Governing equations for electro-conjugate fluid flow

NASA Astrophysics Data System (ADS)

Hosoda, K.; Takemura, K.; Fukagata, K.; Yokota, S.; Edamura, K.

2013-12-01

An electro-conjugation fluid (ECF) is a kind of dielectric liquid, which generates a powerful flow when high DC voltage is applied with tiny electrodes. This study deals with the derivation of the governing equations for electro-conjugate fluid flow based on the Korteweg-Helmholtz (KH) equation which represents the force in dielectric liquid subjected to high DC voltage. The governing equations consist of the Gauss's law, charge conservation with charge recombination, the KH equation, the continuity equation and the incompressible Navier-Stokes equations. The KH equation consists of coulomb force, dielectric constant gradient force and electrostriction force. The governing equation gives the distribution of electric field, charge density and flow velocity. In this study, direct numerical simulation (DNS) is used in order to get these distribution at arbitrary time. Successive over-relaxation (SOR) method is used in analyzing Gauss's law and constrained interpolation pseudo-particle (CIP) method is used in analyzing charge conservation with charge recombination. The third order Runge-Kutta method and conservative second-order-accurate finite difference method is used in analyzing the Navier-Stokes equations with the KH equation. This study also deals with the measurement of ECF ow generated with a symmetrical pole electrodes pair which are made of 0.3 mm diameter piano wire. Working fluid is FF-1EHA2 which is an ECF family. The flow is observed from the both electrodes, i.e., the flow collides in between the electrodes. The governing equation successfully calculates mean flow velocity in between the collector pole electrode and the colliding region by the numerical simulation.

Asymptotic research of transonic gas flows

NASA Astrophysics Data System (ADS)

Velmisov, Petr A.; Tamarova, Yuliya A.

2017-12-01

The article is dedicated to the development asymptotic theory of gas flowing at speed next to sound velocity, particularly of gas transonic flows, i.e. the flows, containing both, subsonic and supersonic areas. The main issue, when styding such flows, are nonlinearity and combined type of equations, describing the transonic flow. Based on asymptotic nonlinear equation obtained in the article, the gas transonic flows is studied, considering transverse disturbance with respect to the main flow. The asymptotic conditions at shock-wave front and conditions on the streamlined surface are found. Moreover, the equation of sound surface and asymptotic formula defining the pressure are recorded. Several exact particular solutions of such equation are given, and their application to solve several tasks of transonic aerodynamics is indicated. Specifically, the polynomial form solution describing gas axisymmetric flows in Laval nozzles with constant acceleration in direction of the nozzle's axis and flow swirling is obtained. The solutions describing the unsteady flow along the channels between spinning surfaces are presented. The asymptotic equation is obtained, describing the flow, appearing during non-separated and separated flow past, closely approximated to cylindrical one. Specific solutions are given, based on which the examples of steady flow are formed.

Design Manual for Microgravity Two-Phase Flow and Heat Transfer

DTIC Science & Technology

1989-10-01

simultaneous solution of two equations. One equation is a dimensionless two-.nhase momentum equation for a separated flow and the other is a dimensionless...created by the flow of the gas over a wave (the Bernoulli effect) is sufficient to lift the waves in a stratified flow to the top of the pipe. A... momentum equation to determine a dimensionless parameter related to the liquid flow rate: 14 [(Ug*Dg*)1(1J*) 2[ [ [ + - 4Y X 2 =9 k (1-16) [U *D1*] -n

Comparison of the Nernst-Planck model and the Poisson-Boltzmann model for electroosmotic flows in microchannels.

PubMed

Park, H M; Lee, J S; Kim, T W

2007-11-15

In the analysis of electroosmotic flows, the internal electric potential is usually modeled by the Poisson-Boltzmann equation. The Poisson-Boltzmann equation is derived from the assumption of thermodynamic equilibrium where the ionic distributions are not affected by fluid flows. Although this is a reasonable assumption for steady electroosmotic flows through straight microchannels, there are some important cases where convective transport of ions has nontrivial effects. In these cases, it is necessary to adopt the Nernst-Planck equation instead of the Poisson-Boltzmann equation to model the internal electric field. In the present work, the predictions of the Nernst-Planck equation are compared with those of the Poisson-Boltzmann equation for electroosmotic flows in various microchannels where the convective transport of ions is not negligible.

Methods for estimating selected spring and fall low-flow frequency statistics for ungaged stream sites in Iowa, based on data through June 2014

USGS Publications Warehouse

Eash, David A.; Barnes, Kimberlee K.; O'Shea, Padraic S.

2016-09-19

A statewide study was led to develop regression equations for estimating three selected spring and three selected fall low-flow frequency statistics for ungaged stream sites in Iowa. The estimation equations developed for the six low-flow frequency statistics include spring (April through June) 1-, 7-, and 30-day mean low flows for a recurrence interval of 10 years and fall (October through December) 1-, 7-, and 30-day mean low flows for a recurrence interval of 10 years. Estimates of the three selected spring statistics are provided for 241 U.S. Geological Survey continuous-record streamgages, and estimates of the three selected fall statistics are provided for 238 of these streamgages, using data through June 2014. Because only 9 years of fall streamflow record were available, three streamgages included in the development of the spring regression equations were not included in the development of the fall regression equations. Because of regulation, diversion, or urbanization, 30 of the 241 streamgages were not included in the development of the regression equations. The study area includes Iowa and adjacent areas within 50 miles of the Iowa border. Because trend analyses indicated statistically significant positive trends when considering the period of record for most of the streamgages, the longest, most recent period of record without a significant trend was determined for each streamgage for use in the study. Geographic information system software was used to measure 63 selected basin characteristics for each of the 211streamgages used to develop the regional regression equations. The study area was divided into three low-flow regions that were defined in a previous study for the development of regional regression equations.Because several streamgages included in the development of regional regression equations have estimates of zero flow calculated from observed streamflow for selected spring and fall low-flow frequency statistics, the final equations for the three low-flow regions were developed using two types of regression analyses—left-censored and generalized-least-squares regression analyses. A total of 211 streamgages were included in the development of nine spring regression equations—three equations for each of the three low-flow regions. A total of 208 streamgages were included in the development of nine fall regression equations—three equations for each of the three low-flow regions. A censoring threshold was used to develop 15 left-censored regression equations to estimate the three fall low-flow frequency statistics for each of the three low-flow regions and to estimate the three spring low-flow frequency statistics for the southern and northwest regions. For the northeast region, generalized-least-squares regression was used to develop three equations to estimate the three spring low-flow frequency statistics. For the northeast region, average standard errors of prediction range from 32.4 to 48.4 percent for the spring equations and average standard errors of estimate range from 56.4 to 73.8 percent for the fall equations. For the northwest region, average standard errors of estimate range from 58.9 to 62.1 percent for the spring equations and from 83.2 to 109.4 percent for the fall equations. For the southern region, average standard errors of estimate range from 43.2 to 64.0 percent for the spring equations and from 78.1 to 78.7 percent for the fall equations.The regression equations are applicable only to stream sites in Iowa with low flows not substantially affected by regulation, diversion, or urbanization and with basin characteristics within the range of those used to develop the equations. The regression equations will be implemented within the U.S. Geological Survey StreamStats Web-based geographic information system application. StreamStats allows users to click on any ungaged stream site and compute estimates of the six selected spring and fall low-flow statistics; in addition, 90-percent prediction intervals and the measured basin characteristics for the ungaged site are provided. StreamStats also allows users to click on any Iowa streamgage to obtain computed estimates for the six selected spring and fall low-flow statistics.

Estimating selected low-flow frequency statistics and harmonic-mean flows for ungaged, unregulated streams in Indiana

USGS Publications Warehouse

Martin, Gary R.; Fowler, Kathleen K.; Arihood, Leslie D.

2016-09-06

Information on low-flow characteristics of streams is essential for the management of water resources. This report provides equations for estimating the 1-, 7-, and 30-day mean low flows for a recurrence interval of 10 years and the harmonic-mean flow at ungaged, unregulated stream sites in Indiana. These equations were developed using the low-flow statistics and basin characteristics for 108 continuous-record streamgages in Indiana with at least 10 years of daily mean streamflow data through the 2011 climate year (April 1 through March 31). The equations were developed in cooperation with the Indiana Department of Environmental Management.Regression techniques were used to develop the equations for estimating low-flow frequency statistics and the harmonic-mean flows on the basis of drainage-basin characteristics. A geographic information system was used to measure basin characteristics for selected streamgages. A final set of 25 basin characteristics measured at all the streamgages were evaluated to choose the best predictors of the low-flow statistics.Logistic-regression equations applicable statewide are presented for estimating the probability that selected low-flow frequency statistics equal zero. These equations use the explanatory variables total drainage area, average transmissivity of the full thickness of the unconsolidated deposits within 1,000 feet of the stream network, and latitude of the basin outlet. The percentage of the streamgage low-flow statistics correctly classified as zero or nonzero using the logistic-regression equations ranged from 86.1 to 88.9 percent.Generalized-least-squares regression equations applicable statewide for estimating nonzero low-flow frequency statistics use total drainage area, the average hydraulic conductivity of the top 70 feet of unconsolidated deposits, the slope of the basin, and the index of permeability and thickness of the Quaternary surficial sediments as explanatory variables. The average standard error of prediction of these regression equations ranges from 55.7 to 61.5 percent.Regional weighted-least-squares regression equations were developed for estimating the harmonic-mean flows by dividing the State into three low-flow regions. The Northern region uses total drainage area and the average transmissivity of the entire thickness of unconsolidated deposits as explanatory variables. The Central region uses total drainage area, the average hydraulic conductivity of the entire thickness of unconsolidated deposits, and the index of permeability and thickness of the Quaternary surficial sediments. The Southern region uses total drainage area and the percent of the basin covered by forest. The average standard error of prediction for these equations ranges from 39.3 to 66.7 percent.The regional regression equations are applicable only to stream sites with low flows unaffected by regulation and to stream sites with drainage basin characteristic values within specified limits. Caution is advised when applying the equations for basins with characteristics near the applicable limits and for basins with karst drainage features and for urbanized basins. Extrapolations near and beyond the applicable basin characteristic limits will have unknown errors that may be large. Equations are presented for use in estimating the 90-percent prediction interval of the low-flow statistics estimated by use of the regression equations at a given stream site.The regression equations are to be incorporated into the U.S. Geological Survey StreamStats Web-based application for Indiana. StreamStats allows users to select a stream site on a map and automatically measure the needed basin characteristics and compute the estimated low-flow statistics and associated prediction intervals.

Regression equations to estimate seasonal flow duration, n-day high-flow frequency, and n-day low-flow frequency at sites in North Dakota using data through water year 2009

USGS Publications Warehouse

Williams-Sether, Tara; Gross, Tara A.

2016-02-09

Seasonal mean daily flow data from 119 U.S. Geological Survey streamflow-gaging stations in North Dakota; the surrounding states of Montana, Minnesota, and South Dakota; and the Canadian provinces of Manitoba and Saskatchewan with 10 or more years of unregulated flow record were used to develop regression equations for flow duration, n-day high flow and n-day low flow using ordinary least-squares and Tobit regression techniques. Regression equations were developed for seasonal flow durations at the 10th, 25th, 50th, 75th, and 90th percent exceedances; the 1-, 7-, and 30-day seasonal mean high flows for the 10-, 25-, and 50-year recurrence intervals; and the 1-, 7-, and 30-day seasonal mean low flows for the 2-, 5-, and 10-year recurrence intervals. Basin and climatic characteristics determined to be significant explanatory variables in one or more regression equations included drainage area, percentage of basin drainage area that drains to isolated lakes and ponds, ruggedness number, stream length, basin compactness ratio, minimum basin elevation, precipitation, slope ratio, stream slope, and soil permeability. The adjusted coefficient of determination for the n-day high-flow regression equations ranged from 55.87 to 94.53 percent. The Chi2 values for the duration regression equations ranged from 13.49 to 117.94, whereas the Chi2 values for the n-day low-flow regression equations ranged from 4.20 to 49.68.

Near-wall modelling of compressible turbulent flows

NASA Technical Reports Server (NTRS)

So, Ronald M. C.

1990-01-01

Work was carried out to formulate near-wall models for the equations governing the transport of the temperature-variance and its dissipation rate. With these equations properly modeled, a foundation is laid for their extension together with the heat-flux equations to compressible flows. This extension is carried out in a manner similar to that used to extend the incompressible near-wall Reynolds-stress models to compressible flows. The methodology used to accomplish the extension of the near-wall Reynolds-stress models is examined and the actual extension of the models for the Reynolds-stress equations and the near-wall dissipation-rate equation to compressible flows is given. Then the formulation of the near-wall models for the equations governing the transport of the temperature variance and its dissipation rate is discussed. Finally, a sample calculation of a flat plate compressible turbulent boundary-layer flow with adiabatic wall boundary condition and a free-stream Mach number of 2.5 using a two-equation near-wall closure is presented. The results show that the near-wall two-equation closure formulated for compressible flows is quite valid and the calculated properties are in good agreement with measurements. Furthermore, the near-wall behavior of the turbulence statistics and structure parameters is consistent with that found in incompressible flows.

Determination of gas & liquid two-phase flow regime transitions in wellbore annulus by virtual mass force coefficient when gas cut

NASA Astrophysics Data System (ADS)

Qu, Junbo; Yan, Tie; Sun, Xiaofeng; Chen, Ye; Pan, Yi

2017-10-01

With the development of drilling technology to deeper stratum, overflowing especially gas cut occurs frequently, and then flow regime in wellbore annulus is from the original drilling fluid single-phase flow into gas & liquid two-phase flow. By using averaged two-fluid model equations and the basic principle of fluid mechanics to establish the continuity equations and momentum conservation equations of gas phase & liquid phase respectively. Relationship between pressure and density of gas & liquid was introduced to obtain hyperbolic equation, and get the expression of the dimensionless eigenvalue of the equation by using the characteristic line method, and analyze wellbore flow regime to get the critical gas content under different virtual mass force coefficients. Results show that the range of equation eigenvalues is getting smaller and smaller with the increase of gas content. When gas content reaches the critical point, the dimensionless eigenvalue of equation has no real solution, and the wellbore flow regime changed from bubble flow to bomb flow. When virtual mass force coefficients are 0.50, 0.60, 0.70 and 0.80 respectively, the critical gas contents are 0.32, 0.34, 0.37 and 0.39 respectively. The higher the coefficient of virtual mass force, the higher gas content in wellbore corresponding to the critical point of transition flow regime, which is in good agreement with previous experimental results. Therefore, it is possible to determine whether there is a real solution of the dimensionless eigenvalue of equation by virtual mass force coefficient and wellbore gas content, from which we can obtain the critical condition of wellbore flow regime transformation. It can provide theoretical support for the accurate judgment of the annular flow regime.

Axisymmetric ideal MHD stellar wind flow

NASA Technical Reports Server (NTRS)

Heinemann, M.; Olbert, S.

1978-01-01

The ideal MHD equations are reduced to a single equation under the assumption of axisymmetric flow. A variational principle from which the equation is derivable is given. The characteristics of the equation are briefly discussed. The equation is used to rederive the theorem of Gussenhoven and Carovillano.

Hypervelocity atmospheric flight: Real gas flow fields

NASA Technical Reports Server (NTRS)

Howe, John T.

1990-01-01

Flight in the atmosphere is examined from the viewpoint of including real gas phenomena in the flow field about a vehicle flying at hypervelocity. That is to say, the flow field is subject not only to compressible phenomena, but is dominated by energetic phenomena. There are several significant features of such a flow field. Spatially, its composition can vary by both chemical and elemental species. The equations which describe the flow field include equations of state and mass, species, elemental, and electric charge continuity; momentum; and energy equations. These are nonlinear, coupled, partial differential equations that were reduced to a relatively compact set of equations of a self-consistent manner (which allows mass addition at the surface at a rate comparable to the free-stream mass flux). The equations and their inputs allow for transport of these quantities relative to the mass-averaged behavior of the flow field. Thus transport of mass by chemical, thermal, pressure, and forced diffusion; transport of momentum by viscosity; and transport of energy by conduction, chemical considerations, viscosity, and radiative transfer are included. The last of these complicate the set of equations by making the energy equation a partial integrodifferential equation. Each phenomenon is considered and represented mathematically by one or more developments. The coefficients which pertain are both thermodynamically and chemically dependent. Solutions of the equations are presented and discussed in considerable detail, with emphasis on severe energetic flow fields. For hypervelocity flight in low-density environments where gaseous reactions proceed at finite rates, chemical nonequilibrium is considered and some illustrations are presented. Finally, flight where the flow field may be out of equilibrium, both chemically and thermodynamically, is presented briefly.

Hypervelocity atmospheric flight: Real gas flow fields

NASA Technical Reports Server (NTRS)

Howe, John T.

1989-01-01

Flight in the atmosphere is examined from the viewpoint of including real gas phenomena in the flow field about a vehicle flying at hypervelocity. That is to say, the flow field is subject not only to compressible phenomena, but is dominated by energetic phenomena. There are several significant features of such a flow field. Spatially, its composition can vary by both chemical and elemental species. The equations which describe the flow field include equations of state and mass, species, elemental, and electric charge continuity; momentum; and energy equations. These are nonlinear, coupled, partial differential equations that have been reduced to a relatively compact set of equations in a self-consistent manner (which allows mass addition at the surface at a rate comparable to the free-stream mass flux). The equations and their inputs allow for transport of these quantities relative to the mass-average behavior of the flow field. Thus transport of mass by chemical, thermal, pressure, and forced diffusion; transport of momentum by viscosity; and transport of energy by conduction, chemical considerations, viscosity, and radiative transfer are included. The last of these complicate the set of equations by making the energy equations a partial integrodifferential equation. Each phenomenon is considered and represented mathematically by one or more developments. The coefficients which pertain are both thermodynamically and chemically dependent. Solutions of the equations are presented and discussed in considerable detail, with emphasis on severe energetic flow fields. Hypervelocity flight in low-density environments where gaseous reactions proceed at finite rates chemical nonequilibrium is considered, and some illustrations are presented. Finally, flight where the flow field may be out of equilibrium, both chemically and thermodynamically, is presented briefly.

On the Representation of Aquifer Compressibility in General Subsurface Flow Codes: How an Alternate Definition of Aquifer Compressibility Matches Results from the Groundwater Flow Equation

NASA Astrophysics Data System (ADS)

Birdsell, D.; Karra, S.; Rajaram, H.

2016-12-01

The governing equations for subsurface flow codes in deformable porous media are derived from the fluid mass balance equation. One class of these codes, which we call general subsurface flow (GSF) codes, does not explicitly track the motion of the solid porous media but does accept general constitutive relations for porosity, density, and fluid flux. Examples of GSF codes include PFLOTRAN, FEHM, STOMP, and TOUGH2. Meanwhile, analytical and numerical solutions based on the groundwater flow equation have assumed forms for porosity, density, and fluid flux. We review the derivation of the groundwater flow equation, which uses the form of Darcy's equation that accounts for the velocity of fluids with respect to solids and defines the soil matrix compressibility accordingly. We then show how GSF codes have a different governing equation if they use the form of Darcy's equation that is written only in terms of fluid velocity. The difference is seen in the porosity change, which is part of the specific storage term in the groundwater flow equation. We propose an alternative definition of soil matrix compressibility to correct for the untracked solid velocity. Simulation results show significantly less error for our new compressibility definition than the traditional compressibility when compared to analytical solutions from the groundwater literature. For example, the error in one calculation for a pumped sandstone aquifer goes from 940 to <70 Pa when the new compressibility is used. Code users and developers need to be aware of assumptions in the governing equations and constitutive relations in subsurface flow codes, and our newly-proposed compressibility function should be incorporated into GSF codes.

On the Representation of Aquifer Compressibility in General Subsurface Flow Codes: How an Alternate Definition of Aquifer Compressibility Matches Results from the Groundwater Flow Equation

NASA Astrophysics Data System (ADS)

Birdsell, D.; Karra, S.; Rajaram, H.

2017-12-01

The governing equations for subsurface flow codes in deformable porous media are derived from the fluid mass balance equation. One class of these codes, which we call general subsurface flow (GSF) codes, does not explicitly track the motion of the solid porous media but does accept general constitutive relations for porosity, density, and fluid flux. Examples of GSF codes include PFLOTRAN, FEHM, STOMP, and TOUGH2. Meanwhile, analytical and numerical solutions based on the groundwater flow equation have assumed forms for porosity, density, and fluid flux. We review the derivation of the groundwater flow equation, which uses the form of Darcy's equation that accounts for the velocity of fluids with respect to solids and defines the soil matrix compressibility accordingly. We then show how GSF codes have a different governing equation if they use the form of Darcy's equation that is written only in terms of fluid velocity. The difference is seen in the porosity change, which is part of the specific storage term in the groundwater flow equation. We propose an alternative definition of soil matrix compressibility to correct for the untracked solid velocity. Simulation results show significantly less error for our new compressibility definition than the traditional compressibility when compared to analytical solutions from the groundwater literature. For example, the error in one calculation for a pumped sandstone aquifer goes from 940 to <70 Pa when the new compressibility is used. Code users and developers need to be aware of assumptions in the governing equations and constitutive relations in subsurface flow codes, and our newly-proposed compressibility function should be incorporated into GSF codes.

Investigation of viscous/inviscid interaction in transonic flow over airfoils with suction

NASA Technical Reports Server (NTRS)

Vemuru, C. S.; Tiwari, S. N.

1988-01-01

The viscous/inviscid interaction over transonic airfoils with and without suction is studied. The streamline angle at the edge of the boundary layer is used to couple the viscous and inviscid flows. The potential flow equations are solved for the inviscid flow field. In the shock region, the Euler equations are solved using the method of integral relations. For this, the potential flow solution is used as the initial and boundary conditions. An integral method is used to solve the laminar boundary-layer equations. Since both methods are integral methods, a continuous interaction is allowed between the outer inviscid flow region and the inner viscous flow region. To avoid the Goldstein singularity near the separation point the laminar boundary-layer equations are derived in an inverse form to obtain solution for the flows with small separations. The displacement thickness distribution is specified instead of the usual pressure distribution to solve the boundry-layer equations. The Euler equations are solved for the inviscid flow using the finite volume technique and the coupling is achieved by a surface transpiration model. A method is developed to apply a minimum amount of suction that is required to have an attached flow on the airfoil. The turbulent boundary layer equations are derived using the bi-logarithmic wall law for mass transfer. The results are found to be in good agreement with available experimental data and with the results of other computational methods.

Peak-flow characteristics of Virginia streams

USGS Publications Warehouse

Austin, Samuel H.; Krstolic, Jennifer L.; Wiegand, Ute

2011-01-01

Peak-flow annual exceedance probabilities, also called probability-percent chance flow estimates, and regional regression equations are provided describing the peak-flow characteristics of Virginia streams. Statistical methods are used to evaluate peak-flow data. Analysis of Virginia peak-flow data collected from 1895 through 2007 is summarized. Methods are provided for estimating unregulated peak flow of gaged and ungaged streams. Station peak-flow characteristics identified by fitting the logarithms of annual peak flows to a Log Pearson Type III frequency distribution yield annual exceedance probabilities of 0.5, 0.4292, 0.2, 0.1, 0.04, 0.02, 0.01, 0.005, and 0.002 for 476 streamgaging stations. Stream basin characteristics computed using spatial data and a geographic information system are used as explanatory variables in regional regression model equations for six physiographic regions to estimate regional annual exceedance probabilities at gaged and ungaged sites. Weighted peak-flow values that combine annual exceedance probabilities computed from gaging station data and from regional regression equations provide improved peak-flow estimates. Text, figures, and lists are provided summarizing selected peak-flow sites, delineated physiographic regions, peak-flow estimates, basin characteristics, regional regression model equations, error estimates, definitions, data sources, and candidate regression model equations. This study supersedes previous studies of peak flows in Virginia.

Topics in structural dynamics: Nonlinear unsteady transonic flows and Monte Carlo methods in acoustics

NASA Technical Reports Server (NTRS)

Haviland, J. K.

1974-01-01

The results are reported of two unrelated studies. The first was an investigation of the formulation of the equations for non-uniform unsteady flows, by perturbation of an irrotational flow to obtain the linear Green's equation. The resulting integral equation was found to contain a kernel which could be expressed as the solution of the adjoint flow equation, a linear equation for small perturbations, but with non-constant coefficients determined by the steady flow conditions. It is believed that the non-uniform flow effects may prove important in transonic flutter, and that in such cases, the use of doublet type solutions of the wave equation would then prove to be erroneous. The second task covered an initial investigation into the use of the Monte Carlo method for solution of acoustical field problems. Computed results are given for a rectangular room problem, and for a problem involving a circular duct with a source located at the closed end.

Unsteady density-current equations for highly curved terrain

NASA Technical Reports Server (NTRS)

Sivakumaran, N. S.; Dressler, R. F.

1989-01-01

New nonlinear partial differential equations containing terrain curvature and its rate of change are derived that describe the flow of an atmospheric density current. Unlike the classical hydraulic-type equations for density currents, the new equations are valid for two-dimensional, gradually varied flow over highly curved terrain, hence suitable for computing unsteady (or steady) flows over arbitrary mountain/valley profiles. The model assumes the atmosphere above the density current exerts a known arbitrary variable pressure upon the unknown interface. Later this is specialized to the varying hydrostatic pressure of the atmosphere above. The new equations yield the variable velocity distribution, the interface position, and the pressure distribution that contains a centrifugal component, often significantly larger than its hydrostatic component. These partial differential equations are hyperbolic, and the characteristic equations and characteristic directions are derived. Using these to form a characteristic mesh, a hypothetical unsteady curved-flow problem is calculated, not based upon observed data, merely as an example to illustrate the simplicity of their application to unsteady flows over mountains.

Exact Solutions to Several Nonlinear Cases of Generalized Grad-Shafranov Equation for Ideal Magnetohydrodynamic Flows in Axisymmetric Domain

NASA Astrophysics Data System (ADS)

Adem, Abdullahi Rashid; Moawad, Salah M.

2018-05-01

In this paper, the steady-state equations of ideal magnetohydrodynamic incompressible flows in axisymmetric domains are investigated. These flows are governed by a second-order elliptic partial differential equation as a type of generalized Grad-Shafranov equation. The problem of finding exact equilibria to the full governing equations in the presence of incompressible mass flows is considered. Two different types of constraints on position variables are presented to construct exact solution classes for several nonlinear cases of the governing equations. Some of the obtained results are checked for their applications to magnetic confinement plasma. Besides, they cover many previous configurations and include new considerations about the nonlinearity of magnetic flux stream variables.

Regional Regression Equations to Estimate Flow-Duration Statistics at Ungaged Stream Sites in Connecticut

USGS Publications Warehouse

Ahearn, Elizabeth A.

2010-01-01

Multiple linear regression equations for determining flow-duration statistics were developed to estimate select flow exceedances ranging from 25- to 99-percent for six 'bioperiods'-Salmonid Spawning (November), Overwinter (December-February), Habitat Forming (March-April), Clupeid Spawning (May), Resident Spawning (June), and Rearing and Growth (July-October)-in Connecticut. Regression equations also were developed to estimate the 25- and 99-percent flow exceedances without reference to a bioperiod. In total, 32 equations were developed. The predictive equations were based on regression analyses relating flow statistics from streamgages to GIS-determined basin and climatic characteristics for the drainage areas of those streamgages. Thirty-nine streamgages (and an additional 6 short-term streamgages and 28 partial-record sites for the non-bioperiod 99-percent exceedance) in Connecticut and adjacent areas of neighboring States were used in the regression analysis. Weighted least squares regression analysis was used to determine the predictive equations; weights were assigned based on record length. The basin characteristics-drainage area, percentage of area with coarse-grained stratified deposits, percentage of area with wetlands, mean monthly precipitation (November), mean seasonal precipitation (December, January, and February), and mean basin elevation-are used as explanatory variables in the equations. Standard errors of estimate of the 32 equations ranged from 10.7 to 156 percent with medians of 19.2 and 55.4 percent to predict the 25- and 99-percent exceedances, respectively. Regression equations to estimate high and median flows (25- to 75-percent exceedances) are better predictors (smaller variability of the residual values around the regression line) than the equations to estimate low flows (less than 75-percent exceedance). The Habitat Forming (March-April) bioperiod had the smallest standard errors of estimate, ranging from 10.7 to 20.9 percent. In contrast, the Rearing and Growth (July-October) bioperiod had the largest standard errors, ranging from 30.9 to 156 percent. The adjusted coefficient of determination of the equations ranged from 77.5 to 99.4 percent with medians of 98.5 and 90.6 percent to predict the 25- and 99-percent exceedances, respectively. Descriptive information on the streamgages used in the regression, measured basin and climatic characteristics, and estimated flow-duration statistics are provided in this report. Flow-duration statistics and the 32 regression equations for estimating flow-duration statistics in Connecticut are stored on the U.S. Geological Survey World Wide Web application ?StreamStats? (http://water.usgs.gov/osw/streamstats/index.html). The regression equations developed in this report can be used to produce unbiased estimates of select flow exceedances statewide.

Transcritical flow of a stratified fluid over topography: analysis of the forced Gardner equation

NASA Astrophysics Data System (ADS)

Kamchatnov, A. M.; Kuo, Y.-H.; Lin, T.-C.; Horng, T.-L.; Gou, S.-C.; Clift, R.; El, G. A.; Grimshaw, R. H. J.

2013-12-01

Transcritical flow of a stratified fluid past a broad localised topographic obstacle is studied analytically in the framework of the forced extended Korteweg--de Vries (eKdV), or Gardner, equation. We consider both possible signs for the cubic nonlinear term in the Gardner equation corresponding to different fluid density stratification profiles. We identify the range of the input parameters: the oncoming flow speed (the Froude number) and the topographic amplitude, for which the obstacle supports a stationary localised hydraulic transition from the subcritical flow upstream to the supercritical flow downstream. Such a localised transcritical flow is resolved back into the equilibrium flow state away from the obstacle with the aid of unsteady coherent nonlinear wave structures propagating upstream and downstream. Along with the regular, cnoidal undular bores occurring in the analogous problem for the single-layer flow modeled by the forced KdV equation, the transcritical internal wave flows support a diverse family of upstream and downstream wave structures, including solibores, rarefaction waves, reversed and trigonometric undular bores, which we describe using the recent development of the nonlinear modulation theory for the (unforced) Gardner equation. The predictions of the developed analytic construction are confirmed by direct numerical simulations of the forced Gardner equation for a broad range of input parameters.

Development of a One-Equation Eddy Viscosity Turbulence Model for Application to Complex Turbulent Flows

NASA Astrophysics Data System (ADS)

Wray, Timothy J.

Computational fluid dynamics (CFD) is routinely used in performance prediction and design of aircraft, turbomachinery, automobiles, and in many other industrial applications. Despite its wide range of use, deficiencies in its prediction accuracy still exist. One critical weakness is the accurate simulation of complex turbulent flows using the Reynolds-Averaged Navier-Stokes equations in conjunction with a turbulence model. The goal of this research has been to develop an eddy viscosity type turbulence model to increase the accuracy of flow simulations for mildly separated flows, flows with rotation and curvature effects, and flows with surface roughness. It is accomplished by developing a new zonal one-equation turbulence model which relies heavily on the flow physics; it is now known in the literature as the Wray-Agarwal one-equation turbulence model. The effectiveness of the new model is demonstrated by comparing its results with those obtained by the industry standard one-equation Spalart-Allmaras model and two-equation Shear-Stress-Transport k - o model and experimental data. Results for subsonic, transonic, and supersonic flows in and about complex geometries are presented. It is demonstrated that the Wray-Agarwal model can provide the industry and CFD researchers an accurate, efficient, and reliable turbulence model for the computation of a large class of complex turbulent flows.

Regression Equations for Estimating Flood Flows at Selected Recurrence Intervals for Ungaged Streams in Pennsylvania

USGS Publications Warehouse

Roland, Mark A.; Stuckey, Marla H.

2008-01-01

Regression equations were developed for estimating flood flows at selected recurrence intervals for ungaged streams in Pennsylvania with drainage areas less than 2,000 square miles. These equations were developed utilizing peak-flow data from 322 streamflow-gaging stations within Pennsylvania and surrounding states. All stations used in the development of the equations had 10 or more years of record and included active and discontinued continuous-record as well as crest-stage partial-record stations. The state was divided into four regions, and regional regression equations were developed to estimate the 2-, 5-, 10-, 50-, 100-, and 500-year recurrence-interval flood flows. The equations were developed by means of a regression analysis that utilized basin characteristics and flow data associated with the stations. Significant explanatory variables at the 95-percent confidence level for one or more regression equations included the following basin characteristics: drainage area; mean basin elevation; and the percentages of carbonate bedrock, urban area, and storage within a basin. The regression equations can be used to predict the magnitude of flood flows for specified recurrence intervals for most streams in the state; however, they are not valid for streams with drainage areas generally greater than 2,000 square miles or with substantial regulation, diversion, or mining activity within the basin. Estimates of flood-flow magnitude and frequency for streamflow-gaging stations substantially affected by upstream regulation are also presented.

Nonlinear storage models of unconfined flow through a shallow aquifer on an inclined base and their quasi-steady flow application

NASA Astrophysics Data System (ADS)

Varvaris, Ioannis; Gravanis, Elias; Koussis, Antonis; Akylas, Evangelos

2013-04-01

Hillslope processes involving flow through an inclined shallow aquifer range from subsurface stormflow to stream base flow (drought flow, or groundwater recession flow). In the case of recharge, the infiltrating water moves vertically as unsaturated flow until it reaches the saturated groundwater, where the flow is approximately parallel to the base of the aquifer. Boussinesq used the Dupuit-Forchheimer (D-F) hydraulic theory to formulate unconfined groundwater flow through a soil layer resting on an impervious inclined bed, deriving a nonlinear equation for the flow rate that consists of a linear gravity-driven component and a quadratic pressure-gradient component. Inserting that flow rate equation into the differential storage balance equation (volume conservation) Boussinesq obtained a nonlinear second-order partial differential equation for the depth. So far however, only few special solutions have been advanced for that governing equation. The nonlinearity of the equation of Boussinesq is the major obstacle to deriving a general analytical solution for the depth profile of unconfined flow on a sloping base with recharge (from which the discharges could be then determined). Henderson and Wooding (1964) were able to obtain an exact analytical solution for steady unconfined flow on a sloping base, with recharge, and their work deserves special note in the realm of solutions of the nonlinear equation of Boussinesq. However, the absence of a general solution for the transient case, which is of practical interest to hydrologists, has been the motivation for developing approximate solutions of the non-linear equation of Boussinesq. In this work, we derive the aquifer storage function by integrating analytically over the aquifer base the depth profiles resulting from the complete nonlinear Boussinesq equation for steady flow. This storage function consists of a linear and a nonlinear outflow-dependent term. Then, we use this physics-based storage function in the transient storage balance over the hillslope, obtaining analytical solutions of the outflow and the storage, for recharge and drainage, via a quasi-steady flow calculation. The hydraulically derived storage model is thus embedded in a quasi-steady approximation of transient unconfined flow in sloping aquifers. We generalise this hydrologic model of groundwater flow by modifying the storage function to be the weighted sum of the linear and the nonlinear storage terms, determining the weighting factor objectively from a known integral quantity of the flow (either an initial volume of water stored in the aquifer or a drained water volume). We demonstrate the validity of this model through comparisons with experimental data and simulation results.

Equations of motion for the variable mass flow-variable exhaust velocity rocket

NASA Technical Reports Server (NTRS)

Tempelman, W. H.

1972-01-01

An equation of motion for a one dimensional rocket is derived as a function of the mass flow rate into the acceleration chamber and the velocity distribution along the chamber, thereby including the transient flow changes in the chamber. The derivation of the mass density requires the introduction of the special time coordinate. The equation of motion is derived from both classical force and momentum approaches and is shown to be consistent with the standard equation expressed in terms of flow parameters at the exit to the acceleration chamber.

Mass conservation: 1-D open channel flow equations

USGS Publications Warehouse

DeLong, Lewis L.

1989-01-01

Unsteady flow simulation in natural rivers is often complicated by meandering channels of compound section. Hydraulic properties and the length of the wetted channel may vary significantly as a meandering river inundates its adjacent floodplain. The one-dimensional, unsteady, open-channel flow equations can be extended to simulate floods in channels of compound section. It will be shown that equations derived from the addition of differential equations individually describing flow in main and overbank channels do not in general conserve mass when overbank and main channels are of different lengths.

Computation of Separated and Unsteady Flows with One- and Two-Equation Turbulence Models

NASA Technical Reports Server (NTRS)

Ekaterinaris, John A.; Menter, Florian R.

1994-01-01

The ability of one- and two-equation turbulence models to predict unsteady separated flows over airfoils is evaluated. An implicit, factorized, upwind-biased numerical scheme is used for the integration of the compressible, Reynolds averaged Navier-Stokes equations. The turbulent eddy viscosity is obtained from the computed mean flowfield by integration of the turbulent field equations. The two-equation turbulence models are discretized in space with an upwind-biased, second order accurate total variation diminishing scheme. One and two-equation turbulence models are first tested for a separated airfoil flow at fixed angle of incidence. The same models are then applied to compute the unsteady flowfields about airfoils undergoing oscillatory motion at low subsonic Mach numbers. Experimental cases where the flow has been tripped at the leading edge and where natural transition was allowed to occur naturally are considered. The more recently developed field-equation turbulence models capture the physics of unsteady separated flow significantly better than the standard kappa-epsilon and kappa-omega models. However, certain differences in the hysteresis effects are obtained. For an untripped high-Reynolds-number flow, it was found necessary to take into account the leading edge transitional flow region in order to capture the correct physical mechanism that leads to dynamic stall.

Methods for estimating selected low-flow frequency statistics for unregulated streams in Kentucky

USGS Publications Warehouse

Martin, Gary R.; Arihood, Leslie D.

2010-01-01

This report provides estimates of, and presents methods for estimating, selected low-flow frequency statistics for unregulated streams in Kentucky including the 30-day mean low flows for recurrence intervals of 2 and 5 years (30Q2 and 30Q5) and the 7-day mean low flows for recurrence intervals of 5, 10, and 20 years (7Q2, 7Q10, and 7Q20). Estimates of these statistics are provided for 121 U.S. Geological Survey streamflow-gaging stations with data through the 2006 climate year, which is the 12-month period ending March 31 of each year. Data were screened to identify the periods of homogeneous, unregulated flows for use in the analyses. Logistic-regression equations are presented for estimating the annual probability of the selected low-flow frequency statistics being equal to zero. Weighted-least-squares regression equations were developed for estimating the magnitude of the nonzero 30Q2, 30Q5, 7Q2, 7Q10, and 7Q20 low flows. Three low-flow regions were defined for estimating the 7-day low-flow frequency statistics. The explicit explanatory variables in the regression equations include total drainage area and the mapped streamflow-variability index measured from a revised statewide coverage of this characteristic. The percentage of the station low-flow statistics correctly classified as zero or nonzero by use of the logistic-regression equations ranged from 87.5 to 93.8 percent. The average standard errors of prediction of the weighted-least-squares regression equations ranged from 108 to 226 percent. The 30Q2 regression equations have the smallest standard errors of prediction, and the 7Q20 regression equations have the largest standard errors of prediction. The regression equations are applicable only to stream sites with low flows unaffected by regulation from reservoirs and local diversions of flow and to drainage basins in specified ranges of basin characteristics. Caution is advised when applying the equations for basins with characteristics near the applicable limits and for basins with karst drainage features.

Kadomtsev−Petviashvili equation for a flow of highly nonisothermal collisionless plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Movsesyants, Yu. B., E-mail: yumovsesyants@gmail.com; Rukhadze, A. A., E-mail: rukh@fpl.gpi.ru; Tyuryukanov, P. M.

2016-01-15

It is shown that the equations of two-fluid electrodynamics for a cold ions flow and Boltzmann electrons in the vicinity of the ion-sound point can be reduced to the Kadomtsev−Petviashvili equation. Examples of two-dimensional equilibria with pole singularities obtained by exactly solving the equations are presented. An exact self-similar solution describing a two-dimensional transonic flow and having no pole singularities is found.

Kadomtsev-Petviashvili equation for a flow of highly nonisothermal collisionless plasma

NASA Astrophysics Data System (ADS)

Movsesyants, Yu. B.; Rukhadze, A. A.; Tyuryukanov, P. M.

2016-01-01

It is shown that the equations of two-fluid electrodynamics for a cold ions flow and Boltzmann electrons in the vicinity of the ion-sound point can be reduced to the Kadomtsev-Petviashvili equation. Examples of two-dimensional equilibria with pole singularities obtained by exactly solving the equations are presented. An exact self-similar solution describing a two-dimensional transonic flow and having no pole singularities is found.

Gauge-invariant flow equation

NASA Astrophysics Data System (ADS)

Wetterich, C.

2018-06-01

We propose a closed gauge-invariant functional flow equation for Yang-Mills theories and quantum gravity that only involves one macroscopic gauge field or metric. It is based on a projection on physical and gauge fluctuations. Deriving this equation from a functional integral we employ the freedom in the precise choice of the macroscopic field and the effective average action in order to realize a closed and simple form of the flow equation.

Calculation of the flow field including boundary layer effects for supersonic mixed compression inlets at angles of attack

NASA Technical Reports Server (NTRS)

Vadyak, J.; Hoffman, J. D.

1982-01-01

The flow field in supersonic mixed compression aircraft inlets at angle of attack is calculated. A zonal modeling technique is employed to obtain the solution which divides the flow field into different computational regions. The computational regions consist of a supersonic core flow, boundary layer flows adjacent to both the forebody/centerbody and cowl contours, and flow in the shock wave boundary layer interaction regions. The zonal modeling analysis is described and some computational results are presented. The governing equations for the supersonic core flow form a hyperbolic system of partial differential equations. The equations for the characteristic surfaces and the compatibility equations applicable along these surfaces are derived. The characteristic surfaces are the stream surfaces, which are surfaces composed of streamlines, and the wave surfaces, which are surfaces tangent to a Mach conoid. The compatibility equations are expressed as directional derivatives along streamlines and bicharacteristics, which are the lines of tangency between a wave surface and a Mach conoid.

Methods for estimating selected low-flow frequency statistics and harmonic mean flows for streams in Iowa

USGS Publications Warehouse

Eash, David A.; Barnes, Kimberlee K.

2017-01-01

A statewide study was conducted to develop regression equations for estimating six selected low-flow frequency statistics and harmonic mean flows for ungaged stream sites in Iowa. The estimation equations developed for the six low-flow frequency statistics include: the annual 1-, 7-, and 30-day mean low flows for a recurrence interval of 10 years, the annual 30-day mean low flow for a recurrence interval of 5 years, and the seasonal (October 1 through December 31) 1- and 7-day mean low flows for a recurrence interval of 10 years. Estimation equations also were developed for the harmonic-mean-flow statistic. Estimates of these seven selected statistics are provided for 208 U.S. Geological Survey continuous-record streamgages using data through September 30, 2006. The study area comprises streamgages located within Iowa and 50 miles beyond the State's borders. Because trend analyses indicated statistically significant positive trends when considering the entire period of record for the majority of the streamgages, the longest, most recent period of record without a significant trend was determined for each streamgage for use in the study. The median number of years of record used to compute each of these seven selected statistics was 35. Geographic information system software was used to measure 54 selected basin characteristics for each streamgage. Following the removal of two streamgages from the initial data set, data collected for 206 streamgages were compiled to investigate three approaches for regionalization of the seven selected statistics. Regionalization, a process using statistical regression analysis, provides a relation for efficiently transferring information from a group of streamgages in a region to ungaged sites in the region. The three regionalization approaches tested included statewide, regional, and region-of-influence regressions. For the regional regression, the study area was divided into three low-flow regions on the basis of hydrologic characteristics, landform regions, and soil regions. A comparison of root mean square errors and average standard errors of prediction for the statewide, regional, and region-of-influence regressions determined that the regional regression provided the best estimates of the seven selected statistics at ungaged sites in Iowa. Because a significant number of streams in Iowa reach zero flow as their minimum flow during low-flow years, four different types of regression analyses were used: left-censored, logistic, generalized-least-squares, and weighted-least-squares regression. A total of 192 streamgages were included in the development of 27 regression equations for the three low-flow regions. For the northeast and northwest regions, a censoring threshold was used to develop 12 left-censored regression equations to estimate the 6 low-flow frequency statistics for each region. For the southern region a total of 12 regression equations were developed; 6 logistic regression equations were developed to estimate the probability of zero flow for the 6 low-flow frequency statistics and 6 generalized least-squares regression equations were developed to estimate the 6 low-flow frequency statistics, if nonzero flow is estimated first by use of the logistic equations. A weighted-least-squares regression equation was developed for each region to estimate the harmonic-mean-flow statistic. Average standard errors of estimate for the left-censored equations for the northeast region range from 64.7 to 88.1 percent and for the northwest region range from 85.8 to 111.8 percent. Misclassification percentages for the logistic equations for the southern region range from 5.6 to 14.0 percent. Average standard errors of prediction for generalized least-squares equations for the southern region range from 71.7 to 98.9 percent and pseudo coefficients of determination for the generalized-least-squares equations range from 87.7 to 91.8 percent. Average standard errors of prediction for weighted-least-squares equations developed for estimating the harmonic-mean-flow statistic for each of the three regions range from 66.4 to 80.4 percent. The regression equations are applicable only to stream sites in Iowa with low flows not significantly affected by regulation, diversion, or urbanization and with basin characteristics within the range of those used to develop the equations. If the equations are used at ungaged sites on regulated streams, or on streams affected by water-supply and agricultural withdrawals, then the estimates will need to be adjusted by the amount of regulation or withdrawal to estimate the actual flow conditions if that is of interest. Caution is advised when applying the equations for basins with characteristics near the applicable limits of the equations and for basins located in karst topography. A test of two drainage-area ratio methods using 31 pairs of streamgages, for the annual 7-day mean low-flow statistic for a recurrence interval of 10 years, indicates a weighted drainage-area ratio method provides better estimates than regional regression equations for an ungaged site on a gaged stream in Iowa when the drainage-area ratio is between 0.5 and 1.4. These regression equations will be implemented within the U.S. Geological Survey StreamStats web-based geographic-information-system tool. StreamStats allows users to click on any ungaged site on a river and compute estimates of the seven selected statistics; in addition, 90-percent prediction intervals and the measured basin characteristics for the ungaged sites also are provided. StreamStats also allows users to click on any streamgage in Iowa and estimates computed for these seven selected statistics are provided for the streamgage.

A root-mean-square pressure fluctuations model for internal flow applications

NASA Technical Reports Server (NTRS)

Chen, Y. S.

1985-01-01

A transport equation for the root-mean-square pressure fluctuations of turbulent flow is derived from the time-dependent momentum equation for incompressible flow. Approximate modeling of this transport equation is included to relate terms with higher order correlations to the mean quantities of turbulent flow. Three empirical constants are introduced in the model. Two of the empirical constants are estimated from homogeneous turbulence data and wall pressure fluctuations measurements. The third constant is determined by comparing the results of large eddy simulations for a plane channel flow and an annulus flow.

Discrete Morse flow for Ricci flow and porous medium equation

NASA Astrophysics Data System (ADS)

Ma, Li; Witt, Ingo

2018-06-01

In this paper, we study the discrete Morse flow for the Ricci flow on the American football, which is the 2-sphere with the north and south poles removed and equipped with a metric g0 of constant scalar curvature, and for the porous medium equation on a bounded regular domain in the plane. We show that under suitable assumptions on the initial metric g(0) one has a weak approximate discrete Morse flow for the approximated Ricci flow and porous medium equation on any time interval.

Peak flow regression equations For small, ungaged streams in Maine: Comparing map-based to field-based variables

USGS Publications Warehouse

Lombard, Pamela J.; Hodgkins, Glenn A.

2015-01-01

Regression equations to estimate peak streamflows with 1- to 500-year recurrence intervals (annual exceedance probabilities from 99 to 0.2 percent, respectively) were developed for small, ungaged streams in Maine. Equations presented here are the best available equations for estimating peak flows at ungaged basins in Maine with drainage areas from 0.3 to 12 square miles (mi2). Previously developed equations continue to be the best available equations for estimating peak flows for basin areas greater than 12 mi2. New equations presented here are based on streamflow records at 40 U.S. Geological Survey streamgages with a minimum of 10 years of recorded peak flows between 1963 and 2012. Ordinary least-squares regression techniques were used to determine the best explanatory variables for the regression equations. Traditional map-based explanatory variables were compared to variables requiring field measurements. Two field-based variables—culvert rust lines and bankfull channel widths—either were not commonly found or did not explain enough of the variability in the peak flows to warrant inclusion in the equations. The best explanatory variables were drainage area and percent basin wetlands; values for these variables were determined with a geographic information system. Generalized least-squares regression was used with these two variables to determine the equation coefficients and estimates of accuracy for the final equations.

A linearized Euler analysis of unsteady flows in turbomachinery

NASA Technical Reports Server (NTRS)

Hall, Kenneth C.; Crawley, Edward F.

1987-01-01

A method for calculating unsteady flows in cascades is presented. The model, which is based on the linearized unsteady Euler equations, accounts for blade loading shock motion, wake motion, and blade geometry. The mean flow through the cascade is determined by solving the full nonlinear Euler equations. Assuming the unsteadiness in the flow is small, then the Euler equations are linearized about the mean flow to obtain a set of linear variable coefficient equations which describe the small amplitude, harmonic motion of the flow. These equations are discretized on a computational grid via a finite volume operator and solved directly subject to an appropriate set of linearized boundary conditions. The steady flow, which is calculated prior to the unsteady flow, is found via a Newton iteration procedure. An important feature of the analysis is the use of shock fitting to model steady and unsteady shocks. Use of the Euler equations with the unsteady Rankine-Hugoniot shock jump conditions correctly models the generation of steady and unsteady entropy and vorticity at shocks. In particular, the low frequency shock displacement is correctly predicted. Results of this method are presented for a variety of test cases. Predicted unsteady transonic flows in channels are compared to full nonlinear Euler solutions obtained using time-accurate, time-marching methods. The agreement between the two methods is excellent for small to moderate levels of flow unsteadiness. The method is also used to predict unsteady flows in cascades due to blade motion (flutter problem) and incoming disturbances (gust response problem).

Equations for estimating selected streamflow statistics in Rhode Island

USGS Publications Warehouse

Bent, Gardner C.; Steeves, Peter A.; Waite, Andrew M.

2014-01-01

The equations, which are based on data from streams with little to no flow alterations, will provide an estimate of the natural flows for a selected site. They will not estimate flows for altered sites with dams, surface-water withdrawals, groundwater withdrawals (pumping wells), diversions, and wastewater discharges. If the equations are used to estimate streamflow statistics for altered sites, the user should adjust the flow estimates for the alterations. The regression equations should be used only for ungaged sites with drainage areas between 0.52 and 294 square miles and stream densities between 0.94 and 3.49 miles per square mile; these are the ranges of the explanatory variables in the equations.

Fragility Analysis of a Concrete Gravity Dam Embedded in Rock and Its System Response Curve Computed by the Analytical Program GDLAD_Foundation

DTIC Science & Technology

2012-06-01

According to the Bernoulli equation for ideal flows, i.e. steady, frictionless, incompressible flows, the total head, H, at any point can be determined...centerline and using the Bernoulli equation for ideal flow with an assumption that the velocity is small, the total head equals the pressure head...the Bernoulli equation for ideal flows, i.e. steady, frictionless, incompressible flows, the total head, H, at any point can be determined by

An implicit numerical scheme for the simulation of internal viscous flows on unstructured grids

NASA Technical Reports Server (NTRS)

Jorgenson, Philip C. E.; Pletcher, Richard H.

1994-01-01

The Navier-Stokes equations are solved numerically for two-dimensional steady viscous laminar flows. The grids are generated based on the method of Delaunay triangulation. A finite-volume approach is used to discretize the conservation law form of the compressible flow equations written in terms of primitive variables. A preconditioning matrix is added to the equations so that low Mach number flows can be solved economically. The equations are time marched using either an implicit Gauss-Seidel iterative procedure or a solver based on a conjugate gradient like method. A four color scheme is employed to vectorize the block Gauss-Seidel relaxation procedure. This increases the memory requirements minimally and decreases the computer time spent solving the resulting system of equations substantially. A factor of 7.6 speed up in the matrix solver is typical for the viscous equations. Numerical results are obtained for inviscid flow over a bump in a channel at subsonic and transonic conditions for validation with structured solvers. Viscous results are computed for developing flow in a channel, a symmetric sudden expansion, periodic tandem cylinders in a cross-flow, and a four-port valve. Comparisons are made with available results obtained by other investigators.

Kinetically reduced local Navier-Stokes equations: an alternative approach to hydrodynamics.

PubMed

Karlin, Iliya V; Tomboulides, Ananias G; Frouzakis, Christos E; Ansumali, Santosh

2006-09-01

An alternative approach, the kinetically reduced local Navier-Stokes (KRLNS) equations for the grand potential and the momentum, is proposed for the simulation of low Mach number flows. The Taylor-Green vortex flow is considered in the KRLNS framework, and compared to the results of the direct numerical simulation of the incompressible Navier-Stokes equations. The excellent agreement between the KRLNS equations and the incompressible nonlocal Navier-Stokes equations for this nontrivial time-dependent flow indicates that the former is a viable alternative for computational fluid dynamics at low Mach numbers.

Pressure model of a four-way spool valve for simulating electrohydraulic control systems

NASA Technical Reports Server (NTRS)

Gebben, V. D.

1976-01-01

An equation that relates the pressure flow characteristics of hydraulic spool valves was developed. The dependent variable is valve output pressure, and the independent variables are spool position and flow. This causal form of equation is preferred in applications that simulate the effects of hydraulic line dynamics. Results from this equation are compared with those from the conventional valve equation, whose dependent variable is flow. A computer program of the valve equations includes spool stops, leakage spool clearances, and dead-zone characteristics of overlap spools.

BHR equations re-derived with immiscible particle effects

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schwarzkopf, John Dennis; Horwitz, Jeremy A.

2015-05-01

Compressible and variable density turbulent flows with dispersed phase effects are found in many applications ranging from combustion to cloud formation. These types of flows are among the most challenging to simulate. While the exact equations governing a system of particles and fluid are known, computational resources limit the scale and detail that can be simulated in this type of problem. Therefore, a common method is to simulate averaged versions of the flow equations, which still capture salient physics and is relatively less computationally expensive. Besnard developed such a model for variable density miscible turbulence, where ensemble-averaging was applied tomore » the flow equations to yield a set of filtered equations. Besnard further derived transport equations for the Reynolds stresses, the turbulent mass flux, and the density-specific volume covariance, to help close the filtered momentum and continuity equations. We re-derive the exact BHR closure equations which include integral terms owing to immiscible effects. Physical interpretations of the additional terms are proposed along with simple models. The goal of this work is to extend the BHR model to allow for the simulation of turbulent flows where an immiscible dispersed phase is non-trivially coupled with the carrier phase.« less

Generalization of Boundary-Layer Momentum-Integral Equations to Three-Dimensional Flows Including Those of Rotating System

NASA Technical Reports Server (NTRS)

Mager, Arthur

1952-01-01

The Navier-Stokes equations of motion and the equation of continuity are transformed so as to apply to an orthogonal curvilinear coordinate system rotating with a uniform angular velocity about an arbitrary axis in space. A usual simplification of these equations as consistent with the accepted boundary-layer theory and an integration of these equations through the boundary layer result in boundary-layer momentum-integral equations for three-dimensional flows that are applicable to either rotating or nonrotating fluid boundaries. These equations are simplified and an approximate solution in closed integral form is obtained for a generalized boundary-layer momentum-loss thickness and flow deflection at the wall in the turbulent case. A numerical evaluation of this solution carried out for data obtained in a curving nonrotating duct shows a fair quantitative agreement with the measures values. The form in which the equations are presented is readily adaptable to cases of steady, three-dimensional, incompressible boundary-layer flow like that over curved ducts or yawed wings; and it also may be used to describe the boundary-layer flow over various rotating surfaces, thus applying to turbomachinery, propellers, and helicopter blades.

An approximate Riemann solver for real gas parabolized Navier-Stokes equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Urbano, Annafederica, E-mail: annafederica.urbano@uniroma1.it; Nasuti, Francesco, E-mail: francesco.nasuti@uniroma1.it

2013-01-15

Under specific assumptions, parabolized Navier-Stokes equations are a suitable mean to study channel flows. A special case is that of high pressure flow of real gases in cooling channels where large crosswise gradients of thermophysical properties occur. To solve the parabolized Navier-Stokes equations by a space marching approach, the hyperbolicity of the system of governing equations is obtained, even for very low Mach number flow, by recasting equations such that the streamwise pressure gradient is considered as a source term. For this system of equations an approximate Roe's Riemann solver is developed as the core of a Godunov type finitemore » volume algorithm. The properties of the approximated Riemann solver, which is a modification of Roe's Riemann solver for the parabolized Navier-Stokes equations, are presented and discussed with emphasis given to its original features introduced to handle fluids governed by a generic real gas EoS. Sample solutions are obtained for low Mach number high compressible flows of transcritical methane, heated in straight long channels, to prove the solver ability to describe flows dominated by complex thermodynamic phenomena.« less

Determining the spill flow discharge of combined sewer overflows using rating curves based on computational fluid dynamics instead of the standard weir equation.

PubMed

Fach, S; Sitzenfrei, R; Rauch, W

2009-01-01

It is state of the art to evaluate and optimise sewer systems with urban drainage models. Since spill flow data is essential in the calibration process of conceptual models it is important to enhance the quality of such data. A wide spread approach is to calculate the spill flow volume by using standard weir equations together with measured water levels. However, these equations are only applicable to combined sewer overflow (CSO) structures, whose weir constructions correspond with the standard weir layout. The objective of this work is to outline an alternative approach to obtain spill flow discharge data based on measurements with a sonic depth finder. The idea is to determine the relation between water level and rate of spill flow by running a detailed 3D computational fluid dynamics (CFD) model. Two real world CSO structures have been chosen due to their complex structure, especially with respect to the weir construction. In a first step the simulation results were analysed to identify flow conditions for discrete steady states. It will be shown that the flow conditions in the CSO structure change after the spill flow pipe acts as a controlled outflow and therefore the spill flow discharge cannot be described with a standard weir equation. In a second step the CFD results will be used to derive rating curves which can be easily applied in everyday practice. Therefore the rating curves are developed on basis of the standard weir equation and the equation for orifice-type outlets. Because the intersection of both equations is not known, the coefficients of discharge are regressed from CFD simulation results. Furthermore, the regression of the CFD simulation results are compared with the one of the standard weir equation by using historic water levels and hydrographs generated with a hydrodynamic model. The uncertainties resulting of the wide spread use of the standard weir equation are demonstrated.

The Use of DNS in Turbulence Modeling

NASA Technical Reports Server (NTRS)

Mansour, Nagi N.; Merriam, Marshal (Technical Monitor)

1997-01-01

The use of Direct numerical simulations (DNS) data in developing and testing turbulence models is reviewed. The data is used to test turbulence models at all levels: algebraic, one-equation, two-equation and full Reynolds stress models were tested. Particular examples on the development of models for the dissipation rate equation are presented. Homogeneous flows are used to test new scaling arguments for the various terms in the dissipation rate equation. The channel flow data is used to develop modifications to the equation model that take into account near-wall effects. DNS of compressible flows under mean compression are used in testing new compressible modifications to the two-equation models.

The effect of magnetohydrodynamic nano fluid flow through porous cylinder

NASA Astrophysics Data System (ADS)

Widodo, Basuki; Arif, Didik Khusnul; Aryany, Deviana; Asiyah, Nur; Widjajati, Farida Agustini; Kamiran

2017-08-01

This paper concerns about the analysis of the effect of magnetohydrodynamic nano fluid flow through horizontal porous cylinder on steady and incompressible condition. Fluid flow is assumed opposite gravity and induced by magnet field. Porous cylinder is assumed had the same depth of porous and was not absorptive. The First thing to do in this research is to build the model of fluid flow to obtain dimentional governing equations. The dimentional governing equations are consist of continuity equation, momentum equation, and energy equation. Furthermore, the dimensional governing equations are converted to non-dimensional governing equation by using non-dimensional parameters and variables. Then, the non-dimensional governing equations are transformed into similarity equations using stream function and solved using Keller-Box method. The result of numerical solution further is obtained by taking variation of magnetic parameter, Prandtl number, porosity parameter, and volume fraction. The numerical results show that velocity profiles increase and temperature profiles decrease when both of the magnetic and the porosity parameter increase. However, the velocity profiles decrease and the temperature profiles increase when both of the magnetic and the porosity parameter increase.

Extension of lattice Boltzmann flux solver for simulation of compressible multi-component flows

NASA Astrophysics Data System (ADS)

Yang, Li-Ming; Shu, Chang; Yang, Wen-Ming; Wang, Yan

2018-05-01

The lattice Boltzmann flux solver (LBFS), which was presented by Shu and his coworkers for solving compressible fluid flow problems, is extended to simulate compressible multi-component flows in this work. To solve the two-phase gas-liquid problems, the model equations with stiffened gas equation of state are adopted. In this model, two additional non-conservative equations are introduced to represent the material interfaces, apart from the classical Euler equations. We first convert the interface equations into the full conservative form by applying the mass equation. After that, we calculate the numerical fluxes of the classical Euler equations by the existing LBFS and the numerical fluxes of the interface equations by the passive scalar approach. Once all the numerical fluxes at the cell interface are obtained, the conservative variables at cell centers can be updated by marching the equations in time and the material interfaces can be identified via the distributions of the additional variables. The numerical accuracy and stability of present scheme are validated by its application to several compressible multi-component fluid flow problems.

Application of the method of lines for solutions of the Navier-Stokes equations using a nonuniform grid distribution

NASA Technical Reports Server (NTRS)

Abolhassani, J. S.; Tiwari, S. N.

1983-01-01

The feasibility of the method of lines for solutions of physical problems requiring nonuniform grid distributions is investigated. To attain this, it is also necessary to investigate the stiffness characteristics of the pertinent equations. For specific applications, the governing equations considered are those for viscous, incompressible, two dimensional and axisymmetric flows. These equations are transformed from the physical domain having a variable mesh to a computational domain with a uniform mesh. The two governing partial differential equations are the vorticity and stream function equations. The method of lines is used to solve the vorticity equation and the successive over relaxation technique is used to solve the stream function equation. The method is applied to three laminar flow problems: the flow in ducts, curved-wall diffusers, and a driven cavity. Results obtained for different flow conditions are in good agreement with available analytical and numerical solutions. The viability and validity of the method of lines are demonstrated by its application to Navier-Stokes equations in the physical domain having a variable mesh.

An advanced kinetic theory for morphing continuum with inner structures

NASA Astrophysics Data System (ADS)

Chen, James

2017-12-01

Advanced kinetic theory with the Boltzmann-Curtiss equation provides a promising tool for polyatomic gas flows, especially for fluid flows containing inner structures, such as turbulence, polyatomic gas flows and others. Although a Hamiltonian-based distribution function was proposed for diatomic gas flow, a general distribution function for the generalized Boltzmann-Curtiss equations and polyatomic gas flow is still out of reach. With assistance from Boltzmann's entropy principle, a generalized Boltzmann-Curtiss distribution for polyatomic gas flow is introduced. The corresponding governing equations at equilibrium state are derived and compared with Eringen's morphing (micropolar) continuum theory derived under the framework of rational continuum thermomechanics. Although rational continuum thermomechanics has the advantages of mathematical rigor and simplicity, the presented statistical kinetic theory approach provides a clear physical picture for what the governing equations represent.

Methods for estimating selected low-flow frequency statistics and mean annual flow for ungaged locations on streams in North Georgia

USGS Publications Warehouse

Gotvald, Anthony J.

2017-01-13

The U.S. Geological Survey, in cooperation with the Georgia Department of Natural Resources, Environmental Protection Division, developed regional regression equations for estimating selected low-flow frequency and mean annual flow statistics for ungaged streams in north Georgia that are not substantially affected by regulation, diversions, or urbanization. Selected low-flow frequency statistics and basin characteristics for 56 streamgage locations within north Georgia and 75 miles beyond the State’s borders in Alabama, Tennessee, North Carolina, and South Carolina were combined to form the final dataset used in the regional regression analysis. Because some of the streamgages in the study recorded zero flow, the final regression equations were developed using weighted left-censored regression analysis to analyze the flow data in an unbiased manner, with weights based on the number of years of record. The set of equations includes the annual minimum 1- and 7-day average streamflow with the 10-year recurrence interval (referred to as 1Q10 and 7Q10), monthly 7Q10, and mean annual flow. The final regional regression equations are functions of drainage area, mean annual precipitation, and relief ratio for the selected low-flow frequency statistics and drainage area and mean annual precipitation for mean annual flow. The average standard error of estimate was 13.7 percent for the mean annual flow regression equation and ranged from 26.1 to 91.6 percent for the selected low-flow frequency equations.The equations, which are based on data from streams with little to no flow alterations, can be used to provide estimates of the natural flows for selected ungaged stream locations in the area of Georgia north of the Fall Line. The regression equations are not to be used to estimate flows for streams that have been altered by the effects of major dams, surface-water withdrawals, groundwater withdrawals (pumping wells), diversions, or wastewater discharges. The regression equations should be used only for ungaged sites with drainage areas between 1.67 and 576 square miles, mean annual precipitation between 47.6 and 81.6 inches, and relief ratios between 0.146 and 0.607; these are the ranges of the explanatory variables used to develop the equations. An attempt was made to develop regional regression equations for the area of Georgia south of the Fall Line by using the same approach used during this study for north Georgia; however, the equations resulted with high average standard errors of estimates and poorly predicted flows below 0.5 cubic foot per second, which may be attributed to the karst topography common in that area.The final regression equations developed from this study are planned to be incorporated into the U.S. Geological Survey StreamStats program. StreamStats is a Web-based geographic information system that provides users with access to an assortment of analytical tools useful for water-resources planning and management, and for engineering design applications, such as the design of bridges. The StreamStats program provides streamflow statistics and basin characteristics for U.S. Geological Survey streamgage locations and ungaged sites of interest. StreamStats also can compute basin characteristics and provide estimates of streamflow statistics for ungaged sites when users select the location of a site along any stream in Georgia.

Prediction of unsteady transonic flow around missile configurations

NASA Technical Reports Server (NTRS)

Nixon, D.; Reisenthel, P. H.; Torres, T. O.; Klopfer, G. H.

1990-01-01

This paper describes the preliminary development of a method for predicting the unsteady transonic flow around missiles at transonic and supersonic speeds, with the final goal of developing a computer code for use in aeroelastic calculations or during maneuvers. The basic equations derived for this method are an extension of those derived by Klopfer and Nixon (1989) for steady flow and are a subset of the Euler equations. In this approach, the five Euler equations are reduced to an equation similar to the three-dimensional unsteady potential equation, and a two-dimensional Poisson equation. In addition, one of the equations in this method is almost identical to the potential equation for which there are well tested computer codes, allowing the development of a prediction method based in part on proved technology.

Development of a three-dimensional supersonic inlet flow analysis

NASA Technical Reports Server (NTRS)

Buggeln, R. C.; Mcdonald, H.; Levy, R.; Kreskovsky, J. P.

1980-01-01

A method for computing three dimensional flow in supersonic inlets is described. An approximate set of governing equations is given for viscous flows which have a primary flow direction. The governing equations are written in general orthogonal coordinates. These equations are modified in the subsonic region of the flow to prevent the phenomenon of branching. Results are presented for the two sample cases: a Mach number equals 2.5 flow in a square duct, and a Mach number equals 3.0 flow in a research jet engine inlet. In the latter case the computed results are compared with the experimental data. A users' manual is included.

Helmholtz-Smoluchowski velocity for viscoelastic electroosmotic flows.

PubMed

Park, H M; Lee, W M

2008-01-15

Many biofluids such as blood and DNA solutions are viscoelastic and exhibit extraordinary flow behaviors, not existing in Newtonian fluids. Adopting appropriate constitutive equations these exotic flow behaviors can be modeled and predicted reasonably using various numerical methods. However, the governing equations for viscoelastic flows are not easily solvable, especially for electroosmotic flows where the streamwise velocity varies rapidly from zero at the wall to a nearly uniform velocity at the outside of the very thin electric double layer. In the present investigation, we have devised a simple method to find the volumetric flow rate of viscoelastic electroosmotic flows through microchannels. It is based on the concept of the Helmholtz-Smoluchowski velocity which is widely adopted in the electroosmotic flows of Newtonian fluids. It is shown that the Helmholtz-Smoluchowski velocity for viscoelastic fluids can be found by solving a simple cubic algebraic equation. The volumetric flow rate obtained using this Helmholtz-Smoluchowski velocity is found to be almost the same as that obtained by solving the governing partial differential equations for various viscoelastic fluids.

Hydrostatic calculations of axisymmetric flow and its stability for the AGCE model

NASA Technical Reports Server (NTRS)

Miller, T. L.; Gall, R. L.

1981-01-01

Baroclinic waves in the atmospherics general circulation experiment (AGCE) apparatus by the use of numerical hydrostatic primitive equation models were determined. The calculation is accomplished by using an axisymmetric primitive equation model to compute, for a given set of experimental parameters, a steady state axisymmetric flow and then testing this axisymmetric flow for stability using a linear primitive equation model. Some axisymmetric flows are presented together with preliminary stability calculations.

A paradigm for modeling and computation of gas dynamics

NASA Astrophysics Data System (ADS)

Xu, Kun; Liu, Chang

2017-02-01

In the continuum flow regime, the Navier-Stokes (NS) equations are usually used for the description of gas dynamics. On the other hand, the Boltzmann equation is applied for the rarefied flow. These two equations are based on distinguishable modeling scales for flow physics. Fortunately, due to the scale separation, i.e., the hydrodynamic and kinetic ones, both the Navier-Stokes equations and the Boltzmann equation are applicable in their respective domains. However, in real science and engineering applications, they may not have such a distinctive scale separation. For example, around a hypersonic flying vehicle, the flow physics at different regions may correspond to different regimes, where the local Knudsen number can be changed significantly in several orders of magnitude. With a variation of flow physics, theoretically a continuous governing equation from the kinetic Boltzmann modeling to the hydrodynamic Navier-Stokes dynamics should be used for its efficient description. However, due to the difficulties of a direct modeling of flow physics in the scale between the kinetic and hydrodynamic ones, there is basically no reliable theory or valid governing equations to cover the whole transition regime, except resolving flow physics always down to the mean free path scale, such as the direct Boltzmann solver and the Direct Simulation Monte Carlo (DSMC) method. In fact, it is an unresolved problem about the exact scale for the validity of the NS equations, especially in the small Reynolds number cases. The computational fluid dynamics (CFD) is usually based on the numerical solution of partial differential equations (PDEs), and it targets on the recovering of the exact solution of the PDEs as mesh size and time step converging to zero. This methodology can be hardly applied to solve the multiple scale problem efficiently because there is no such a complete PDE for flow physics through a continuous variation of scales. For the non-equilibrium flow study, the direct modeling methods, such as DSMC, particle in cell, and smooth particle hydrodynamics, play a dominant role to incorporate the flow physics into the algorithm construction directly. It is fully legitimate to combine the modeling and computation together without going through the process of constructing PDEs. In other words, the CFD research is not only to obtain the numerical solution of governing equations but to model flow dynamics as well. This methodology leads to the unified gas-kinetic scheme (UGKS) for flow simulation in all flow regimes. Based on UGKS, the boundary for the validation of the Navier-Stokes equations can be quantitatively evaluated. The combination of modeling and computation provides a paradigm for the description of multiscale transport process.

Thermoelastic-plastic flow equations in general coordinates

DOE PAGES

Blaschke, Daniel N.; Preston, Dean L.

2018-03-28

The equations governing the thermoelastic-plastic flow of isotropic solids in the Prandtl- Reuss and small anisotropy approximations in Cartesian coordinates are generalized to arbitrary coordinate systems. In applications the choice of coordinates is dictated by the symmetry of the solid flow. The generally invariant equations are evaluated in spherical, cylindrical (including uniaxial), and both prolate and oblate spheroidal coordinates.

Regularity of the 3D Navier-Stokes equations with viewpoint of 2D flow

NASA Astrophysics Data System (ADS)

Bae, Hyeong-Ohk

2018-04-01

The regularity of 2D Navier-Stokes flow is well known. In this article we study the relationship of 3D and 2D flow, and the regularity of the 3D Naiver-Stokes equations with viewpoint of 2D equations. We consider the problem in the Cartesian and in the cylindrical coordinates.

Thermoelastic-plastic flow equations in general coordinates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Blaschke, Daniel N.; Preston, Dean L.

The equations governing the thermoelastic-plastic flow of isotropic solids in the Prandtl- Reuss and small anisotropy approximations in Cartesian coordinates are generalized to arbitrary coordinate systems. In applications the choice of coordinates is dictated by the symmetry of the solid flow. The generally invariant equations are evaluated in spherical, cylindrical (including uniaxial), and both prolate and oblate spheroidal coordinates.

Multigrid calculation of three-dimensional turbomachinery flows

NASA Technical Reports Server (NTRS)

Caughey, David A.

1989-01-01

Research was performed in the general area of computational aerodynamics, with particular emphasis on the development of efficient techniques for the solution of the Euler and Navier-Stokes equations for transonic flows through the complex blade passages associated with turbomachines. In particular, multigrid methods were developed, using both explicit and implicit time-stepping schemes as smoothing algorithms. The specific accomplishments of the research have included: (1) the development of an explicit multigrid method to solve the Euler equations for three-dimensional turbomachinery flows based upon the multigrid implementation of Jameson's explicit Runge-Kutta scheme (Jameson 1983); (2) the development of an implicit multigrid scheme for the three-dimensional Euler equations based upon lower-upper factorization; (3) the development of a multigrid scheme using a diagonalized alternating direction implicit (ADI) algorithm; (4) the extension of the diagonalized ADI multigrid method to solve the Euler equations of inviscid flow for three-dimensional turbomachinery flows; and also (5) the extension of the diagonalized ADI multigrid scheme to solve the Reynolds-averaged Navier-Stokes equations for two-dimensional turbomachinery flows.

Finite-volume method with lattice Boltzmann flux scheme for incompressible porous media flow at the representative-elementary-volume scale.

PubMed

Hu, Yang; Li, Decai; Shu, Shi; Niu, Xiaodong

2016-02-01

Based on the Darcy-Brinkman-Forchheimer equation, a finite-volume computational model with lattice Boltzmann flux scheme is proposed for incompressible porous media flow in this paper. The fluxes across the cell interface are calculated by reconstructing the local solution of the generalized lattice Boltzmann equation for porous media flow. The time-scaled midpoint integration rule is adopted to discretize the governing equation, which makes the time step become limited by the Courant-Friedricks-Lewy condition. The force term which evaluates the effect of the porous medium is added to the discretized governing equation directly. The numerical simulations of the steady Poiseuille flow, the unsteady Womersley flow, the circular Couette flow, and the lid-driven flow are carried out to verify the present computational model. The obtained results show good agreement with the analytical, finite-difference, and/or previously published solutions.

Mixed Convection Opposing Flow in a Vertical Porous Annulus-Two Temperature Model

NASA Astrophysics Data System (ADS)

Al-Rashed, Abdullah A. AA; J, Salman Ahmed N.; Khaleed, H. M. T.; Yunus Khan, T. M.; NazimAhamed, K. S.

2016-09-01

The opposing flow in a porous medium refers to a condition when the forcing velocity flows in opposite direction to thermal buoyancy obstructing the buoyant force. The present research refers to the effect of opposing flow in a vertical porous annulus embedded with fluid saturated porous medium. The thermal non-equilibrium approach with Darcy modal is considered. The boundary conditions are such that the inner radius is heated with constant temperature Tw the outer radius is maintained at constant temperature Tc. The coupled nonlinear partial differential equations such as momentum equation, energy equation for fluid and energy equation for solid are solved using the finite element method. The opposing flow variation of average Nusselt number with respect to radius ratio Rr, Aspect ratioAr and Radiation parameter Rd for different values of Peclet number Pe are investigated. It is found that the flow behavior is quite different from that of aiding flow.

Computation of oscillating airfoil flows with one- and two-equation turbulence models

NASA Technical Reports Server (NTRS)

Ekaterinaris, J. A.; Menter, F. R.

1994-01-01

The ability of one- and two-equation turbulence models to predict unsteady separated flows over airfoils is evaluated. An implicit, factorized, upwind-biased numerical scheme is used for the integration of the compressible, Reynolds-averaged Navier-Stokes equations. The turbulent eddy viscosity is obtained from the computed mean flowfield by integration of the turbulent field equations. One- and two-equation turbulence models are first tested for a separated airfoil flow at fixed angle of incidence. The same models are then applied to compute the unsteady flowfields about airfoils undergoing oscillatory motion at low subsonic Mach numbers. Experimental cases where the flow has been tripped at the leading-edge and where natural transition was allowed to occur naturally are considered. The more recently developed turbulence models capture the physics of unsteady separated flow significantly better than the standard kappa-epsilon and kappa-omega models. However, certain differences in the hysteresis effects are observed. For an untripped high-Reynolds-number flow, it was found necessary to take into account the leading-edge transitional flow region to capture the correct physical mechanism that leads to dynamic stall.

A Gas-Kinetic Scheme for Reactive Flows

NASA Technical Reports Server (NTRS)

Lian,Youg-Sheng; Xu, Kun

1998-01-01

In this paper, the gas-kinetic BGK scheme for the compressible flow equations is extended to chemical reactive flow. The mass fraction of the unburnt gas is implemented into the gas kinetic equation by assigning a new internal degree of freedom to the particle distribution function. The new variable can be also used to describe fluid trajectory for the nonreactive flows. Due to the gas-kinetic BGK model, the current scheme basically solves the Navier-Stokes chemical reactive flow equations. Numerical tests validate the accuracy and robustness of the current kinetic method.

Computation of incompressible viscous flows through turbopump components

NASA Technical Reports Server (NTRS)

Kiris, Cetin; Chang, Leon

1993-01-01

Flow through pump components, such as an inducer and an impeller, is efficiently simulated by solving the incompressible Navier-Stokes equations. The solution method is based on the pseudocompressibility approach and uses an implicit-upwind differencing scheme together with the Gauss-Seidel line relaxation method. the equations are solved in steadily rotating reference frames and the centrifugal force and the Coriolis force are added to the equation of motion. Current computations use a one-equation Baldwin-Barth turbulence model which is derived from a simplified form of the standard k-epsilon model equations. The resulting computer code is applied to the flow analysis inside a generic rocket engine pump inducer, a fuel pump impeller, and SSME high pressure fuel turbopump impeller. Numerical results of inducer flow are compared with experimental measurements. In the fuel pump impeller, the effect of downstream boundary conditions is investigated. Flow analyses at 80 percent, 100 percent, and 120 percent of design conditions are presented.

A note on the solutions of some nonlinear equations arising in third-grade fluid flows: an exact approach.

PubMed

Aziz, Taha; Mahomed, F M

2014-01-01

In this communication, we utilize some basic symmetry reductions to transform the governing nonlinear partial differential equations arising in the study of third-grade fluid flows into ordinary differential equations. We obtain some simple closed-form steady-state solutions of these reduced equations. Our solutions are valid for the whole domain [0,∞) and also satisfy the physical boundary conditions. We also present the numerical solutions for some of the underlying equations. The graphs corresponding to the essential physical parameters of the flow are presented and discussed.

Derivation of Inviscid Quasi-geostrophic Equation from Rotational Compressible Magnetohydrodynamic Flows

NASA Astrophysics Data System (ADS)

Kwon, Young-Sam; Lin, Ying-Chieh; Su, Cheng-Fang

2018-04-01

In this paper, we consider the compressible models of magnetohydrodynamic flows giving rise to a variety of mathematical problems in many areas. We derive a rigorous quasi-geostrophic equation governed by magnetic field from the rotational compressible magnetohydrodynamic flows with the well-prepared initial data. It is a first derivation of quasi-geostrophic equation governed by the magnetic field, and the tool is based on the relative entropy method. This paper covers two results: the existence of the unique local strong solution of quasi-geostrophic equation with the good regularity and the derivation of a quasi-geostrophic equation.

A Note on the Solutions of Some Nonlinear Equations Arising in Third-Grade Fluid Flows: An Exact Approach

PubMed Central

Mahomed, F. M.

2014-01-01

In this communication, we utilize some basic symmetry reductions to transform the governing nonlinear partial differential equations arising in the study of third-grade fluid flows into ordinary differential equations. We obtain some simple closed-form steady-state solutions of these reduced equations. Our solutions are valid for the whole domain [0,∞) and also satisfy the physical boundary conditions. We also present the numerical solutions for some of the underlying equations. The graphs corresponding to the essential physical parameters of the flow are presented and discussed. PMID:25143962

Numerical optimization using flow equations.

PubMed

Punk, Matthias

2014-12-01

We develop a method for multidimensional optimization using flow equations. This method is based on homotopy continuation in combination with a maximum entropy approach. Extrema of the optimizing functional correspond to fixed points of the flow equation. While ideas based on Bayesian inference such as the maximum entropy method always depend on a prior probability, the additional step in our approach is to perform a continuous update of the prior during the homotopy flow. The prior probability thus enters the flow equation only as an initial condition. We demonstrate the applicability of this optimization method for two paradigmatic problems in theoretical condensed matter physics: numerical analytic continuation from imaginary to real frequencies and finding (variational) ground states of frustrated (quantum) Ising models with random or long-range antiferromagnetic interactions.

Numerical optimization using flow equations

NASA Astrophysics Data System (ADS)

Punk, Matthias

2014-12-01

We develop a method for multidimensional optimization using flow equations. This method is based on homotopy continuation in combination with a maximum entropy approach. Extrema of the optimizing functional correspond to fixed points of the flow equation. While ideas based on Bayesian inference such as the maximum entropy method always depend on a prior probability, the additional step in our approach is to perform a continuous update of the prior during the homotopy flow. The prior probability thus enters the flow equation only as an initial condition. We demonstrate the applicability of this optimization method for two paradigmatic problems in theoretical condensed matter physics: numerical analytic continuation from imaginary to real frequencies and finding (variational) ground states of frustrated (quantum) Ising models with random or long-range antiferromagnetic interactions.

Turbulence Modeling Validation, Testing, and Development

NASA Technical Reports Server (NTRS)

Bardina, J. E.; Huang, P. G.; Coakley, T. J.

1997-01-01

The primary objective of this work is to provide accurate numerical solutions for selected flow fields and to compare and evaluate the performance of selected turbulence models with experimental results. Four popular turbulence models have been tested and validated against experimental data often turbulent flows. The models are: (1) the two-equation k-epsilon model of Wilcox, (2) the two-equation k-epsilon model of Launder and Sharma, (3) the two-equation k-omega/k-epsilon SST model of Menter, and (4) the one-equation model of Spalart and Allmaras. The flows investigated are five free shear flows consisting of a mixing layer, a round jet, a plane jet, a plane wake, and a compressible mixing layer; and five boundary layer flows consisting of an incompressible flat plate, a Mach 5 adiabatic flat plate, a separated boundary layer, an axisymmetric shock-wave/boundary layer interaction, and an RAE 2822 transonic airfoil. The experimental data for these flows are well established and have been extensively used in model developments. The results are shown in the following four sections: Part A describes the equations of motion and boundary conditions; Part B describes the model equations, constants, parameters, boundary conditions, and numerical implementation; and Parts C and D describe the experimental data and the performance of the models in the free-shear flows and the boundary layer flows, respectively.

Finite elements and finite differences for transonic flow calculations

NASA Technical Reports Server (NTRS)

Hafez, M. M.; Murman, E. M.; Wellford, L. C.

1978-01-01

The paper reviews the chief finite difference and finite element techniques used for numerical solution of nonlinear mixed elliptic-hyperbolic equations governing transonic flow. The forms of the governing equations for unsteady two-dimensional transonic flow considered are the Euler equation, the full potential equation in both conservative and nonconservative form, the transonic small-disturbance equation in both conservative and nonconservative form, and the hodograph equations for the small-disturbance case and the full-potential case. Finite difference methods considered include time-dependent methods, relaxation methods, semidirect methods, and hybrid methods. Finite element methods include finite element Lax-Wendroff schemes, implicit Galerkin method, mixed variational principles, dual iterative procedures, optimal control methods and least squares.

A model for closing the inviscid form of the average-passage equation system

NASA Technical Reports Server (NTRS)

Adamczyk, J. J.; Mulac, R. A.; Celestina, M. L.

1985-01-01

A mathematical model is proposed for closing or mathematically completing the system of equations which describes the time average flow field through the blade passages of multistage turbomachinery. These equations referred to as the average passage equation system govern a conceptual model which has proven useful in turbomachinery aerodynamic design and analysis. The closure model is developed so as to insure a consistency between these equations and the axisymmetric through flow equations. The closure model was incorporated into a computer code for use in simulating the flow field about a high speed counter rotating propeller and a high speed fan stage. Results from these simulations are presented.

Theoretical and computational analyses of LNG evaporator

NASA Astrophysics Data System (ADS)

Chidambaram, Palani Kumar; Jo, Yang Myung; Kim, Heuy Dong

2017-04-01

Theoretical and numerical analysis on the fluid flow and heat transfer inside a LNG evaporator is conducted in this work. Methane is used instead of LNG as the operating fluid. This is because; methane constitutes over 80% of natural gas. The analytical calculations are performed using simple mass and energy balance equations. The analytical calculations are made to assess the pressure and temperature variations in the steam tube. Multiphase numerical simulations are performed by solving the governing equations (basic flow equations of continuity, momentum and energy equations) in a portion of the evaporator domain consisting of a single steam pipe. The flow equations are solved along with equations of species transport. Multiphase modeling is incorporated using VOF method. Liquid methane is the primary phase. It vaporizes into the secondary phase gaseous methane. Steam is another secondary phase which flows through the heating coils. Turbulence is modeled by a two equation turbulence model. Both the theoretical and numerical predictions are seen to match well with each other. Further parametric studies are planned based on the current research.

Computational Fluid Mechanics

NASA Technical Reports Server (NTRS)

Hassan, H. A.

1988-01-01

A one-equation turbulence model based on the turbulent kinetic energy equation is presented. The model is motivated by the success of the Johnson-King model and incorporates a number of features uncovered by Simpson's experiments on separated flows. Based on the results obtained, the model duplicates the success of algebraic models in attached flow regions and outperforms the two-equation models in detached flow regions.

Incompressible viscous flow simulations of the NFAC wind tunnel

NASA Technical Reports Server (NTRS)

Champney, Joelle Milene

1986-01-01

The capabilities of an existing 3-D incompressible Navier-Stokes flow solver, INS3D, are extended and improved to solve turbulent flows through the incorporation of zero- and two-equation turbulence models. The two-equation model equations are solved in their high Reynolds number form and utilize wall functions in the treatment of solid wall boundary conditions. The implicit approximate factorization scheme is modified to improve the stability of the two-equation solver. Applications to the 3-D viscous flow inside the 80 by 120 feet open return wind tunnel of the National Full Scale Aerodynamics Complex (NFAC) are discussed and described.

Methods for estimating flow-duration and annual mean-flow statistics for ungaged streams in Oklahoma

USGS Publications Warehouse

Esralew, Rachel A.; Smith, S. Jerrod

2010-01-01

Flow statistics can be used to provide decision makers with surface-water information needed for activities such as water-supply permitting, flow regulation, and other water rights issues. Flow statistics could be needed at any location along a stream. Most often, streamflow statistics are needed at ungaged sites, where no flow data are available to compute the statistics. Methods are presented in this report for estimating flow-duration and annual mean-flow statistics for ungaged streams in Oklahoma. Flow statistics included the (1) annual (period of record), (2) seasonal (summer-autumn and winter-spring), and (3) 12 monthly duration statistics, including the 20th, 50th, 80th, 90th, and 95th percentile flow exceedances, and the annual mean-flow (mean of daily flows for the period of record). Flow statistics were calculated from daily streamflow information collected from 235 streamflow-gaging stations throughout Oklahoma and areas in adjacent states. A drainage-area ratio method is the preferred method for estimating flow statistics at an ungaged location that is on a stream near a gage. The method generally is reliable only if the drainage-area ratio of the two sites is between 0.5 and 1.5. Regression equations that relate flow statistics to drainage-basin characteristics were developed for the purpose of estimating selected flow-duration and annual mean-flow statistics for ungaged streams that are not near gaging stations on the same stream. Regression equations were developed from flow statistics and drainage-basin characteristics for 113 unregulated gaging stations. Separate regression equations were developed by using U.S. Geological Survey streamflow-gaging stations in regions with similar drainage-basin characteristics. These equations can increase the accuracy of regression equations used for estimating flow-duration and annual mean-flow statistics at ungaged stream locations in Oklahoma. Streamflow-gaging stations were grouped by selected drainage-basin characteristics by using a k-means cluster analysis. Three regions were identified for Oklahoma on the basis of the clustering of gaging stations and a manual delineation of distinguishable hydrologic and geologic boundaries: Region 1 (western Oklahoma excluding the Oklahoma and Texas Panhandles), Region 2 (north- and south-central Oklahoma), and Region 3 (eastern and central Oklahoma). A total of 228 regression equations (225 flow-duration regressions and three annual mean-flow regressions) were developed using ordinary least-squares and left-censored (Tobit) multiple-regression techniques. These equations can be used to estimate 75 flow-duration statistics and annual mean-flow for ungaged streams in the three regions. Drainage-basin characteristics that were statistically significant independent variables in the regression analyses were (1) contributing drainage area; (2) station elevation; (3) mean drainage-basin elevation; (4) channel slope; (5) percentage of forested canopy; (6) mean drainage-basin hillslope; (7) soil permeability; and (8) mean annual, seasonal, and monthly precipitation. The accuracy of flow-duration regression equations generally decreased from high-flow exceedance (low-exceedance probability) to low-flow exceedance (high-exceedance probability) . This decrease may have happened because a greater uncertainty exists for low-flow estimates and low-flow is largely affected by localized geology that was not quantified by the drainage-basin characteristics selected. The standard errors of estimate of regression equations for Region 1 (western Oklahoma) were substantially larger than those standard errors for other regions, especially for low-flow exceedances. These errors may be a result of greater variability in low flow because of increased irrigation activities in this region. Regression equations may not be reliable for sites where the drainage-basin characteristics are outside the range of values of independent vari

Numerical Study on Electroosmotic Flow in Trapezoidal Microchannels

NASA Astrophysics Data System (ADS)

Zuo, C. C.; Ji, F.; Wang, L. F.

The analysis of electroosmotic flow mechanism in trapezoidal microchannels is performed in this work. The coupled Poisson-Boltzmann equation, Laplace equation, and modified Navier-Stokes equation are solved by finite volume method to describe distribution of electroosmotic flow. The detailed numerical results show that the salt concentration and applied electrical potential have great effects on the fundamental characteristics of elelctroosmotic flow. The most important finding is that the corner and wall effects in trapezoidal microchannels are stronger than those in rectangular microchannels.

Aerodynamic optimization by simultaneously updating flow variables and design parameters with application to advanced propeller designs

NASA Technical Reports Server (NTRS)

Rizk, Magdi H.

1988-01-01

A scheme is developed for solving constrained optimization problems in which the objective function and the constraint function are dependent on the solution of the nonlinear flow equations. The scheme updates the design parameter iterative solutions and the flow variable iterative solutions simultaneously. It is applied to an advanced propeller design problem with the Euler equations used as the flow governing equations. The scheme's accuracy, efficiency and sensitivity to the computational parameters are tested.

Selected Streamflow Statistics and Regression Equations for Predicting Statistics at Stream Locations in Monroe County, Pennsylvania

USGS Publications Warehouse

Thompson, Ronald E.; Hoffman, Scott A.

2006-01-01

A suite of 28 streamflow statistics, ranging from extreme low to high flows, was computed for 17 continuous-record streamflow-gaging stations and predicted for 20 partial-record stations in Monroe County and contiguous counties in north-eastern Pennsylvania. The predicted statistics for the partial-record stations were based on regression analyses relating inter-mittent flow measurements made at the partial-record stations indexed to concurrent daily mean flows at continuous-record stations during base-flow conditions. The same statistics also were predicted for 134 ungaged stream locations in Monroe County on the basis of regression analyses relating the statistics to GIS-determined basin characteristics for the continuous-record station drainage areas. The prediction methodology for developing the regression equations used to estimate statistics was developed for estimating low-flow frequencies. This study and a companion study found that the methodology also has application potential for predicting intermediate- and high-flow statistics. The statistics included mean monthly flows, mean annual flow, 7-day low flows for three recurrence intervals, nine flow durations, mean annual base flow, and annual mean base flows for two recurrence intervals. Low standard errors of prediction and high coefficients of determination (R2) indicated good results in using the regression equations to predict the statistics. Regression equations for the larger flow statistics tended to have lower standard errors of prediction and higher coefficients of determination (R2) than equations for the smaller flow statistics. The report discusses the methodologies used in determining the statistics and the limitations of the statistics and the equations used to predict the statistics. Caution is indicated in using the predicted statistics for small drainage area situations. Study results constitute input needed by water-resource managers in Monroe County for planning purposes and evaluation of water-resources availability.

A sensitivity equation approach to shape optimization in fluid flows

NASA Technical Reports Server (NTRS)

Borggaard, Jeff; Burns, John

1994-01-01

A sensitivity equation method to shape optimization problems is applied. An algorithm is developed and tested on a problem of designing optimal forebody simulators for a 2D, inviscid supersonic flow. The algorithm uses a BFGS/Trust Region optimization scheme with sensitivities computed by numerically approximating the linear partial differential equations that determine the flow sensitivities. Numerical examples are presented to illustrate the method.

Poiseuille equation for steady flow of fractal fluid

NASA Astrophysics Data System (ADS)

Tarasov, Vasily E.

2016-07-01

Fractal fluid is considered in the framework of continuous models with noninteger dimensional spaces (NIDS). A recently proposed vector calculus in NIDS is used to get a description of fractal fluid flow in pipes with circular cross-sections. The Navier-Stokes equations of fractal incompressible viscous fluids are used to derive a generalization of the Poiseuille equation of steady flow of fractal media in pipe.

A review of at rest droplet growth equations for condensing nitrogen in transonic cryogenic wind tunnels

NASA Technical Reports Server (NTRS)

Hall, R. M.; Kramer, S. A.

1979-01-01

Droplet growth equations are reviewed in the free-molecular, transition, and continuum flow regimes with the assumption that the droplets are at rest with respect to the vapor. As comparison calculations showed, it was important to use a growth equation designed for the flow regime of interest. Otherwise, a serious over-prediction of droplet growth may result. The growth equation by Gyarmathy appeared to be applicable throughout the flow regimes and involved no iteration. His expression also avoided the uncertainty associated with selecting a mass accommodation coefficient and consequently involved less uncertainty in specifying adjustable parameters than many of the other growth equations.

Unsteady boundary layer flow over a sphere in a porous medium

NASA Astrophysics Data System (ADS)

Mohammad, Nurul Farahain; Waini, Iskandar; Kasim, Abdul Rahman Mohd; Majid, Nurazleen Abdul

2017-08-01

This study focuses on the problem of unsteady boundary layer flow over a sphere in a porous medium. The governing equations which consists of a system of dimensional partial differential equations is applied with dimensionless parameter in order to attain non-dimensional partial differential equations. Later, the similarity transformation is performed in order to attain nonsimilar governing equations. Afterwards, the nonsimilar governing equations are solved numerically by using the Keller-Box method in Octave programme. The effect of porosity parameter is examined on separation time, velocity profile and skin friction of the unsteady flow. The results attained are presented in the form of table and graph.

Computational flow development for unsteady viscous flows: Foundation of the numerical method

NASA Technical Reports Server (NTRS)

Bratanow, T.; Spehert, T.

1978-01-01

A procedure is presented for effective consideration of viscous effects in computational development of high Reynolds number flows. The procedure is based on the interpretation of the Navier-Stokes equations as vorticity transport equations. The physics of the flow was represented in a form suitable for numerical analysis. Lighthill's concept for flow development for computational purposes was adapted. The vorticity transport equations were cast in a form convenient for computation. A statement for these equations was written using the method of weighted residuals and applying the Galerkin criterion. An integral representation of the induced velocity was applied on the basis of the Biot-Savart law. Distribution of new vorticity, produced at wing surfaces over small computational time intervals, was assumed to be confined to a thin region around the wing surfaces.

Aerodynamic Analyses Requiring Advanced Computers, Part 1

NASA Technical Reports Server (NTRS)

1975-01-01

Papers are presented which deal with results of theoretical research on aerodynamic flow problems requiring the use of advanced computers. Topics discussed include: viscous flows, boundary layer equations, turbulence modeling and Navier-Stokes equations, and internal flows.

THE BERNOULLI EQUATION AND COMPRESSIBLE FLOW THEORIES

EPA Science Inventory

The incompressible Bernoulli equation is an analytical relationship between pressure, kinetic energy, and potential energy. As perhaps the simplest and most useful statement for describing laminar flow, it buttresses numerous incompressible flow models that have been developed ...

Simulation of groundwater flow and streamflow depletion in the Branch Brook, Merriland River, and parts of the Mousam River watersheds in southern Maine

USGS Publications Warehouse

Nielsen, Martha G.; Locke, Daniel B.

2015-01-01

The study evaluated two different methods of calculating in-stream flow requirements for Branch Brook and the Merriland River—a set of statewide equations used to calculate monthly median flows and the MOVE.1 record-extension technique used on site-specific streamflow measurements. The August median in-stream flow requirement in the Merriland River was calculated as 7.18 ft3/s using the statewide equations but was 3.07 ft3/s using the MOVE.1 analysis. In Branch Brook, the August median in-stream flow requirements were calculated as 20.3 ft3/s using the statewide equations and 11.8 ft3/s using the MOVE.1 analysis. In each case, using site-specific data yields an estimate of in-stream flow that is much lower than an estimate the statewide equations provide.

Scour assessments and sediment-transport simulation for selected bridge sites in South Dakota

USGS Publications Warehouse

Niehus, C.A.

1996-01-01

Scour at bridges is a major concern in the design of new bridges and in the evaluation of structural stability of existing bridges. Equations for estimating pier, contraction, and abutment scour have been developed from numerous laboratory studies using sand-bed flumes, but little verification of these scour equations has been done for actual rivers with various bed conditions. This report describes the results of reconnaissance and detailed scour assessments and a sediment-transport simulation for selected bridge sites in South Dakota. Reconnaissance scour assessments were done during 1991 for 32 bridge sites. The reconnaissance assessments for each bridge site included compilation of general and structural data, field inspection to record and measure pertinent scour variables, and evaluation of scour susceptibility using various scour-index forms. Observed pier scour at the 32 sites ranged from 0 to 7 feet, observed contraction scour ranged from 0 to 4 feet, and observed abutment scour ranged from 0 to 10 feet. Thirteen bridge sites having high potential for scour were selected for detailed assessments, which were accomplished during 1992-95. These detailed assessments included prediction of scour depths for 2-, 100-, and 500-year flows using selected published scour equations; measurement of scour during high flows; comparison of measured and predicted scour; and identification of which scour equations best predict actual scour. The medians of predicted pier-scour depth at each of the 13 bridge sites (using 13 scour equations) ranged from 2.4 to 6.8 feet for the 2-year flows and ranged from 3.4 to 13.3 feet for the 500-year flows. The maximum pier scour measured during high flows ranged from 0 to 8.5 feet. Statistical comparison (Spearman rank correlation) of predicted pier-scour depths (using flow data col- lected during scour measurements) indicate that the Laursen, Shen (method b), Colorado State University, and Blench (method b) equations correlate closer with measured scour than do the other prediction equations. The predicted pier-scour depths using the Varzeliotis and Carstens equations have weak statistical rela- tions with measured scour depths. Medians of predicted pier-scour depth from the Shen (method a), Chitale, Bata, and Carstens equations are statistically equal to the median of measured pier-scour depths, based on the Wilcoxon signed-ranks test. The medians of contraction scour depth at each of the 13 bridge sites (using one equation) ranged from -0.1 foot for the 2- year flows to 23.2 feet for the 500-year flows. The maximum contraction scour measured during high flows ranged from 0 to 3.0 feet. The contraction- scour prediction equation substantially overestimated the scour depths in almost all comparisons with the measured scour depths. A significant reason for this discrepancy is due to the wide flood plain (as wide as 5,000 feet) at most of the bridge sites that were investigated. One possible way to reduce this effect for bridge design is to make a decision on what is the effective approach section and thereby limit the size of the bridge flow approach width. The medians of abutment-scour depth at each of the 13 bridge sites (using five equations) ranged from 8.2 to 16.5 feet for the 2-year flows and ranged from 5.7 to 41 feet for the 500-year flows. The maximum abutment scour measured during high flows ranged from 0 to 4.0 feet. The abutment-scour prediction equations also substantially overestimated the scour depths in almost all comparisons with the measured scour depths. The Liu and others (live bed) equation predicted abutment-scour depths substantially lower than the other four abutment-scour equations and closer to the actual measured scour depths. However, this equation at times predicted greater scour depths for 2-year flows than it did for 500-year flows, making its use highly questionable. Again, limiting the bridge flow approach width would produce more reasonable predicted abutment scour.

A theoretical analysis of fluid flow and energy transport in hydrothermal systems

USGS Publications Warehouse

Faust, Charles R.; Mercer, James W.

1977-01-01

A mathematical derivation for fluid flow and energy transport in hydrothermal systems is presented. Specifically, the mathematical model describes the three-dimensional flow of both single- and two-phase, single-component water and the transport of heat in porous media. The derivation begins with the point balance equations for mass, momentum, and energy. These equations are then averaged over a finite volume to obtain the macroscopic balance equations for a porous medium. The macroscopic equations are combined by appropriate constitutive relationships to form two similified partial differential equations posed in terms of fluid pressure and enthalpy. A two-dimensional formulation of the simplified equations is also derived by partial integration in the vertical dimension. (Woodard-USGS)

Review of literature on the finite-element solution of the equations of two-dimensional surface-water flow in the horizontal plane

USGS Publications Warehouse

Lee, Jonathan K.; Froehlich, David C.

1987-01-01

Published literature on the application of the finite-element method to solving the equations of two-dimensional surface-water flow in the horizontal plane is reviewed in this report. The finite-element method is ideally suited to modeling two-dimensional flow over complex topography with spatially variable resistance. A two-dimensional finite-element surface-water flow model with depth and vertically averaged velocity components as dependent variables allows the user great flexibility in defining geometric features such as the boundaries of a water body, channels, islands, dikes, and embankments. The following topics are reviewed in this report: alternative formulations of the equations of two-dimensional surface-water flow in the horizontal plane; basic concepts of the finite-element method; discretization of the flow domain and representation of the dependent flow variables; treatment of boundary conditions; discretization of the time domain; methods for modeling bottom, surface, and lateral stresses; approaches to solving systems of nonlinear equations; techniques for solving systems of linear equations; finite-element alternatives to Galerkin's method of weighted residuals; techniques of model validation; and preparation of model input data. References are listed in the final chapter.

Methods for estimating low-flow statistics for Massachusetts streams

USGS Publications Warehouse

Ries, Kernell G.; Friesz, Paul J.

2000-01-01

Methods and computer software are described in this report for determining flow duration, low-flow frequency statistics, and August median flows. These low-flow statistics can be estimated for unregulated streams in Massachusetts using different methods depending on whether the location of interest is at a streamgaging station, a low-flow partial-record station, or an ungaged site where no data are available. Low-flow statistics for streamgaging stations can be estimated using standard U.S. Geological Survey methods described in the report. The MOVE.1 mathematical method and a graphical correlation method can be used to estimate low-flow statistics for low-flow partial-record stations. The MOVE.1 method is recommended when the relation between measured flows at a partial-record station and daily mean flows at a nearby, hydrologically similar streamgaging station is linear, and the graphical method is recommended when the relation is curved. Equations are presented for computing the variance and equivalent years of record for estimates of low-flow statistics for low-flow partial-record stations when either a single or multiple index stations are used to determine the estimates. The drainage-area ratio method or regression equations can be used to estimate low-flow statistics for ungaged sites where no data are available. The drainage-area ratio method is generally as accurate as or more accurate than regression estimates when the drainage-area ratio for an ungaged site is between 0.3 and 1.5 times the drainage area of the index data-collection site. Regression equations were developed to estimate the natural, long-term 99-, 98-, 95-, 90-, 85-, 80-, 75-, 70-, 60-, and 50-percent duration flows; the 7-day, 2-year and the 7-day, 10-year low flows; and the August median flow for ungaged sites in Massachusetts. Streamflow statistics and basin characteristics for 87 to 133 streamgaging stations and low-flow partial-record stations were used to develop the equations. The streamgaging stations had from 2 to 81 years of record, with a mean record length of 37 years. The low-flow partial-record stations had from 8 to 36 streamflow measurements, with a median of 14 measurements. All basin characteristics were determined from digital map data. The basin characteristics that were statistically significant in most of the final regression equations were drainage area, the area of stratified-drift deposits per unit of stream length plus 0.1, mean basin slope, and an indicator variable that was 0 in the eastern region and 1 in the western region of Massachusetts. The equations were developed by use of weighted-least-squares regression analyses, with weights assigned proportional to the years of record and inversely proportional to the variances of the streamflow statistics for the stations. Standard errors of prediction ranged from 70.7 to 17.5 percent for the equations to predict the 7-day, 10-year low flow and 50-percent duration flow, respectively. The equations are not applicable for use in the Southeast Coastal region of the State, or where basin characteristics for the selected ungaged site are outside the ranges of those for the stations used in the regression analyses. A World Wide Web application was developed that provides streamflow statistics for data collection stations from a data base and for ungaged sites by measuring the necessary basin characteristics for the site and solving the regression equations. Output provided by the Web application for ungaged sites includes a map of the drainage-basin boundary determined for the site, the measured basin characteristics, the estimated streamflow statistics, and 90-percent prediction intervals for the estimates. An equation is provided for combining regression and correlation estimates to obtain improved estimates of the streamflow statistics for low-flow partial-record stations. An equation is also provided for combining regression and drainage-area ratio estimates to obtain improved e

Free surface profiles in river flows: Can standard energy-based gradually-varied flow computations be pursued?

NASA Astrophysics Data System (ADS)

Cantero, Francisco; Castro-Orgaz, Oscar; Garcia-Marín, Amanda; Ayuso, José Luis; Dey, Subhasish

2015-10-01

Is the energy equation for gradually-varied flow the best approximation for the free surface profile computations in river flows? Determination of flood inundation in rivers and natural waterways is based on the hydraulic computation of flow profiles. This is usually done using energy-based gradually-varied flow models, like HEC-RAS, that adopts a vertical division method for discharge prediction in compound channel sections. However, this discharge prediction method is not so accurate in the context of advancements over the last three decades. This paper firstly presents a study of the impact of discharge prediction on the gradually-varied flow computations by comparing thirteen different methods for compound channels, where both energy and momentum equations are applied. The discharge, velocity distribution coefficients, specific energy, momentum and flow profiles are determined. After the study of gradually-varied flow predictions, a new theory is developed to produce higher-order energy and momentum equations for rapidly-varied flow in compound channels. These generalized equations enable to describe the flow profiles with more generality than the gradually-varied flow computations. As an outcome, results of gradually-varied flow provide realistic conclusions for computations of flow in compound channels, showing that momentum-based models are in general more accurate; whereas the new theory developed for rapidly-varied flow opens a new research direction, so far not investigated in flows through compound channels.

Steady-state flow distribution and monthly flow duration in selected branches of St. Clair and Detroit rivers within the Great Lakes waterway

USGS Publications Warehouse

Holtschlag, D.J.; Koschik, J.A.

2001-01-01

St. Clair and Detroit Rivers are connecting channels between Lake Huron and Lake Erie in the Great Lakes waterway, and form part of the boundary between the United States and Canada. St. Clair River, the upper connecting channel, drains 222,400 square miles and has an average flow of about 182,000 cubic feet per second. Water from St. Clair River combines with local inflows and discharges into Lake St. Clair before flowing into Detroit River. In some reaches of St. Clair and Detroit Rivers, islands and dikes split the flow into two to four branches. Even when the flow in a reach is known, proportions of flows within individual branches of a reach are uncertain. Simple linear regression equations, subject to a flow continuity constraint, are developed to provide estimators of these proportions and flows. The equations are based on 533 paired measurements of flow in 13 reaches forming 31 branches. The equations provide a means for computing the expected values and uncertainties of steady-state flows on the basis of flow conditions specified at the upstream boundaries of the waterway. In 7 upstream reaches, flow is considered fixed because it can be determined on the basis of flows specified at waterway boundaries and flow continuity. In these reaches, the uncertainties of flow proportions indicated by the regression equations can be used directly to determine the uncertainties of the corresponding flows. In the remaining 6 downstream reaches, flow is considered uncertain because these reaches do not receive flow from all the branches of an upstream reach, or they receive flow from some branches of more than one upstream reach. Monte Carlo simulation analysis is used to quantify this increase in uncertainty associated with the propagation of uncertainties from upstream reaches to downstream reaches. To eliminate the need for Monte Carlo simulations for routine calculations, polynomial regression equations are developed to approximate the variation in uncertainties as a function of flow at the headwaters of St. Clair River. Finally, monthly flow-duration data on the main channels of St. Clair and Detroit Rivers are used with the equations developed in this report to estimate the steady-state flow-duration characteristics of selected branches.

Numerical Modeling of Interstitial Fluid Flow Coupled with Blood Flow through a Remodeled Solid Tumor Microvascular Network

PubMed Central

Soltani, M.; Chen, P.

2013-01-01

Modeling of interstitial fluid flow involves processes such as fluid diffusion, convective transport in extracellular matrix, and extravasation from blood vessels. To date, majority of microvascular flow modeling has been done at different levels and scales mostly on simple tumor shapes with their capillaries. However, with our proposed numerical model, more complex and realistic tumor shapes and capillary networks can be studied. Both blood flow through a capillary network, which is induced by a solid tumor, and fluid flow in tumor’s surrounding tissue are formulated. First, governing equations of angiogenesis are implemented to specify the different domains for the network and interstitium. Then, governing equations for flow modeling are introduced for different domains. The conservation laws for mass and momentum (including continuity equation, Darcy’s law for tissue, and simplified Navier–Stokes equation for blood flow through capillaries) are used for simulating interstitial and intravascular flows and Starling’s law is used for closing this system of equations and coupling the intravascular and extravascular flows. This is the first study of flow modeling in solid tumors to naturalistically couple intravascular and extravascular flow through a network. This network is generated by sprouting angiogenesis and consisting of one parent vessel connected to the network while taking into account the non-continuous behavior of blood, adaptability of capillary diameter to hemodynamics and metabolic stimuli, non-Newtonian blood flow, and phase separation of blood flow in capillary bifurcation. The incorporation of the outlined components beyond the previous models provides a more realistic prediction of interstitial fluid flow pattern in solid tumors and surrounding tissues. Results predict higher interstitial pressure, almost two times, for realistic model compared to the simplified model. PMID:23840579

Turbulence modeling for hypersonic flows

NASA Technical Reports Server (NTRS)

Marvin, J. G.; Coakley, T. J.

1989-01-01

Turbulence modeling for high speed compressible flows is described and discussed. Starting with the compressible Navier-Stokes equations, methods of statistical averaging are described by means of which the Reynolds-averaged Navier-Stokes equations are developed. Unknown averages in these equations are approximated using various closure concepts. Zero-, one-, and two-equation eddy viscosity models, algebraic stress models and Reynolds stress transport models are discussed. Computations of supersonic and hypersonic flows obtained using several of the models are discussed and compared with experimental results. Specific examples include attached boundary layer flows, shock wave boundary layer interactions and compressible shear layers. From these examples, conclusions regarding the status of modeling and recommendations for future studies are discussed.

A high-resolution Godunov method for compressible multi-material flow on overlapping grids

NASA Astrophysics Data System (ADS)

Banks, J. W.; Schwendeman, D. W.; Kapila, A. K.; Henshaw, W. D.

2007-04-01

A numerical method is described for inviscid, compressible, multi-material flow in two space dimensions. The flow is governed by the multi-material Euler equations with a general mixture equation of state. Composite overlapping grids are used to handle complex flow geometry and block-structured adaptive mesh refinement (AMR) is used to locally increase grid resolution near shocks and material interfaces. The discretization of the governing equations is based on a high-resolution Godunov method, but includes an energy correction designed to suppress numerical errors that develop near a material interface for standard, conservative shock-capturing schemes. The energy correction is constructed based on a uniform-pressure-velocity flow and is significant only near the captured interface. A variety of two-material flows are presented to verify the accuracy of the numerical approach and to illustrate its use. These flows assume an equation of state for the mixture based on the Jones-Wilkins-Lee (JWL) forms for the components. This equation of state includes a mixture of ideal gases as a special case. Flow problems considered include unsteady one-dimensional shock-interface collision, steady interaction of a planar interface and an oblique shock, planar shock interaction with a collection of gas-filled cylindrical inhomogeneities, and the impulsive motion of the two-component mixture in a rigid cylindrical vessel.

A numerical study of nonlinear waves in a transcritical flow of stratified fluid past an obstacle

NASA Astrophysics Data System (ADS)

Hanazaki, Hideshi

1992-10-01

A numerical study of the flow of stratified fluid past an obstacle in a horizontal channel is described. Upstream advancing of waves near critically (resonance) appears in the case of ordinary two-layer flow, in which case the flow is described well by the solution of the forced extended Korteweg-de Vries (KdV) equation which has a cubic nonlinear term. It is shown theoretically that the upstream waves in the general two-layer flow cannot be well described by the forced KdV equation except when the wave amplitude is very small. The critical-level flow is also governed by the forced extended KdV equation. However, because of the smallness of the coefficient of the quadratic nonlinear term, the bore cannot propagate upstream at exact resonance. The results for the linearly stratified Boussinesq flow show good agreement with the solution of the Grimshaw and Yi (1991) equation, at least for exact resonance.

Calculations of separated 3-D flows with a pressure-staggered Navier-Stokes equations solver

NASA Technical Reports Server (NTRS)

Kim, S.-W.

1991-01-01

A Navier-Stokes equations solver based on a pressure correction method with a pressure-staggered mesh and calculations of separated three-dimensional flows are presented. It is shown that the velocity pressure decoupling, which occurs when various pressure correction algorithms are used for pressure-staggered meshes, is caused by the ill-conditioned discrete pressure correction equation. The use of a partial differential equation for the incremental pressure eliminates the velocity pressure decoupling mechanism by itself and yields accurate numerical results. Example flows considered are a three-dimensional lid driven cavity flow and a laminar flow through a 90 degree bend square duct. For the lid driven cavity flow, the present numerical results compare more favorably with the measured data than those obtained using a formally third order accurate quadratic upwind interpolation scheme. For the curved duct flow, the present numerical method yields a grid independent solution with a very small number of grid points. The calculated velocity profiles are in good agreement with the measured data.

Conservation-form equations of unsteady open-channel flow

USGS Publications Warehouse

Lai, C.; Baltzer, R.A.; Schaffranek, R.W.

2002-01-01

The unsteady open-channel flow equations are typically expressed in a variety of forms due to the imposition of differing assumptions, use of varied dependent variables, and inclusion of different source/sink terms. Questions often arise as to whether a particular equation set is expressed in a form consistent with the conservation-law definition. The concept of conservation form is developed to clarify the meaning mathematically. Six sets of unsteady-flow equations typically used in engineering practice are presented and their conservation properties are identified and discussed. Results of the theoretical development and analysis of the equations are substantiated in a set of numerical experiments conducted using alternate equation forms. Findings of these analytical and numerical efforts demonstrate that the choice of dependent variable is the fundamental factor determining the nature of the conservation properties of any particular equation form.

A GENERAL MASS-CONSERVATIVE NUMERICAL SOLUTION FOR THE UNSATURATED FLOW EQUATION

EPA Science Inventory

Numerical approximations based on different forms of the governing partial differential equation can lead to significantly different results for unsaturated flow problems. Numerical solution based on the standard h-based form of Richards equation generally yields poor results, ch...

Numerical solutions of Navier-Stokes equations for a Butler wing

NASA Technical Reports Server (NTRS)

Abolhassani, J. S.; Tiwari, S. N.

1985-01-01

The flow field is simulated on the surface of a given delta wing (Butler wing) at zero incident in a uniform stream. The simulation is done by integrating a set of flow field equations. This set of equations governs the unsteady, viscous, compressible, heat conducting flow of an ideal gas. The equations are written in curvilinear coordinates so that the wing surface is represented accurately. These equations are solved by the finite difference method, and results obtained for high-speed freestream conditions are compared with theoretical and experimental results. In this study, the Navier-Stokes equations are solved numerically. These equations are unsteady, compressible, viscous, and three-dimensional without neglecting any terms. The time dependency of the governing equations allows the solution to progress naturally for an arbitrary initial initial guess to an asymptotic steady state, if one exists. The equations are transformed from physical coordinates to the computational coordinates, allowing the solution of the governing equations in a rectangular parallel-piped domain. The equations are solved by the MacCormack time-split technique which is vectorized and programmed to run on the CDC VPS 32 computer.

Convergence of the flow of a chemically reacting gaseous mixture to incompressible Euler equations in a unbounded domain

NASA Astrophysics Data System (ADS)

Kwon, Young-Sam

2017-12-01

The flow of chemically reacting gaseous mixture is associated with a variety of phenomena and processes. We study the combined quasineutral and inviscid limit from the flow of chemically reacting gaseous mixture governed by Poisson equation to incompressible Euler equations with the ill-prepared initial data in the unbounded domain R^2× T. Furthermore, the convergence rates are obtained.

Modification of equation of motion of fluid-conveying pipe for laminar and turbulent flow profiles

NASA Astrophysics Data System (ADS)

Guo, C. Q.; Zhang, C. H.; Païdoussis, M. P.

2010-07-01

Considering the non-uniformity of the flow velocity distribution in fluid-conveying pipes caused by the viscosity of real fluids, the centrifugal force term in the equation of motion of the pipe is modified for laminar and turbulent flow profiles. The flow-profile-modification factors are found to be 1.333, 1.015-1.040 and 1.035-1.055 for laminar flow in circular pipes, turbulent flow in smooth-wall circular pipes and turbulent flow in rough-wall circular pipes, respectively. The critical flow velocities for divergence in the above-mentioned three cases are found to be 13.4%, 0.74-1.9% and 1.7-2.6%, respectively, lower than that with plug flow, while those for flutter are even lower, which could reach 36% for the laminar flow profile. By introducing two new concepts of equivalent flow velocity and equivalent mass, fluid-conveying pipe problems with different flow profiles can be solved with the equation of motion for plug flow.

Some aspects of steam-water flow simulation in geothermal wells

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shulyupin, Alexander N.

1996-01-24

Actual aspects of steam-water simulation in geothermal wells are considered: necessary quality of a simulator, flow regimes, mass conservation equation, momentum conservation equation, energy conservation equation and condition equations. Shortcomings of traditional hydraulic approach are noted. Main questions of simulator development by the hydraulic approach are considered. New possibilities of a simulation with the structure approach employment are noted.

Low-flow characteristics of Virginia streams

USGS Publications Warehouse

Austin, Samuel H.; Krstolic, Jennifer L.; Wiegand, Ute

2011-01-01

Low-flow annual non-exceedance probabilities (ANEP), called probability-percent chance (P-percent chance) flow estimates, regional regression equations, and transfer methods are provided describing the low-flow characteristics of Virginia streams. Statistical methods are used to evaluate streamflow data. Analysis of Virginia streamflow data collected from 1895 through 2007 is summarized. Methods are provided for estimating low-flow characteristics of gaged and ungaged streams. The 1-, 4-, 7-, and 30-day average streamgaging station low-flow characteristics for 290 long-term, continuous-record, streamgaging stations are determined, adjusted for instances of zero flow using a conditional probability adjustment method, and presented for non-exceedance probabilities of 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, 0.2, 0.1, 0.05, 0.02, 0.01, and 0.005. Stream basin characteristics computed using spatial data and a geographic information system are used as explanatory variables in regional regression equations to estimate annual non-exceedance probabilities at gaged and ungaged sites and are summarized for 290 long-term, continuous-record streamgaging stations, 136 short-term, continuous-record streamgaging stations, and 613 partial-record streamgaging stations. Regional regression equations for six physiographic regions use basin characteristics to estimate 1-, 4-, 7-, and 30-day average low-flow annual non-exceedance probabilities at gaged and ungaged sites. Weighted low-flow values that combine computed streamgaging station low-flow characteristics and annual non-exceedance probabilities from regional regression equations provide improved low-flow estimates. Regression equations developed using the Maintenance of Variance with Extension (MOVE.1) method describe the line of organic correlation (LOC) with an appropriate index site for low-flow characteristics at 136 short-term, continuous-record streamgaging stations and 613 partial-record streamgaging stations. Monthly streamflow statistics computed on the individual daily mean streamflows of selected continuous-record streamgaging stations and curves describing flow-duration are presented. Text, figures, and lists are provided summarizing low-flow estimates, selected low-flow sites, delineated physiographic regions, basin characteristics, regression equations, error estimates, definitions, and data sources. This study supersedes previous studies of low flows in Virginia.

Density-velocity equations with bulk modulus for computational hydro-acoustics

NASA Astrophysics Data System (ADS)

Lin, Po-Hsien; Chen, Yung-Yu; John Yu, S.-T.

2014-02-01

This paper reports a new set of model equations for Computational Hydro Acoustics (CHA). The governing equations include the continuity and the momentum equations. The definition of bulk modulus is used to relate density with pressure. For 3D flow fields, there are four equations with density and velocity components as the unknowns. The inviscid equations are proved to be hyperbolic because an arbitrary linear combination of the three Jacobian matrices is diagonalizable and has a real spectrum. The left and right eigenvector matrices are explicitly derived. Moreover, an analytical form of the Riemann invariants are derived. The model equations are indeed suitable for modeling wave propagation in low-speed, nearly incompressible air and water flows. To demonstrate the capability of the new formulation, we use the CESE method to solve the 2D equations for aeolian tones generated by air flows passing a circular cylinder at Re = 89,000, 46,000, and 22,000. Numerical results compare well with previously published data. By simply changing the value of the bulk modulus, the same code is then used to calculate three cases of water flows passing a cylinder at Re = 89,000, 67,000, and 44,000.

A computer code for multiphase all-speed transient flows in complex geometries. MAST version 1.0

NASA Technical Reports Server (NTRS)

Chen, C. P.; Jiang, Y.; Kim, Y. M.; Shang, H. M.

1991-01-01

The operation of the MAST code, which computes transient solutions to the multiphase flow equations applicable to all-speed flows, is described. Two-phase flows are formulated based on the Eulerian-Lagrange scheme in which the continuous phase is described by the Navier-Stokes equation (or Reynolds equations for turbulent flows). Dispersed phase is formulated by a Lagrangian tracking scheme. The numerical solution algorithms utilized for fluid flows is a newly developed pressure-implicit algorithm based on the operator-splitting technique in generalized nonorthogonal coordinates. This operator split allows separate operation on each of the variable fields to handle pressure-velocity coupling. The obtained pressure correction equation has the hyperbolic nature and is effective for Mach numbers ranging from the incompressible limit to supersonic flow regimes. The present code adopts a nonstaggered grid arrangement; thus, the velocity components and other dependent variables are collocated at the same grid. A sequence of benchmark-quality problems, including incompressible, subsonic, transonic, supersonic, gas-droplet two-phase flows, as well as spray-combustion problems, were performed to demonstrate the robustness and accuracy of the present code.

Navier-Stokes Computations With One-Equation Turbulence Model for Flows Along Concave Wall Surfaces

NASA Technical Reports Server (NTRS)

Wang, Chi R.

2005-01-01

This report presents the use of a time-marching three-dimensional compressible Navier-Stokes equation numerical solver with a one-equation turbulence model to simulate the flow fields developed along concave wall surfaces without and with a downstream extension flat wall surface. The 3-D Navier- Stokes numerical solver came from the NASA Glenn-HT code. The one-equation turbulence model was derived from the Spalart and Allmaras model. The computational approach was first calibrated with the computations of the velocity and Reynolds shear stress profiles of a steady flat plate boundary layer flow. The computational approach was then used to simulate developing boundary layer flows along concave wall surfaces without and with a downstream extension wall. The author investigated the computational results of surface friction factors, near surface velocity components, near wall temperatures, and a turbulent shear stress component in terms of turbulence modeling, computational mesh configurations, inlet turbulence level, and time iteration step. The computational results were compared with existing measurements of skin friction factors, velocity components, and shear stresses of the developing boundary layer flows. With a fine computational mesh and a one-equation model, the computational approach could predict accurately the skin friction factors, near surface velocity and temperature, and shear stress within the flows. The computed velocity components and shear stresses also showed the vortices effect on the velocity variations over a concave wall. The computed eddy viscosities at the near wall locations were also compared with the results from a two equation turbulence modeling technique. The inlet turbulence length scale was found to have little effect on the eddy viscosities at locations near the concave wall surface. The eddy viscosities, from the one-equation and two-equation modeling, were comparable at most stream-wise stations. The present one-equation turbulence model is an effective approach for turbulence modeling in the near solid wall surface region of flow over a concave wall.

Nozzle Flow with Vibrational Nonequilibrium. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Landry, John Gary

1995-01-01

Flow of nitrogen gas through a converging-diverging nozzle is simulated. The flow is modeled using the Navier-Stokes equations that have been modified for vibrational nonequilibrium. The energy equation is replaced by two equations. One equation accounts for energy effects due to the translational and rotational degrees of freedom, and the other accounts for the affects due to the vibrational degree of freedom. The energy equations are coupled by a relaxation time which measures the time required for the vibrational energy component to equilibrate with the translational and rotational energy components. An improved relaxation time is used in this thesis. The equations are solved numerically using the Steger-Warming flux vector splitting method and the Implicit MacCormack method. The results show that uniform flow is produced outside of the boundary layer. Nonequilibrium exists in both the converging and diverging nozzle sections. The boundary layer region is characterized by a marked increase in translational-rotational temperature. The vibrational temperature remains frozen downstream of the nozzle, except in the boundary layer.

The pdf approach to turbulent flow

NASA Technical Reports Server (NTRS)

Kollmann, W.

1990-01-01

This paper provides a detailed discussion of the theory and application of probability density function (pdf) methods, which provide a complete statistical description of turbulent flow fields at a single point or a finite number of points. The basic laws governing the flow of Newtonian fluids are set up in the Eulerian and the Lagrangian frame, and the exact and linear equations for the characteristic functionals in those frames are discussed. Pdf equations in both frames are derived as Fourier transforms of the equations of the characteristic functions. Possible formulations for the nonclosed terms in the pdf equation are discussed, their properties are assessed, and closure modes for the molecular-transport and the fluctuating pressure-gradient terms are reviewed. The application of pdf methods to turbulent combustion flows, supersonic flows, and the interaction of turbulence with shock waves is discussed.

A compressible Navier-Stokes solver with two-equation and Reynolds stress turbulence closure models

NASA Technical Reports Server (NTRS)

Morrison, Joseph H.

1992-01-01

This report outlines the development of a general purpose aerodynamic solver for compressible turbulent flows. Turbulent closure is achieved using either two equation or Reynolds stress transportation equations. The applicable equation set consists of Favre-averaged conservation equations for the mass, momentum and total energy, and transport equations for the turbulent stresses and turbulent dissipation rate. In order to develop a scheme with good shock capturing capabilities, good accuracy and general geometric capabilities, a multi-block cell centered finite volume approach is used. Viscous fluxes are discretized using a finite volume representation of a central difference operator and the source terms are treated as an integral over the control volume. The methodology is validated by testing the algorithm on both two and three dimensional flows. Both the two equation and Reynolds stress models are used on a two dimensional 10 degree compression ramp at Mach 3, and the two equation model is used on the three dimensional flow over a cone at angle of attack at Mach 3.5. With the development of this algorithm, it is now possible to compute complex, compressible high speed flow fields using both two equation and Reynolds stress turbulent closure models, with the capability of eventually evaluating their predictive performance.

A Study of Two-Equation Turbulence Models on the Elliptic Streamline Flow

NASA Technical Reports Server (NTRS)

Blaisdell, Gregory A.; Qin, Jim H.; Shariff, Karim; Rai, Man Mohan (Technical Monitor)

1995-01-01

Several two-equation turbulence models are compared to data from direct numerical simulations (DNS) of the homogeneous elliptic streamline flow, which combines rotation and strain. The models considered include standard two-equation models and models with corrections for rotational effects. Most of the rotational corrections modify the dissipation rate equation to account for the reduced dissipation rate in rotating turbulent flows, however, the DNS data shows that the production term in the turbulent kinetic energy equation is not modeled correctly by these models. Nonlinear relations for the Reynolds stresses are considered as a means of modifying the production term. Implications for the modeling of turbulent vortices will be discussed.

Regression equations for estimating flood flows for the 2-, 10-, 25-, 50-, 100-, and 500-Year recurrence intervals in Connecticut

USGS Publications Warehouse

Ahearn, Elizabeth A.

2004-01-01

Multiple linear-regression equations were developed to estimate the magnitudes of floods in Connecticut for recurrence intervals ranging from 2 to 500 years. The equations can be used for nonurban, unregulated stream sites in Connecticut with drainage areas ranging from about 2 to 715 square miles. Flood-frequency data and hydrologic characteristics from 70 streamflow-gaging stations and the upstream drainage basins were used to develop the equations. The hydrologic characteristics?drainage area, mean basin elevation, and 24-hour rainfall?are used in the equations to estimate the magnitude of floods. Average standard errors of prediction for the equations are 31.8, 32.7, 34.4, 35.9, 37.6 and 45.0 percent for the 2-, 10-, 25-, 50-, 100-, and 500-year recurrence intervals, respectively. Simplified equations using only one hydrologic characteristic?drainage area?also were developed. The regression analysis is based on generalized least-squares regression techniques. Observed flows (log-Pearson Type III analysis of the annual maximum flows) from five streamflow-gaging stations in urban basins in Connecticut were compared to flows estimated from national three-parameter and seven-parameter urban regression equations. The comparison shows that the three- and seven- parameter equations used in conjunction with the new statewide equations generally provide reasonable estimates of flood flows for urban sites in Connecticut, although a national urban flood-frequency study indicated that the three-parameter equations significantly underestimated flood flows in many regions of the country. Verification of the accuracy of the three-parameter or seven-parameter national regression equations using new data from Connecticut stations was beyond the scope of this study. A technique for calculating flood flows at streamflow-gaging stations using a weighted average also is described. Two estimates of flood flows?one estimate based on the log-Pearson Type III analyses of the annual maximum flows at the gaging station, and the other estimate from the regression equation?are weighted together based on the years of record at the gaging station and the equivalent years of record value determined from the regression. Weighted averages of flood flows for the 2-, 10-, 25-, 50-, 100-, and 500-year recurrence intervals are tabulated for the 70 streamflow-gaging stations used in the regression analysis. Generally, weighted averages give the most accurate estimate of flood flows at gaging stations. An evaluation of the Connecticut's streamflow-gaging network was performed to determine whether the spatial coverage and range of geographic and hydrologic conditions are adequately represented for transferring flood characteristics from gaged to ungaged sites. Fifty-one of 54 stations in the current (2004) network support one or more flood needs of federal, state, and local agencies. Twenty-five of 54 stations in the current network are considered high-priority stations by the U.S. Geological Survey because of their contribution to the longterm understanding of floods, and their application for regionalflood analysis. Enhancements to the network to improve overall effectiveness for regionalization can be made by increasing the spatial coverage of gaging stations, establishing stations in regions of the state that are not well-represented, and adding stations in basins with drainage area sizes not represented. Additionally, the usefulness of the network for characterizing floods can be maintained and improved by continuing operation at the current stations because flood flows can be more accurately estimated at stations with continuous, long-term record.

Rotordynamic coefficients for labyrinth seals calculated by means of a finite difference technique

NASA Technical Reports Server (NTRS)

Nordmann, R.; Weiser, P.

1989-01-01

The compressible, turbulent, time dependent and three dimensional flow in a labyrinth seal can be described by the Navier-Stokes equations in conjunction with a turbulence model. Additionally, equations for mass and energy conservation and an equation of state are required. To solve these equations, a perturbation analysis is performed yielding zeroth order equations for centric shaft position and first order equations describing the flow field for small motions around the seal center. For numerical solution a finite difference method is applied to the zeroth and first order equations resulting in leakage and dynamic seal coefficients respectively.

Stability analysis of shallow wake flows

NASA Astrophysics Data System (ADS)

Kolyshkin, A. A.; Ghidaoui, M. S.

2003-11-01

Experimentally observed periodic structures in shallow (i.e. bounded) wake flows are believed to appear as a result of hydrodynamic instability. Previously published studies used linear stability analysis under the rigid-lid assumption to investigate the onset of instability of wakes in shallow water flows. The objectives of this paper are: (i) to provide a preliminary assessment of the accuracy of the rigid-lid assumption; (ii) to investigate the influence of the shape of the base flow profile on the stability characteristics; (iii) to formulate the weakly nonlinear stability problem for shallow wake flows and show that the evolution of the instability is governed by the Ginzburg Landau equation; and (iv) to establish the connection between weakly nonlinear analysis and the observed flow patterns in shallow wake flows which are reported in the literature. It is found that the relative error in determining the critical value of the shallow wake stability parameter induced by the rigid-lid assumption is below 10% for the practical range of Froude number. In addition, it is shown that the shape of the velocity profile has a large influence on the stability characteristics of shallow wakes. Starting from the rigid-lid shallow-water equations and using the method of multiple scales, an amplitude evolution equation for the most unstable mode is derived. The resulting equation has complex coefficients and is of Ginzburg Landau type. An example calculation of the complex coefficients of the Ginzburg Landau equation confirms the existence of a finite equilibrium amplitude, where the unstable mode evolves with time into a limit-cycle oscillation. This is consistent with flow patterns observed by Ingram & Chu (1987), Chen & Jirka (1995), Balachandar et al. (1999), and Balachandar & Tachie (2001). Reasonable agreement is found between the saturation amplitude obtained from the Ginzburg Landau equation under some simplifying assumptions and the numerical data of Grubi[sbreve]ic et al. (1995). Such consistency provides further evidence that experimentally observed structures in shallow wake flows may be described by the nonlinear Ginzburg Landau equation. Previous works have found similar consistency between the Ginzburg Landau model and experimental data for the case of deep (i.e. unbounded) wake flows. However, it must be emphasized that much more information is required to confirm the appropriateness of the Ginzburg Landau equation in describing shallow wake flows.

Numerical Study of High Speed Viscous Flows.

DTIC Science & Technology

1986-12-01

freestream Renolds number p density (7 arbitrary saftey factor used in equation (48) T local temperature t time shear stress u velocity component tangent...field, where the undisturbed flow conditions are used. The third boundary condition is applied far downstream of the body where the flow is weakly...8217(xy) (24) where and 𔄁 are defined in the List of Symbols. When the above transformation is applied to equation (16) the following equation

Analysis of eccentric annular incompressible seals. II - Effects of eccentricity on rotordynamic coefficients

NASA Technical Reports Server (NTRS)

Nelson, C. C.; Nguyen, D. T.

1987-01-01

A new analysis procedure has been presented which solves for the flow variables of an annular pressure seal in which the rotor has a large static displacement (eccentricity) from the centered position. The present paper incorporates the solutions to investigate the effect of eccentricity on the rotordynamic coefficients. The analysis begins with a set of governing equations based on a turbulent bulk-flow model and Moody's friction factor equation. Perturbations of the flow variables yields a set of zeroth- and first-order equations. After integration of the zeroth-order equations, the resulting zeroth-order flow variables are used as input in the solution of the first-order equations. Further integration of the first order pressures yields the eccentric rotordynamic coefficients. The results from this procedure compare well with available experimental and theoretical data, with accuracy just as good or slightly better than the predictions based on a finite-element model.

Development of one-equation transition/turbulence models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Edwards, J.R.; Roy, C.J.; Blottner, F.G.

2000-01-14

This paper reports on the development of a unified one-equation model for the prediction of transitional and turbulent flows. An eddy viscosity--transport equation for nonturbulent fluctuation growth based on that proposed by Warren and Hassan is combined with the Spalart-Allmaras one-equation model for turbulent fluctuation growth. Blending of the two equations is accomplished through a multidimensional intermittency function based on the work of Dhawan and Narasimha. The model predicts both the onset and extent of transition. Low-speed test cases include transitional flow over a flat plate, a single element airfoil, and a multi-element airfoil in landing configuration. High-speed test casesmore » include transitional Mach 3.5 flow over a 5{degree} cone and Mach 6 flow over a flared-cone configuration. Results are compared with experimental data, and the grid-dependence of selected predictions is analyzed.« less

Cascade flow analysis by Navier-Stokes equation

NASA Astrophysics Data System (ADS)

Nozaki, Osamu

1987-06-01

As the performance of the large electronic computer has improved, numerical simulation of the flow around the blade of the aircraft, for instance, is being actively conducted. In the compressor and turbine cascades of aircraft engine, multiple blades are put side by side closely, and the pressure gradient in the flow direction is large. Thus they have more complicated properties than the independent blade. At present, therefore, it is the mainstream to use potential, Euler's equation, etc., as the basic equation but, for knowing the phenomenon caused by the viscosity like the interference of shock waves and boundary layers, it is necessary to solve the Navier-Stokes (N-S) equation. A two-dimensional cascade analysis program was developed by the N-S equation by expanding the two-dimensional high Reynolds number transonic profile analysis code NSFOIL and the lattice formation program AFMESH for the independent blade, which were already developed so as to fit the cascade flow.

Foundations of radiation hydrodynamics

NASA Astrophysics Data System (ADS)

Mihalas, D.; Mihalas, B. W.

This book is the result of an attempt, over the past few years, to gather the basic tools required to do research on radiating flows in astrophysics. The microphysics of gases is discussed, taking into account the equation of state of a perfect gas, the first and second law of thermodynamics, the thermal properties of a perfect gas, the distribution function and Boltzmann's equation, the collision integral, the Maxwellian velocity distribution, Boltzmann's H-theorem, the time of relaxation, and aspects of classical statistical mechanics. Other subjects explored are related to the dynamics of ideal fluids, the dynamics of viscous and heat-conducting fluids, relativistic fluid flow, waves, shocks, winds, radiation and radiative transfer, the equations of radiation hydrodynamics, and radiating flows. Attention is given to small-amplitude disturbances, nonlinear flows, the interaction of radiation and matter, the solution of the transfer equation, acoustic waves, acoustic-gravity waves, basic concepts of special relativity, and equations of motion and energy.

A modified Dodge algorithm for the parabolized Navier-Stokes equation and compressible duct flows

NASA Technical Reports Server (NTRS)

Cooke, C. H.

1981-01-01

A revised version of Dodge's split-velocity method for numerical calculation of compressible duct flow was developed. The revision incorporates balancing of mass flow rates on each marching step in order to maintain front-to-back continuity during the calculation. The (checkerboard) zebra algorithm is applied to solution of the three dimensional continuity equation in conservative form. A second-order A-stable linear multistep method is employed in effecting a marching solution of the parabolized momentum equations. A checkerboard iteration is used to solve the resulting implicit nonlinear systems of finite-difference equations which govern stepwise transition. Qualitive agreement with analytical predictions and experimental results was obtained for some flows with well-known solutions.

A compressible solution of the Navier-Stokes equations for turbulent flow about an airfoil

NASA Technical Reports Server (NTRS)

Shamroth, S. J.; Gibeling, H. J.

1979-01-01

A compressible time dependent solution of the Navier-Stokes equations including a transition turbulence model is obtained for the isolated airfoil flow field problem. The equations are solved by a consistently split linearized block implicit scheme. A nonorthogonal body-fitted coordinate system is used which has maximum resolution near the airfoil surface and in the region of the airfoil leading edge. The transition turbulence model is based upon the turbulence kinetic energy equation and predicts regions of laminar, transitional, and turbulent flow. Mean flow field and turbulence field results are presented for an NACA 0012 airfoil at zero and nonzero incidence angles of Reynolds number up to one million and low subsonic Mach numbers.

Analysis of atmospheric flow over a surface protrusion using the turbulence kinetic energy equation

NASA Technical Reports Server (NTRS)

Frost, W.; Harper, W. L.; Fichtl, G. H.

1975-01-01

Atmospheric flow fields resulting from a semi-elliptical surface obstruction in an otherwise horizontally homogeneous statistically stationary flow are modelled with the boundary-layer/Boussinesq-approximation of the governing equation of fluid mechanics. The turbulence kinetic energy equation is used to determine the dissipative effects of turbulent shear on the mean flow. Mean-flow results are compared with those given in a previous paper where the same problem was attacked using a Prandtl mixing-length hypothesis. Iso-lines of turbulence kinetic energy and turbulence intensity are plotted in the plane of the flow. They highlight regions of high turbulence intensity in the stagnation zone and sharp gradients in intensity along the transition from adverse to favourable pressure gradient.

Flow Behavior and Constitutive Equation of Ti-6.5Al-2Sn-4Zr-4Mo-1W-0.2Si Titanium Alloy

NASA Astrophysics Data System (ADS)

Yang, Xuemei; Guo, Hongzhen; Liang, Houquan; Yao, Zekun; Yuan, Shichong

2016-04-01

In order to get a reliable constitutive equation for the finite element simulation, flow behavior of Ti-6.5Al-2Sn-4Zr-4Mo-1W-0.2Si alloy under high temperature was investigated by carrying a series of isothermal compression tests at temperatures of 1153-1293 K and strain rates of 0.01-10.0 s-1 on the Gleeble-1500 simulator. Results showed that the true stress-strain curves exhibited peaks at small strains, after which the flow stress decreased monotonically. Ultimately, the flow curves reached steady state at the strain of 0.6, showing a dynamic flow softening phenomenon. The effects of strain rate, temperature, and strain on the flow behavior were researched by establishing a constitutive equation. The relations among stress exponent, deformation activation energy, and strain were preliminarily discussed by using strain rate sensitivity exponent and dynamic recrystallization kinetics curve. Stress values predicted by the modified constitutive equation showed a good agreement with the experimental ones. The correlation coefficient ( R) and average absolute relative error (AARE) were 98.2% and 4.88%, respectively, which confirmed that the modified constitutive equation could give an accurate estimation of the flow stress for BT25y titanium alloy.

Separation of acoustic waves in isentropic flow perturbations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Henke, Christian, E-mail: christian.henke@atlas-elektronik.com

2015-04-15

The present contribution investigates the mechanisms of sound generation and propagation in the case of highly-unsteady flows. Based on the linearisation of the isentropic Navier–Stokes equation around a new pathline-averaged base flow, it is demonstrated for the first time that flow perturbations of a non-uniform flow can be split into acoustic and vorticity modes, with the acoustic modes being independent of the vorticity modes. Therefore, we can propose this acoustic perturbation as a general definition of sound. As a consequence of the splitting result, we conclude that the present acoustic perturbation is propagated by the convective wave equation and fulfilsmore » Lighthill’s acoustic analogy. Moreover, we can define the deviations of the Navier–Stokes equation from the convective wave equation as “true” sound sources. In contrast to other authors, no assumptions on a slowly varying or irrotational flow are necessary. Using a symmetry argument for the conservation laws, an energy conservation result and a generalisation of the sound intensity are provided. - Highlights: • First splitting of non-uniform flows in acoustic and non-acoustic components. • These result leads to a generalisation of sound which is compatible with Lighthill’s acoustic analogy. • A closed equation for the generation and propagation of sound is given.« less

A two-layer model for buoyant inertial displacement flows in inclined pipes

NASA Astrophysics Data System (ADS)

Etrati, Ali; Frigaard, Ian A.

2018-02-01

We investigate the inertial flows found in buoyant miscible displacements using a two-layer model. From displacement flow experiments in inclined pipes, it has been observed that for significant ranges of Fr and Re cos β/Fr, a two-layer, stratified flow develops with the heavier fluid moving at the bottom of the pipe. Due to significant inertial effects, thin-film/lubrication models developed for laminar, viscous flows are not effective for predicting these flows. Here we develop a displacement model that addresses this shortcoming. The complete model for the displacement flow consists of mass and momentum equations for each fluid, resulting in a set of four non-linear equations. By integrating over each layer and eliminating the pressure gradient, we reduce the system to two equations for the area and mean velocity of the heavy fluid layer. The wall and interfacial stresses appear as source terms in the reduced system. The final system of equations is solved numerically using a robust, shock-capturing scheme. The equations are stabilized to remove non-physical instabilities. A linear stability analysis is able to predict the onset of instabilities at the interface and together with numerical solution, is used to study displacement effectiveness over different parametric regimes. Backflow and instability onset predictions are made for different viscosity ratios.

The Soil Foam Drainage Equation - an alternative model for unsaturated flow in porous media

NASA Astrophysics Data System (ADS)

Assouline, Shmuel; Lehmann, Peter; Hoogland, Frouke; Or, Dani

2017-04-01

The analogy between the geometry and dynamics of wet foam drainage and gravity drainage of unsaturated porous media expands modeling capabilities for capillary flows and supplements the standard Richards equation representation. The governing equation for draining foam (or a soil variant termed the soil foam drainage equation - SFDE) obviates the need for macroscopic unsaturated hydraulic conductivity function by an explicit account of diminishing flow pathway sizes as the medium gradually drains. Potential advantages of the proposed drainage foam formalism include direct description of transient flow without requiring constitutive functions; evolution of capillary cross sections that provides consistent description of self-regulating internal fluxes (e.g., towards field capacity); and a more intuitive geometrical picture of capillary flow across textural boundaries. We will present new and simple analytical expressions for drainage rates and volumes from unsaturated porous media subjected to different boundary conditions that are in good agreement with the numerical solution of the SFDE and experimental results. The foam drainage methodology expands the range of tools available for describing and quantifying unsaturated flows and provides geometrically tractable links between evolution of liquid configuration and flow dynamics in unsaturated porous media. The resulting geometrical representation of capillary drainage could improve understanding of colloid and pathogen transport. The explicit geometrical interpretation of flow pathways underlying the hydraulic functions used by the Richards equation offers new insights that benefit both approaches.

A High-Resolution Godunov Method for Compressible Multi-Material Flow on Overlapping Grids

DOE Office of Scientific and Technical Information (OSTI.GOV)

Banks, J W; Schwendeman, D W; Kapila, A K

2006-02-13

A numerical method is described for inviscid, compressible, multi-material flow in two space dimensions. The flow is governed by the multi-material Euler equations with a general mixture equation of state. Composite overlapping grids are used to handle complex flow geometry and block-structured adaptive mesh refinement (AMR) is used to locally increase grid resolution near shocks and material interfaces. The discretization of the governing equations is based on a high-resolution Godunov method, but includes an energy correction designed to suppress numerical errors that develop near a material interface for standard, conservative shock-capturing schemes. The energy correction is constructed based on amore » uniform pressure-velocity flow and is significant only near the captured interface. A variety of two-material flows are presented to verify the accuracy of the numerical approach and to illustrate its use. These flows assume an equation of state for the mixture based on Jones-Wilkins-Lee (JWL) forms for the components. This equation of state includes a mixture of ideal gases as a special case. Flow problems considered include unsteady one-dimensional shock-interface collision, steady interaction of an planar interface and an oblique shock, planar shock interaction with a collection of gas-filled cylindrical inhomogeneities, and the impulsive motion of the two-component mixture in a rigid cylindrical vessel.« less

Breakdown of the conservative potential equation

NASA Technical Reports Server (NTRS)

Salas, M. D.; Gumbert, C. R.

1986-01-01

The conservative full-potential equation is used to study transonic flow over five airfoil sections. The results of the study indicate that once shock are present in the flow, the qualitative approximation is different from that observed with the Euler equations. The difference in behavior of the potential eventually leads to multiple solutions.

Theoretical fluid dynamics

NASA Astrophysics Data System (ADS)

Shivamoggi, B. K.

This book is concerned with a discussion of the dynamical behavior of a fluid, and is addressed primarily to graduate students and researchers in theoretical physics and applied mathematics. A review of basic concepts and equations of fluid dynamics is presented, taking into account a fluid model of systems, the objective of fluid dynamics, the fluid state, description of the flow field, volume forces and surface forces, relative motion near a point, stress-strain relation, equations of fluid flows, surface tension, and a program for analysis of the governing equations. The dynamics of incompressible fluid flows is considered along with the dynamics of compressible fluid flows, the dynamics of viscous fluid flows, hydrodynamic stability, and dynamics of turbulence. Attention is given to the complex-variable method, three-dimensional irrotational flows, vortex flows, rotating flows, water waves, applications to aerodynamics, shock waves, potential flows, the hodograph method, flows at low and high Reynolds numbers, the Jeffrey-Hamel flow, and the capillary instability of a liquid jet.

Numerical simulation of steady and unsteady asymmetric vortical flow

NASA Technical Reports Server (NTRS)

Kandil, Osama A.; Wong, Tin-Chee; Liu, C. H.

1992-01-01

The unsteady, compressible, thin-layer, Navier-Stokes (NS) equations are solved to simulate steady and unsteady, asymmetric, vortical laminar flow around cones at high incidences and supersonic Mach numbers. The equations are solved by using an implicit, upwind, flux-difference splitting (FDS), finite-volume scheme. The locally conical flow assumption is used and the solutions are obtained by forcing the conserved components of the flowfield vector to be equal at two axial stations located at 0.95 and 1.0. Computational examples cover steady and unsteady asymmetric flows around a circular cone and its control using side strakes. The unsteady asymmetric flow solution around the circular cone has also been validated using the upwind, flux-vector splitting (FVS) scheme with the thin-layer NS equations and the upwind FDS with the full NS equations. The results are in excellent agreement with each other. Unsteady asymmetric flows are also presented for elliptic- and diamond-section cones, which model asymmetric vortex shedding around round- and sharp-edged delta winds.

A New Formulation of Time Domain Boundary Integral Equation for Acoustic Wave Scattering in the Presence of a Uniform Mean Flow

NASA Technical Reports Server (NTRS)

Hu, Fang; Pizzo, Michelle E.; Nark, Douglas M.

2017-01-01

It has been well-known that under the assumption of a constant uniform mean flow, the acoustic wave propagation equation can be formulated as a boundary integral equation, in both the time domain and the frequency domain. Compared with solving partial differential equations, numerical methods based on the boundary integral equation have the advantage of a reduced spatial dimension and, hence, requiring only a surface mesh. However, the constant uniform mean flow assumption, while convenient for formulating the integral equation, does not satisfy the solid wall boundary condition wherever the body surface is not aligned with the uniform mean flow. In this paper, we argue that the proper boundary condition for the acoustic wave should not have its normal velocity be zero everywhere on the solid surfaces, as has been applied in the literature. A careful study of the acoustic energy conservation equation is presented that shows such a boundary condition in fact leads to erroneous source or sink points on solid surfaces not aligned with the mean flow. A new solid wall boundary condition is proposed that conserves the acoustic energy and a new time domain boundary integral equation is derived. In addition to conserving the acoustic energy, another significant advantage of the new equation is that it is considerably simpler than previous formulations. In particular, tangential derivatives of the solution on the solid surfaces are no longer needed in the new formulation, which greatly simplifies numerical implementation. Furthermore, stabilization of the new integral equation by Burton-Miller type reformulation is presented. The stability of the new formulation is studied theoretically as well as numerically by an eigenvalue analysis. Numerical solutions are also presented that demonstrate the stability of the new formulation.

Peak-flow frequency relations and evaluation of the peak-flow gaging network in Nebraska

USGS Publications Warehouse

Soenksen, Philip J.; Miller, Lisa D.; Sharpe, Jennifer B.; Watton, Jason R.

1999-01-01

Estimates of peak-flow magnitude and frequency are required for the efficient design of structures that convey flood flows or occupy floodways, such as bridges, culverts, and roads. The U.S. Geological Survey, in cooperation with the Nebraska Department of Roads, conducted a study to update peak-flow frequency analyses for selected streamflow-gaging stations, develop a new set of peak-flow frequency relations for ungaged streams, and evaluate the peak-flow gaging-station network for Nebraska. Data from stations located in or within about 50 miles of Nebraska were analyzed using guidelines of the Interagency Advisory Committee on Water Data in Bulletin 17B. New generalized skew relations were developed for use in frequency analyses of unregulated streams. Thirty-three drainage-basin characteristics related to morphology, soils, and precipitation were quantified using a geographic information system, related computer programs, and digital spatial data.For unregulated streams, eight sets of regional regression equations relating drainage-basin to peak-flow characteristics were developed for seven regions of the state using a generalized least squares procedure. Two sets of regional peak-flow frequency equations were developed for basins with average soil permeability greater than 4 inches per hour, and six sets of equations were developed for specific geographic areas, usually based on drainage-basin boundaries. Standard errors of estimate for the 100-year frequency equations (1percent probability) ranged from 12.1 to 63.8 percent. For regulated reaches of nine streams, graphs of peak flow for standard frequencies and distance upstream of the mouth were estimated.The regional networks of streamflow-gaging stations on unregulated streams were analyzed to evaluate how additional data might affect the average sampling errors of the newly developed peak-flow equations for the 100-year frequency occurrence. Results indicated that data from new stations, rather than more data from existing stations, probably would produce the greatest reduction in average sampling errors of the equations.

Turbulence Model Selection for Low Reynolds Number Flows

PubMed Central

2016-01-01

One of the major flow phenomena associated with low Reynolds number flow is the formation of separation bubbles on an airfoil’s surface. NACA4415 airfoil is commonly used in wind turbines and UAV applications. The stall characteristics are gradual compared to thin airfoils. The primary criterion set for this work is the capture of laminar separation bubble. Flow is simulated for a Reynolds number of 120,000. The numerical analysis carried out shows the advantages and disadvantages of a few turbulence models. The turbulence models tested were: one equation Spallart Allmars (S-A), two equation SST K-ω, three equation Intermittency (γ) SST, k-kl-ω and finally, the four equation transition γ-Reθ SST. However, the variation in flow physics differs between these turbulence models. Procedure to establish the accuracy of the simulation, in accord with previous experimental results, has been discussed in detail. PMID:27104354

Electroosmotic flow and mixing in microchannels with the lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Tang, G. H.; Li, Zhuo; Wang, J. K.; He, Y. L.; Tao, W. Q.

2006-11-01

Understanding the electroosmotic flow in microchannels is of both fundamental and practical significance for the design and optimization of various microfluidic devices to control fluid motion. In this paper, a lattice Boltzmann equation, which recovers the nonlinear Poisson-Boltzmann equation, is used to solve the electric potential distribution in the electrolytes, and another lattice Boltzmann equation, which recovers the Navier-Stokes equation including the external force term, is used to solve the velocity fields. The method is validated by the electric potential distribution in the electrolytes and the pressure driven pulsating flow. Steady-state and pulsating electroosmotic flows in two-dimensional parallel uniform and nonuniform charged microchannels are studied with this lattice Boltzmann method. The simulation results show that the heterogeneous surface potential distribution and the electroosmotic pulsating flow can induce chaotic advection and thus enhance the mixing in microfluidic systems efficiently.

Turbulence Model Selection for Low Reynolds Number Flows.

PubMed

Aftab, S M A; Mohd Rafie, A S; Razak, N A; Ahmad, K A

2016-01-01

One of the major flow phenomena associated with low Reynolds number flow is the formation of separation bubbles on an airfoil's surface. NACA4415 airfoil is commonly used in wind turbines and UAV applications. The stall characteristics are gradual compared to thin airfoils. The primary criterion set for this work is the capture of laminar separation bubble. Flow is simulated for a Reynolds number of 120,000. The numerical analysis carried out shows the advantages and disadvantages of a few turbulence models. The turbulence models tested were: one equation Spallart Allmars (S-A), two equation SST K-ω, three equation Intermittency (γ) SST, k-kl-ω and finally, the four equation transition γ-Reθ SST. However, the variation in flow physics differs between these turbulence models. Procedure to establish the accuracy of the simulation, in accord with previous experimental results, has been discussed in detail.

SCORE-EVET: a computer code for the multidimensional transient thermal-hydraulic analysis of nuclear fuel rod arrays. [BWR; PWR

DOE Office of Scientific and Technical Information (OSTI.GOV)

Benedetti, R. L.; Lords, L. V.; Kiser, D. M.

1978-02-01

The SCORE-EVET code was developed to study multidimensional transient fluid flow in nuclear reactor fuel rod arrays. The conservation equations used were derived by volume averaging the transient compressible three-dimensional local continuum equations in Cartesian coordinates. No assumptions associated with subchannel flow have been incorporated into the derivation of the conservation equations. In addition to the three-dimensional fluid flow equations, the SCORE-EVET code ocntains: (a) a one-dimensional steady state solution scheme to initialize the flow field, (b) steady state and transient fuel rod conduction models, and (c) comprehensive correlation packages to describe fluid-to-fuel rod interfacial energy and momentum exchange. Velocitymore » and pressure boundary conditions can be specified as a function of time and space to model reactor transient conditions such as a hypothesized loss-of-coolant accident (LOCA) or flow blockage.« less

Second order modeling of boundary-free turbulent shear flows

NASA Technical Reports Server (NTRS)

Shih, T.-H.; Chen, Y.-Y.; Lumley, J. L.

1991-01-01

A set of realizable second order models for boundary-free turbulent flows is presented. The constraints on second order models based on the realizability principle are re-examined. The rapid terms in the pressure correlations for both the Reynolds stress and the passive scalar flux equations are constructed to exactly satisfy the joint realizability. All other model terms (return-to-isotropy, third moments, and terms in the dissipation equations) already satisfy realizability. To correct the spreading rate of the axisymmetric jet, an extra term is added to the dissipation equation which accounts for the effect of mean vortex stretching on dissipation. The test flows used in this study are the mixing shear layer, plane jet, axisymmetric jet, and plane wake. The numerical solutions show that the unified model equations predict all these flows reasonably. It is expected that these models would be suitable for more complex and critical flows.

Ensemble Averaged Probability Density Function (APDF) for Compressible Turbulent Reacting Flows

NASA Technical Reports Server (NTRS)

Shih, Tsan-Hsing; Liu, Nan-Suey

2012-01-01

In this paper, we present a concept of the averaged probability density function (APDF) for studying compressible turbulent reacting flows. The APDF is defined as an ensemble average of the fine grained probability density function (FG-PDF) with a mass density weighting. It can be used to exactly deduce the mass density weighted, ensemble averaged turbulent mean variables. The transport equation for APDF can be derived in two ways. One is the traditional way that starts from the transport equation of FG-PDF, in which the compressible Navier- Stokes equations are embedded. The resulting transport equation of APDF is then in a traditional form that contains conditional means of all terms from the right hand side of the Navier-Stokes equations except for the chemical reaction term. These conditional means are new unknown quantities that need to be modeled. Another way of deriving the transport equation of APDF is to start directly from the ensemble averaged Navier-Stokes equations. The resulting transport equation of APDF derived from this approach appears in a closed form without any need for additional modeling. The methodology of ensemble averaging presented in this paper can be extended to other averaging procedures: for example, the Reynolds time averaging for statistically steady flow and the Reynolds spatial averaging for statistically homogeneous flow. It can also be extended to a time or spatial filtering procedure to construct the filtered density function (FDF) for the large eddy simulation (LES) of compressible turbulent reacting flows.

Numerical analysis of field-modulated electroosmotic flows in microchannels with arbitrary numbers and configurations of discrete electrodes.

PubMed

Chao, Kan; Chen, Bo; Wu, Jiankang

2010-12-01

The formation of an electric double layer and electroosmosis are important theoretic foundations associated with microfluidic systems. Field-modulated electroosmotic flows in microchannels can be obtained by applying modulating electric fields in a direction perpendicular to a channel wall. This paper presents a systematic numerical analysis of modulated electroosmotic flows in a microchannel with discrete electrodes on the basis of the Poisson equation of electric fields in a liquid-solid coupled domain, the Navier-Stokes equation of liquid flow, and the Nernst-Planck equation of ion transport. These equations are nonlinearly coupled and are simultaneously solved numerically for the electroosmotic flow velocity, electric potential, and ion concentrations in the microchannel. A number of numerical examples of modulated electroosmotic flows in microchannels with discrete electrodes are presented, including single electrodes, symmetric/asymmetric double electrodes, and triple electrodes. Numerical results indicate that chaotic circulation flows, micro-vortices, and effective fluid mixing can be realized in microchannels by applying modulating electric fields with various electrode configurations. The interaction of a modulating field with an applied field along the channel is also discussed.

Numerical computation of viscous flow about unconventional airfoil shapes

NASA Technical Reports Server (NTRS)

Ahmed, S.; Tannehill, J. C.

1990-01-01

A new two-dimensional computer code was developed to analyze the viscous flow around unconventional airfoils at various Mach numbers and angles of attack. The Navier-Stokes equations are solved using an implicit, upwind, finite-volume scheme. Both laminar and turbulent flows can be computed. A new nonequilibrium turbulence closure model was developed for computing turbulent flows. This two-layer eddy viscosity model was motivated by the success of the Johnson-King model in separated flow regions. The influence of history effects are described by an ordinary differential equation developed from the turbulent kinetic energy equation. The performance of the present code was evaluated by solving the flow around three airfoils using the Reynolds time-averaged Navier-Stokes equations. Excellent results were obtained for both attached and separated flows about the NACA 0012 airfoil, the RAE 2822 airfoil, and the Integrated Technology A 153W airfoil. Based on the comparison of the numerical solutions with the available experimental data, it is concluded that the present code in conjunction with the new nonequilibrium turbulence model gives excellent results.

A new lumped-parameter model for flow in unsaturated dual-porosity media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zimmerman, Robert W.; Hadgu, Teklu; Bodvarsson, Gudmundur S.

A new lumped-parameter approach to simulating unsaturated flow processes in dual-porosity media such as fractured rocks or aggregated soils is presented. Fluid flow between the fracture network and the matrix blocks is described by a non-linear equation that relates the imbibition rate to the local difference in liquid-phase pressure between the fractures and the matrix blocks. Unlike a Warren-Root-type equation, this equation is accurate in both the early and late time regimes. The fracture/matrix interflow equation has been incorporated into an existing unsaturated flow simulator, to serve as a source/sink term for fracture gridblocks. Flow processes are then simulated usingmore » only fracture gridblocks in the computational grid. This new lumped-parameter approach has been tested on two problems involving transient flow in fractured/porous media, and compared with simulations performed using explicit discretization of the matrix blocks. The new procedure seems to accurately simulate flow processes in unsaturated fractured rocks, and typically requires an order of magnitude less computational time than do simulations using fully-discretized matrix blocks. [References: 37]« less

Simulations of Fluvial Landscapes

NASA Astrophysics Data System (ADS)

Cattan, D.; Birnir, B.

2013-12-01

The Smith-Bretherton-Birnir (SBB) model for fluvial landsurfaces consists of a pair of partial differential equations, one governing water flow and one governing the sediment flow. Numerical solutions of these equations have been shown to provide realistic models in the evolution of fluvial landscapes. Further analysis of these equations shows that they possess scaling laws (Hack's Law) that are known to exist in nature. However, the simulations are highly dependent on the numerical methods used; with implicit methods exhibiting the correct scaling laws, but the explicit methods fail to do so. These equations, and the resulting models, help to bridge the gap between the deterministic and the stochastic theories of landscape evolution. Slight modifications of the SBB equations make the results of the model more realistic. By modifying the sediment flow equation, the model obtains more pronounced meandering rivers. Typical landsurface with rivers.

Textbook Multigrid Efficiency for the Steady Euler Equations

NASA Technical Reports Server (NTRS)

Roberts, Thomas W.; Sidilkover, David; Swanson, R. C.

2004-01-01

A fast multigrid solver for the steady incompressible Euler equations is presented. Unlike time-marching schemes, this approach uses relaxation of the steady equations. Application of this method results in a discretization that correctly distinguishes between the advection and elliptic parts of the operator, allowing efficient smoothers to be constructed. Solvers for both unstructured triangular grids and structured quadrilateral grids have been written. Computations for channel flow and flow over a nonlifting airfoil have computed. Using Gauss-Seidel relaxation ordered in the flow direction, textbook multigrid convergence rates of nearly one order-of-magnitude residual reduction per multigrid cycle are achieved, independent of the grid spacing. This approach also may be applied to the compressible Euler equations and the incompressible Navier-Stokes equations.

Bypass Transitional Flow Calculations Using a Navier-Stokes Solver and Two-Equation Models

NASA Technical Reports Server (NTRS)

Liuo, William W.; Shih, Tsan-Hsing; Povinelli, L. A. (Technical Monitor)

2000-01-01

Bypass transitional flows over a flat plate were simulated using a Navier-Stokes solver and two equation models. A new model for the bypass transition, which occurs in cases with high free stream turbulence intensity (TI), is described. The new transition model is developed by including an intermittency correction function to an existing two-equation turbulence model. The advantages of using Navier-Stokes equations, as opposed to boundary-layer equations, in bypass transition simulations are also illustrated. The results for two test flows over a flat plate with different levels of free stream turbulence intensity are reported. Comparisons with the experimental measurements show that the new model can capture very well both the onset and the length of bypass transition.

Effective equations and the inverse cascade theory for Kolmogorov flows

NASA Technical Reports Server (NTRS)

Weinan, E.; Shu, Chi-Wang

1992-01-01

We study the two dimensional Kolmogorov flows in the limit as the forcing frequency goes to infinity. Direct numerical simulation indicates that the low frequency energy spectrum evolves to a universal kappa (exp -4) decay law. We derive effective equations governing the behavior of the large scale flow quantities. We then present numerical evidence that with smooth initial data, the solution to the effective equation develops a kappa (exp -4) type singularity at a finite time. This gives a convenient explanation for the kappa (exp -4) decay law exhibited by the original Kolmogorov flows.

Three-phase Power Flow Calculation of Low Voltage Distribution Network Considering Characteristics of Residents Load

NASA Astrophysics Data System (ADS)

Wang, Yaping; Lin, Shunjiang; Yang, Zhibin

2017-05-01

In the traditional three-phase power flow calculation of the low voltage distribution network, the load model is described as constant power. Since this model cannot reflect the characteristics of actual loads, the result of the traditional calculation is always different from the actual situation. In this paper, the load model in which dynamic load represented by air conditioners parallel with static load represented by lighting loads is used to describe characteristics of residents load, and the three-phase power flow calculation model is proposed. The power flow calculation model includes the power balance equations of three-phase (A,B,C), the current balance equations of phase 0, and the torque balancing equations of induction motors in air conditioners. And then an alternating iterative algorithm of induction motor torque balance equations with each node balance equations is proposed to solve the three-phase power flow model. This method is applied to an actual low voltage distribution network of residents load, and by the calculation of three different operating states of air conditioners, the result demonstrates the effectiveness of the proposed model and the algorithm.

On the Divergence of the Velocity Vector in Real-Gas Flow

NASA Technical Reports Server (NTRS)

Bellan, Josette

2009-01-01

A theoretical study was performed addressing the degree of applicability or inapplicability, to a real gas, of the occasionally stated belief that for an ideal gas, incompressibility is synonymous with a zero or very low Mach number. The measure of compressibility used in this study is the magnitude of the divergence of the flow velocity vector [V(bar) (raised dot) u (where u is the flow velocity)]. The study involves a mathematical derivation that begins with the governing equations of flow and involves consideration of equations of state, thermodynamics, and fluxes of heat, mass, and the affected molecular species. The derivation leads to an equation for the volume integral of (V(bar) (raised dot) u)(sup 2) that indicates contributions of several thermodynamic, hydrodynamic, and species-flux effects to compressibility and reveals differences between real and ideal gases. An analysis of the equation leads to the conclusion that for a real gas, incompressibility is not synonymous with zero or very small Mach number. Therefore, it is further concluded, the contributions to compressibility revealed by the derived equation should be taken into account in simulations of real-gas flows.

Simulation of 2D rarefied gas flows based on the numerical solution of the Boltzmann equation

NASA Astrophysics Data System (ADS)

Poleshkin, Sergey O.; Malkov, Ewgenij A.; Kudryavtsev, Alexey N.; Shershnev, Anton A.; Bondar, Yevgeniy A.; Kohanchik, A. A.

2017-10-01

There are various methods for calculating rarefied gas flows, in particular, statistical methods and deterministic methods based on the finite-difference solutions of the Boltzmann nonlinear kinetic equation and on the solutions of model kinetic equations. There is no universal method; each has its disadvantages in terms of efficiency or accuracy. The choice of the method depends on the problem to be solved and on parameters of calculated flows. Qualitative theoretical arguments help to determine the range of parameters of effectively solved problems for each method; however, it is advisable to perform comparative tests of calculations of the classical problems performed by different methods and with different parameters to have quantitative confirmation of this reasoning. The paper provides the results of the calculations performed by the authors with the help of the Direct Simulation Monte Carlo method and finite-difference methods of solving the Boltzmann equation and model kinetic equations. Based on this comparison, conclusions are made on selecting a particular method for flow simulations in various ranges of flow parameters.

Method for estimating low-flow characteristics of ungaged streams in Indiana

USGS Publications Warehouse

Arihood, Leslie D.; Glatfelter, Dale R.

1991-01-01

Equations for estimating the 7-day, 2-year and 7oday, 10-year low flows at sites on ungaged streams are presented. Regression analysis was used to develop equations relating basin characteristics and low-flow characteristics at 82 gaging stations. Significant basin characteristics in the equations are contributing drainage area and flow-duration ratio, which is the 20-percent flow duration divided by the 90-percent flow duration. Flow-duration ratio has been regionalized for Indiana on a plate. Ratios for use in the equations are obtained from the plate. Drainage areas are determined from maps or are obtained from reports. The predictive capability of the method was determined by tests of the equations and of the flow-duration ratios on the plate. The accuracy of the equations alone was tested by estimating the low-flow characteristics at 82 gaging stations where flow-duration ratio is already known. In this case, the standard errors of estimate for 7-day, 2-year and 7-day, 10-year low flows are 19 and 28 percent. When flow-duration ratios for the 82 gaging stations are obtained from the map, the standard errors are 46 and 61 percent. However, when stations having drainage areas of less than 10 square miles are excluded from the test, the standard errors decrease to 38 and 49 percent. Standard errors increase when stations with small basins are included, probably because some of the flow-duration ratios obtained for these small basins are incorrect. Local geology and its effect on the ratio are not adequately reflected on the plate, which shows the regional variation in flow-duration ratio. In all the tests, no bias is apparent areally, with increasing drainage area or with increasing ratio. Guidelines and limitations should be considered when using the method. The method can be applied only at sites in the northern and central physiographic zones of the State. Low-flow characteristics cannot be estimated for regulated streams unless the amount of regulation is known so that the estimated low-flow characteristic can be adjusted. The method is most accurate for sites having drainage areas ranging from 10 to 1,000 square miles and for predictions of 7-day, 10-year low flows ranging from 0.5 to 340 cubic feet per second.

Method for estimating low-flow characteristics of ungaged streams in Indiana

USGS Publications Warehouse

Arihood, L.D.; Glatfelter, D.R.

1986-01-01

Equations for estimating the 7-day, 2-yr and 7-day, 10-yr low flows at sites on ungaged streams are presented. Regression analysis was used to develop equations relating basin characteristics and low flow characteristics at 82 gaging stations. Significant basin characteristics in the equations are contributing drainage area and flow duration ratio, which is the 20% flow duration divided by the 90% flow duration. Flow duration ratio has been regionalized for Indiana on a plate. Ratios for use in the equations are obtained from this plate. Drainage areas are determined from maps or are obtained from reports. The predictive capability of the method was determined by tests of the equations and of the flow duration ratios on the plate. The accuracy of the equations alone was tested by estimating the low flow characteristics at 82 gaging stations where flow duration ratio is already known. In this case, the standard errors of estimate for 7-day, 2-yr and 7-day, 10-yr low flows are 19% and 28%. When flow duration ratios for the 82 gaging stations are obtained from the map, the standard errors are 46% and 61%. However, when stations with drainage areas < 10 sq mi are excluded from the test, the standard errors reduce to 38% and 49%. Standard errors increase when stations with small basins are included, probably because some of the flow duration ratios obtained for these small basins are incorrect. Local geology and its effect on the ratio are not adequately reflected on the plate, which shows the regional variation in flow duration ratio. In all the tests, no bias is apparent areally, with increasing drainage area or with increasing ratio. Guidelines and limitations should be considered when using the method. The method can be applied only at sites in the northern and the central physiographic zones of the state. Low flow characteristics cannot be estimated for regulated streams unless the amount of regulation is known so that the estimated low flow characteristic can be adjusted. The method is most accurate for sites with drainage areas ranging from 10 to 1,000 sq mi and for predictions of 7-day, 10-yr low flows ranging from 0.5 to 340 cu ft/sec. (Author 's abstract)

A modified Dodge algorithm for the parabolized Navier-Stokes equations and compressible duct flows

NASA Technical Reports Server (NTRS)

Cooke, C. H.; Dwoyer, D. M.

1983-01-01

A revised version of Dodge's split-velocity method for numerical calculation of compressible duct flow was developed. The revision incorporates balancing of mass flow rates on each marching step in order to maintain front-to-back continuity during the calculation. The (checkerboard) zebra algorithm is applied to solution of the three dimensional continuity equation in conservative form. A second-order A-stable linear multistep method is employed in effecting a marching solution of the parabolized momentum equations. A checkerboard iteration is used to solve the resulting implicit nonlinear systems of finite-difference equations which govern stepwise transition. Qualitative agreement with analytical predictions and experimental results was obtained for some flows with well-known solutions. Previously announced in STAR as N82-16363

Unsteady free surface flow in porous media: One-dimensional model equations including vertical effects and seepage face

NASA Astrophysics Data System (ADS)

Di Nucci, Carmine

2018-05-01

This note examines the two-dimensional unsteady isothermal free surface flow of an incompressible fluid in a non-deformable, homogeneous, isotropic, and saturated porous medium (with zero recharge and neglecting capillary effects). Coupling a Boussinesq-type model for nonlinear water waves with Darcy's law, the two-dimensional flow problem is solved using one-dimensional model equations including vertical effects and seepage face. In order to take into account the seepage face development, the system equations (given by the continuity and momentum equations) are completed by an integral relation (deduced from the Cauchy theorem). After testing the model against data sets available in the literature, some numerical simulations, concerning the unsteady flow through a rectangular dam (with an impermeable horizontal bottom), are presented and discussed.

A modified dodge algorithm for the parabolized Navier-Stokes equations and compressible duct flows

NASA Technical Reports Server (NTRS)

Cooke, C. H.

1981-01-01

A revised version of a split-velocity method for numerical calculation of compressible duct flow was developed. The revision incorporates balancing of mass flow rates on each marching step in order to maintain front-to-back continuity during the calculation. The (checkerboard) zebra algorithm is applied to solution of the three-dimensional continuity equation in conservative form. A second-order A-stable linear multistep method is employed in effecting a marching solution of the parabolized momentum equations. A checkerboard successive overrelaxation iteration is used to solve the resulting implicit nonlinear systems of finite-difference equations which govern stepwise transition.

Estimates of streamflow characteristics for selected small streams, Baker River basin, Washington

USGS Publications Warehouse

Williams, John R.

1987-01-01

Regression equations were used to estimate streamflow characteristics at eight ungaged sites on small streams in the Baker River basin in the North Cascade Mountains, Washington, that could be suitable for run-of-the-river hydropower development. The regression equations were obtained by relating known streamflow characteristics at 25 gaging stations in nearby basins to several physical and climatic variables that could be easily measured in gaged or ungaged basins. The known streamflow characteristics were mean annual flows, 1-, 3-, and 7-day low flows and high flows, mean monthly flows, and flow duration. Drainage area and mean annual precipitation were not the most significant variables in all the regression equations. Variance in the low flows and the summer mean monthly flows was reduced by including an index of glacierized area within the basin as a third variable. Standard errors of estimate of the regression equations ranged from 25 to 88%, and the largest errors were associated with the low flow characteristics. Discharge measurements made at the eight sites near midmonth each month during 1981 were used to estimate monthly mean flows at the sites for that period. These measurements also were correlated with concurrent daily mean flows from eight operating gaging stations. The correlations provided estimates of mean monthly flows that compared reasonably well with those estimated by the regression analyses. (Author 's abstract)

Solution of transonic flows by an integro-differential equation method

NASA Technical Reports Server (NTRS)

Ogana, W.

1978-01-01

Solutions of steady transonic flow past a two-dimensional airfoil are obtained from a singular integro-differential equation which involves a tangential derivative of the perturbation velocity potential. Subcritical flows are solved by taking central differences everywhere. For supercritical flows with shocks, central differences are taken in subsonic flow regions and backward differences in supersonic flow regions. The method is applied to a nonlifting parabolic-arc airfoil and to a lifting NACA 0012 airfoil. Results compare favorably with those of finite-difference schemes.

Analytic solutions for Long's equation and its generalization

NASA Astrophysics Data System (ADS)

Humi, Mayer

2017-12-01

Two-dimensional, steady-state, stratified, isothermal atmospheric flow over topography is governed by Long's equation. Numerical solutions of this equation were derived and used by several authors. In particular, these solutions were applied extensively to analyze the experimental observations of gravity waves. In the first part of this paper we derive an extension of this equation to non-isothermal flows. Then we devise a transformation that simplifies this equation. We show that this simplified equation admits solitonic-type solutions in addition to regular gravity waves. These new analytical solutions provide new insights into the propagation and amplitude of gravity waves over topography.

Turbulent boundary layers with secondary flow

NASA Technical Reports Server (NTRS)

Grushwitz, E.

1984-01-01

An experimental analysis of the boundary layer on a plane wall, along which the flow occurs, whose potential flow lines are curved in plane parallel to the wall is discussed. According to the equation frequently applied to boundary layers in a plane flow, which is usually obtained by using the pulse law, a generalization is derived which is valid for boundary layers with spatial flow. The wall shear stresses were calculated with this equation.

A dual potential formulation of the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Gegg, S. G.; Pletcher, R. H.; Steger, J. L.

1989-01-01

A dual potential formulation for numerically solving the Navier-Stokes equations is developed and presented. The velocity field is decomposed using a scalar and vector potential. Vorticity and dilatation are used as the dependent variables in the momentum equations. Test cases in two dimensions verify the capability to solve flows using approximations from potential flow to full Navier-Stokes simulations. A three-dimensional incompressible flow formulation is also described. An interesting feature of this approach to solving the Navier-Stokes equations is the decomposition of the velocity field into a rotational part (vector potential) and an irrotational part (scalar potential). The Helmholtz decomposition theorem allows this splitting of the velocity field. This approach has had only limited use since it increases the number of dependent variables in the solution. However, it has often been used for incompressible flows where the solution scheme is known to be fast and accurate. This research extends the usage of this method to fully compressible Navier-Stokes simulations by using the dilatation variable along with vorticity. A time-accurate, iterative algorithm is used for the uncoupled solution of the governing equations. Several levels of flow approximation are available within the framework of this method. Potential flow, Euler and full Navier-Stokes solutions are possible using the dual potential formulation. Solution efficiency can be enhanced in a straightforward way. For some flows, the vorticity and/or dilatation may be negligible in certain regions (e.g., far from a viscous boundary in an external flow). It is possible to drop the calculation of these variables then and optimize the solution speed. Also, efficient Poisson solvers are available for the potentials. The relative merits of non-primitive variables versus primitive variables for solution of the Navier-Stokes equations are also discussed.

On the propagation of decaying planar shock and blast waves through non-uniform channels

NASA Astrophysics Data System (ADS)

Peace, J. T.; Lu, F. K.

2018-05-01

The propagation of planar decaying shock and blast waves in non-uniform channels is investigated with the use of a two-equation approximation of the generalized CCW theory. The effects of flow non-uniformity for the cases of an arbitrary strength decaying shock and blast wave in the strong shock limit are considered. Unlike the original CCW theory, the two-equation approximation takes into account the effects of initial temporal flow gradients in the flow properties behind the shock as the shock encounters an area change. A generalized order-of-magnitude analysis is carried out to analyze under which conditions the classical area-Mach (A-M) relation and two-equation approximation are valid given a time constant of decay for the flow properties behind the shock. It is shown that the two-equation approximation extends the applicability of the CCW theory to problems where flow non-uniformity behind the shock is orders of magnitude above that for appropriate use of the A-M relation. The behavior of the two-equation solution is presented for converging and diverging channels and compared against the A-M relation. It is shown that the second-order approximation and A-M relation have good agreement for converging geometries, such that the influence of flow non-uniformity behind the shock is negligible compared to the effects of changing area. Alternatively, the two-equation approximation is shown to be strongly dependent on the initial magnitude of flow non-uniformity in diverging geometries. Further, in diverging geometries, the inclusion of flow non-uniformity yields shock solutions that tend toward an acoustic wave faster than that predicted by the A-M relation.

An approximately factored incremental strategy for calculating consistent discrete aerodynamic sensitivity derivatives

NASA Technical Reports Server (NTRS)

Korivi, V. M.; Taylor, A. C., III; Newman, P. A.; Hou, G. J.-W.; Jones, H. E.

1992-01-01

An incremental strategy is presented for iteratively solving very large systems of linear equations, which are associated with aerodynamic sensitivity derivatives for advanced CFD codes. It is shown that the left-hand side matrix operator and the well-known factorization algorithm used to solve the nonlinear flow equations can also be used to efficiently solve the linear sensitivity equations. Two airfoil problems are considered as an example: subsonic low Reynolds number laminar flow and transonic high Reynolds number turbulent flow.

Numerical solution of the two-dimensional time-dependent incompressible Euler equations

NASA Technical Reports Server (NTRS)

Whitfield, David L.; Taylor, Lafayette K.

1994-01-01

A numerical method is presented for solving the artificial compressibility form of the 2D time-dependent incompressible Euler equations. The approach is based on using an approximate Riemann solver for the cell face numerical flux of a finite volume discretization. Characteristic variable boundary conditions are developed and presented for all boundaries and in-flow out-flow situations. The system of algebraic equations is solved using the discretized Newton-relaxation (DNR) implicit method. Numerical results are presented for both steady and unsteady flow.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Isa, Sharena Mohamad; Ali, Anati

In this paper, the hydromagnetic flow of dusty fluid over a vertical stretching sheet with thermal radiation is investigated. The governing partial differential equations are reduced to nonlinear ordinary differential equations using similarity transformation. These nonlinear ordinary differential equations are solved numerically using Runge-Kutta Fehlberg fourth-fifth order method (RKF45 Method). The behavior of velocity and temperature profiles of hydromagnetic fluid flow of dusty fluid is analyzed and discussed for different parameters of interest such as unsteady parameter, fluid-particle interaction parameter, the magnetic parameter, radiation parameter and Prandtl number on the flow.

Navier-Stokes computation of compressible turbulent flows with a second order closure

NASA Technical Reports Server (NTRS)

Dingus, C.; Kollmann, W.

1991-01-01

The objective was the development of a complete second order closure for wall bounded flows, including all components of the dissipation rate tensor and a numerical solution procedure for the resulting system of equations. The main topics discussed are the closure of the pressure correlations and the viscous destruction terms in the dissipation rate equations and the numerical solution scheme based on a block-tridiagonal solver for the nine equations required for the prediction of plane or axisymmetric flows.

Basic lubrication equations

NASA Technical Reports Server (NTRS)

Hamrock, B. J.; Dowson, D.

1981-01-01

Lubricants, usually Newtonian fluids, are assumed to experience laminar flow. The basic equations used to describe the flow are the Navier-Stokes equation of motion. The study of hydrodynamic lubrication is, from a mathematical standpoint, the application of a reduced form of these Navier-Stokes equations in association with the continuity equation. The Reynolds equation can also be derived from first principles, provided of course that the same basic assumptions are adopted in each case. Both methods are used in deriving the Reynolds equation, and the assumptions inherent in reducing the Navier-Stokes equations are specified. Because the Reynolds equation contains viscosity and density terms and these properties depend on temperature and pressure, it is often necessary to couple the Reynolds with energy equation. The lubricant properties and the energy equation are presented. Film thickness, a parameter of the Reynolds equation, is a function of the elastic behavior of the bearing surface. The governing elasticity equation is therefore presented.

Advancements in engineering turbulence modeling

NASA Technical Reports Server (NTRS)

Shih, T.-H.

1991-01-01

Some new developments in two-equation models and second order closure models are presented. Two-equation models (k-epsilon models) have been widely used in computational fluid dynamics (CFD) for engineering problems. Most of low-Reynolds number two-equation models contain some wall-distance damping functions to account for the effect of wall on turbulence. However, this often causes the confusion and difficulties in computing flows with complex geometry and also needs an ad hoc treatment near the separation and reattachment points. A set of modified two-equation models is proposed to remove the aforementioned shortcomings. The calculations using various two-equation models are compared with direct numerical simulations of channel flow and flat boundary layers. Development of a second order closure model is also discussed with emphasis on the modeling of pressure related correlation terms and dissipation rates in the second moment equations. All the existing models poorly predict the normal stresses near the wall and fail to predict the 3-D effect of mean flow on the turbulence (e.g. decrease in the shear stress caused by the cross flow in the boundary layer). The newly developed second order near-wall turbulence model is described and is capable of capturing the near-wall behavior of turbulence as well as the effect of 3-D mean flow on the turbulence.

Multi-scale diffuse interface modeling of multi-component two-phase flow with partial miscibility

NASA Astrophysics Data System (ADS)

Kou, Jisheng; Sun, Shuyu

2016-08-01

In this paper, we introduce a diffuse interface model to simulate multi-component two-phase flow with partial miscibility based on a realistic equation of state (e.g. Peng-Robinson equation of state). Because of partial miscibility, thermodynamic relations are used to model not only interfacial properties but also bulk properties, including density, composition, pressure, and realistic viscosity. As far as we know, this effort is the first time to use diffuse interface modeling based on equation of state for modeling of multi-component two-phase flow with partial miscibility. In numerical simulation, the key issue is to resolve the high contrast of scales from the microscopic interface composition to macroscale bulk fluid motion since the interface has a nanoscale thickness only. To efficiently solve this challenging problem, we develop a multi-scale simulation method. At the microscopic scale, we deduce a reduced interfacial equation under reasonable assumptions, and then we propose a formulation of capillary pressure, which is consistent with macroscale flow equations. Moreover, we show that Young-Laplace equation is an approximation of this capillarity formulation, and this formulation is also consistent with the concept of Tolman length, which is a correction of Young-Laplace equation. At the macroscopical scale, the interfaces are treated as discontinuous surfaces separating two phases of fluids. Our approach differs from conventional sharp-interface two-phase flow model in that we use the capillary pressure directly instead of a combination of surface tension and Young-Laplace equation because capillarity can be calculated from our proposed capillarity formulation. A compatible condition is also derived for the pressure in flow equations. Furthermore, based on the proposed capillarity formulation, we design an efficient numerical method for directly computing the capillary pressure between two fluids composed of multiple components. Finally, numerical tests are carried out to verify the effectiveness of the proposed multi-scale method.

Multi-scale diffuse interface modeling of multi-component two-phase flow with partial miscibility

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kou, Jisheng; Sun, Shuyu, E-mail: shuyu.sun@kaust.edu.sa; School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049

2016-08-01

In this paper, we introduce a diffuse interface model to simulate multi-component two-phase flow with partial miscibility based on a realistic equation of state (e.g. Peng–Robinson equation of state). Because of partial miscibility, thermodynamic relations are used to model not only interfacial properties but also bulk properties, including density, composition, pressure, and realistic viscosity. As far as we know, this effort is the first time to use diffuse interface modeling based on equation of state for modeling of multi-component two-phase flow with partial miscibility. In numerical simulation, the key issue is to resolve the high contrast of scales from themore » microscopic interface composition to macroscale bulk fluid motion since the interface has a nanoscale thickness only. To efficiently solve this challenging problem, we develop a multi-scale simulation method. At the microscopic scale, we deduce a reduced interfacial equation under reasonable assumptions, and then we propose a formulation of capillary pressure, which is consistent with macroscale flow equations. Moreover, we show that Young–Laplace equation is an approximation of this capillarity formulation, and this formulation is also consistent with the concept of Tolman length, which is a correction of Young–Laplace equation. At the macroscopical scale, the interfaces are treated as discontinuous surfaces separating two phases of fluids. Our approach differs from conventional sharp-interface two-phase flow model in that we use the capillary pressure directly instead of a combination of surface tension and Young–Laplace equation because capillarity can be calculated from our proposed capillarity formulation. A compatible condition is also derived for the pressure in flow equations. Furthermore, based on the proposed capillarity formulation, we design an efficient numerical method for directly computing the capillary pressure between two fluids composed of multiple components. Finally, numerical tests are carried out to verify the effectiveness of the proposed multi-scale method.« less

Effect of helicity on the correlation time of large scales in turbulent flows

NASA Astrophysics Data System (ADS)

Cameron, Alexandre; Alexakis, Alexandros; Brachet, Marc-Étienne

2017-11-01

Solutions of the forced Navier-Stokes equation have been conjectured to thermalize at scales larger than the forcing scale, similar to an absolute equilibrium obtained for the spectrally truncated Euler equation. Using direct numeric simulations of Taylor-Green flows and general-periodic helical flows, we present results on the probability density function, energy spectrum, autocorrelation function, and correlation time that compare the two systems. In the case of highly helical flows, we derive an analytic expression describing the correlation time for the absolute equilibrium of helical flows that is different from the E-1 /2k-1 scaling law of weakly helical flows. This model predicts a new helicity-based scaling law for the correlation time as τ (k ) ˜H-1 /2k-1 /2 . This scaling law is verified in simulations of the truncated Euler equation. In simulations of the Navier-Stokes equations the large-scale modes of forced Taylor-Green symmetric flows (with zero total helicity and large separation of scales) follow the same properties as absolute equilibrium including a τ (k ) ˜E-1 /2k-1 scaling for the correlation time. General-periodic helical flows also show similarities between the two systems; however, the largest scales of the forced flows deviate from the absolute equilibrium solutions.

Finite element analysis and computer graphics visualization of flow around pitching and plunging airfoils

NASA Technical Reports Server (NTRS)

Bratanow, T.; Ecer, A.

1973-01-01

A general computational method for analyzing unsteady flow around pitching and plunging airfoils was developed. The finite element method was applied in developing an efficient numerical procedure for the solution of equations describing the flow around airfoils. The numerical results were employed in conjunction with computer graphics techniques to produce visualization of the flow. The investigation involved mathematical model studies of flow in two phases: (1) analysis of a potential flow formulation and (2) analysis of an incompressible, unsteady, viscous flow from Navier-Stokes equations.

Navier-Stokes-like equations for traffic flow.

PubMed

Velasco, R M; Marques, W

2005-10-01

The macroscopic traffic flow equations derived from the reduced Paveri-Fontana equation are closed starting with the maximization of the informational entropy. The homogeneous steady state taken as a reference is obtained for a specific model of the desired velocity and a kind of Chapman-Enskog method is developed to calculate the traffic pressure at the Navier-Stokes level. Numerical solution of the macroscopic traffic equations is obtained and its characteristics are analyzed.

Density Weighted FDF Equations for Simulations of Turbulent Reacting Flows

NASA Technical Reports Server (NTRS)

Shih, Tsan-Hsing; Liu, Nan-Suey

2011-01-01

In this report, we briefly revisit the formulation of density weighted filtered density function (DW-FDF) for large eddy simulation (LES) of turbulent reacting flows, which was proposed by Jaberi et al. (Jaberi, F.A., Colucci, P.J., James, S., Givi, P. and Pope, S.B., Filtered mass density function for Large-eddy simulation of turbulent reacting flows, J. Fluid Mech., vol. 401, pp. 85-121, 1999). At first, we proceed the traditional derivation of the DW-FDF equations by using the fine grained probability density function (FG-PDF), then we explore another way of constructing the DW-FDF equations by starting directly from the compressible Navier-Stokes equations. We observe that the terms which are unclosed in the traditional DW-FDF equations are now closed in the newly constructed DW-FDF equations. This significant difference and its practical impact on the computational simulations may deserve further studies.

A simple, direct derivation and proof of the validity of the SLLOD equations of motion for generalized homogeneous flows.

PubMed

Daivis, Peter J; Todd, B D

2006-05-21

We present a simple and direct derivation of the SLLOD equations of motion for molecular simulations of general homogeneous flows. We show that these equations of motion (1) generate the correct particle trajectories, (2) conserve the total thermal momentum without requiring the center of mass to be located at the origin, and (3) exactly generate the required energy dissipation. These equations of motion are compared with the g-SLLOD and p-SLLOD equations of motion, which are found to be deficient. Claims that the SLLOD equations of motion are incorrect for elongational flows are critically examined and found to be invalid. It is confirmed that the SLLOD equations are, in general, non-Hamiltonian. We derive a Hamiltonian from which they can be obtained in the special case of a symmetric velocity gradient tensor. In this case, it is possible to perform a canonical transformation that results in the well-known DOLLS tensor Hamiltonian.

Aerodynamic Characteristics of Controls.

DTIC Science & Technology

1979-09-01

efforts. CONTENT 1. Introduction 2. Subsonic attached flow 3. Transonic attached flow 4. Supersonic attached flow 5. Leading edge vortex flow 6... introduction of these loading functions the integral-equation is reduced to a system of linear equations where the scale factors of the loading... introduction of different regions of influence for the subsonic and the supersonic case 1511. In the unsteady case this brings no difficulties since these

A coupled implicit method for chemical non-equilibrium flows at all speeds

NASA Technical Reports Server (NTRS)

Shuen, Jian-Shun; Chen, Kuo-Huey; Choi, Yunho

1993-01-01

The present time-accurate coupled-solution procedure addresses the chemical nonequilibrium Navier-Stokes equations over a wide Mach-number range uses, in conjunction with the strong conservation form of the governing equations, five unknown primitive variables. The numerical tests undertaken address steady convergent-divergent nozzle flows with air dissociation/recombination, dump combustor flows with n-pentane/air chemistry, and unsteady nonreacting cavity flows.

Well-posed continuum equations for granular flow with compressibility and μ(I)-rheology

NASA Astrophysics Data System (ADS)

Barker, T.; Schaeffer, D. G.; Shearer, M.; Gray, J. M. N. T.

2017-05-01

Continuum modelling of granular flow has been plagued with the issue of ill-posed dynamic equations for a long time. Equations for incompressible, two-dimensional flow based on the Coulomb friction law are ill-posed regardless of the deformation, whereas the rate-dependent μ(I)-rheology is ill-posed when the non-dimensional inertial number I is too high or too low. Here, incorporating ideas from critical-state soil mechanics, we derive conditions for well-posedness of partial differential equations that combine compressibility with I-dependent rheology. When the I-dependence comes from a specific friction coefficient μ(I), our results show that, with compressibility, the equations are well-posed for all deformation rates provided that μ(I) satisfies certain minimal, physically natural, inequalities.

A computer code for three-dimensional incompressible flows using nonorthogonal body-fitted coordinate systems

NASA Technical Reports Server (NTRS)

Chen, Y. S.

1986-01-01

In this report, a numerical method for solving the equations of motion of three-dimensional incompressible flows in nonorthogonal body-fitted coordinate (BFC) systems has been developed. The equations of motion are transformed to a generalized curvilinear coordinate system from which the transformed equations are discretized using finite difference approximations in the transformed domain. The hybrid scheme is used to approximate the convection terms in the governing equations. Solutions of the finite difference equations are obtained iteratively by using a pressure-velocity correction algorithm (SIMPLE-C). Numerical examples of two- and three-dimensional, laminar and turbulent flow problems are employed to evaluate the accuracy and efficiency of the present computer code. The user's guide and computer program listing of the present code are also included.

Well-posed continuum equations for granular flow with compressibility and μ(I)-rheology

PubMed Central

Schaeffer, D. G.; Shearer, M.; Gray, J. M. N. T.

2017-01-01

Continuum modelling of granular flow has been plagued with the issue of ill-posed dynamic equations for a long time. Equations for incompressible, two-dimensional flow based on the Coulomb friction law are ill-posed regardless of the deformation, whereas the rate-dependent μ(I)-rheology is ill-posed when the non-dimensional inertial number I is too high or too low. Here, incorporating ideas from critical-state soil mechanics, we derive conditions for well-posedness of partial differential equations that combine compressibility with I-dependent rheology. When the I-dependence comes from a specific friction coefficient μ(I), our results show that, with compressibility, the equations are well-posed for all deformation rates provided that μ(I) satisfies certain minimal, physically natural, inequalities. PMID:28588402

Relationships between basic soils-engineering equations and basic ground-water flow equations

USGS Publications Warehouse

Jorgensen, Donald G.

1980-01-01

The many varied though related terms developed by ground-water hydrologists and by soils engineers are useful to each discipline, but their differences in terminology hinder the use of related information in interdisciplinary studies. Equations for the Terzaghi theory of consolidation and equations for ground-water flow are identical under specific conditions. A combination of the two sets of equations relates porosity to void ratio and relates the modulus of elasticity to the coefficient of compressibility, coefficient of volume compressibility, compression index, coefficient of consolidation, specific storage, and ultimate compaction. Also, transient ground-water flow is related to coefficient of consolidation, rate of soil compaction, and hydraulic conductivity. Examples show that soils-engineering data and concepts are useful to solution of problems in ground-water hydrology.

Well-posed continuum equations for granular flow with compressibility and μ(I)-rheology.

PubMed

Barker, T; Schaeffer, D G; Shearer, M; Gray, J M N T

2017-05-01

Continuum modelling of granular flow has been plagued with the issue of ill-posed dynamic equations for a long time. Equations for incompressible, two-dimensional flow based on the Coulomb friction law are ill-posed regardless of the deformation, whereas the rate-dependent μ ( I )-rheology is ill-posed when the non-dimensional inertial number I is too high or too low. Here, incorporating ideas from critical-state soil mechanics, we derive conditions for well-posedness of partial differential equations that combine compressibility with I -dependent rheology. When the I -dependence comes from a specific friction coefficient μ ( I ), our results show that, with compressibility, the equations are well-posed for all deformation rates provided that μ ( I ) satisfies certain minimal, physically natural, inequalities.

A rigorous solution of the Navier-Stokes equations for unsteady viscous flow at high Reynolds numbers around oscillating airfoils

NASA Technical Reports Server (NTRS)

Bratanow, T.; Aksu, H.; Spehert, T.

1975-01-01

A method based on the Navier-Stokes equations was developed for analyzing the unsteady incompressible viscous flow around oscillating airfoils at high Reynolds numbers. The Navier-Stokes equations have been integrated in their classical Helmholtz vorticity transport equation form, and the instantaneous velocity field at each time step was determined by the solution of Poisson's equation. A refined finite element was utilized to allow for a conformable solution of the stream function and its first space derivatives at the element interfaces. A corresponding set of accurate boundary conditions was applied; thus obtaining a rigorous solution for the velocity field. The details of the computational procedure and examples of computed results describing the unsteady flow characteristics around the airfoil are presented.

Sensitivity analysis for aeroacoustic and aeroelastic design of turbomachinery blades

NASA Technical Reports Server (NTRS)

Lorence, Christopher B.; Hall, Kenneth C.

1995-01-01

A new method for computing the effect that small changes in the airfoil shape and cascade geometry have on the aeroacoustic and aeroelastic behavior of turbomachinery cascades is presented. The nonlinear unsteady flow is assumed to be composed of a nonlinear steady flow plus a small perturbation unsteady flow that is harmonic in time. First, the full potential equation is used to describe the behavior of the nonlinear mean (steady) flow through a two-dimensional cascade. The small disturbance unsteady flow through the cascade is described by the linearized Euler equations. Using rapid distortion theory, the unsteady velocity is split into a rotational part that contains the vorticity and an irrotational part described by a scalar potential. The unsteady vorticity transport is described analytically in terms of the drift and stream functions computed from the steady flow. Hence, the solution of the linearized Euler equations may be reduced to a single inhomogeneous equation for the unsteady potential. The steady flow and small disturbance unsteady flow equations are discretized using bilinear quadrilateral isoparametric finite elements. The nonlinear mean flow solution and streamline computational grid are computed simultaneously using Newton iteration. At each step of the Newton iteration, LU decomposition is used to solve the resulting set of linear equations. The unsteady flow problem is linear, and is also solved using LU decomposition. Next, a sensitivity analysis is performed to determine the effect small changes in cascade and airfoil geometry have on the mean and unsteady flow fields. The sensitivity analysis makes use of the nominal steady and unsteady flow LU decompositions so that no additional matrices need to be factored. Hence, the present method is computationally very efficient. To demonstrate how the sensitivity analysis may be used to redesign cascades, a compressor is redesigned for improved aeroelastic stability and two different fan exit guide vanes are redesigned for reduced downstream radiated noise. In addition, a framework detailing how the two-dimensional version of the method may be used to redesign three-dimensional geometries is presented.

Development of a One-Equation Transition/Turbulence Model

DOE Office of Scientific and Technical Information (OSTI.GOV)

EDWARDS,JACK R.; ROY,CHRISTOPHER J.; BLOTTNER,FREDERICK G.

2000-09-26

This paper reports on the development of a unified one-equation model for the prediction of transitional and turbulent flows. An eddy viscosity - transport equation for non-turbulent fluctuation growth based on that proposed by Warren and Hassan (Journal of Aircraft, Vol. 35, No. 5) is combined with the Spalart-Allmaras one-equation model for turbulent fluctuation growth. Blending of the two equations is accomplished through a multidimensional intermittence function based on the work of Dhawan and Narasimha (Journal of Fluid Mechanics, Vol. 3, No. 4). The model predicts both the onset and extent of transition. Low-speed test cases include transitional flow overmore » a flat plate, a single element airfoil, and a multi-element airfoil in landing configuration. High-speed test cases include transitional Mach 3.5 flow over a 5{degree} cone and Mach 6 flow over a flared-cone configuration. Results are compared with experimental data, and the spatial accuracy of selected predictions is analyzed.« less

The Evolution of Finite Amplitude Wavetrains in Plane Channel Flow

NASA Technical Reports Server (NTRS)

Hewitt, R. E.; Hall, P.

1996-01-01

We consider a viscous incompressible fluid flow driven between two parallel plates by a constant pressure gradient. The flow is at a finite Reynolds number, with an 0(l) disturbance in the form of a traveling wave. A phase equation approach is used to discuss the evolution of slowly varying fully nonlinear two dimensional wavetrains. We consider uniform wavetrains in detail, showing that the development of a wavenumber perturbation is governed by Burgers equation in most cases. The wavenumber perturbation theory, constructed using the phase equation approach for a uniform wavetrain, is shown to be distinct from an amplitude perturbation expansion about the periodic flow. In fact we show that the amplitude equation contains only linear terms and is simply the heat equation. We review, briefly, the well known dynamics of Burgers equation, which imply that both shock structures and finite time singularities of the wavenumber perturbation can occur with respect to the slow scales. Numerical computations have been performed to identify areas of the (wavenumber, Reynolds number, energy) neutral surface for which each of these possibilities can occur. We note that the evolution equations will breakdown under certain circumstances, in particular for a weakly nonlinear secondary flow. Finally we extend the theory to three dimensions and discuss the limit of a weak spanwise dependence for uniform wavetrains, showing that two functions are required to describe the evolution. These unknowns are a phase and a pressure function which satisfy a pair of linearly coupled partial differential equations. The results obtained from applying the same analysis to the fully three dimensional problem are included as an appendix.

Equation for wave processes in inhomogeneous moving media and functional solution of the acoustic tomography problem based on it

NASA Astrophysics Data System (ADS)

Rumyantseva, O. D.; Shurup, A. S.

2017-01-01

The paper considers the derivation of the wave equation and Helmholtz equation for solving the tomographic problem of reconstruction combined scalar-vector inhomogeneities describing perturbations of the sound velocity and absorption, the vector field of flows, and perturbations of the density of the medium. Restrictive conditions under which the obtained equations are meaningful are analyzed. Results of numerical simulation of the two-dimensional functional-analytical Novikov-Agaltsov algorithm for reconstructing the flow velocity using the the obtained Helmholtz equation are presented.

Unsteady Analysis of Separated Aerodynamic Flows Using an Unstructured Multigrid Algorithm

NASA Technical Reports Server (NTRS)

Pelaez, Juan; Mavriplis, Dimitri J.; Kandil, Osama

2001-01-01

An implicit method for the computation of unsteady flows on unstructured grids is presented. The resulting nonlinear system of equations is solved at each time step using an agglomeration multigrid procedure. The method allows for arbitrarily large time steps and is efficient in terms of computational effort and storage. Validation of the code using a one-equation turbulence model is performed for the well-known case of flow over a cylinder. A Detached Eddy Simulation model is also implemented and its performance compared to the one equation Spalart-Allmaras Reynolds Averaged Navier-Stokes (RANS) turbulence model. Validation cases using DES and RANS include flow over a sphere and flow over a NACA 0012 wing including massive stall regimes. The project was driven by the ultimate goal of computing separated flows of aerodynamic interest, such as massive stall or flows over complex non-streamlined geometries.

Dip and anisotropy effects on flow using a vertically skewed model grid.

PubMed

Hoaglund, John R; Pollard, David

2003-01-01

Darcy flow equations relating vertical and bedding-parallel flow to vertical and bedding-parallel gradient components are derived for a skewed Cartesian grid in a vertical plane, correcting for structural dip given the principal hydraulic conductivities in bedding-parallel and bedding-orthogonal directions. Incorrect-minus-correct flow error results are presented for ranges of structural dip (0 < or = theta < or = 90) and gradient directions (0 < or = phi < or = 360). The equations can be coded into ground water models (e.g., MODFLOW) that can use a skewed Cartesian coordinate system to simulate flow in structural terrain with deformed bedding planes. Models modified with these equations will require input arrays of strike and dip, and a solver that can handle off-diagonal hydraulic conductivity terms.

Calculations of Laminar Heat Transfer Around Cylinders of Arbitrary Cross Section and Transpiration-Cooled Walls with Application to Turbine Blade Cooling

NASA Technical Reports Server (NTRS)

Eckert, E.R.G.; Livingood, John N.B.

1951-01-01

An approximate method for development of flow and thermal boundary layers in laminar regime on cylinders with arbitrary cross section and transpiration-cooled walls is obtained by use of Karman's integrated momentum equation and an analogous heat-flow equation. Incompressible flow with constant property values throughout boundary layer is assumed. Shape parameters for approximated velocity and temperature profiles and functions necessary for solution of boundary-layer equations are presented as charts, reducing calculations to a minimum. The method is applied to determine local heat-transfer coefficients and surface temperature-cooled turbine blades for a given flow rate. Coolant flow distributions necessary for maintaining uniform blade temperatures are also determined.

Numerical simulations of three-dimensional laminar flow over a backward facing step; flow near side walls

NASA Technical Reports Server (NTRS)

Steinthorsson, Erlendur; Liou, Meng-Sing; Povinelli, Louis A.; Arnone, Andrea

1993-01-01

This paper reports the results of numerical simulations of steady, laminar flow over a backward-facing step. The governing equations used in the simulations are the full 'compressible' Navier-Stokes equations, solutions to which were computed by using a cell-centered, finite volume discretization. The convection terms of the governing equations were discretized by using the Advection Upwind Splitting Method (AUSM), whereas the diffusion terms were discretized using central differencing formulas. The validity and accuracy of the numerical solutions were verified by comparing the results to existing experimental data for flow at identical Reynolds numbers in the same back step geometry. The paper focuses attention on the details of the flow field near the side wall of the geometry.

Progress and supercomputing in computational fluid dynamics; Proceedings of U.S.-Israel Workshop, Jerusalem, Israel, December 1984

NASA Technical Reports Server (NTRS)

Murman, E. M. (Editor); Abarbanel, S. S. (Editor)

1985-01-01

Current developments and future trends in the application of supercomputers to computational fluid dynamics are discussed in reviews and reports. Topics examined include algorithm development for personal-size supercomputers, a multiblock three-dimensional Euler code for out-of-core and multiprocessor calculations, simulation of compressible inviscid and viscous flow, high-resolution solutions of the Euler equations for vortex flows, algorithms for the Navier-Stokes equations, and viscous-flow simulation by FEM and related techniques. Consideration is given to marching iterative methods for the parabolized and thin-layer Navier-Stokes equations, multigrid solutions to quasi-elliptic schemes, secondary instability of free shear flows, simulation of turbulent flow, and problems connected with weather prediction.

Comparison of Mars Science Laboratory Reaction Control System Jet Computations With Flow Visualization and Velocimetry

NASA Technical Reports Server (NTRS)

Bathel, Brett F.; Danehy, Paul M.; Johansen, Craig T.; Ashcraft, Scott W.; Novak, Luke A.

2013-01-01

Numerical predictions of the Mars Science Laboratory reaction control system jets interacting with a Mach 10 hypersonic flow are compared to experimental nitric oxide planar laser-induced fluorescence data. The steady Reynolds Averaged Navier Stokes equations using the Baldwin-Barth one-equation turbulence model were solved using the OVERFLOW code. The experimental fluorescence data used for comparison consists of qualitative two-dimensional visualization images, qualitative reconstructed three-dimensional flow structures, and quantitative two-dimensional distributions of streamwise velocity. Through modeling of the fluorescence signal equation, computational flow images were produced and directly compared to the qualitative fluorescence data.

A nonperturbative approximation for the moderate Reynolds number Navier–Stokes equations

PubMed Central

Roper, Marcus; Brenner, Michael P.

2009-01-01

The nonlinearity of the Navier–Stokes equations makes predicting the flow of fluid around rapidly moving small bodies highly resistant to all approaches save careful experiments or brute force computation. Here, we show how a linearization of the Navier–Stokes equations captures the drag-determining features of the flow and allows simplified or analytical computation of the drag on bodies up to Reynolds number of order 100. We illustrate the utility of this linearization in 2 practical problems that normally can only be tackled with sophisticated numerical methods: understanding flow separation in the flow around a bluff body and finding drag-minimizing shapes. PMID:19211800

A nonperturbative approximation for the moderate Reynolds number Navier-Stokes equations.

PubMed

Roper, Marcus; Brenner, Michael P

2009-03-03

The nonlinearity of the Navier-Stokes equations makes predicting the flow of fluid around rapidly moving small bodies highly resistant to all approaches save careful experiments or brute force computation. Here, we show how a linearization of the Navier-Stokes equations captures the drag-determining features of the flow and allows simplified or analytical computation of the drag on bodies up to Reynolds number of order 100. We illustrate the utility of this linearization in 2 practical problems that normally can only be tackled with sophisticated numerical methods: understanding flow separation in the flow around a bluff body and finding drag-minimizing shapes.

Multigrid Relaxation of a Factorizable, Conservative Discretization of the Compressible Flow Equations

NASA Technical Reports Server (NTRS)

Roberts, Thomas W.; Sidilkover, David; Thomas, J. L.

2000-01-01

The second-order factorizable discretization of the compressible Euler equations developed by Sidilkover is extended to conservation form on general curvilinear body-fitted grids. The discrete equations are solved by symmetric collective Gauss-Seidel relaxation and FAS multigrid. Solutions for flow in a channel with Mach numbers ranging from 0.0001 to a supercritical Mach number are shown, demonstrating uniform convergence rates and no loss of accuracy in the incompressible limit. A solution for the flow around the leading edge of a semi-infinite parabolic body demonstrates that the scheme maintains rapid convergence for a flow containing a stagnation point.

Median and Low-Flow Characteristics for Streams under Natural and Diverted Conditions, Northeast Maui, Hawaii

USGS Publications Warehouse

Gingerich, Stephen B.

2005-01-01

Flow-duration statistics under natural (undiverted) and diverted flow conditions were estimated for gaged and ungaged sites on 21 streams in northeast Maui, Hawaii. The estimates were made using the optimal combination of continuous-record gaging-station data, low-flow measurements, and values determined from regression equations developed as part of this study. Estimated 50- and 95-percent flow duration statistics for streams are presented and the analyses done to develop and evaluate the methods used in estimating the statistics are described. Estimated streamflow statistics are presented for sites where various amounts of streamflow data are available as well as for locations where no data are available. Daily mean flows were used to determine flow-duration statistics for continuous-record stream-gaging stations in the study area following U.S. Geological Survey established standard methods. Duration discharges of 50- and 95-percent were determined from total flow and base flow for each continuous-record station. The index-station method was used to adjust all of the streamflow records to a common, long-term period. The gaging station on West Wailuaiki Stream (16518000) was chosen as the index station because of its record length (1914-2003) and favorable geographic location. Adjustments based on the index-station method resulted in decreases to the 50-percent duration total flow, 50-percent duration base flow, 95-percent duration total flow, and 95-percent duration base flow computed on the basis of short-term records that averaged 7, 3, 4, and 1 percent, respectively. For the drainage basin of each continuous-record gaged site and selected ungaged sites, morphometric, geologic, soil, and rainfall characteristics were quantified using Geographic Information System techniques. Regression equations relating the non-diverted streamflow statistics to basin characteristics of the gaged basins were developed using ordinary-least-squares regression analyses. Rainfall rate, maximum basin elevation, and the elongation ratio of the basin were the basin characteristics used in the final regression equations for 50-percent duration total flow and base flow. Rainfall rate and maximum basin elevation were used in the final regression equations for the 95-percent duration total flow and base flow. The relative errors between observed and estimated flows ranged from 10 to 20 percent for the 50-percent duration total flow and base flow, and from 29 to 56 percent for the 95-percent duration total flow and base flow. The regression equations developed for this study were used to determine the 50-percent duration total flow, 50-percent duration base flow, 95-percent duration total flow, and 95-percent duration base flow at selected ungaged diverted and undiverted sites. Estimated streamflow, prediction intervals, and standard errors were determined for 48 ungaged sites in the study area and for three gaged sites west of the study area. Relative errors were determined for sites where measured values of 95-percent duration discharge of total flow were available. East of Keanae Valley, the 95-percent duration discharge equation generally underestimated flow, and within and west of Keanae Valley, the equation generally overestimated flow. Reduction in 50- and 95-percent flow-duration values in stream reaches affected by diversions throughout the study area average 58 to 60 percent.

Prediction of Undsteady Flows in Turbomachinery Using the Linearized Euler Equations on Deforming Grids

NASA Technical Reports Server (NTRS)

Clark, William S.; Hall, Kenneth C.

1994-01-01

A linearized Euler solver for calculating unsteady flows in turbomachinery blade rows due to both incident gusts and blade motion is presented. The model accounts for blade loading, blade geometry, shock motion, and wake motion. Assuming that the unsteadiness in the flow is small relative to the nonlinear mean solution, the unsteady Euler equations can be linearized about the mean flow. This yields a set of linear variable coefficient equations that describe the small amplitude harmonic motion of the fluid. These linear equations are then discretized on a computational grid and solved using standard numerical techniques. For transonic flows, however, one must use a linear discretization which is a conservative linearization of the non-linear discretized Euler equations to ensure that shock impulse loads are accurately captured. Other important features of this analysis include a continuously deforming grid which eliminates extrapolation errors and hence, increases accuracy, and a new numerically exact, nonreflecting far-field boundary condition treatment based on an eigenanalysis of the discretized equations. Computational results are presented which demonstrate the computational accuracy and efficiency of the method and demonstrate the effectiveness of the deforming grid, far-field nonreflecting boundary conditions, and shock capturing techniques. A comparison of the present unsteady flow predictions to other numerical, semi-analytical, and experimental methods shows excellent agreement. In addition, the linearized Euler method presented requires one or two orders-of-magnitude less computational time than traditional time marching techniques making the present method a viable design tool for aeroelastic analyses.

Stability of the line preserving flows

NASA Astrophysics Data System (ADS)

Figura, Przemysław

2017-11-01

We examine the equations that are used to describe flows which preserve field lines. We study what happens if we introduce perturbations to the governing equations. The stability of the line preserving flows in the case of the magneto-fluids permeated by magnetic fields is strictly connected to the non-null magnetic reconnection processes. In most of our study we use the Euler potential representation of the external magnetic field. We provide general expressions for the perturbations of the Euler potentials that describe the magnetic field. Similarly, we provide expressions for the case of steady flow as well as we obtain certain conditions required for the stability of the flow. In addition, for steady flows we formulate conditions under which the perturbations of the external field are negligible and the field may be described by its initial unperturbed form. Then we consider the flow equation that transforms quantities from the laboratory coordinate system to the related external field coordinate system. We introduce perturbations to the equation and obtain its simplified versions for the case of a steady flow. For a given system, use of this method allows us to simplify the considerations provided that some part of the system may be described as a perturbation. Next, to study regions favourable for the magnetic reconnection to occur we introduce a deviation vector to the basic line preserving flows condition equation. We provide expressions of the vector for some simplifying cases. This method allows us to examine if given perturbations either stabilise the system or induce magnetic reconnection. To illustrate some of our results we study two examples, namely a simple laboratory plasma flow and a simple planetary magnetosphere model.

Creeping gaseous flows through elastic tube and annulus micro-configurations

NASA Astrophysics Data System (ADS)

Elbaz, Shai; Jacob, Hila; Gat, Amir

2016-11-01

Gaseous flows in elastic micro-configurations is relevant to biological systems (e.g. alveolar ducts in the lungs) as well as to applications such as gas actuated soft micro-robots. We here examine the effect of low-Mach-number compressibility on creeping gaseous axial flows through linearly elastic tube and annulus micro-configurations. For steady flows, the leading-order effects of elasticity on the pressure distribution and mass-flux are obtained. For transient flow in a tube with small deformations, elastic effects are shown to be negligible in leading order due to compressibility. We then examine transient flows in annular configurations where the deformation is significant compared with the gap between the inner and outer cylinders defining the annulus. Both compressibility and elasticity are obtained as dominant terms interacting with viscosity. For a sudden flux impulse, the governing non-linear leading order diffusion equation is initially approximated by a porous-medium-equation of order 2.5 for the pressure square. However, as the fluid expand and the pressure decreases, the governing equation degenerates to a porous-medium-equation of order 2 for the pressure.

Diffusion of chemically reactive species in MHD oscillatory flow with thermal radiation in the presence of constant suction and injection

NASA Astrophysics Data System (ADS)

Sasikumar, J.; Bhuvaneshwari, S.; Govindarajan, A.

2018-04-01

In this project, it is proposed to investigate the effect of suction/injection on the unsteady oscillatory flow of an incompressible viscous electrically conducting fluid through a channel filled with porous medium and non-uniform wall temperature. The fluid is subjected to a uniform magnetic field normal to the channel and the velocity slip at the cold plate is taken into consideration. With the assumption of magnetic Reynolds number to be very small, the induced magnetic field is neglected. Assuming pressure gradient to be oscillatory across the ends of the channel, resulting flow as unsteady oscillatory flow. Under the usual Bousinessq approximation, a mathematical model representing this fluid flow consisting of governing equations with boundary conditions will be developed. Closed form solutions of the dimensionless governing equations of the fluid flow, namely momentum equation, energy equation and species concentration can be obtained . The effects of heat radiation and chemical reaction with suction and injection on temperature, velocity and species concentration profiles will be analysed with tables and graphs.

An interaction algorithm for prediction of mean and fluctuating velocities in two-dimensional aerodynamic wake flows

NASA Technical Reports Server (NTRS)

Baker, A. J.; Orzechowski, J. A.

1980-01-01

A theoretical analysis is presented yielding sets of partial differential equations for determination of turbulent aerodynamic flowfields in the vicinity of an airfoil trailing edge. A four phase interaction algorithm is derived to complete the analysis. Following input, the first computational phase is an elementary viscous corrected two dimensional potential flow solution yielding an estimate of the inviscid-flow induced pressure distribution. Phase C involves solution of the turbulent two dimensional boundary layer equations over the trailing edge, with transition to a two dimensional parabolic Navier-Stokes equation system describing the near-wake merging of the upper and lower surface boundary layers. An iteration provides refinement of the potential flow induced pressure coupling to the viscous flow solutions. The final phase is a complete two dimensional Navier-Stokes analysis of the wake flow in the vicinity of a blunt-bases airfoil. A finite element numerical algorithm is presented which is applicable to solution of all partial differential equation sets of inviscid-viscous aerodynamic interaction algorithm. Numerical results are discussed.

Extraction of skin-friction fields from surface flow visualizations as an inverse problem

NASA Astrophysics Data System (ADS)

Liu, Tianshu

2013-12-01

Extraction of high-resolution skin-friction fields from surface flow visualization images as an inverse problem is discussed from a unified perspective. The surface flow visualizations used in this study are luminescent oil-film visualization and heat-transfer and mass-transfer visualizations with temperature- and pressure-sensitive paints (TSPs and PSPs). The theoretical foundations of these global methods are the thin-oil-film equation and the limiting forms of the energy- and mass-transport equations at a wall, which are projected onto the image plane to provide the relationships between a skin-friction field and the relevant quantities measured by using an imaging system. Since these equations can be re-cast in the same mathematical form as the optical flow equation, they can be solved by using the variational method in the image plane to extract relative or normalized skin-friction fields from images. Furthermore, in terms of instrumentation, essentially the same imaging system for measurements of luminescence can be used in these surface flow visualizations. Examples are given to demonstrate the applications of these methods in global skin-friction diagnostics of complex flows.

Application of the Green's function method for 2- and 3-dimensional steady transonic flows

NASA Technical Reports Server (NTRS)

Tseng, K.

1984-01-01

A Time-Domain Green's function method for the nonlinear time-dependent three-dimensional aerodynamic potential equation is presented. The Green's theorem is being used to transform the partial differential equation into an integro-differential-delay equation. Finite-element and finite-difference methods are employed for the spatial and time discretizations to approximate the integral equation by a system of differential-delay equations. Solution may be obtained by solving for this nonlinear simultaneous system of equations in time. This paper discusses the application of the method to the Transonic Small Disturbance Equation and numerical results for lifting and nonlifting airfoils and wings in steady flows are presented.

Approach to the origin of turbulence on the basis of two-point kinetic theory

NASA Technical Reports Server (NTRS)

Tsuge, S.

1974-01-01

Equations for the fluctuation correlation in an incompressible shear flow are derived on the basis of kinetic theory, utilizing the two-point distribution function which obeys the BBGKY hierarchy equation truncated with the hypothesis of 'ternary' molecular chaos. The step from the molecular to the hydrodynamic description is accomplished by a moment expansion which is a two-point version of the thirteen-moment method, and which leads to a series of correlation equations, viz., the two-point counterparts of the continuity equation, the Navier-Stokes equation, etc. For almost parallel shearing flows the two-point equation is separable and reduces to two Orr-Sommerfeld equations with different physical implications.

Vacuum-bag-only processing of composites

NASA Astrophysics Data System (ADS)

Thomas, Shad

Ultrasonic imaging in the C-scan mode in conjunction with the amplitude of the reflected signal was used to measure flow rates of an epoxy resin film penetrating through the thickness of single layers of woven carbon fabric. Assemblies, comprised of a single layer of fabric and film, were vacuum-bagged and ultrasonically scanned in a water tank during impregnation at 50°C, 60°C, 70°C, and 80°C. Measured flow rates were plotted versus inverse viscosity to determine the permeability in the thin film, non-saturated system. The results demonstrated that ultrasonic imaging in the C-scan mode is an effective method of measuring z-direction resin flow through a single layer of fabric. The permeability values determined in this work were consistent with permeability values reported in the literature. Capillary flow was not observed at the temperatures and times required for pressurized flow to occur. The flow rate at 65°C was predicted from the linear plot of flow rate versus inverse viscosity. The effects of fabric architecture on through-thickness flow rates during impregnation of an epoxy resin film were measured by ultrasonic imaging. Multilayered laminates comprised of woven carbon fabrics and epoxy films (prepregs) were fabricated by vacuum-bagging. Ultrasonic imaging was performed in a heated water tank (65°C) during impregnation. Impregnation rates showed a strong dependence on fabric architecture, despite similar areal densities. Impregnation rates are directly affected by inter-tow spacing and tow nesting, which depend on fabric architecture, and are indirectly affected by areal densities. A new method of predicting resin infusion rates in prepreg and resin film infusion processes was proposed. The Stokes equation was used to derive an equation to predict the impregnation rate of laminates as a function of fabric architecture. Flow rate data previously measured by ultrasound was analyzed with the new equation and the Kozeny-Carman equation. A fiber interaction parameter was determined as a function of fabric architecture. The derived equation is straight-forward to use, unlike the Kozeny-Carman equation. The results demonstrated that the newly derived equation can be used to predict the resin infusion rate of multilayer laminates.

Numerical Study of Pressure Field in Laterally Closed Industrial Buildings with Curved Metallic Roofs due to the Wind Effect by FEM and European Rule Comparison

NASA Astrophysics Data System (ADS)

Nieto, P. J. García; del Coz Díaz, J. J.; Vilán, J. A. Vilán; Placer, C. Casqueiro

2009-08-01

In this paper, an evaluation of distribution of the air pressure is determined throughout the laterally closed industrial buildings with curved metallic roofs due to the wind effect by the finite element method (FEM). The non-linearity is due to Reynolds-averaged Navier-Stokes (RANS) equations that govern the turbulent flow. The Navier-Stokes equations are non-linear partial differential equations and this non-linearity makes most problems difficult to solve and is part of the cause of turbulence. The RANS equations are time-averaged equations of motion for fluid flow. They are primarily used while dealing with turbulent flows. Turbulence is a highly complex physical phenomenon that is pervasive in flow problems of scientific and engineering concern like this one. In order to solve the RANS equations a two-equation model is used: the standard k-ɛ model. The calculation has been carried out keeping in mind the following assumptions: turbulent flow, an exponential-like wind speed profile with a maximum velocity of 40 m/s at 10 m reference height, and different heights of the building ranging from 6 to 10 meters. Finally, the forces and moments are determined on the cover, as well as the distribution of pressures on the same one, comparing the numerical results obtained with the Spanish CTE DB SE-AE, Spanish NBE AE-88 and European standard rules, giving place to the conclusions that are exposed in the study.

Ventilation equations for improved exothermic process control.

PubMed

McKernan, John L; Ellenbecker, Michael J

2007-04-01

Exothermic or heated processes create potentially unsafe work environments for an estimated 5-10 million American workers each year. Excessive heat and process contaminants have the potential to cause acute health effects such as heat stroke, and chronic effects such as manganism in welders. Although millions of workers are exposed to exothermic processes, insufficient attention has been given to continuously improving engineering technologies for these processes to provide effective and efficient control. Currently there is no specific occupational standard established by OSHA regarding exposure to heat from exothermic processes, therefore it is important to investigate techniques that can mitigate known and potential adverse occupational health effects. The current understanding of engineering controls for exothermic processes is primarily based on a book chapter written by W. C. L. Hemeon in 1955. Improvements in heat transfer and meteorological theory necessary to design improved process controls have occurred since this time. The research presented involved a review of the physical properties, heat transfer and meteorological theories governing buoyant air flow created by exothermic processes. These properties and theories were used to identify parameters and develop equations required for the determination of buoyant volumetric flow to assist in improving ventilation controls. Goals of this research were to develop and describe a new (i.e. proposed) flow equation, and compare it to currently accepted ones by Hemeon and the American Conference of Governmental Industrial Hygienists (ACGIH). Numerical assessments were conducted to compare solutions from the proposed equations for plume area, mean velocity and flow to those from the ACGIH and Hemeon. Parameters were varied for the dependent variables and solutions from the proposed, ACGIH, and Hemeon equations for plume area, mean velocity and flow were analyzed using a randomized complete block statistical design (ANOVA). Results indicate that the proposed plume mean velocity equation provides significantly greater means than either the ACGIH or Hemeon equations throughout the range of parameters investigated. The proposed equations for plume area and flow also provide significantly greater means than either the ACGIH or Hemeon equations at distances >1 m above exothermic processes. With an accurate solution for the total volumetric flow, ventilation engineers and practicing industrial hygienists are equipped with the necessary information to design and size hoods, as well as place them at an optimal distance from the source to provide adequate control of the rising plume. The equations developed will allow researchers and practitioners to determine the critical control parameters for exothermic processes, such as the exhaust flow necessary to improve efficacy and efficiency, while ensuring adequate worker protection.

Finite element analysis of low speed viscous and inviscid aerodynamic flows

NASA Technical Reports Server (NTRS)

Baker, A. J.; Manhardt, P. D.

1977-01-01

A weak interaction solution algorithm was established for aerodynamic flow about an isolated airfoil. Finite element numerical methodology was applied to solution of each of differential equations governing potential flow, and viscous and turbulent boundary layer and wake flow downstream of the sharp trailing edge. The algorithm accounts for computed viscous displacement effects on the potential flow. Closure for turbulence was accomplished using both first and second order models. The COMOC finite element fluid mechanics computer program was modified to solve the identified equation systems for two dimensional flows. A numerical program was completed to determine factors affecting solution accuracy, convergence and stability for the combined potential, boundary layer, and parabolic Navier-Stokes equation systems. Good accuracy and convergence are demonstrated. Each solution is obtained within the identical finite element framework of COMOC.

A calculation procedure for viscous flow in turbomachines, volume 3. [computer programs

NASA Technical Reports Server (NTRS)

Khalil, I.; Sheoran, Y.; Tabakoff, W.

1980-01-01

A method for analyzing the nonadiabatic viscous flow through turbomachine blade passages was developed. The field analysis is based upon the numerical integration of the full incompressible Navier-Stokes equations, together with the energy equation on the blade-to-blade surface. A FORTRAN IV computer program was written based on this method. The numerical code used to solve the governing equations employs a nonorthogonal boundary fitted coordinate system. The flow may be axial, radial or mixed and there may be a change in stream channel thickness in the through-flow direction. The inputs required for two FORTRAN IV programs are presented. The first program considers laminar flows and the second can handle turbulent flows. Numerical examples are included to illustrate the use of the program, and to show the results that are obtained.

Algorithms for the Euler and Navier-Stokes equations for supercomputers

NASA Technical Reports Server (NTRS)

Turkel, E.

1985-01-01

The steady state Euler and Navier-Stokes equations are considered for both compressible and incompressible flow. Methods are found for accelerating the convergence to a steady state. This acceleration is based on preconditioning the system so that it is no longer time consistent. In order that the acceleration technique be scheme-independent, this preconditioning is done at the differential equation level. Applications are presented for very slow flows and also for the incompressible equations.

An Initial Investigation of the Effects of Turbulence Models on the Convergence of the RK/Implicit Scheme

NASA Technical Reports Server (NTRS)

Swanson, R. C.; Rossow, C.-C.

2008-01-01

A three-stage Runge-Kutta (RK) scheme with multigrid and an implicit preconditioner has been shown to be an effective solver for the fluid dynamic equations. This scheme has been applied to both the compressible and essentially incompressible Reynolds-averaged Navier-Stokes (RANS) equations using the algebraic turbulence model of Baldwin and Lomax (BL). In this paper we focus on the convergence of the RK/implicit scheme when the effects of turbulence are represented by either the Spalart-Allmaras model or the Wilcox k-! model, which are frequently used models in practical fluid dynamic applications. Convergence behavior of the scheme with these turbulence models and the BL model are directly compared. For this initial investigation we solve the flow equations and the partial differential equations of the turbulence models indirectly coupled. With this approach we examine the convergence behavior of each system. Both point and line symmetric Gauss-Seidel are considered for approximating the inverse of the implicit operator of the flow solver. To solve the turbulence equations we use a diagonally dominant alternating direction implicit (DDADI) scheme. Computational results are presented for three airfoil flow cases and comparisons are made with experimental data. We demonstrate that the two-dimensional RANS equations and transport-type equations for turbulence modeling can be efficiently solved with an indirectly coupled algorithm that uses the RK/implicit scheme for the flow equations.

Peak-flow frequency for tributaries of the Colorado River downstream of Austin, Texas

USGS Publications Warehouse

Asquith, William H.

1998-01-01

Peak-flow frequency for 38 stations with at least 8 years of data in natural (unregulated and nonurbanized) basins was estimated on the basis of annual peak-streamflow data through water year 1995. Peak-flow frequency represents the peak discharges for recurrence intervals of 2, 5, 10, 25, 50, 100, 250, and 500 years. The peak-flow frequency and drainage basin characteristics for the stations were used to develop two sets of regression equations to estimate peak-flow frequency for tributaries of the Colorado River in the study area. One set of equations was developed for contributing drainage areas less than 32 square miles, and another set was developed for contributing drainage areas greater than 32 square miles. A procedure is presented to estimate the peak discharge at sites where both sets of equations are considered applicable. Additionally, procedures are presented to compute the 50-, 67-, and 90-percent prediction interval for any estimation from the equations.

Glottal flow through a two-mass model: comparison of Navier-Stokes solutions with simplified models.

PubMed

de Vries, M P; Schutte, H K; Veldman, A E P; Verkerke, G J

2002-04-01

A new numerical model of the vocal folds is presented based on the well-known two-mass models of the vocal folds. The two-mass model is coupled to a model of glottal airflow based on the incompressible Navier-Stokes equations. Glottal waves are produced using different initial glottal gaps and different subglottal pressures. Fundamental frequency, glottal peak flow, and closed phase of the glottal waves have been compared with values known from the literature. The phonation threshold pressure was determined for different initial glottal gaps. The phonation threshold pressure obtained using the flow model with Navier-Stokes equations corresponds better to values determined in normal phonation than the phonation threshold pressure obtained using the flow model based on the Bernoulli equation. Using the Navier-Stokes equations, an increase of the subglottal pressure causes the fundamental frequency and the glottal peak flow to increase, whereas the fundamental frequency in the Bernoulli-based model does not change with increasing pressure.

A study of the viscous and nonadiabatic flow in radial turbines

NASA Technical Reports Server (NTRS)

Khalil, I.; Tabakoff, W.

1981-01-01

A method for analyzing the viscous nonadiabatic flow within turbomachine rotors is presented. The field analysis is based upon the numerical integration of the incompressible Navier-Stokes equations together with the energy equation over the rotors blade-to-blade stream channels. The numerical code used to solve the governing equations employs a nonorthogonal boundary fitted coordinate system that suits the most complicated blade geometries. Effects of turbulence are modeled with two equations; one expressing the development of the turbulence kinetic energy and the other its dissipation rate. The method of analysis is applied to a radial inflow turbine. The solution obtained indicates the severity of the complex interaction mechanism that occurs between different flow regimes (i.e., boundary layers, recirculating eddies, separation zones, etc.). Comparison with nonviscous flow solutions tend to justify strongly the inadequacy of using the latter with standard boundary layer techniques to obtain viscous flow details within turbomachine rotors. Capabilities and limitations of the present method of analysis are discussed.

Pdf - Transport equations for chemically reacting flows

NASA Technical Reports Server (NTRS)

Kollmann, W.

1989-01-01

The closure problem for the transport equations for pdf and the characteristic functions of turbulent, chemically reacting flows is addressed. The properties of the linear and closed equations for the characteristic functional for Eulerian and Lagrangian variables are established, and the closure problem for the finite-dimensional case is discussed for pdf and characteristic functions. It is shown that the closure for the scalar dissipation term in the pdf equation developed by Dopazo (1979) and Kollmann et al. (1982) results in a single integral, in contrast to the pdf, where double integration is required. Some recent results using pdf methods obtained for turbulent flows with combustion, including effects of chemical nonequilibrium, are discussed.

Evaluation of aerodynamic characteristics of a coupled fluid-structure system using generalized Bernoulli’s principle: An application to vocal folds vibration

PubMed Central

Zhang, Lucy T.; Yang, Jubiao

2017-01-01

In this work we explore the aerodynamics flow characteristics of a coupled fluid-structure interaction system using a generalized Bernoulli equation derived directly from the Cauchy momentum equations. Unlike the conventional Bernoulli equation where incompressible, inviscid, and steady flow conditions are assumed, this generalized Bernoulli equation includes the contributions from compressibility, viscous, and unsteadiness, which could be essential in defining aerodynamic characteristics. The application of the derived Bernoulli’s principle is on a fully-coupled fluid-structure interaction simulation of the vocal folds vibration. The coupled system is simulated using the immersed finite element method where compressible Navier-Stokes equations are used to describe the air and an elastic pliable structure to describe the vocal fold. The vibration of the vocal fold works to open and close the glottal flow. The aerodynamics flow characteristics are evaluated using the derived Bernoulli’s principles for a vibration cycle in a carefully partitioned control volume based on the moving structure. The results agree very well to experimental observations, which validate the strategy and its use in other types of flow characteristics that involve coupled fluid-structure interactions. PMID:29527541

Transonic flow of steam with non-equilibrium and homogenous condensation

NASA Astrophysics Data System (ADS)

Virk, Akashdeep Singh; Rusak, Zvi

2017-11-01

A small-disturbance model for studying the physical behavior of a steady transonic flow of steam with non-equilibrium and homogeneous condensation around a thin airfoil is derived. The steam thermodynamic behavior is described by van der Waals equation of state. The water condensation rate is calculated according to classical nucleation and droplet growth models. The current study is based on an asymptotic analysis of the fluid flow and condensation equations and boundary conditions in terms of the small thickness of the airfoil, small angle of attack, closeness of upstream flow Mach number to unity and small amount of condensate. The asymptotic analysis gives the similarity parameters that govern the problem. The flow field may be described by a non-homogeneous transonic small-disturbance equation coupled with a set of four ordinary differential equations for the calculation of the condensate mass fraction. An iterative numerical scheme which combines Murman & Cole's (1971) method with Simpson's integration rule is applied to solve the coupled system of equations. The model is used to study the effects of energy release from condensation on the aerodynamic performance of airfoils operating at high pressures and temperatures and near the vapor-liquid saturation conditions.

Evaluation of aerodynamic characteristics of a coupled fluid-structure system using generalized Bernoulli's principle: An application to vocal folds vibration.

PubMed

Zhang, Lucy T; Yang, Jubiao

2016-12-01

In this work we explore the aerodynamics flow characteristics of a coupled fluid-structure interaction system using a generalized Bernoulli equation derived directly from the Cauchy momentum equations. Unlike the conventional Bernoulli equation where incompressible, inviscid, and steady flow conditions are assumed, this generalized Bernoulli equation includes the contributions from compressibility, viscous, and unsteadiness, which could be essential in defining aerodynamic characteristics. The application of the derived Bernoulli's principle is on a fully-coupled fluid-structure interaction simulation of the vocal folds vibration. The coupled system is simulated using the immersed finite element method where compressible Navier-Stokes equations are used to describe the air and an elastic pliable structure to describe the vocal fold. The vibration of the vocal fold works to open and close the glottal flow. The aerodynamics flow characteristics are evaluated using the derived Bernoulli's principles for a vibration cycle in a carefully partitioned control volume based on the moving structure. The results agree very well to experimental observations, which validate the strategy and its use in other types of flow characteristics that involve coupled fluid-structure interactions.

Methods for estimating magnitude and frequency of peak flows for natural streams in Utah

USGS Publications Warehouse

Kenney, Terry A.; Wilkowske, Chris D.; Wright, Shane J.

2007-01-01

Estimates of the magnitude and frequency of peak streamflows is critical for the safe and cost-effective design of hydraulic structures and stream crossings, and accurate delineation of flood plains. Engineers, planners, resource managers, and scientists need accurate estimates of peak-flow return frequencies for locations on streams with and without streamflow-gaging stations. The 2-, 5-, 10-, 25-, 50-, 100-, 200-, and 500-year recurrence-interval flows were estimated for 344 unregulated U.S. Geological Survey streamflow-gaging stations in Utah and nearby in bordering states. These data along with 23 basin and climatic characteristics computed for each station were used to develop regional peak-flow frequency and magnitude regression equations for 7 geohydrologic regions of Utah. These regression equations can be used to estimate the magnitude and frequency of peak flows for natural streams in Utah within the presented range of predictor variables. Uncertainty, presented as the average standard error of prediction, was computed for each developed equation. Equations developed using data from more than 35 gaging stations had standard errors of prediction that ranged from 35 to 108 percent, and errors for equations developed using data from less than 35 gaging stations ranged from 50 to 357 percent.

Numerical solution of the Saint-Venant equations by an efficient hybrid finite-volume/finite-difference method

NASA Astrophysics Data System (ADS)

Lai, Wencong; Khan, Abdul A.

2018-04-01

A computationally efficient hybrid finite-volume/finite-difference method is proposed for the numerical solution of Saint-Venant equations in one-dimensional open channel flows. The method adopts a mass-conservative finite volume discretization for the continuity equation and a semi-implicit finite difference discretization for the dynamic-wave momentum equation. The spatial discretization of the convective flux term in the momentum equation employs an upwind scheme and the water-surface gradient term is discretized using three different schemes. The performance of the numerical method is investigated in terms of efficiency and accuracy using various examples, including steady flow over a bump, dam-break flow over wet and dry downstream channels, wetting and drying in a parabolic bowl, and dam-break floods in laboratory physical models. Numerical solutions from the hybrid method are compared with solutions from a finite volume method along with analytic solutions or experimental measurements. Comparisons demonstrates that the hybrid method is efficient, accurate, and robust in modeling various flow scenarios, including subcritical, supercritical, and transcritical flows. In this method, the QUICK scheme for the surface slope discretization is more accurate and less diffusive than the center difference and the weighted average schemes.

Stability of mixing layers

NASA Technical Reports Server (NTRS)

Tam, Christopher; Krothapalli, A

1993-01-01

The research program for the first year of this project (see the original research proposal) consists of developing an explicit marching scheme for solving the parabolized stability equations (PSE). Performing mathematical analysis of the computational algorithm including numerical stability analysis and the determination of the proper boundary conditions needed at the boundary of the computation domain are implicit in the task. Before one can solve the parabolized stability equations for high-speed mixing layers, the mean flow must first be found. In the past, instability analysis of high-speed mixing layer has mostly been performed on mean flow profiles calculated by the boundary layer equations. In carrying out this project, it is believed that the boundary layer equations might not give an accurate enough nonparallel, nonlinear mean flow needed for parabolized stability analysis. A more accurate mean flow can, however, be found by solving the parabolized Navier-Stokes equations. The advantage of the parabolized Navier-Stokes equations is that its accuracy is consistent with the PSE method. Furthermore, the method of solution is similar. Hence, the major part of the effort of the work of this year has been devoted to the development of an explicit numerical marching scheme for the solution of the Parabolized Navier-Stokes equation as applied to the high-seed mixing layer problem.

Self-Similar Compressible Free Vortices

NASA Technical Reports Server (NTRS)

vonEllenrieder, Karl

1998-01-01

Lie group methods are used to find both exact and numerical similarity solutions for compressible perturbations to all incompressible, two-dimensional, axisymmetric vortex reference flow. The reference flow vorticity satisfies an eigenvalue problem for which the solutions are a set of two-dimensional, self-similar, incompressible vortices. These solutions are augmented by deriving a conserved quantity for each eigenvalue, and identifying a Lie group which leaves the reference flow equations invariant. The partial differential equations governing the compressible perturbations to these reference flows are also invariant under the action of the same group. The similarity variables found with this group are used to determine the decay rates of the velocities and thermodynamic variables in the self-similar flows, and to reduce the governing partial differential equations to a set of ordinary differential equations. The ODE's are solved analytically and numerically for a Taylor vortex reference flow, and numerically for an Oseen vortex reference flow. The solutions are used to examine the dependencies of the temperature, density, entropy, dissipation and radial velocity on the Prandtl number. Also, experimental data on compressible free vortex flow are compared to the analytical results, the evolution of vortices from initial states which are not self-similar is discussed, and the energy transfer in a slightly-compressible vortex is considered.

OVERSMART Reporting Tool for Flow Computations Over Large Grid Systems

NASA Technical Reports Server (NTRS)

Kao, David L.; Chan, William M.

2012-01-01

Structured grid solvers such as NASA's OVERFLOW compressible Navier-Stokes flow solver can generate large data files that contain convergence histories for flow equation residuals, turbulence model equation residuals, component forces and moments, and component relative motion dynamics variables. Most of today's large-scale problems can extend to hundreds of grids, and over 100 million grid points. However, due to the lack of efficient tools, only a small fraction of information contained in these files is analyzed. OVERSMART (OVERFLOW Solution Monitoring And Reporting Tool) provides a comprehensive report of solution convergence of flow computations over large, complex grid systems. It produces a one-page executive summary of the behavior of flow equation residuals, turbulence model equation residuals, and component forces and moments. Under the automatic option, a matrix of commonly viewed plots such as residual histograms, composite residuals, sub-iteration bar graphs, and component forces and moments is automatically generated. Specific plots required by the user can also be prescribed via a command file or a graphical user interface. Output is directed to the user s computer screen and/or to an html file for archival purposes. The current implementation has been targeted for the OVERFLOW flow solver, which is used to obtain a flow solution on structured overset grids. The OVERSMART framework allows easy extension to other flow solvers.

Lubrication Flows.

ERIC Educational Resources Information Center

Papanastasiou, Tasos C.

1989-01-01

Discusses fluid mechanics for undergraduates including the differential Navier-Stokes equations, dimensional analysis and simplified dimensionless numbers, control volume principles, the Reynolds lubrication equation for confined and free surface flows, capillary pressure, and simplified perturbation techniques. Provides a vertical dip coating…

Regionalisation of low flow frequency curves for the Peninsular Malaysia

NASA Astrophysics Data System (ADS)

Mamun, Abdullah A.; Hashim, Alias; Daoud, Jamal I.

2010-02-01

SUMMARYRegional maps and equations for the magnitude and frequency of 1, 7 and 30-day low flows were derived and are presented in this paper. The river gauging stations of neighbouring catchments that produced similar low flow frequency curves were grouped together. As such, the Peninsular Malaysia was divided into seven low flow regions. Regional equations were developed using the multivariate regression technique. An empirical relationship was developed for mean annual minimum flow as a function of catchment area, mean annual rainfall and mean annual evaporation. The regional equations exhibited good coefficient of determination ( R2 > 0.90). Three low flow frequency curves showing the low, mean and high limits for each region were proposed based on a graphical best-fit technique. Knowing the catchment area, mean annual rainfall and evaporation in the region, design low flows of different durations can be easily estimated for the ungauged catchments. This procedure is expected to overcome the problem of data unavailability in estimating low flows in the Peninsular Malaysia.

A Green's function formulation for a nonlinear potential flow solution applicable to transonic flow

NASA Technical Reports Server (NTRS)

Baker, A. J.; Fox, C. H., Jr.

1977-01-01

Routine determination of inviscid subsonic flow fields about wing-body-tail configurations employing a Green's function approach for numerical solution of the perturbation velocity potential equation is successfully extended into the high subsonic subcritical flow regime and into the shock-free supersonic flow regime. A modified Green's function formulation, valid throughout a range of Mach numbers including transonic, that takes an explicit accounting of the intrinsic nonlinearity in the parent governing partial differential equations is developed. Some considerations pertinent to flow field predictions in the transonic flow regime are discussed.

Dynamic characteristics of a two-stage variable-mass flexible missile with internal flow

NASA Technical Reports Server (NTRS)

Meirovitch, L.; Bankovskis, J.

1972-01-01

A general formulation of the dynamical problems associated with powered flight of a two stage flexible, variable-mass missile with internal flow, discrete masses, and aerodynamic forces is presented. The formulation comprises six ordinary differential equations for the rigid body motion, 3n ordinary differential equations for the n discrete masses and three partial differential equations with the appropriate boundary conditions for the elastic motion. This set of equations is modified to represent a single stage flexible, variable-mass missile with internal flow and aerodynamic forces. The rigid-body motion consists then of three translations and three rotations, whereas the elastic motion is defined by one longitudinal and two flexural displacements, the latter about two orthogonal transverse axes. The differential equations are nonlinear and, in addition, they possess time-dependent coefficients due to the mass variation.

Application of viscous-inviscid interaction methods to transonic turbulent flows

NASA Technical Reports Server (NTRS)

Lee, D.; Pletcher, R. H.

1986-01-01

Two different viscous-inviscid interaction schemes were developed for the analysis of steady, turbulent, transonic, separated flows over axisymmetric bodies. The viscous and inviscid solutions are coupled through the displacement concept using a transpiration velocity approach. In the semi-inverse interaction scheme, the viscous and inviscid equations are solved in an explicitly separate manner and the displacement thickness distribution is iteratively updated by a simple coupling algorithm. In the simultaneous interaction method, local solutions of viscous and inviscid equations are treated simultaneously, and the displacement thickness is treated as an unknown and is obtained as a part of the solution through a global iteration procedure. The inviscid flow region is described by a direct finite-difference solution of a velocity potential equation in conservative form. The potential equation is solved on a numerically generated mesh by an approximate factorization (AF2) scheme in the semi-inverse interaction method and by a successive line overrelaxation (SLOR) scheme in the simultaneous interaction method. The boundary-layer equations are used for the viscous flow region. The continuity and momentum equations are solved inversely in a coupled manner using a fully implicit finite-difference scheme.

Modelling gas dynamics in 1D ducts with abrupt area change

NASA Astrophysics Data System (ADS)

Menina, R.; Saurel, R.; Zereg, M.; Houas, L.

2011-09-01

Most gas dynamic computations in industrial ducts are done in one dimension with cross-section-averaged Euler equations. This poses a fundamental difficulty as soon as geometrical discontinuities are present. The momentum equation contains a non-conservative term involving a surface pressure integral, responsible for momentum loss. Definition of this integral is very difficult from a mathematical standpoint as the flow may contain other discontinuities (shocks, contact discontinuities). From a physical standpoint, geometrical discontinuities induce multidimensional vortices that modify the surface pressure integral. In the present paper, an improved 1D flow model is proposed. An extra energy (or entropy) equation is added to the Euler equations expressing the energy and turbulent pressure stored in the vortices generated by the abrupt area variation. The turbulent energy created by the flow-area change interaction is determined by a specific estimate of the surface pressure integral. Model's predictions are compared with 2D-averaged results from numerical solution of the Euler equations. Comparison with shock tube experiments is also presented. The new 1D-averaged model improves the conventional cross-section-averaged Euler equations and is able to reproduce the main flow features.

Ensemble modeling of stochastic unsteady open-channel flow in terms of its time-space evolutionary probability distribution - Part 1: theoretical development

NASA Astrophysics Data System (ADS)

Dib, Alain; Kavvas, M. Levent

2018-03-01

The Saint-Venant equations are commonly used as the governing equations to solve for modeling the spatially varied unsteady flow in open channels. The presence of uncertainties in the channel or flow parameters renders these equations stochastic, thus requiring their solution in a stochastic framework in order to quantify the ensemble behavior and the variability of the process. While the Monte Carlo approach can be used for such a solution, its computational expense and its large number of simulations act to its disadvantage. This study proposes, explains, and derives a new methodology for solving the stochastic Saint-Venant equations in only one shot, without the need for a large number of simulations. The proposed methodology is derived by developing the nonlocal Lagrangian-Eulerian Fokker-Planck equation of the characteristic form of the stochastic Saint-Venant equations for an open-channel flow process, with an uncertain roughness coefficient. A numerical method for its solution is subsequently devised. The application and validation of this methodology are provided in a companion paper, in which the statistical results computed by the proposed methodology are compared against the results obtained by the Monte Carlo approach.

Real-Gas Effects on Binary Mixing Layers

NASA Technical Reports Server (NTRS)

Okong'o, Nora; Bellan, Josette

2003-01-01

This paper presents a computational study of real-gas effects on the mean flow and temporal stability of heptane/nitrogen and oxygen/hydrogen mixing layers at supercritical pressures. These layers consist of two counterflowing free streams of different composition, temperature, and density. As in related prior studies reported in NASA Tech Briefs, the governing conservation equations were the Navier-Stokes equations of compressible flow plus equations for the conservation of total energy and of chemical- species masses. In these equations, the expressions for heat fluxes and chemical-species mass fluxes were derived from fluctuation-dissipation theory and incorporate Soret and Dufour effects. Similarity equations for the streamwise velocity, temperature, and mass fractions were derived as approximations to the governing equations. Similarity profiles showed important real-gas, non-ideal-mixture effects, particularly for temperature, in departing from the error-function profile, which is the similarity solution for incompressible flow. The temperature behavior was attributed to real-gas thermodynamics and variations in Schmidt and Prandtl numbers. Temporal linear inviscid stability analyses were performed using the similarity and error-function profiles as the mean flow. For the similarity profiles, the growth rates were found to be larger and the wavelengths of highest instability shorter, relative to those of the errorfunction profiles and to those obtained from incompressible-flow stability analysis. The range of unstable wavelengths was found to be larger for the similarity profiles than for the error-function profiles

A depth-averaged debris-flow model that includes the effects of evolving dilatancy: II. Numerical predictions and experimental tests.

USGS Publications Warehouse

George, David L.; Iverson, Richard M.

2014-01-01

We evaluate a new depth-averaged mathematical model that is designed to simulate all stages of debris-flow motion, from initiation to deposition. A companion paper shows how the model’s five governing equations describe simultaneous evolution of flow thickness, solid volume fraction, basal pore-fluid pressure, and two components of flow momentum. Each equation contains a source term that represents the influence of state-dependent granular dilatancy. Here we recapitulate the equations and analyze their eigenstructure to show that they form a hyperbolic system with desirable stability properties. To solve the equations we use a shock-capturing numerical scheme with adaptive mesh refinement, implemented in an open-source software package we call D-Claw. As tests of D-Claw, we compare model output with results from two sets of large-scale debris-flow experiments. One set focuses on flow initiation from landslides triggered by rising pore-water pressures, and the other focuses on downstream flow dynamics, runout, and deposition. D-Claw performs well in predicting evolution of flow speeds, thicknesses, and basal pore-fluid pressures measured in each type of experiment. Computational results illustrate the critical role of dilatancy in linking coevolution of the solid volume fraction and pore-fluid pressure, which mediates basal Coulomb friction and thereby regulates debris-flow dynamics.

One-dimensional drift-flux model and constitutive equations for relative motion between phases in various two-phase flow regimes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ishii, M.

1977-10-01

In view of the practical importance of the drift-flux model for two-phase flow analysis in general and in the analysis of nuclear-reactor transients and accidents in particular, the kinematic constitutive equation for the drift velocity has been studied for various two-phase flow regimes. The constitutive equation that specifies the relative motion between phases in the drift-flux model has been derived by taking into account the interfacial geometry, the body-force field, shear stresses, and the interfacial momentum transfer, since these macroscopic effects govern the relative velocity between phases. A comparison of the model with various experimental data over various flow regimesmore » and a wide range of flow parameters shows a satisfactory agreement.« less

Boundary-layer computational model for predicting the flow and heat transfer in sudden expansions

NASA Technical Reports Server (NTRS)

Lewis, J. P.; Pletcher, R. H.

1986-01-01

Fully developed turbulent and laminar flows through symmetric planar and axisymmetric expansions with heat transfer were modeled using a finite-difference discretization of the boundary-layer equations. By using the boundary-layer equations to model separated flow in place of the Navier-Stokes equations, computational effort was reduced permitting turbulence modelling studies to be economically carried out. For laminar flow, the reattachment length was well predicted for Reynolds numbers as low as 20 and the details of the trapped eddy were well predicted for Reynolds numbers above 200. For turbulent flows, the Boussinesq assumption was used to express the Reynolds stresses in terms of a turbulent viscosity. Near-wall algebraic turbulence models based on Prandtl's-mixing-length model and the maximum Reynolds shear stress were compared.

The attenuation of sound by turbulence in internal flows.

PubMed

Weng, Chenyang; Boij, Susann; Hanifi, Ardeshir

2013-06-01

The attenuation of sound waves due to interaction with low Mach number turbulent boundary layers in internal flows (channel or pipe flow) is examined. Dynamic equations for the turbulent Reynolds stress on the sound wave are derived, and the analytical solution to the equation provides a frequency dependent eddy viscosity model. This model is used to predict the attenuation of sound propagating in fully developed turbulent pipe flow. The predictions are shown to compare well with the experimental data. The proposed dynamic equation shows that the turbulence behaves like a viscoelastic fluid in the interaction process, and that the ratio of turbulent relaxation time near the wall and the sound wave period is the parameter that controls the characteristics of the attenuation induced by the turbulent flow.

Multiloop functional renormalization group for general models

NASA Astrophysics Data System (ADS)

Kugler, Fabian B.; von Delft, Jan

2018-02-01

We present multiloop flow equations in the functional renormalization group (fRG) framework for the four-point vertex and self-energy, formulated for a general fermionic many-body problem. This generalizes the previously introduced vertex flow [F. B. Kugler and J. von Delft, Phys. Rev. Lett. 120, 057403 (2018), 10.1103/PhysRevLett.120.057403] and provides the necessary corrections to the self-energy flow in order to complete the derivative of all diagrams involved in the truncated fRG flow. Due to its iterative one-loop structure, the multiloop flow is well suited for numerical algorithms, enabling improvement of many fRG computations. We demonstrate its equivalence to a solution of the (first-order) parquet equations in conjunction with the Schwinger-Dyson equation for the self-energy.

The turbulent mean-flow, Reynolds-stress, and heat flux equations in mass-averaged dependent variables

NASA Technical Reports Server (NTRS)

Rubesin, M. W.; Rose, W. C.

1973-01-01

The time-dependent, turbulent mean-flow, Reynolds stress, and heat flux equations in mass-averaged dependent variables are presented. These equations are given in conservative form for both generalized orthogonal and axisymmetric coordinates. For the case of small viscosity and thermal conductivity fluctuations, these equations are considerably simpler than the general Reynolds system of dependent variables for a compressible fluid and permit a more direct extension of low speed turbulence modeling to computer codes describing high speed turbulence fields.

Full Equations (FEQ) model for the solution of the full, dynamic equations of motion for one-dimensional unsteady flow in open channels and through control structures

USGS Publications Warehouse

Franz, Delbert D.; Melching, Charles S.

1997-01-01

The Full EQuations (FEQ) model is a computer program for solution of the full, dynamic equations of motion for one-dimensional unsteady flow in open channels and through control structures. A stream system that is simulated by application of FEQ is subdivided into stream reaches (branches), parts of the stream system for which complete information on flow and depth are not required (dummy branches), and level-pool reservoirs. These components are connected by special features; that is, hydraulic control structures, including junctions, bridges, culverts, dams, waterfalls, spillways, weirs, side weirs, and pumps. The principles of conservation of mass and conservation of momentum are used to calculate the flow and depth throughout the stream system resulting from known initial and boundary conditions by means of an implicit finite-difference approximation at fixed points (computational nodes). The hydraulic characteristics of (1) branches including top width, area, first moment of area with respect to the water surface, conveyance, and flux coefficients and (2) special features (relations between flow and headwater and (or) tail-water elevations, including the operation of variable-geometry structures) are stored in function tables calculated in the companion program, Full EQuations UTiLities (FEQUTL). Function tables containing other information used in unsteady-flow simulation (boundary conditions, tributary inflows or outflows, gate settings, correction factors, characteristics of dummy branches and level-pool reservoirs, and wind speed and direction) are prepared by the user as detailed in this report. In the iterative solution scheme for flow and depth throughout the stream system, an interpolation of the function tables corresponding to the computational nodes throughout the stream system is done in the model. FEQ can be applied in the simulation of a wide range of stream configurations (including loops), lateral-inflow conditions, and special features. The accuracy and convergence of the numerical routines in the model are demonstrated for the case of laboratory measurements of unsteady flow in a sewer pipe. Verification of the routines in the model for field data on the Fox River in northeastern Illinois also is briefly discussed. The basic principles of unsteady-flow modeling and the relation between steady flow and unsteady flow are presented. Assumptions and the limitations of the model also are presented. The schematization of the stream system and the conversion of the physical characteristics of the stream reaches and a wide range of special features into function tables for model applications are described. The modified dynamic-wave equation used in FEQ for unsteady flow in curvilinear channels with drag on minor hydraulic structures and channel constrictions determined from an equivalent energy slope is developed. The matrix equation relating flows and depths at computational nodes throughout the stream system by the continuity (conservation of mass) and modified dynamic-wave equations is illustrated for four sequential examples. The solution of the matrix equation by Newton's method is discussed. Finally, the input for FEQ and the error messages and warnings issued are presented.

Estimation of low-flow statistics at ungaged sites on streams in the Lower Hudson River Basin, New York, from data in geographic information systems

USGS Publications Warehouse

Randall, Allan D.; Freehafer, Douglas A.

2017-08-02

A variety of watershed properties available in 2015 from geographic information systems were tested in regression equations to estimate two commonly used statistical indices of the low flow of streams, namely the lowest flows averaged over 7 consecutive days that have a 1 in 10 and a 1 in 2 chance of not being exceeded in any given year (7-day, 10-year and 7-day, 2-year low flows). The equations were based on streamflow measurements in 51 watersheds in the Lower Hudson River Basin of New York during the years 1958–1978, when the number of streamflow measurement sites on unregulated streams was substantially greater than in subsequent years. These low-flow indices are chiefly a function of the area of surficial sand and gravel in the watershed; more precisely, 7-day, 10-year and 7-day, 2-year low flows both increase in proportion to the area of sand and gravel deposited by glacial meltwater, whereas 7-day, 2-year low flows also increase in proportion to the area of postglacial alluvium. Both low-flow statistics are also functions of mean annual runoff (a measure of net water input to the watershed from precipitation) and area of swamps and poorly drained soils in or adjacent to surficial sand and gravel (where groundwater recharge is unlikely and riparian water loss to evapotranspiration is substantial). Small but significant refinements in estimation accuracy resulted from the inclusion of two indices of stream geometry, channel slope and length, in the regression equations. Most of the regression analysis was undertaken with the ordinary least squares method, but four equations were replicated by using weighted least squares to provide a more realistic appraisal of the precision of low-flow estimates. The most accurate estimation equations tested in this study explain nearly 84 and 87 percent of the variation in 7-day, 10-year and 7-day, 2-year low flows, respectively, with standard errors of 0.032 and 0.050 cubic feet per second per square mile. The equations use natural values of streamflow and watershed properties; logarithmic transformations yielded less accurate equations inconsistent with some conceptualized relationships.

Computation of the stability derivatives via CFD and the sensitivity equations

NASA Astrophysics Data System (ADS)

Lei, Guo-Dong; Ren, Yu-Xin

2011-04-01

The method to calculate the aerodynamic stability derivates of aircrafts by using the sensitivity equations is extended to flows with shock waves in this paper. Using the newly developed second-order cell-centered finite volume scheme on the unstructured-grid, the unsteady Euler equations and sensitivity equations are solved simultaneously in a non-inertial frame of reference, so that the aerodynamic stability derivatives can be calculated for aircrafts with complex geometries. Based on the numerical results, behavior of the aerodynamic sensitivity parameters near the shock wave is discussed. Furthermore, the stability derivatives are analyzed for supersonic and hypersonic flows. The numerical results of the stability derivatives are found in good agreement with theoretical results for supersonic flows, and variations of the aerodynamic force and moment predicted by the stability derivatives are very close to those obtained by CFD simulation for both supersonic and hypersonic flows.

Solution of a few nonlinear problems in aerodynamics by the finite elements and functional least squares methods. Ph.D. Thesis - Paris Univ.; [mathematical models of transonic flow using nonlinear equations

NASA Technical Reports Server (NTRS)

Periaux, J.

1979-01-01

The numerical simulation of the transonic flows of idealized fluids and of incompressible viscous fluids, by the nonlinear least squares methods is presented. The nonlinear equations, the boundary conditions, and the various constraints controlling the two types of flow are described. The standard iterative methods for solving a quasi elliptical nonlinear equation with partial derivatives are reviewed with emphasis placed on two examples: the fixed point method applied to the Gelder functional in the case of compressible subsonic flows and the Newton method used in the technique of decomposition of the lifting potential. The new abstract least squares method is discussed. It consists of substituting the nonlinear equation by a problem of minimization in a H to the minus 1 type Sobolev functional space.

A Galerkin least squares approach to viscoelastic flow.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rao, Rekha R.; Schunk, Peter Randall

2015-10-01

A Galerkin/least-squares stabilization technique is applied to a discrete Elastic Viscous Stress Splitting formulation of for viscoelastic flow. From this, a possible viscoelastic stabilization method is proposed. This method is tested with the flow of an Oldroyd-B fluid past a rigid cylinder, where it is found to produce inaccurate drag coefficients. Furthermore, it fails for relatively low Weissenberg number indicating it is not suited for use as a general algorithm. In addition, a decoupled approach is used as a way separating the constitutive equation from the rest of the system. A Pressure Poisson equation is used when the velocity andmore » pressure are sought to be decoupled, but this fails to produce a solution when inflow/outflow boundaries are considered. However, a coupled pressure-velocity equation with a decoupled constitutive equation is successful for the flow past a rigid cylinder and seems to be suitable as a general-use algorithm.« less

Finite element computation of a viscous compressible free shear flow governed by the time dependent Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Cooke, C. H.; Blanchard, D. K.

1975-01-01

A finite element algorithm for solution of fluid flow problems characterized by the two-dimensional compressible Navier-Stokes equations was developed. The program is intended for viscous compressible high speed flow; hence, primitive variables are utilized. The physical solution was approximated by trial functions which at a fixed time are piecewise cubic on triangular elements. The Galerkin technique was employed to determine the finite-element model equations. A leapfrog time integration is used for marching asymptotically from initial to steady state, with iterated integrals evaluated by numerical quadratures. The nonsymmetric linear systems of equations governing time transition from step-to-step are solved using a rather economical block iterative triangular decomposition scheme. The concept was applied to the numerical computation of a free shear flow. Numerical results of the finite-element method are in excellent agreement with those obtained from a finite difference solution of the same problem.

Conjugate Compressible Fluid Flow and Heat Transfer in Ducts

NASA Technical Reports Server (NTRS)

Cross, M. F.

2011-01-01

A computational approach to modeling transient, compressible fluid flow with heat transfer in long, narrow ducts is presented. The primary application of the model is for analyzing fluid flow and heat transfer in solid propellant rocket motor nozzle joints during motor start-up, but the approach is relevant to a wide range of analyses involving rapid pressurization and filling of ducts. Fluid flow is modeled through solution of the spatially one-dimensional, transient Euler equations. Source terms are included in the governing equations to account for the effects of wall friction and heat transfer. The equation solver is fully-implicit, thus providing greater flexibility than an explicit solver. This approach allows for resolution of pressure wave effects on the flow as well as for fast calculation of the steady-state solution when a quasi-steady approach is sufficient. Solution of the one-dimensional Euler equations with source terms significantly reduces computational run times compared to general purpose computational fluid dynamics packages solving the Navier-Stokes equations with resolved boundary layers. In addition, conjugate heat transfer is more readily implemented using the approach described in this paper than with most general purpose computational fluid dynamics packages. The compressible flow code has been integrated with a transient heat transfer solver to analyze heat transfer between the fluid and surrounding structure. Conjugate fluid flow and heat transfer solutions are presented. The author is unaware of any previous work available in the open literature which uses the same approach described in this paper.

Use of digital land-cover data from the Landsat satellite in estimating streamflow characteristics in the Cumberland Plateau of Tennessee

USGS Publications Warehouse

Hollyday, E.F.; Hansen, G.R.

1983-01-01

Streamflow may be estimated with regression equations that relate streamflow characteristics to characteristics of the drainage basin. A statistical experiment was performed to compare the accuracy of equations using basin characteristics derived from maps and climatological records (control group equations) with the accuracy of equations using basin characteristics derived from Landsat data as well as maps and climatological records (experimental group equations). Results show that when the equations in both groups are arranged into six flow categories, there is no substantial difference in accuracy between control group equations and experimental group equations for this particular site where drainage area accounts for more than 90 percent of the variance in all streamflow characteristics (except low flows and most annual peak logarithms). (USGS)

Solution of the Burnett equations for hypersonic flows near the continuum limit

NASA Technical Reports Server (NTRS)

Imlay, Scott T.

1992-01-01

The INCA code, a three-dimensional Navier-Stokes code for analysis of hypersonic flowfields, was modified to analyze the lower reaches of the continuum transition regime, where the Navier-Stokes equations become inaccurate and Monte Carlo methods become too computationally expensive. The two-dimensional Burnett equations and the three-dimensional rotational energy transport equation were added to the code and one- and two-dimensional calculations were performed. For the structure of normal shock waves, the Burnett equations give consistently better results than Navier-Stokes equations and compare reasonably well with Monte Carlo methods. For two-dimensional flow of Nitrogen past a circular cylinder the Burnett equations predict the total drag reasonably well. Care must be taken, however, not to exceed the range of validity of the Burnett equations.

Modeling of high pressure arc-discharge with a fully-implicit Navier-Stokes stabilized finite element flow solver

NASA Astrophysics Data System (ADS)

Sahai, A.; Mansour, N. N.; Lopez, B.; Panesi, M.

2017-05-01

This work addresses the modeling of high pressure electric discharge in an arc-heated wind tunnel. The combined numerical solution of Poisson’s equation, radiative transfer equations, and the set of Favre-averaged thermochemical nonequilibrium Navier-Stokes equations allows for the determination of the electric, radiation, and flow fields, accounting for their mutual interaction. Semi-classical statistical thermodynamics is used to determine the plasma thermodynamic properties, while transport properties are obtained from kinetic principles with the Chapman-Enskog method. A multi-temperature formulation is used to account for thermal non-equilibrium. Finally, the turbulence closure of the flow equations is obtained by means of the Spalart-Allmaras model, which requires the solution of an additional scalar transport equation. A Streamline upwind Petrov-Galerkin stabilized finite element formulation is employed to solve the Navier-Stokes equation. The electric field equation is solved using the standard Galerkin formulation. A stable formulation for the radiative transfer equations is obtained using the least-squares finite element method. The developed simulation framework has been applied to investigate turbulent plasma flows in the 20 MW Aerodynamic Heating Facility at NASA Ames Research Center. The current model is able to predict the process of energy addition and re-distribution due to Joule heating and thermal radiation, resulting in a hot central core surrounded by colder flow. The use of an unsteady three-dimensional treatment also allows the asymmetry due to a dynamic electric arc attachment point in the cathode chamber to be captured accurately. The current work paves the way for detailed estimation of operating characteristics for arc-heated wind tunnels which are critical in testing thermal protection systems.

Kinetically reduced local Navier-Stokes equations for simulation of incompressible viscous flows.

PubMed

Borok, S; Ansumali, S; Karlin, I V

2007-12-01

Recently, another approach to study incompressible fluid flow was suggested [S. Ansumali, I. Karlin, and H. Ottinger, Phys. Rev. Lett. 94, 080602 (2005)]-the kinetically reduced local Navier-Stokes (KRLNS) equations. We consider a simplified two-dimensional KRLNS system and compare it with Chorin's artificial compressibility method. A comparison of the two methods for steady state computation of the flow in a lid-driven cavity at various Reynolds numbers shows that the results from both methods are in good agreement with each other. However, in the transient flow, it is demonstrated that the KRLNS equations correctly describe the time evolution of the velocity and of the pressure, unlike the artificial compressibility method.

Instability of Poiseuille flow at extreme Mach numbers: linear analysis and simulations.

PubMed

Xie, Zhimin; Girimaji, Sharath S

2014-04-01

We develop the perturbation equations to describe instability evolution in Poiseuille flow at the limit of very high Mach numbers. At this limit the equation governing the flow is the pressure-released Navier-Stokes equation. The ensuing semianalytical solution is compared against simulations performed using the gas-kinetic method (GKM), resulting in excellent agreement. A similar comparison between analytical and computational results of small perturbation growth is performed at the incompressible (zero Mach number) limit, again leading to excellent agreement. The study accomplishes two important goals: it (i) contrasts the small perturbation evolution in Poiseuille flows at extreme Mach numbers and (ii) provides important verification of the GKM simulation scheme.

BMS3 invariant fluid dynamics at null infinity

NASA Astrophysics Data System (ADS)

Penna, Robert F.

2018-02-01

We revisit the boundary dynamics of asymptotically flat, three dimensional gravity. The boundary is governed by a momentum conservation equation and an energy conservation equation, which we interpret as fluid equations, following the membrane paradigm. We reformulate the boundary’s equations of motion as Hamiltonian flow on the dual of an infinite-dimensional, semi-direct product Lie algebra equipped with a Lie–Poisson bracket. This gives the analogue for boundary fluid dynamics of the Marsden–Ratiu–Weinstein formulation of the compressible Euler equations on a manifold, M, as Hamiltonian flow on the dual of the Lie algebra of \

Computation of Sound Propagation by Boundary Element Method

NASA Technical Reports Server (NTRS)

Guo, Yueping

2005-01-01

This report documents the development of a Boundary Element Method (BEM) code for the computation of sound propagation in uniform mean flows. The basic formulation and implementation follow the standard BEM methodology; the convective wave equation and the boundary conditions on the surfaces of the bodies in the flow are formulated into an integral equation and the method of collocation is used to discretize this equation into a matrix equation to be solved numerically. New features discussed here include the formulation of the additional terms due to the effects of the mean flow and the treatment of the numerical singularities in the implementation by the method of collocation. The effects of mean flows introduce terms in the integral equation that contain the gradients of the unknown, which is undesirable if the gradients are treated as additional unknowns, greatly increasing the sizes of the matrix equation, or if numerical differentiation is used to approximate the gradients, introducing numerical error in the computation. It is shown that these terms can be reformulated in terms of the unknown itself, making the integral equation very similar to the case without mean flows and simple for numerical implementation. To avoid asymptotic analysis in the treatment of numerical singularities in the method of collocation, as is conventionally done, we perform the surface integrations in the integral equation by using sub-triangles so that the field point never coincide with the evaluation points on the surfaces. This simplifies the formulation and greatly facilitates the implementation. To validate the method and the code, three canonic problems are studied. They are respectively the sound scattering by a sphere, the sound reflection by a plate in uniform mean flows and the sound propagation over a hump of irregular shape in uniform flows. The first two have analytical solutions and the third is solved by the method of Computational Aeroacoustics (CAA), all of which are used to compare the BEM solutions. The comparisons show very good agreements and validate the accuracy of the BEM approach implemented here.

Numerical techniques for the solution of the compressible Navier-Stokes equations and implementation of turbulence models. [separated turbulent boundary layer flow problems

NASA Technical Reports Server (NTRS)

Baldwin, B. S.; Maccormack, R. W.; Deiwert, G. S.

1975-01-01

The time-splitting explicit numerical method of MacCormack is applied to separated turbulent boundary layer flow problems. Modifications of this basic method are developed to counter difficulties associated with complicated geometry and severe numerical resolution requirements of turbulence model equations. The accuracy of solutions is investigated by comparison with exact solutions for several simple cases. Procedures are developed for modifying the basic method to improve the accuracy. Numerical solutions of high-Reynolds-number separated flows over an airfoil and shock-separated flows over a flat plate are obtained. A simple mixing length model of turbulence is used for the transonic flow past an airfoil. A nonorthogonal mesh of arbitrary configuration facilitates the description of the flow field. For the simpler geometry associated with the flat plate, a rectangular mesh is used, and solutions are obtained based on a two-equation differential model of turbulence.

A finite difference method for the solution of the transonic flow around harmonically oscillating wings

NASA Technical Reports Server (NTRS)

Ehlers, E. F.

1974-01-01

A finite difference method for the solution of the transonic flow about a harmonically oscillating wing is presented. The partial differential equation for the unsteady transonic flow was linearized by dividing the flow into separate steady and unsteady perturbation velocity potentials and by assuming small amplitudes of harmonic oscillation. The resulting linear differential equation is of mixed type, being elliptic or hyperbolic whereever the steady flow equation is elliptic or hyperbolic. Central differences were used for all derivatives except at supersonic points where backward differencing was used for the streamwise direction. Detailed formulas and procedures are described in sufficient detail for programming on high speed computers. To test the method, the problem of the oscillating flap on a NACA 64A006 airfoil was programmed. The numerical procedure was found to be stable and convergent even in regions of local supersonic flow with shocks.

On compressible and piezo-viscous flow in thin porous media.

PubMed

Pérez-Ràfols, F; Wall, P; Almqvist, A

2018-01-01

In this paper, we study flow through thin porous media as in, e.g. seals or fractures. It is often useful to know the permeability of such systems. In the context of incompressible and iso-viscous fluids, the permeability is the constant of proportionality relating the total flow through the media to the pressure drop. In this work, we show that it is also relevant to define a constant permeability when compressible and/or piezo-viscous fluids are considered. More precisely, we show that the corresponding nonlinear equation describing the flow of any compressible and piezo-viscous fluid can be transformed into a single linear equation. Indeed, this linear equation is the same as the one describing the flow of an incompressible and iso-viscous fluid. By this transformation, the total flow can be expressed as the product of the permeability and a nonlinear function of pressure, which represents a generalized pressure drop.

Linearly exact parallel closures for slab geometry

NASA Astrophysics Data System (ADS)

Ji, Jeong-Young; Held, Eric D.; Jhang, Hogun

2013-08-01

Parallel closures are obtained by solving a linearized kinetic equation with a model collision operator using the Fourier transform method. The closures expressed in wave number space are exact for time-dependent linear problems to within the limits of the model collision operator. In the adiabatic, collisionless limit, an inverse Fourier transform is performed to obtain integral (nonlocal) parallel closures in real space; parallel heat flow and viscosity closures for density, temperature, and flow velocity equations replace Braginskii's parallel closure relations, and parallel flow velocity and heat flow closures for density and temperature equations replace Spitzer's parallel transport relations. It is verified that the closures reproduce the exact linear response function of Hammett and Perkins [Phys. Rev. Lett. 64, 3019 (1990)] for Landau damping given a temperature gradient. In contrast to their approximate closures where the vanishing viscosity coefficient numerically gives an exact response, our closures relate the heat flow and nonvanishing viscosity to temperature and flow velocity (gradients).

The development of a three-dimensional partially elliptic flow computer program for combustor research

NASA Technical Reports Server (NTRS)

Pan, Y. S.

1978-01-01

A three dimensional, partially elliptic, computer program was developed. Without requiring three dimensional computer storage locations for all flow variables, the partially elliptic program is capable of predicting three dimensional combustor flow fields with large downstream effects. The program requires only slight increase of computer storage over the parabolic flow program from which it was developed. A finite difference formulation for a three dimensional, fully elliptic, turbulent, reacting, flow field was derived. Because of the negligible diffusion effects in the main flow direction in a supersonic combustor, the set of finite-difference equations can be reduced to a partially elliptic form. Only the pressure field was governed by an elliptic equation and requires three dimensional storage; all other dependent variables are governed by parabolic equations. A numerical procedure which combines a marching integration scheme with an iterative scheme for solving the elliptic pressure was adopted.

Unsteady electroosmosis in a microchannel with Poisson-Boltzmann charge distribution.

PubMed

Chang, Chien C; Kuo, Chih-Yu; Wang, Chang-Yi

2011-11-01

The present study is concerned with unsteady electroosmotic flow (EOF) in a microchannel with the electric charge distribution described by the Poisson-Boltzmann (PB) equation. The nonlinear PB equation is solved by a systematic perturbation with respect to the parameter λ which measures the strength of the wall zeta potential relative to the thermal potential. In the small λ limits (λ<1), we recover the linearized PB equation - the Debye-Hückel approximation. The solutions obtained by using only three terms in the perturbation series are shown to be accurate with errors <1% for λ up to 2. The accurate solution to the PB equation is then used to solve the electrokinetic fluid transport equation for two types of unsteady flow: transient flow driven by a suddenly applied voltage and oscillatory flow driven by a time-harmonic voltage. The solution for the transient flow has important implications on EOF as an effective means for transporting electrolytes in microchannels with various electrokinetic widths. On the other hand, the solution for the oscillatory flow is shown to have important physical implications on EOF in mixing electrolytes in terms of the amplitude and phase of the resulting time-harmonic EOF rate, which depends on the applied frequency and the electrokinetic width of the microchannel as well as on the parameter λ. Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Computation of turbulent boundary layer flows with an algebraic stress turbulence model

NASA Technical Reports Server (NTRS)

Kim, Sang-Wook; Chen, Yen-Sen

1986-01-01

An algebraic stress turbulence model is presented, characterized by the following: (1) the eddy viscosity expression is derived from the Reynolds stress turbulence model; (2) the turbulent kinetic energy dissipation rate equation is improved by including a production range time scale; and (3) the diffusion coefficients for turbulence equations are adjusted so that the kinetic energy profile extends further into the free stream region found in most experimental data. The turbulent flow equations were solved using a finite element method. Examples include: fully developed channel flow, fully developed pipe flow, flat plate boundary layer flow, plane jet exhausting into a moving stream, circular jet exhausting into a moving stream, and wall jet flow. Computational results compare favorably with experimental data for most of the examples considered. Significantly improved results were obtained for the plane jet flow, the circular jet flow, and the wall jet flow; whereas the remainder are comparable to those obtained by finite difference methods using the standard kappa-epsilon turbulence model. The latter seems to be promising with further improvement of the expression for the eddy viscosity coefficient.

CONSTITUTIVE BEHAVIOR OF AS-QUENCHED Al-Cu-Mn ALLOY

NASA Astrophysics Data System (ADS)

Yang, Xia-Wei; Zhu, Jing-Chuan; Nong, Zhi-Sheng; Ye, Mao; Lai, Zhong-Hong; Liu, Yong

2013-07-01

The hot flow stress of as-quenched Al-Cu-Mn alloy was modeled using the constitutive equations. The as-quenched Al-Cu-Mn alloy were treated with isothermal hot compression tests in the temperature range of 350-500°C, the strain rate range of 0.001-1 s-1. The hyperbolic sine equation was found to be appropriate for flow stress modeling and prediction. Based on the hyperbolic sine equation, a constitutive equation is a relation between 0.2 pct yield stress and deformation conditions (strain rate and deformation temperature) was established. The corresponding hot deformation activation energy (Q) for as-quenched Al-Cu-Mn alloy was determined to be 251.314 kJ/mol. Parameters of constitutive equation of as-quenched Al-Cu-Mn alloy were calculated at different small strains (≤ 0.01). The calculated flow stresses from the constitutive equation are in good agreement with the experimental results. Therefore, this constitutive equation can be used as an accurate temperature-stress model to solve the problems of quench distortion of Al-Cu-Mn alloy parts.

Numerical Investigation of Two-Phase Flows With Charged Droplets in Electrostatic Field

NASA Technical Reports Server (NTRS)

Kim, Sang-Wook

1996-01-01

A numerical method to solve two-phase turbulent flows with charged droplets in an electrostatic field is presented. The ensemble-averaged Navier-Stokes equations and the electrostatic potential equation are solved using a finite volume method. The transitional turbulence field is described using multiple-time-scale turbulence equations. The equations of motion of droplets are solved using a Lagrangian particle tracking scheme, and the inter-phase momentum exchange is described by the Particle-In-Cell scheme. The electrostatic force caused by an applied electrical potential is calculated using the electrostatic field obtained by solving a Laplacian equation and the force exerted by charged droplets is calculated using the Coulombic force equation. The method is applied to solve electro-hydrodynamic sprays. The calculated droplet velocity distributions for droplet dispersions occurring in a stagnant surrounding are in good agreement with the measured data. For droplet dispersions occurring in a two-phase flow, the droplet trajectories are influenced by aerodynamic forces, the Coulombic force, and the applied electrostatic potential field.

Rarefied gas flows through a curved channel: Application of a diffusion-type equation

NASA Astrophysics Data System (ADS)

Aoki, Kazuo; Takata, Shigeru; Tatsumi, Eri; Yoshida, Hiroaki

2010-11-01

Rarefied gas flows through a curved two-dimensional channel, caused by a pressure or a temperature gradient, are investigated numerically by using a macroscopic equation of convection-diffusion type. The equation, which was derived systematically from the Bhatnagar-Gross-Krook model of the Boltzmann equation and diffuse-reflection boundary condition in a previous paper [K. Aoki et al., "A diffusion model for rarefied flows in curved channels," Multiscale Model. Simul. 6, 1281 (2008)], is valid irrespective of the degree of gas rarefaction when the channel width is much shorter than the scale of variations of physical quantities and curvature along the channel. Attention is also paid to a variant of the Knudsen compressor that can produce a pressure raise by the effect of the change of channel curvature and periodic temperature distributions without any help of moving parts. In the process of analysis, the macroscopic equation is (partially) extended to the case of the ellipsoidal-statistical model of the Boltzmann equation.

Input guide for computer programs to generate thermodynamic data for air and Freon CF4

NASA Technical Reports Server (NTRS)

Tevepaugh, J. A.; Penny, M. M.; Baker, L. R., Jr.

1975-01-01

FORTRAN computer programs were developed to calculate the thermodynamic properties of Freon 14 and air for isentropic expansion from given plenum conditions. Thermodynamic properties for air are calculated with equations derived from the Beattie-Bridgeman nonstandard equation of state and, for Freon 14, with equations derived from the Redlich-Quang nonstandard equation of state. These two gases are used in scale model testing of model rocket nozzle flow fields which requires simulation of the prototype plume shape with a cold flow test approach. Utility of the computer programs for use in analytical prediction of flow fields is enhanced by arranging card or tape output of the data in a format compatible with a method-of-characteristics computer program.

A review of physically based models for soil erosion by water

NASA Astrophysics Data System (ADS)

Le, Minh-Hoang; Cerdan, Olivier; Sochala, Pierre; Cheviron, Bruno; Brivois, Olivier; Cordier, Stéphane

2010-05-01

Physically-based models rely on fundamental physical equations describing stream flow and sediment and associated nutrient generation in a catchment. This paper reviews several existing erosion and sediment transport approaches. The process of erosion include soil detachment, transport and deposition, we present various forms of equations and empirical formulas used when modelling and quantifying each of these processes. In particular, we detail models describing rainfall and infiltration effects and the system of equations to describe the overland flow and the evolution of the topography. We also present the formulas for the flow transport capacity and the erodibility functions. Finally, we present some recent numerical schemes to approach the shallow water equations and it's coupling with infiltration and erosion source terms.

On the Representation of the Porosity-Pressure Relationship in General Subsurface Flow Codes

DOE PAGES

Birdsell, Daniel Traver; Karra, Satish; Rajaram, Harihar

2018-01-11

The governing equations for subsurface flow codes in a deformable porous media are derived from the balance of fluid mass and Darcy's equation. One class of these codes, which we call general subsurface flow codes (GSFs), allow for more general constitutive relations for material properties such as porosity, permeability and density. Examples of GSFs include PFLOTRAN, FEHM, TOUGH2, STOMP, and some reservoir simulators such as BOAST. Depending on the constitutive relations used in GSFs, an inconsistency arises between the standard groundwater flow equation and the governing equation of GSFs, and we clarify that the reason for this inconsistency is becausemore » the Darcy's equation used in the GSFs should account for the velocity of fluid with respect to solid. Due to lack of awareness of this inconsistency, users of the GSFs tend to use a porosity-pressure relationship that comes from the standard groundwater flow equation and assumes that the relative velocity is already accounted for. For the Theis problem, we show that using this traditional relationship in the GSFs leads to significantly large errors. We propose an alternate porosity-pressure relationship that is consistent with the derivation of the governing equations in the GSFs where the solid velocity is not tracked, and show that, with this relationship, the results are more accurate for the Theis problem. In conclusion, the purpose of this note is to make the users and developers of these GSFs aware of this inconsistency and to advocate that the alternate porosity model derived here should be incorporated in GSFs.« less

Macroscopic momentum and mechanical energy equations for incompressible single-phase flow in porous media.

PubMed

Paéz-García, Catherine Teresa; Valdés-Parada, Francisco J; Lasseux, Didier

2017-02-01

Modeling flow in porous media is usually focused on the governing equations for mass and momentum transport, which yield the velocity and pressure at the pore or Darcy scales. However, in many applications, it is important to determine the work (or power) needed to induce flow in porous media, and this can be achieved when the mechanical energy equation is taken into account. At the macroscopic scale, this equation may be postulated to be the result of the inner product of Darcy's law and the seepage velocity. However, near the porous medium boundaries, this postulate seems questionable due to the spatial variations of the effective properties (velocity, permeability, porosity, etc.). In this work we derive the macroscopic mechanical energy equation using the method of volume averaging for the simple case of incompressible single-phase flow in porous media. Our analysis shows that the result of averaging the pore-scale version of the mechanical energy equation at the Darcy scale is not, in general, the expected product of Darcy's law and the seepage velocity. As a matter of fact, this result is only applicable in the bulk region of the porous medium and, in the derivation of this result, the properties of the permeability tensor are determinant. Furthermore, near the porous medium boundaries, a more novel version of the mechanical energy equation is obtained, which incorporates additional terms that take into account the rapid variations of structural properties taking place in this particular portion of the system. This analysis can be applied to multiphase and compressible flows in porous media and in many other multiscale systems.

On the wall-normal velocity of the compressible boundary-layer equations

NASA Technical Reports Server (NTRS)

Pruett, C. David

1991-01-01

Numerical methods for the compressible boundary-layer equations are facilitated by transformation from the physical (x,y) plane to a computational (xi,eta) plane in which the evolution of the flow is 'slow' in the time-like xi direction. The commonly used Levy-Lees transformation results in a computationally well-behaved problem for a wide class of non-similar boundary-layer flows, but it complicates interpretation of the solution in physical space. Specifically, the transformation is inherently nonlinear, and the physical wall-normal velocity is transformed out of the problem and is not readily recovered. In light of recent research which shows mean-flow non-parallelism to significantly influence the stability of high-speed compressible flows, the contribution of the wall-normal velocity in the analysis of stability should not be routinely neglected. Conventional methods extract the wall-normal velocity in physical space from the continuity equation, using finite-difference techniques and interpolation procedures. The present spectrally-accurate method extracts the wall-normal velocity directly from the transformation itself, without interpolation, leaving the continuity equation free as a check on the quality of the solution. The present method for recovering wall-normal velocity, when used in conjunction with a highly-accurate spectral collocation method for solving the compressible boundary-layer equations, results in a discrete solution which is extraordinarily smooth and accurate, and which satisfies the continuity equation nearly to machine precision. These qualities make the method well suited to the computation of the non-parallel mean flows needed by spatial direct numerical simulations (DNS) and parabolized stability equation (PSE) approaches to the analysis of stability.

On the Representation of the Porosity-Pressure Relationship in General Subsurface Flow Codes

NASA Astrophysics Data System (ADS)

Birdsell, Daniel T.; Karra, Satish; Rajaram, Harihar

2018-02-01

The governing equations for subsurface flow codes in a deformable porous media are derived from the balance of fluid mass and Darcy's equation. One class of these codes, which we call general subsurface flow codes (GSFs), allow for more general constitutive relations for material properties such as porosity, permeability and density. Examples of GSFs include PFLOTRAN, FEHM, TOUGH2, STOMP, and some reservoir simulators such as BOAST. Depending on the constitutive relations used in GSFs, an inconsistency arises between the standard groundwater flow equation and the governing equation of GSFs, and we clarify that the reason for this inconsistency is because the Darcy's equation used in the GSFs should account for the velocity of fluid with respect to solid. Due to lack of awareness of this inconsistency, users of the GSFs tend to use a porosity-pressure relationship that comes from the standard groundwater flow equation and assumes that the relative velocity is already accounted for. For the Theis problem, we show that using this traditional relationship in the GSFs leads to significantly large errors. We propose an alternate porosity-pressure relationship that is consistent with the derivation of the governing equations in the GSFs where the solid velocity is not tracked, and show that, with this relationship, the results are more accurate for the Theis problem. The purpose of this note is to make the users and developers of these GSFs aware of this inconsistency and to advocate that the alternate porosity model derived here should be incorporated in GSFs.

On the Representation of the Porosity-Pressure Relationship in General Subsurface Flow Codes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Birdsell, Daniel Traver; Karra, Satish; Rajaram, Harihar

The governing equations for subsurface flow codes in a deformable porous media are derived from the balance of fluid mass and Darcy's equation. One class of these codes, which we call general subsurface flow codes (GSFs), allow for more general constitutive relations for material properties such as porosity, permeability and density. Examples of GSFs include PFLOTRAN, FEHM, TOUGH2, STOMP, and some reservoir simulators such as BOAST. Depending on the constitutive relations used in GSFs, an inconsistency arises between the standard groundwater flow equation and the governing equation of GSFs, and we clarify that the reason for this inconsistency is becausemore » the Darcy's equation used in the GSFs should account for the velocity of fluid with respect to solid. Due to lack of awareness of this inconsistency, users of the GSFs tend to use a porosity-pressure relationship that comes from the standard groundwater flow equation and assumes that the relative velocity is already accounted for. For the Theis problem, we show that using this traditional relationship in the GSFs leads to significantly large errors. We propose an alternate porosity-pressure relationship that is consistent with the derivation of the governing equations in the GSFs where the solid velocity is not tracked, and show that, with this relationship, the results are more accurate for the Theis problem. In conclusion, the purpose of this note is to make the users and developers of these GSFs aware of this inconsistency and to advocate that the alternate porosity model derived here should be incorporated in GSFs.« less

Estimating Selected Streamflow Statistics Representative of 1930-2002 in West Virginia

USGS Publications Warehouse

Wiley, Jeffrey B.

2008-01-01

Regional equations and procedures were developed for estimating 1-, 3-, 7-, 14-, and 30-day 2-year; 1-, 3-, 7-, 14-, and 30-day 5-year; and 1-, 3-, 7-, 14-, and 30-day 10-year hydrologically based low-flow frequency values for unregulated streams in West Virginia. Regional equations and procedures also were developed for estimating the 1-day, 3-year and 4-day, 3-year biologically based low-flow frequency values; the U.S. Environmental Protection Agency harmonic-mean flows; and the 10-, 25-, 50-, 75-, and 90-percent flow-duration values. Regional equations were developed using ordinary least-squares regression using statistics from 117 U.S. Geological Survey continuous streamflow-gaging stations as dependent variables and basin characteristics as independent variables. Equations for three regions in West Virginia - North, South-Central, and Eastern Panhandle - were determined. Drainage area, precipitation, and longitude of the basin centroid are significant independent variables in one or more of the equations. Estimating procedures are presented for determining statistics at a gaging station, a partial-record station, and an ungaged location. Examples of some estimating procedures are presented.

Low-Dispersion Scheme for Nonlinear Acoustic Waves in Nonuniform Flow

NASA Technical Reports Server (NTRS)

Baysal, Oktay; Kaushik, Dinesh K.; Idres, Moumen

1997-01-01

The linear dispersion-relation-preserving scheme and its boundary conditions have been extended to the nonlinear Euler equations. This allowed computing, a nonuniform flowfield and a nonlinear acoustic wave propagation in such a medium, by the same scheme. By casting all the equations, boundary conditions, and the solution scheme in generalized curvilinear coordinates, the solutions were made possible for non-Cartesian domains and, for the better deployment of the grid points, nonuniform grid step sizes could be used. It has been tested for a number of simple initial-value and periodic-source problems. A simple demonstration of the difference between a linear and nonlinear propagation was conducted. The wall boundary condition, derived from the momentum equations and implemented through a pressure at a ghost point, and the radiation boundary condition, derived from the asymptotic solution to the Euler equations, have proven to be effective for the nonlinear equations and nonuniform flows. The nonreflective characteristic boundary conditions also have shown success but limited to the nonlinear waves in no mean flow, and failed for nonlinear waves in nonuniform flow.

Effect of homogenous-heterogeneous reactions on MHD Prandtl fluid flow over a stretching sheet

NASA Astrophysics Data System (ADS)

Khan, Imad; Malik, M. Y.; Hussain, Arif; Salahuddin, T.

An analysis is performed to explore the effects of homogenous-heterogeneous reactions on two-dimensional flow of Prandtl fluid over a stretching sheet. In present analysis, we used the developed model of homogeneous-heterogeneous reactions in boundary layer flow. The mathematical configuration of presented flow phenomenon yields the nonlinear partial differential equations. Using scaling transformations, the governing partial differential equations (momentum equation and homogenous-heterogeneous reactions equations) are transformed into non-linear ordinary differential equations (ODE's). Then, resulting non-linear ODE's are solved by computational scheme known as shooting method. The quantitative and qualitative manners of concerned physical quantities (velocity, concentration and drag force coefficient) are examined under prescribed physical constrained through figures and tables. It is observed that velocity profile enhances verses fluid parameters α and β while Hartmann number reduced it. The homogeneous and heterogeneous reactions parameters have reverse effects on concentration profile. Concentration profile shows retarding behavior for large values of Schmidt number. Skin fraction coefficient enhances with increment in Hartmann number H and fluid parameter α .

Discrete Ricci Flow in Higher Dimensions

DTIC Science & Technology

2015-02-01

simplicial version of the RF equations. The definition of these SRF equations required a subtile definition of the Ricci tensor as we needed to... definition of congestion in networks. This definition mirrors the Wang and Yau definition for quasi-local energy and momentum in general relativity. In... definition and associated corollary: Definition 1. We define the dual-edge Regge-Ricci flow equation for any compact, piecewise–flat simplicial geometry

Numerical Solution for Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Warsi, Z. U. A.; Weed, R. A.; Thompson, J. F.

1982-01-01

Carefully selected blend of computational techniques solves complete set of equations for viscous, unsteady, hypersonic flow in general curvilinear coordinates. New algorithm has tested computation of axially directed flow about blunt body having shape similar to that of such practical bodies as wide-body aircraft or artillery shells. Method offers significant computational advantages because of conservation-law form of equations and because it reduces amount of metric data required.

An entropy correction method for unsteady full potential flows with strong shocks

NASA Technical Reports Server (NTRS)

Whitlow, W., Jr.; Hafez, M. M.; Osher, S. J.

1986-01-01

An entropy correction method for the unsteady full potential equation is presented. The unsteady potential equation is modified to account for entropy jumps across shock waves. The conservative form of the modified equation is solved in generalized coordinates using an implicit, approximate factorization method. A flux-biasing differencing method, which generates the proper amounts of artificial viscosity in supersonic regions, is used to discretize the flow equations in space. Comparisons between the present method and solutions of the Euler equations and between the present method and experimental data are presented. The comparisons show that the present method more accurately models solutions of the Euler equations and experiment than does the isentropic potential formulation.

Numerical solution of nonlinear partial differential equations of mixed type. [finite difference approximation

NASA Technical Reports Server (NTRS)

Jameson, A.

1976-01-01

A review is presented of some recently developed numerical methods for the solution of nonlinear equations of mixed type. The methods considered use finite difference approximations to the differential equation. Central difference formulas are employed in the subsonic zone and upwind difference formulas are used in the supersonic zone. The relaxation method for the small disturbance equation is discussed and a description is given of difference schemes for the potential flow equation in quasi-linear form. Attention is also given to difference schemes for the potential flow equation in conservation form, the analysis of relaxation schemes by the time dependent analogy, the accelerated iterative method, and three-dimensional calculations.

Mobility statistics and automated hazard mapping for debris flows and rock avalanches

USGS Publications Warehouse

Griswold, Julia P.; Iverson, Richard M.

2008-01-01

Power-law equations that are physically motivated and statistically tested and calibrated provide a basis for forecasting areas likely to be inundated by debris flows, rock avalanches, and lahars with diverse volumes. The equations A=α1V2/3 and B=α2V2/3 are based on the postulate that the maximum valley cross-sectional area (A) and total valley planimetric area (B) likely to be inundated by a flow depend only on its volume (V) and the topography of the flow path. Testing of these equations involves determining whether or not they fit data for documented flows satisfactorily, and calibration entails determining best-fit values of the coefficients α1 and α2 for debris flows, rock avalanches, and lahars. This report describes statistical testing and calibration of the equations by using field data compiled from many sources, and it describes application of the equations to delineation of debris-flow hazard zones. Statistical results show that for each type of flow (debris flows, rock avalanches, and lahars), the dependence of A and B on V is described well by power laws with exponents equal to 2/3. This value of the exponent produces fits that are effectively indistinguishable from the best fits obtained by using adjustable power-law exponents. Statistically calibrated values of the coefficients α1 and α2 provide scale-invariant indices of the relative mobilities of rock avalanches (α1 = 0.2, α2 = 20), nonvolcanic debris flows (α1 = 0.1, α2 = 20), and lahars (α1 = 0.05, α2 = 200). These values show, for example, that a lahar of specified volume can be expected to inundate a planimetric area ten times larger than that inundated by a rock avalanche or nonvolcanic debris flow of the same volume. The utility of the calibrated debris-flow inundation equations A=0.1V2/3 and B=20V2/3 is demonstrated by using them within the GIS program LAHARZ to delineate nested hazard zones for future debris flows in an area bordering the Umpqua River in the south-central Oregon Coast Range. This application requires use of high-resolution topographic data derived form LIDAR surveys, knowledge of local geology to specify a suitable range of prospective debris-flow volumes, and development and use of a new algorithm for identification of prospective debris-flow source areas in finely dissected terrain.

A model for simulation of flow in singular and interconnected channels

USGS Publications Warehouse

Schaffranek, Raymond W.; Baltzer, R.A.; Goldberg, D.E.

1981-01-01

A one-dimensional numerical model is presented for simulating the unsteady flow in singular riverine or estuarine reaches and in networks of reaches composed of interconnected channels. The model is both general and flexible in that it can be used to simulate a wide range of flow conditions for various channel configurations. The channel geometry of the network to be modeled should be sufficiently simple so as to lend itself to characterization in one spatial dimension. The flow must be substantially homogenous in density, and hydrostatic pressure must prevail everywhere in the network channels. The slope of each channel bottom ought to be mild and reasonably constant over its length so that the flow remains subcritical. The model accommodates tributary inflows and diversions and includes the effects of wind shear on the water surface as a forcing function in the flow equations. Water-surface elevations and flow discharges are computed at channel junctions, as well as at specified intermediate locations within the network channels. The one-dimensional branch-network flow model uses a four-point, implicit, finite-difference approximation of the unsteady-flow equations. The flow equations are linearized over a time step, and branch transformations are formulated that describe the relationship between the unknowns at the end points of the channels. The resultant matrix of branch-transformation equations and required boundary-condition equations is solved by Gaussian elimination using maximum pivot strategy. Five example applications of the flow model are illustrated. The applications cover such diverse conditions as a singular upland river reach in which unsteady flow results from hydropower regulations, coastal rivers composed of sequentially connected reaches subject to unsteady tide-driven flow, and a multiply connected network of channels whose flow is principally governed by wind tides and seiches in adjoining lakes. The report includes a listing of the FORTRAN IV computer program and a description of the input data requirements. Model supporting programs for the processing and input of initial and boundary-value data are identified, various model output formats are illustrated, and instructions are given to permit the production of graphical output using the line printer, electromechanical pen plotters, cathode-ray-tube display units, or microfilm recorders.

Modeling self-consistent multi-class dynamic traffic flow

NASA Astrophysics Data System (ADS)

Cho, Hsun-Jung; Lo, Shih-Ching

2002-09-01

In this study, we present a systematic self-consistent multiclass multilane traffic model derived from the vehicular Boltzmann equation and the traffic dispersion model. The multilane domain is considered as a two-dimensional space and the interaction among vehicles in the domain is described by a dispersion model. The reason we consider a multilane domain as a two-dimensional space is that the driving behavior of road users may not be restricted by lanes, especially motorcyclists. The dispersion model, which is a nonlinear Poisson equation, is derived from the car-following theory and the equilibrium assumption. Under the concept that all kinds of users share the finite section, the density is distributed on a road by the dispersion model. In addition, the dynamic evolution of the traffic flow is determined by the systematic gas-kinetic model derived from the Boltzmann equation. Multiplying Boltzmann equation by the zeroth, first- and second-order moment functions, integrating both side of the equation and using chain rules, we can derive continuity, motion and variance equation, respectively. However, the second-order moment function, which is the square of the individual velocity, is employed by previous researches does not have physical meaning in traffic flow. Although the second-order expansion results in the velocity variance equation, additional terms may be generated. The velocity variance equation we propose is derived from multiplying Boltzmann equation by the individual velocity variance. It modifies the previous model and presents a new gas-kinetic traffic flow model. By coupling the gas-kinetic model and the dispersion model, a self-consistent system is presented.

A fast iterative scheme for the linearized Boltzmann equation

NASA Astrophysics Data System (ADS)

Wu, Lei; Zhang, Jun; Liu, Haihu; Zhang, Yonghao; Reese, Jason M.

2017-06-01

Iterative schemes to find steady-state solutions to the Boltzmann equation are efficient for highly rarefied gas flows, but can be very slow to converge in the near-continuum flow regime. In this paper, a synthetic iterative scheme is developed to speed up the solution of the linearized Boltzmann equation by penalizing the collision operator L into the form L = (L + Nδh) - Nδh, where δ is the gas rarefaction parameter, h is the velocity distribution function, and N is a tuning parameter controlling the convergence rate. The velocity distribution function is first solved by the conventional iterative scheme, then it is corrected such that the macroscopic flow velocity is governed by a diffusion-type equation that is asymptotic-preserving into the Navier-Stokes limit. The efficiency of this new scheme is assessed by calculating the eigenvalue of the iteration, as well as solving for Poiseuille and thermal transpiration flows. We find that the fastest convergence of our synthetic scheme for the linearized Boltzmann equation is achieved when Nδ is close to the average collision frequency. The synthetic iterative scheme is significantly faster than the conventional iterative scheme in both the transition and the near-continuum gas flow regimes. Moreover, due to its asymptotic-preserving properties, the synthetic iterative scheme does not need high spatial resolution in the near-continuum flow regime, which makes it even faster than the conventional iterative scheme. Using this synthetic scheme, with the fast spectral approximation of the linearized Boltzmann collision operator, Poiseuille and thermal transpiration flows between two parallel plates, through channels of circular/rectangular cross sections and various porous media are calculated over the whole range of gas rarefaction. Finally, the flow of a Ne-Ar gas mixture is solved based on the linearized Boltzmann equation with the Lennard-Jones intermolecular potential for the first time, and the difference between these results and those using the hard-sphere potential is discussed.

A logistic regression equation for estimating the probability of a stream in Vermont having intermittent flow

USGS Publications Warehouse

Olson, Scott A.; Brouillette, Michael C.

2006-01-01

A logistic regression equation was developed for estimating the probability of a stream flowing intermittently at unregulated, rural stream sites in Vermont. These determinations can be used for a wide variety of regulatory and planning efforts at the Federal, State, regional, county and town levels, including such applications as assessing fish and wildlife habitats, wetlands classifications, recreational opportunities, water-supply potential, waste-assimilation capacities, and sediment transport. The equation will be used to create a derived product for the Vermont Hydrography Dataset having the streamflow characteristic of 'intermittent' or 'perennial.' The Vermont Hydrography Dataset is Vermont's implementation of the National Hydrography Dataset and was created at a scale of 1:5,000 based on statewide digital orthophotos. The equation was developed by relating field-verified perennial or intermittent status of a stream site during normal summer low-streamflow conditions in the summer of 2005 to selected basin characteristics of naturally flowing streams in Vermont. The database used to develop the equation included 682 stream sites with drainage areas ranging from 0.05 to 5.0 square miles. When the 682 sites were observed, 126 were intermittent (had no flow at the time of the observation) and 556 were perennial (had flowing water at the time of the observation). The results of the logistic regression analysis indicate that the probability of a stream having intermittent flow in Vermont is a function of drainage area, elevation of the site, the ratio of basin relief to basin perimeter, and the areal percentage of well- and moderately well-drained soils in the basin. Using a probability cutpoint (a lower probability indicates the site has perennial flow and a higher probability indicates the site has intermittent flow) of 0.5, the logistic regression equation correctly predicted the perennial or intermittent status of 116 test sites 85 percent of the time.

Methods for estimating peak-flow frequencies at ungaged sites in Montana based on data through water year 2011: Chapter F in Montana StreamStats

USGS Publications Warehouse

Sando, Roy; Sando, Steven K.; McCarthy, Peter M.; Dutton, DeAnn M.

2016-04-05

The U.S. Geological Survey (USGS), in cooperation with the Montana Department of Natural Resources and Conservation, completed a study to update methods for estimating peak-flow frequencies at ungaged sites in Montana based on peak-flow data at streamflow-gaging stations through water year 2011. The methods allow estimation of peak-flow frequencies (that is, peak-flow magnitudes, in cubic feet per second, associated with annual exceedance probabilities of 66.7, 50, 42.9, 20, 10, 4, 2, 1, 0.5, and 0.2 percent) at ungaged sites. The annual exceedance probabilities correspond to 1.5-, 2-, 2.33-, 5-, 10-, 25-, 50-, 100-, 200-, and 500-year recurrence intervals, respectively.Regional regression analysis is a primary focus of Chapter F of this Scientific Investigations Report, and regression equations for estimating peak-flow frequencies at ungaged sites in eight hydrologic regions in Montana are presented. The regression equations are based on analysis of peak-flow frequencies and basin characteristics at 537 streamflow-gaging stations in or near Montana and were developed using generalized least squares regression or weighted least squares regression.All of the data used in calculating basin characteristics that were included as explanatory variables in the regression equations were developed for and are available through the USGS StreamStats application (http://water.usgs.gov/osw/streamstats/) for Montana. StreamStats is a Web-based geographic information system application that was created by the USGS to provide users with access to an assortment of analytical tools that are useful for water-resource planning and management. The primary purpose of the Montana StreamStats application is to provide estimates of basin characteristics and streamflow characteristics for user-selected ungaged sites on Montana streams. The regional regression equations presented in this report chapter can be conveniently solved using the Montana StreamStats application.Selected results from this study were compared with results of previous studies. For most hydrologic regions, the regression equations reported for this study had lower mean standard errors of prediction (in percent) than the previously reported regression equations for Montana. The equations presented for this study are considered to be an improvement on the previously reported equations primarily because this study (1) included 13 more years of peak-flow data; (2) included 35 more streamflow-gaging stations than previous studies; (3) used a detailed geographic information system (GIS)-based definition of the regulation status of streamflow-gaging stations, which allowed better determination of the unregulated peak-flow records that are appropriate for use in the regional regression analysis; (4) included advancements in GIS and remote-sensing technologies, which allowed more convenient calculation of basin characteristics and investigation of many more candidate basin characteristics; and (5) included advancements in computational and analytical methods, which allowed more thorough and consistent data analysis.This report chapter also presents other methods for estimating peak-flow frequencies at ungaged sites. Two methods for estimating peak-flow frequencies at ungaged sites located on the same streams as streamflow-gaging stations are described. Additionally, envelope curves relating maximum recorded annual peak flows to contributing drainage area for each of the eight hydrologic regions in Montana are presented and compared to a national envelope curve. In addition to providing general information on characteristics of large peak flows, the regional envelope curves can be used to assess the reasonableness of peak-flow frequency estimates determined using the regression equations.

Techniques for estimating streamflow characteristics in the Eastern and Interior coal provinces of the United States

USGS Publications Warehouse

Wetzel, Kim L.; Bettandorff, J.M.

1986-01-01

Techniques are presented for estimating various streamflow characteristics, such as peak flows, mean monthly and annual flows, flow durations, and flow volumes, at ungaged sites on unregulated streams in the Eastern Coal region. Streamflow data and basin characteristics for 629 gaging stations were used to develop multiple-linear-regression equations. Separate equations were developed for the Eastern and Interior Coal Provinces. Drainage area is an independent variable common to all equations. Other variables needed, depending on the streamflow characteristic, are mean annual precipitation, mean basin elevation, main channel length, basin storage, main channel slope, and forest cover. A ratio of the observed 50- to 90-percent flow durations was used in the development of relations to estimate low-flow frequencies in the Eastern Coal Province. Relations to estimate low flows in the Interior Coal Province are not presented because the standard errors were greater than 0.7500 log units and were considered to be of poor reliability.

Analytical and experimental study of mean flow and turbulence characteristics inside the passages of an axial flow inducer

NASA Technical Reports Server (NTRS)

Gorton, C. A.; Lakshminarayana, B.

1974-01-01

The effort conducted to gather additional understanding of the complex inviscid and viscid effects existing within the passages of a three-bladed axial flow inducer operating at a flow coefficient of 0.065 is summarized. The experimental investigations included determination of the blade static pressure and blade limiting streamline angle distributions, and measurement of the three components of mean velocity, turbulence intensities and turbulence stresses at locations inside the inducer blade passage utilizing a rotating three-sensor hotwire probe. Applicable equations were derived for the hotwire data reduction analysis and solved numerically to obtain the appropriate flow parameters. Analytical investigations were conducted to predict the three-dimensional inviscid flow in the inducer by numerically solving the exact equations of motion, and to approximately predict the three-dimensional viscid flow by incorporating the dominant viscous terms into the exact equations. The analytical results are compared with the experimental measurements and design values where appropriate.

Forebody and afterbody solutions of the Navier-Stokes equations for supersonic flow over blunt bodies in a generalized orthogonal coordinate system

NASA Technical Reports Server (NTRS)

Gnoffo, P. A.

1978-01-01

A coordinate transformation, which can approximate many different two-dimensional and axisymmetric body shapes with an analytic function, is used as a basis for solving the Navier-Stokes equations for the purpose of predicting 0 deg angle of attack supersonic flow fields. The transformation defines a curvilinear, orthogonal coordinate system in which coordinate lines are perpendicular to the body and the body is defined by one coordinate line. This system is mapped in to a rectangular computational domain in which the governing flow field equations are solved numerically. Advantages of this technique are that the specification of boundary conditions are simplified and, most importantly, the entire flow field can be obtained, including flow in the wake. Good agreement has been obtained with experimental data for pressure distributions, density distributions, and heat transfer over spheres and cylinders in supersonic flow. Approximations to the Viking aeroshell and to a candidate Jupiter probe are presented and flow fields over these shapes are calculated.

Three-dimensional elliptic grid generation for an F-16

NASA Technical Reports Server (NTRS)

Sorenson, Reese L.

1988-01-01

A case history depicting the effort to generate a computational grid for the simulation of transonic flow about an F-16 aircraft at realistic flight conditions is presented. The flow solver for which this grid is designed is a zonal one, using the Reynolds averaged Navier-Stokes equations near the surface of the aircraft, and the Euler equations in regions removed from the aircraft. A body conforming global grid, suitable for the Euler equation, is first generated using 3-D Poisson equations having inhomogeneous terms modeled after the 2-D GRAPE code. Regions of the global grid are then designated for zonal refinement as appropriate to accurately model the flow physics. Grid spacing suitable for solution of the Navier-Stokes equations is generated in the refinement zones by simple subdivision of the given coarse grid intervals. That grid generation project is described, with particular emphasis on the global coarse grid.

A Comparison of Experimental and Theoretical Results for Labyrinth Gas Seals. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Scharrer, Joseph Kirk

1987-01-01

The basic equations are derived for a two control volume model for compressible flow in a labyrinth seal. The flow is assumed to be completely turbulent and isoenergetic. The wall friction factors are determined using the Blasius formula. Jet flow theory is used for the calculation of the recirculation velocity in the cavity. Linearized zeroth and first order perturbation equations are developed for small motion about a centered position by an expansion in the eccentricity ratio. The zeroth order pressure distribution is found by satisfying the leakage equation. The circumferential velocity distribution is determined by satisfying the momentum equations. The first order equations are solved by a separation of variable solution. Integration of the resultant pressure distribution along and around the seal defines the reaction force developed by the seal and the corresponding dynamic coefficients. The results of this analysis are compared to experimental test results.

Analysis of Three-Dimensional, Nonlinear Development of Wave-Like Structure in a Compressible Round Jet

NASA Technical Reports Server (NTRS)

Dahl, Milo D.; Mankbadi, Reda R.

2002-01-01

An analysis of the nonlinear development of the large-scale structures or instability waves in compressible round jets was conducted using the integral energy method. The equations of motion were decomposed into two sets of equations; one set governing the mean flow motion and the other set governing the large-scale structure motion. The equations in each set were then combined to derive kinetic energy equations that were integrated in the radial direction across the jet after the boundary-layer approximations were applied. Following the application of further assumptions regarding the radial shape of the mean flow and the large structures, equations were derived that govern the nonlinear, streamwise development of the large structures. Using numerically generated mean flows, calculations show the energy exchanges and the effects of the initial amplitude on the coherent structure development in the jet.

Surface-slip equations for multicomponent, nonequilibrium air flow

NASA Technical Reports Server (NTRS)

Gupta, Roop N.; Scott, Carl D.; Moss, James N.; Goglia, Gene

1985-01-01

Equations are presented for the surface slip (or jump) values of species concentration, pressure, velocity, and temperature in the low-Reynolds-number, high-altitude flight regime of a space vehicle. These are obtained from closed-form solutions of the mass, momentum, and energy flux equations using the Chapman-Enskog velocity distribution function. This function represents a solution of the Boltzmann equation in the Navier-Stokes approximation. The analysis, obtained for nonequilibrium multicomponent air flow, includes the finite-rate surface catalytic recombination and changes in the internal energy during reflection from the surface. Expressions for the various slip quantities have been obtained in a form which can readily be employed in flow-field computations. A consistent set of equations is provided for multicomponent, binary, and single species mixtures. Expression is also provided for the finite-rate species-concentration boundary condition for a multicomponent mixture in absence of slip.

A new lumped-parameter approach to simulating flow processes in unsaturated dual-porosity media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zimmerman, R.W.; Hadgu, T.; Bodvarsson, G.S.

We have developed a new lumped-parameter dual-porosity approach to simulating unsaturated flow processes in fractured rocks. Fluid flow between the fracture network and the matrix blocks is described by a nonlinear equation that relates the imbibition rate to the local difference in liquid-phase pressure between the fractures and the matrix blocks. This equation is a generalization of the Warren-Root equation, but unlike the Warren-Root equation, is accurate in both the early and late time regimes. The fracture/matrix interflow equation has been incorporated into a computational module, compatible with the TOUGH simulator, to serve as a source/sink term for fracture elements.more » The new approach achieves accuracy comparable to simulations in which the matrix blocks are discretized, but typically requires an order of magnitude less computational time.« less

Estimating peak-flow frequency statistics for selected gaged and ungaged sites in naturally flowing streams and rivers in Idaho

USGS Publications Warehouse

Wood, Molly S.; Fosness, Ryan L.; Skinner, Kenneth D.; Veilleux, Andrea G.

2016-06-27

The U.S. Geological Survey, in cooperation with the Idaho Transportation Department, updated regional regression equations to estimate peak-flow statistics at ungaged sites on Idaho streams using recent streamflow (flow) data and new statistical techniques. Peak-flow statistics with 80-, 67-, 50-, 43-, 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent annual exceedance probabilities (1.25-, 1.50-, 2.00-, 2.33-, 5.00-, 10.0-, 25.0-, 50.0-, 100-, 200-, and 500-year recurrence intervals, respectively) were estimated for 192 streamgages in Idaho and bordering States with at least 10 years of annual peak-flow record through water year 2013. The streamgages were selected from drainage basins with little or no flow diversion or regulation. The peak-flow statistics were estimated by fitting a log-Pearson type III distribution to records of annual peak flows and applying two additional statistical methods: (1) the Expected Moments Algorithm to help describe uncertainty in annual peak flows and to better represent missing and historical record; and (2) the generalized Multiple Grubbs Beck Test to screen out potentially influential low outliers and to better fit the upper end of the peak-flow distribution. Additionally, a new regional skew was estimated for the Pacific Northwest and used to weight at-station skew at most streamgages. The streamgages were grouped into six regions (numbered 1_2, 3, 4, 5, 6_8, and 7, to maintain consistency in region numbering with a previous study), and the estimated peak-flow statistics were related to basin and climatic characteristics to develop regional regression equations using a generalized least squares procedure. Four out of 24 evaluated basin and climatic characteristics were selected for use in the final regional peak-flow regression equations.Overall, the standard error of prediction for the regional peak-flow regression equations ranged from 22 to 132 percent. Among all regions, regression model fit was best for region 4 in west-central Idaho (average standard error of prediction=46.4 percent; pseudo-R2>92 percent) and region 5 in central Idaho (average standard error of prediction=30.3 percent; pseudo-R2>95 percent). Regression model fit was poor for region 7 in southern Idaho (average standard error of prediction=103 percent; pseudo-R2<78 percent) compared to other regions because few streamgages in region 7 met the criteria for inclusion in the study, and the region’s semi-arid climate and associated variability in precipitation patterns causes substantial variability in peak flows.A drainage area ratio-adjustment method, using ratio exponents estimated using generalized least-squares regression, was presented as an alternative to the regional regression equations if peak-flow estimates are desired at an ungaged site that is close to a streamgage selected for inclusion in this study. The alternative drainage area ratio-adjustment method is appropriate for use when the drainage area ratio between the ungaged and gaged sites is between 0.5 and 1.5.The updated regional peak-flow regression equations had lower total error (standard error of prediction) than all regression equations presented in a 1982 study and in four of six regions presented in 2002 and 2003 studies in Idaho. A more extensive streamgage screening process used in the current study resulted in fewer streamgages used in the current study than in the 1982, 2002, and 2003 studies. Fewer streamgages used and the selection of different explanatory variables were likely causes of increased error in some regions compared to previous studies, but overall, regional peak‑flow regression model fit was generally improved for Idaho. The revised statistical procedures and increased streamgage screening applied in the current study most likely resulted in a more accurate representation of natural peak-flow conditions.The updated, regional peak-flow regression equations will be integrated in the U.S. Geological Survey StreamStats program to allow users to estimate basin and climatic characteristics and peak-flow statistics at ungaged locations of interest. StreamStats estimates peak-flow statistics with quantifiable certainty only when used at sites with basin and climatic characteristics within the range of input variables used to develop the regional regression equations. Both the regional regression equations and StreamStats should be used to estimate peak-flow statistics only in naturally flowing, relatively unregulated streams without substantial local influences to flow, such as large seeps, springs, or other groundwater-surface water interactions that are not widespread or characteristic of the respective region.

Flume experimental evaluation of the effect of rill flow path tortuosity on rill roughness based on the Manning–Strickler equation

USDA-ARS?s Scientific Manuscript database

Numerous soil erosion models compute concentrated flow hydraulics based on the Manning–Strickler equation (v = kSt R2/3 I1/2) even though the range of the application on rill flow is unclear. Unconfined rill morphologies generate local friction effects and consequently spatially variable rill roughn...

High speed flow past wings

NASA Technical Reports Server (NTRS)

Norstrud, H.

1973-01-01

The analytical solution to the transonic small perturbation equation which describes steady compressible flow past finite wings at subsonic speeds can be expressed as a nonlinear integral equation with the perturbation velocity potential as the unknown function. This known formulation is substituted by a system of nonlinear algebraic equations to which various methods are applicable for its solution. Due to the presence of mathematical discontinuities in the flow solutions, however, a main computational difficulty was to ensure uniqueness of the solutions when local velocities on the wing exceeded the speed of sound. For continuous solutions this was achieved by embedding the algebraic system in an one-parameter operator homotopy in order to apply the method of parametric differentiation. The solution to the initial system of equations appears then as a solution to a Cauchy problem where the initial condition is related to the accompanying incompressible flow solution. In using this technique, however, a continuous dependence of the solution development on the initial data is lost when the solution reaches the minimum bifurcation point. A steepest descent iteration technique was therefore, added to the computational scheme for the calculation of discontinuous flow solutions. Results for purely subsonic flows and supersonic flows with and without compression shocks are given and compared with other available theoretical solutions.

Investigation of supersonic chemically reacting and radiating channel flow

NASA Technical Reports Server (NTRS)

Mani, Mortaza; Tiwari, Surendra N.

1988-01-01

The 2-D time-dependent Navier-Stokes equations are used to investigate supersonic flows undergoing finite rate chemical reaction and radiation interaction for a hydrogen-air system. The explicit multistage finite volume technique of Jameson is used to advance the governing equations in time until convergence is achieved. The chemistry source term in the species equation is treated implicitly to alleviate the stiffness associated with fast reactions. The multidimensional radiative transfer equations for a nongray model are provided for a general configuration and then reduced for a planar geometry. Both pseudo-gray and nongray models are used to represent the absorption-emission characteristics of the participating species. The supersonic inviscid and viscous, nonreacting flows are solved by employing the finite volume technique of Jameson and the unsplit finite difference scheme of MacCormack. The specified problem considered is of the flow in a channel with a 10 deg compression-expansion ramp. The calculated results are compared with those of an upwind scheme. The problem of chemically reacting and radiating flows are solved for the flow of premixed hydrogen-air through a channel with parallel boundaries, and a channel with a compression corner. Results obtained for specific conditions indicate that the radiative interaction can have a significant influence on the entire flow field.

Supersonic flow calculation using a Reynolds-stress and an eddy thermal diffusivity turbulence model

NASA Technical Reports Server (NTRS)

Sommer, T. P.; So, R. M. C.; Zhang, H. S.

1993-01-01

A second-order model for the velocity field and a two-equation model for the temperature field are used to calculate supersonic boundary layers assuming negligible real gas effects. The modeled equations are formulated on the basis of an incompressible assumption and then extended to supersonic flows by invoking Morkovin's hypothesis, which proposes that compressibility effects are completely accounted for by mean density variations alone. In order to calculate the near-wall flow accurately, correction functions are proposed to render the modeled equations asymptotically consistent with the behavior of the exact equations near a wall and, at the same time, display the proper dependence on the molecular Prandtl number. Thus formulated, the near-wall second order turbulence model for heat transfer is applicable to supersonic flows with different Prandtl numbers. The model is validated against flows with different Prandtl numbers and supersonic flows with free-stream Mach numbers as high as 10 and wall temperature ratios as low as 0.3. Among the flow cases considered, the momentum thickness Reynolds number varies from approximately 4,000 to approximately 21,000. Good correlation with measurements of mean velocity, temperature, and its variance is obtained. Discernible improvements in the law-of-the-wall are observed, especially in the range where the big-law applies.

Fluid-structure interaction analysis on the effect of vessel wall hypertrophy and stiffness on the blood flow in carotid artery bifurcation

NASA Astrophysics Data System (ADS)

Lee, Sang Hoon; Choi, Hyoung Gwon; Yoo, Jung Yul

2012-11-01

The effect of artery wall hypertrophy and stiffness on the flow field is investigated using three-dimensional finite element method for simulating the blood flow. To avoid the complexity due to the necessity of additional mechanical constraints, we use the combined formulation which includes both the fluid and structural equations of motion into single coupled variational equation. A P2P1 Galerkin finite element method is used to solve the Navier-Stokes equations for fluid flow and arbitrary Lagrangian-Eulerian formulation is used to achieve mesh movement. The Newmark method is employed for solving the dynamic equilibrium equations for linear elastic solid mechanics. The pulsatile, incompressible flows of Newtonian fluids constrained in the flexible wall are analyzed with Womersley velocity profile at the inlet and constant pressure at the outlet. The study shows that the stiffness of carotid artery wall affects significantly the flow phenomena during the pulse cycle. Similarly, it is found that the flow field is also strongly influenced by wall hypertrophy. This work was supported by Mid-career Researcher Program and Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2009-0079936 & 2011-0029613).

Eigenmodes of Ducted Flows With Radially-Dependent Axial and Swirl Velocity Components

NASA Technical Reports Server (NTRS)

Kousen, Kenneth A.

1999-01-01

This report characterizes the sets of small disturbances possible in cylindrical and annular ducts with mean flow whose axial and tangential components vary arbitrarily with radius. The linearized equations of motion are presented and discussed, and then exponential forms for the axial, circumferential, and time dependencies of any unsteady disturbances are assumed. The resultant equations form a generalized eigenvalue problem, the solution of which yields the axial wavenumbers and radial mode shapes of the unsteady disturbances. Two numerical discretizations are applied to the system of equations: (1) a spectral collocation technique based on Chebyshev polynomial expansions on the Gauss-Lobatto points, and (2) second and fourth order finite differences on uniform grids. The discretized equations are solved using a standard eigensystem package employing the QR algorithm. The eigenvalues fall into two primary categories: a discrete set (analogous to the acoustic modes found in uniform mean flows) and a continuous band (analogous to convected disturbances in uniform mean flows) where the phase velocities of the disturbances correspond to the local mean flow velocities. Sample mode shapes and eigensystem distributions are presented for both sheared axial and swirling flows. The physics of swirling flows is examined with reference to hydrodynamic stability and completeness of the eigensystem expansions. The effect of assuming exponential dependence in the axial direction is discussed.

A Second Law Based Unstructured Finite Volume Procedure for Generalized Flow Simulation

NASA Technical Reports Server (NTRS)

Majumdar, Alok

1998-01-01

An unstructured finite volume procedure has been developed for steady and transient thermo-fluid dynamic analysis of fluid systems and components. The procedure is applicable for a flow network consisting of pipes and various fittings where flow is assumed to be one dimensional. It can also be used to simulate flow in a component by modeling a multi-dimensional flow using the same numerical scheme. The flow domain is discretized into a number of interconnected control volumes located arbitrarily in space. The conservation equations for each control volume account for the transport of mass, momentum and entropy from the neighboring control volumes. In addition, they also include the sources of each conserved variable and time dependent terms. The source term of entropy equation contains entropy generation due to heat transfer and fluid friction. Thermodynamic properties are computed from the equation of state of a real fluid. The system of equations is solved by a hybrid numerical method which is a combination of simultaneous Newton-Raphson and successive substitution schemes. The paper also describes the application and verification of the procedure by comparing its predictions with the analytical and numerical solution of several benchmark problems.

Comparison of Themodynamic and Transport Property Models for Computing Equilibrium High Enthalpy Flows

NASA Astrophysics Data System (ADS)

Ramasahayam, Veda Krishna Vyas; Diwakar, Anant; Bodi, Kowsik

2017-11-01

To study the flow of high temperature air in vibrational and chemical equilibrium, accurate models for thermodynamic state and transport phenomena are required. In the present work, the performance of a state equation model and two mixing rules for determining equilibrium air thermodynamic and transport properties are compared with that of curve fits. The thermodynamic state model considers 11 species which computes flow chemistry by an iterative process and the mixing rules considered for viscosity are Wilke and Armaly-Sutton. The curve fits of Srinivasan, which are based on Grabau type transition functions, are chosen for comparison. A two-dimensional Navier-Stokes solver is developed to simulate high enthalpy flows with numerical fluxes computed by AUSM+-up. The accuracy of state equation model and curve fits for thermodynamic properties is determined using hypersonic inviscid flow over a circular cylinder. The performance of mixing rules and curve fits for viscosity are compared using hypersonic laminar boundary layer prediction on a flat plate. It is observed that steady state solutions from state equation model and curve fits match with each other. Though curve fits are significantly faster the state equation model is more general and can be adapted to any flow composition.

Acquisition and correlation of cryogenic nitrogen mass flow data through a multiple orifice Joule-Thomson device

NASA Astrophysics Data System (ADS)

Papell, S. Stephen; Saiyed, Naseem H.; Nyland, Ted W.

1990-05-01

Liquid nitrogen mass flow rate, pressure drop, and temperature drop data were obtained for a series of multiple orifice Joule-Thomson devices, known as Visco Jets, over a wide range of flow resistance. The test rig used to acquire the data was designed to minimize heat transfer so that fluid expansion through the Visco Jets would be isenthalpic. The data include a range of fluid inlet pressures from 30 to 60 psia, fluid inlet temperatures from 118 to 164 R, outlet pressures from 2.8 to 55.8 psia, outlet temperatures from 117 to 162 R and flow rate from 0.04 to 4.0 lbm/hr of nitrogen. A flow rate equation supplied by the manufacturer was found to accurately predict single-phase (noncavitating) liquid nitrogen flow through the Visco Jets. For cavitating flow, the manufacturer's equation was found to be inaccurate. Greatly improved results were achieved with a modified version of the single-phase equation. The modification consists of a multiplication factor to the manufacturer's equation equal to one minus the downstream quality on an isenthalpic expansion of the fluid across the Visco Jet. For a range of flow resistances represented by Visco Jet Lohm ratings between 17,600 and 80,000, 100 percent of the single-phase data and 85 percent of the two-phase data fall within + or - 10 percent of predicted values.

Computation of high Reynolds number internal/external flows

NASA Technical Reports Server (NTRS)

Cline, M. C.; Wilmoth, R. G.

1981-01-01

A general, user oriented computer program, called VNAP2, has been developed to calculate high Reynolds number, internal/external flows. VNAP2 solves the two-dimensional, time-dependent Navier-Stokes equations. The turbulence is modeled with either a mixing-length, a one transport equation, or a two transport equation model. Interior grid points are computed using the explicit MacCormack scheme with special procedures to speed up the calculation in the fine grid. All boundary conditions are calculated using a reference plane characteristic scheme with the viscous terms treated as source terms. Several internal, and internal/external flow calculations are presented.

Computation of high Reynolds number internal/external flows

NASA Technical Reports Server (NTRS)

Cline, M. C.; Wilmoth, R. G.

1981-01-01

A general, user oriented computer program, called VNAP2, was developed to calculate high Reynolds number, internal/ external flows. The VNAP2 program solves the two dimensional, time dependent Navier-Stokes equations. The turbulence is modeled with either a mixing-length, a one transport equation, or a two transport equation model. Interior grid points are computed using the explicit MacCormack Scheme with special procedures to speed up the calculation in the fine grid. All boundary conditions are calculated using a reference plane characteristic scheme with the viscous terms treated as source terms. Several internal, external, and internal/external flow calculations are presented.

Computation of high Reynolds number internal/external flows

NASA Technical Reports Server (NTRS)

Cline, M. C.; Wilmoth, R. G.

1981-01-01

A general, user oriented computer program, called VNAF2, developed to calculate high Reynolds number internal/external flows is described. The program solves the two dimensional, time dependent Navier-Stokes equations. Turbulence is modeled with either a mixing length, a one transport equation, or a two transport equation model. Interior grid points are computed using the explicit MacCormack scheme with special procedures to speed up the calculation in the fine grid. All boundary conditions are calculated using a reference plane characteristic scheme with the viscous terms treated as source terms. Several internal, external, and internal/external flow calculations are presented.

A direct method for the solution of unsteady two-dimensional incompressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Ghia, K. N.; Osswald, G. A.; Ghia, U.

1983-01-01

The unsteady incompressible Navier-Stokes equations are formulated in terms of vorticity and stream function in generalized curvilinear orthogonal coordinates to facilitiate analysis of flow configurations with general geometries. The numerical method developed solves the conservative form of the transport equation using the alternating-direction implicit method, whereas the stream-function equation is solved by direct block Gaussian elimination. The method is applied to a model problem of flow over a back-step in a doubly infinite channel, using clustered conformal coordinates. One-dimensional stretching functions, dependent on the Reynolds number and the asymptotic behavior of the flow, are used to provide suitable grid distribution in the separation and reattachment regions, as well as in the inflow and outflow regions. The optimum grid distribution selected attempts to honor the multiple length scales of the separated-flow model problem. The asymptotic behavior of the finite-differenced transport equation near infinity is examined and the numerical method is carefully developed so as to lead to spatially second-order accurate wiggle-free solutions, i.e., with minimum dispersive error. Results have been obtained in the entire laminar range for the backstep channel and are in good agreement with the available experimental data for this flow problem.

Sensitivity Analysis for Steady State Groundwater Flow Using Adjoint Operators

NASA Astrophysics Data System (ADS)

Sykes, J. F.; Wilson, J. L.; Andrews, R. W.

1985-03-01

Adjoint sensitivity theory is currently being considered as a potential method for calculating the sensitivity of nuclear waste repository performance measures to the parameters of the system. For groundwater flow systems, performance measures of interest include piezometric heads in the vicinity of a waste site, velocities or travel time in aquifers, and mass discharge to biosphere points. The parameters include recharge-discharge rates, prescribed boundary heads or fluxes, formation thicknesses, and hydraulic conductivities. The derivative of a performance measure with respect to the system parameters is usually taken as a measure of sensitivity. To calculate sensitivities, adjoint sensitivity equations are formulated from the equations describing the primary problem. The solution of the primary problem and the adjoint sensitivity problem enables the determination of all of the required derivatives and hence related sensitivity coefficients. In this study, adjoint sensitivity theory is developed for equations of two-dimensional steady state flow in a confined aquifer. Both the primary flow equation and the adjoint sensitivity equation are solved using the Galerkin finite element method. The developed computer code is used to investigate the regional flow parameters of the Leadville Formation of the Paradox Basin in Utah. The results illustrate the sensitivity of calculated local heads to the boundary conditions. Alternatively, local velocity related performance measures are more sensitive to hydraulic conductivities.

The use of direct numerical simulation data in turbulence modeling

NASA Technical Reports Server (NTRS)

Mansour, N. N.

1991-01-01

Direct numerical simulations (DNS) of turbulent flows provide a complete data base to develop and to test turbulence models. In this article, the progress made in developing models for the dissipation rate equation is reviewed. New scaling arguments for the various terms in the dissipation rate equation were tested using data from DNS of homogeneous shear flows. Modifications to the epsilon-equation model that take into account near-wall effects were developed using DNS of turbulent channel flows. Testing of new models for flows under mean compression was carried out using data from DNS of isotropically compressed turbulence. In all of these studies the data from the simulations was essential in guiding the model development. The next generation of DNS will be at higher Reynolds numbers, and will undoubtedly lead to improved models for computations of flows of practical interest.

Direct modeling for computational fluid dynamics

NASA Astrophysics Data System (ADS)

Xu, Kun

2015-06-01

All fluid dynamic equations are valid under their modeling scales, such as the particle mean free path and mean collision time scale of the Boltzmann equation and the hydrodynamic scale of the Navier-Stokes (NS) equations. The current computational fluid dynamics (CFD) focuses on the numerical solution of partial differential equations (PDEs), and its aim is to get the accurate solution of these governing equations. Under such a CFD practice, it is hard to develop a unified scheme that covers flow physics from kinetic to hydrodynamic scales continuously because there is no such governing equation which could make a smooth transition from the Boltzmann to the NS modeling. The study of fluid dynamics needs to go beyond the traditional numerical partial differential equations. The emerging engineering applications, such as air-vehicle design for near-space flight and flow and heat transfer in micro-devices, do require further expansion of the concept of gas dynamics to a larger domain of physical reality, rather than the traditional distinguishable governing equations. At the current stage, the non-equilibrium flow physics has not yet been well explored or clearly understood due to the lack of appropriate tools. Unfortunately, under the current numerical PDE approach, it is hard to develop such a meaningful tool due to the absence of valid PDEs. In order to construct multiscale and multiphysics simulation methods similar to the modeling process of constructing the Boltzmann or the NS governing equations, the development of a numerical algorithm should be based on the first principle of physical modeling. In this paper, instead of following the traditional numerical PDE path, we introduce direct modeling as a principle for CFD algorithm development. Since all computations are conducted in a discretized space with limited cell resolution, the flow physics to be modeled has to be done in the mesh size and time step scales. Here, the CFD is more or less a direct construction of discrete numerical evolution equations, where the mesh size and time step will play dynamic roles in the modeling process. With the variation of the ratio between mesh size and local particle mean free path, the scheme will capture flow physics from the kinetic particle transport and collision to the hydrodynamic wave propagation. Based on the direct modeling, a continuous dynamics of flow motion will be captured in the unified gas-kinetic scheme. This scheme can be faithfully used to study the unexplored non-equilibrium flow physics in the transition regime.

Discharge rating equation and hydraulic characteristics of standard Denil fishways

USGS Publications Warehouse

Odeh, M.

2003-01-01

This paper introduces a new equation to predict discharge capacity in the commonly used Denil fishway using water surface elevation in the upstream reservoir and fishway width and slope as the independent variables. A dimensionless discharge coefficient based only on the physical slope of the fishway is introduced. The discharge equation is based on flow physics, dimensional analysis, and experiments with three full-scale fishways of different sizes. Hydraulic characteristics of flow inside these fishways are discussed. Water velocities decreased by more than 50% and remained relatively unchanged in the fully developed flow downstream of the vena contracta region, near the upstream baffle where fish exit the fishway. Engineers and biologists need to be aware of this fact and ensure that fish can negotiate the vena contracta velocities rather than velocities within the developed flow region only. Discharge capacity was directly proportional to the fishway width and slope. The new equation is a design tool for engineers and field biologists, especially when designing a fishway based on flow availability in conjunction with the swimming capabilities of target fish species.

Euler/Navier-Stokes calculations of transonic flow past fixed- and rotary-wing aircraft configurations

NASA Technical Reports Server (NTRS)

Deese, J. E.; Agarwal, R. K.

1989-01-01

Computational fluid dynamics has an increasingly important role in the design and analysis of aircraft as computer hardware becomes faster and algorithms become more efficient. Progress is being made in two directions: more complex and realistic configurations are being treated and algorithms based on higher approximations to the complete Navier-Stokes equations are being developed. The literature indicates that linear panel methods can model detailed, realistic aircraft geometries in flow regimes where this approximation is valid. As algorithms including higher approximations to the Navier-Stokes equations are developed, computer resource requirements increase rapidly. Generation of suitable grids become more difficult and the number of grid points required to resolve flow features of interest increases. Recently, the development of large vector computers has enabled researchers to attempt more complex geometries with Euler and Navier-Stokes algorithms. The results of calculations for transonic flow about a typical transport and fighter wing-body configuration using thin layer Navier-Stokes equations are described along with flow about helicopter rotor blades using both Euler/Navier-Stokes equations.

Cattaneo-Christov heat flux effect on hydromagnetic radiative Oldroyd-B liquid flow across a cone/wedge in the presence of cross-diffusion

NASA Astrophysics Data System (ADS)

Gnaneswara Reddy, M.

2018-01-01

The present article scrutinizes the prominent characteristics of the Cattaneo-Christov heat flux on magnetohydrodynamic Oldroyd-B radiative liquid flow over two different geometries. The effects of cross-diffusion are considered in the modeling of species and energy equations. Similarity transformations are employed to transmute the governing flow, species and energy equations into a set of nonlinear ordinary differential equations (ODEs) with the appropriate boundary conditions. The final system of dimensionless equations is resolved numerically by utilizing the R-K-Fehlberg numerical approach. The behaviors of all physical pertinent flow controlling variables on the three flow distributions are analyzed through plots. The obtained numerical results have been compared with earlier published work and reveal good agreement. The Deborah numbers γ1 and γ2 have quite opposite effects on velocity and energy fields. The increase in thermal relaxation parameter β corresponds to a decrease in the fluid temperature. This study has salient applications in heat and mass transfer manufacturing system processing for energy conversion.

Numerical simulation of axisymmetric turbulent flow in combustors and diffusors. Ph.D. Thesis. Final Report

NASA Technical Reports Server (NTRS)

Yung, Chain Nan

1988-01-01

A method for predicting turbulent flow in combustors and diffusers is developed. The Navier-Stokes equations, incorporating a turbulence kappa-epsilon model equation, were solved in a nonorthogonal curvilinear coordinate system. The solution applied the finite volume method to discretize the differential equations and utilized the SIMPLE algorithm iteratively to solve the differenced equations. A zonal grid method, wherein the flow field was divided into several subsections, was developed. This approach permitted different computational schemes to be used in the various zones. In addition, grid generation was made a more simple task. However, treatment of the zonal boundaries required special handling. Boundary overlap and interpolating techniques were used and an adjustment of the flow variables was required to assure conservation of mass, momentum and energy fluxes. The numerical accuracy was assessed using different finite differencing methods, i.e., hybrid, quadratic upwind and skew upwind, to represent the convection terms. Flows in different geometries of combustors and diffusers were simulated and results compared with experimental data and good agreement was obtained.

A lumped model of venting during thermal runaway in a cylindrical Lithium Cobalt Oxide lithium-ion cell

NASA Astrophysics Data System (ADS)

Coman, Paul T.; Rayman, Sean; White, Ralph E.

2016-03-01

This paper presents a mathematical model built for analyzing the intricate thermal behavior of a 18650 LCO (Lithium Cobalt Oxide) battery cell during thermal runaway when venting of the electrolyte and contents of the jelly roll (ejecta) is considered. The model consists of different ODEs (Ordinary Differential Equations) describing reaction rates and electrochemical reactions, as well as the isentropic flow equations for describing electrolyte venting. The results are validated against experimental findings from Golubkov et al. [1] [Andrey W. Golubkov, David Fuchs, Julian Wagner, Helmar Wiltsche, Christoph Stangl, Gisela Fauler, Gernot Voitice Alexander Thaler and Viktor Hacker, RSC Advances, 4:3633-3642, 2014] for two cases - with flow and without flow. The results show that if the isentropic flow equations are not included in the model, the thermal runaway is triggered prematurely at the point where venting should occur. This shows that the heat dissipation due to ejection of electrolyte and jelly roll contents has a significant contribution. When the flow equations are included, the model shows good agreement with the experiment and therefore proving the importance of including venting.

The stationary flow in a heterogeneous compliant vessel network

NASA Astrophysics Data System (ADS)

Filoche, Marcel; Florens, Magali

2011-09-01

We introduce a mathematical model of the hydrodynamic transport into systems consisting in a network of connected flexible pipes. In each pipe of the network, the flow is assumed to be steady and one-dimensional. The fluid-structure interaction is described through tube laws which relate the pipe diameter to the pressure difference across the pipe wall. We show that the resulting one-dimensional differential equation describing the flow in the pipe can be exactly integrated if one is able to estimate averages of the Reynolds number along the pipe. The differential equation is then transformed into a non linear scalar equation relating pressures at both ends of the pipe and the flow rate in the pipe. These equations are coupled throughout the network with mass conservation equations for the flow and zero pressure losses at the branching points of the network. This allows us to derive a general model for the computation of the flow into very large inhomogeneous networks consisting of several thousands of flexible pipes. This model is then applied to perform numerical simulations of the human lung airway system at exhalation. The topology of the system and the tube laws are taken from morphometric and physiological data in the literature. We find good qualitative and quantitative agreement between the simulation results and flow-volume loops measured in real patients. In particular, expiratory flow limitation which is an essential characteristic of forced expiration is found to be well reproduced by our simulations. Finally, a mathematical model of a pathology (Chronic Obstructive Pulmonary Disease) is introduced which allows us to quantitatively assess the influence of a moderate or severe alteration of the airway compliances.

Laminar and turbulent flow computations of Type 4 shock-shock interference aerothermal loads using unstructured grids

NASA Technical Reports Server (NTRS)

Vemaganti, Gururaja R.

1994-01-01

This report presents computations for the Type 4 shock-shock interference flow under laminar and turbulent conditions using unstructured grids. Mesh adaptation was accomplished by remeshing, refinement, and mesh movement. Two two-equation turbulence models were used to analyze turbulent flows. The mean flow governing equations and the turbulence governing equations are solved in a coupled manner. The solution algorithm and the details pertaining to its implementation on unstructured grids are described. Computations were performed at two different freestream Reynolds numbers at a freestream Mach number of 11. Effects of the variation in the impinging shock location are studied. The comparison of the results in terms of wall heat flux and wall pressure distributions is presented.

Implementation of Advanced Two Equation Turbulence Models in the USM3D Unstructured Flow Solver

NASA Technical Reports Server (NTRS)

Wang, Qun-Zhen; Massey, Steven J.; Abdol-Hamid, Khaled S.

2000-01-01

USM3D is a widely-used unstructured flow solver for simulating inviscid and viscous flows over complex geometries. The current version (version 5.0) of USM3D, however, does not have advanced turbulence models to accurately simulate complicated flow. We have implemented two modified versions of the original Jones and Launder k-epsilon "two-equation" turbulence model and the Girimaji algebraic Reynolds stress model in USM3D. Tests have been conducted for three flat plate boundary layer cases, a RAE2822 airfoil and an ONERA M6 wing. The results are compared with those from direct numerical simulation, empirical formulae, theoretical results, and the existing Spalart-Allmaras one-equation model.

A composite velocity procedure for the compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Khosla, P. K.; Rubin, S. G.

1982-01-01

A new boundary-layer relaxation procedure is presented. In the spirit of the theory of matched asymptotic expansions, a multiplicative composite of the appropriate velocity representations for the inviscid and viscous regions is prescribed. The resulting equations are structured so that far from the surface of the body the momentum equations lead to the Bernoulli relation for the pressure, while the continuity equation reduces to the familiar compressible potential equation. Close to the body surface, the governing equations and solution techniques are characteristic of those describing interacting boundary-layers; although, the full Navier-Stokes equations are considered here. Laminar flow calculations for the subsonic flow over an axisymmetric boattail simulator geometry are presented for a variety of Reynolds and Mach numbers. A strongly implicit solution method is applied for the coupled velocity components.

An exact solution for axial flow in cylindrically symmetric, steady-state detonation in polytropic explosive with an arbitrary rate of decomposition

NASA Astrophysics Data System (ADS)

Cowperthwaite, M.

1994-03-01

Methods of differential geometry and Bernoulli's equation, written as B=0, are used to develop a new approach for constructing an exact solution for axial flow in a classical, two-dimensional, ZND detonation wave in a polytropic explosive with an arbitrary rate of decomposition. This geometric approach is fundamentally different from the traditional approaches to this axial flow problem formulated by Wood and Kirkwood (WK) and Fickett and Davis (FD), and gives equations for the axial particle velocity (u), the sound speed (c), the pressure (p), and the density (ρ), that are expressed in terms of the detonation velocity (D), the extent of decomposition (λ), the polytropic index (K), and two nonideal parameters ɛ3 and ɛ1, and reduce to the equations for steady-state, one-dimensional detonation as ɛ3 and ɛ1 approach zero. In contrast to the FD approach, the equations for u and c are obtained from first integrals of a tangent vector à on (u,c,λ) space, and the invariant condition, ÃB=aB=0, bypasses the FD eigenvalue problem by defining ɛ3 in terms of the detonation velocity deficit D/D∞ and K. In contrast to the WK approach, the equations for p and ρ are obtained from equations expressing the conservation of axial momentum and energy. Because the equations for these flow variables are derived without using the conservation of mass, the axial radial particle velocity gradient (war) associated with the flow can be obtained from the continuity equation without making approximations. The relationship between ɛ1 and ɛ3 that closes the solution is obtained from equations expressing constraints imposed on the axial flow at the shock front by the axial and radial momentum equations, the curved shock and the decomposition rate law, and a particular solution is constructed from the ɛ1-ɛ3 relationship determined by a prescribed rate law and value of K. Properties of particular solutions are presented to provide a better understanding of two-dimensional detonation, and a new axial condition for detonation failure is used to show that detonation failure can occur before the curve relating D/D∞ to the axial radius of curvature of the shock (Sa) becomes infinite.

Numerical and experimental investigation of the 3D free surface flow in a model Pelton turbine

NASA Astrophysics Data System (ADS)

Fiereder, R.; Riemann, S.; Schilling, R.

2010-08-01

This investigation focuses on the numerical and experimental analysis of the 3D free surface flow in a Pelton turbine. In particular, two typical flow conditions occurring in a full scale Pelton turbine - a configuration with a straight inlet as well as a configuration with a 90 degree elbow upstream of the nozzle - are considered. Thereby, the effect of secondary flow due to the 90 degree bending of the upstream pipe on the characteristics of the jet is explored. The hybrid flow field consists of pure liquid flow within the conduit and free surface two component flow of the liquid jet emerging out of the nozzle into air. The numerical results are validated against experimental investigations performed in the laboratory of the Institute of Fluid Mechanics (FLM). For the numerical simulation of the flow the in-house unstructured fully parallelized finite volume solver solver3D is utilized. An advanced interface capturing model based on the classic Volume of Fluid method is applied. In order to ensure sharp interface resolution an additional convection term is added to the transport equation of the volume fraction. A collocated variable arrangement is used and the set of non-linear equations, containing fluid conservation equations and model equations for turbulence and volume fraction, are solved in a segregated manner. For pressure-velocity coupling the SIMPLE and PISO algorithms are implemented. Detailed analysis of the observed flow patterns in the jet and of the jet geometry are presented.

Blood Flow through an Open-Celled Foam

NASA Astrophysics Data System (ADS)

Ortega, Jason; Maitland, Duncan

2011-11-01

The Hazen-Dupuit-Darcy (HDD) equation is commonly used in engineering applications to model the pressure gradient of flow through a porous media. One major advantage of this equation is that it simplifies the complex geometric details of the porous media into two coefficients: the permeability, K, and form factor, C. However through this simplification, the flow details within the porous media are no longer accessible, making it difficult to study the phenomena that contribute to changes in K and C due to clotting of blood flow. To obtain a more detailed understanding of blood flow through a porous media, a direct assessment of the complex interstitial geometry and flow is required. In this study, we solve the Navier-Stokes equations for Newtonian and non-Newtonian blood flow through an open-celled foam geometry obtained from a micro-CT scan. The nominal strut size of the foam sample is of O(10e-5) m and the corresponding Reynolds number based upon this length ranges up to O(10). Fitting the pressure gradient vs. Darcy velocity data with the HDD equation demonstrates that both viscous and inertial forces play an important role in the flow through the foam at these Reynolds numbers. Recirculation zones are observed to form in the wake of the pore struts, producing regions of flow characterized by both low shear rates and long fluid residence times, factors of which have been shown in previous studies to promote blood clotting.

Stable Algorithm For Estimating Airdata From Flush Surface Pressure Measurements

NASA Technical Reports Server (NTRS)

Whitmore, Stephen, A. (Inventor); Cobleigh, Brent R. (Inventor); Haering, Edward A., Jr. (Inventor)

2001-01-01

An airdata estimation and evaluation system and method, including a stable algorithm for estimating airdata from nonintrusive surface pressure measurements. The airdata estimation and evaluation system is preferably implemented in a flush airdata sensing (FADS) system. The system and method of the present invention take a flow model equation and transform it into a triples formulation equation. The triples formulation equation eliminates the pressure related states from the flow model equation by strategically taking the differences of three surface pressures, known as triples. This triples formulation equation is then used to accurately estimate and compute vital airdata from nonintrusive surface pressure measurements.

Aerodynamic Design Optimization on Unstructured Meshes Using the Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Nielsen, Eric J.; Anderson, W. Kyle

1998-01-01

A discrete adjoint method is developed and demonstrated for aerodynamic design optimization on unstructured grids. The governing equations are the three-dimensional Reynolds-averaged Navier-Stokes equations coupled with a one-equation turbulence model. A discussion of the numerical implementation of the flow and adjoint equations is presented. Both compressible and incompressible solvers are differentiated and the accuracy of the sensitivity derivatives is verified by comparing with gradients obtained using finite differences. Several simplifying approximations to the complete linearization of the residual are also presented, and the resulting accuracy of the derivatives is examined. Demonstration optimizations for both compressible and incompressible flows are given.

Turbulent Flow Validation in the Helios Strand Solver

DTIC Science & Technology

2014-01-07

usual (̄) notation is omitted for simplicity). The pressure is obtained from the ideal gas equation of state given as: P = (γ−1) [ Et − 1 2 ρ ( u2 + v2...2. SA-RANS System The state vector and flux vectors including those of the SA model equation for three-dimensional flow are explicitly given as: u...number, PrT is the turbulent Prandtl number, and T is the temperature. The ideal gas equation of state , p = ρRT is used to close the equations . IV.A

Exact solutions of the Navier-Stokes equations generalized for flow in porous media

NASA Astrophysics Data System (ADS)

Daly, Edoardo; Basser, Hossein; Rudman, Murray

2018-05-01

Flow of Newtonian fluids in porous media is often modelled using a generalized version of the full non-linear Navier-Stokes equations that include additional terms describing the resistance to flow due to the porous matrix. Because this formulation is becoming increasingly popular in numerical models, exact solutions are required as a benchmark of numerical codes. The contribution of this study is to provide a number of non-trivial exact solutions of the generalized form of the Navier-Stokes equations for parallel flow in porous media. Steady-state solutions are derived in the case of flows in a medium with constant permeability along the main direction of flow and a constant cross-stream velocity in the case of both linear and non-linear drag. Solutions are also presented for cases in which the permeability changes in the direction normal to the main flow. An unsteady solution for a flow with velocity driven by a time-periodic pressure gradient is also derived. These solutions form a basis for validating computational models across a wide range of Reynolds and Darcy numbers.

Becoming angular momentum density flow through nonlinear mass transfer into a gravitating spheroidal body

NASA Astrophysics Data System (ADS)

Krot, A. M.

2009-04-01

A statistical theory for a cosmological body forming based on the spheroidal body model has been proposed in the works [1]-[4]. This work studies a slowly evolving process of gravitational condensation of a spheroidal body from an infinitely distributed gas-dust substance in space. The equation for an initial evolution of mass density function of a gas-dust cloud is considered here. It is found this equation coincides completely with the analogous equation for a slowly gravitational compressed spheroidal body [5]. A conductive flow in dissipative systems was investigated by I. Prigogine in his works (see, for example, [6], [7]). As it has been found in [2], [5], there exists a conductive antidiffusion flow in a slowly compressible gravitating spheroidal body. Applying the equation of continuity to this conductive flow density we obtain a linear antidiffusion equation [5]. However, if an intensity of conductive flow density increases sharply then the linear antidiffusion equation becomes a nonlinear one. Really, it was pointed to [6] analogous linear equations of diffusion or thermal conductivity transform in nonlinear equations respectively. In this case, the equation of continuity describes a nonlinear mass flow being a source of instabilities into a gravitating spheroidal body because the gravitational compression factor G is a function of not only time but a mass density. Using integral substitution we can reduce a nonlinear antidiffusion equation to the linear antidiffusion equation relative to a new function. If the factor G can be considered as a specific angular momentum then the new function is an angular momentum density. Thus, a nonlinear momentum density flow induces a flow of angular momentum density because streamlines of moving continuous substance come close into a gravitating spheroidal body. Really, the streamline approach leads to more tight interactions of "liquid particles" that implies a superposition of their specific angular momentums. This superposition forms an antidiffusion flow of an angular momentum density into a gravitating spheroidal body. References: [1] Krot, A.M. The statistical model of gravitational interaction of particles. Achievement in Modern Radioelectronics (spec.issue"Cosmic Radiophysics", Moscow), 1996, no.8, pp. 66-81 (in Russian). [2] Krot, A.M. Statistical description of gravitational field: a new approach. Proc. SPIE's 14th Annual Intern.Symp. "AeroSense", Orlando, Florida, USA, 2000, vol.4038, pp.1318-1329. [3] Krot, A.M. The statistical model of rotating and gravitating spheroidal body with the point of view of general relativity. Proc.35th COSPAR Scientific Assembly, Paris, France, 2004, Abstract A-00162. [4] Krot, A. The statistical approach to exploring formation of Solar system. Proc.EGU General Assembly, Vienna, Austria, 2006, Geophys.Res.Abstracts, vol.8, A-00216; SRef-ID: 1607-7962/gra/. [5] Krot, A.M. A statistical approach to investigate the formation of the solar system. Chaos, Solitons and Fractals, 2008, doi:10.1016/j.chaos.2008.06.014. [6] Glansdorff, P. and Prigogine, I. Thermodynamic Theory of Structure, Stability and Fluctuations. London, 1971. [7] Nicolis, G. and Prigogine, I. Self-organization in Nonequilibrium Systems:From Dissipative Structures to Order through Fluctuation. John Willey and Sons, New York etc., 1977.

Solution of the Euler equations with viscous-inviscid interaction for high Reynolds number transonic flow past wing/body configurations

NASA Technical Reports Server (NTRS)

Koenig, Keith

1986-01-01

The theoretical and numerical bases of a program for the solution of the Euler equations with viscous-inviscid interaction for high Reynolds number transonic flow past wing/body configurations are explained. The emphasis is upon the logic behind the equation development. The program is fully detailed so that the user can quickly become familiar with its operation.

A boundary integral approach in primitive variables for free surface flows

NASA Astrophysics Data System (ADS)

Casciola, C.; Piva, R.

The boundary integral formulation, very efficient for free surface potential flows, was considered for its possible extension to rotational flows either inviscid or viscous. We first analyze a general formulation for unsteady Navier-Stokes equations in primitive variables, which reduces to a representation for the Euler equations in the limiting case of Reynolds infinity. A first simplified model for rotational flows, obtained by decoupling kinematics and dynamics, reduces the integral equations to a known kinematical form whose mathematical and numerical properties have been studied. The dynamics equations to complete the model are obtained for the free surface and the wake. A simple and efficient scheme for the study of the non linear evolution of the wave system and its interaction with the body wake is presented. A steady state version for the calculation of the wave resistance is also reported. A second model was proposed for the simulation of rotational separated regions, by coupling the integral equations in velocity with an integral equation for the vorticity at the body boundary. The same procedure may be extended to include the diffusion of the vorticity in the flowfield. The vortex shedding from a cylindrical body in unsteady motion is discussed, as a first application of the model.

A novel method to measure regional muscle blood flow continuously using NIRS kinetics information

PubMed Central

Nioka, Shoko; Kime, Ryotaro; Sunar, Ulas; Im, Joohee; Izzetoglu, Meltem; Zhang, Jun; Alacam, Burak; Chance, Britton

2006-01-01

Background This article introduces a novel method to continuously monitor regional muscle blood flow by using Near Infrared Spectroscopy (NIRS). We demonstrate the feasibility of the new method in two ways: (1) by applying this new method of determining blood flow to experimental NIRS data during exercise and ischemia; and, (2) by simulating muscle oxygenation and blood flow values using these newly developed equations during recovery from exercise and ischemia. Methods Deoxy (Hb) and oxyhemoglobin (HbO2), located in the blood ofthe skeletal muscle, carry two internal relationships between blood flow and oxygen consumption. One is a mass transfer principle and the other describes a relationship between oxygen consumption and Hb kinetics in a two-compartment model. To monitor blood flow continuously, we transfer these two relationships into two equations and calculate the blood flow with the differential information of HbO2 and Hb. In addition, these equations are used to simulate the relationship between blood flow and reoxygenation kinetics after cuff ischemia and a light exercise. Nine healthy subjects volunteered for the cuff ischemia, light arm exercise and arm exercise with cuff ischemia for the experimental study. Results Analysis of experimental data of both cuff ischemia and light exercise using the new equations show greater blood flow (four to six times more than resting values) during recovery, agreeing with previous findings. Further, the simulation and experimental studies of cuff ischemia and light exercise agree with each other. Conclusion We demonstrate the accuracy of this new method by showing that the blood flow obtained from the method agrees with previous data as well as with simulated data. We conclude that this novel continuous blood flow monitoring method can provide blood flow information non-invasively with NIRS. PMID:16704736

Experimental study on interfacial area transport in downward two-phase flow

NASA Astrophysics Data System (ADS)

Wang, Guanyi

In view of the importance of two group interfacial area transport equations and lack of corresponding accurate downward flow database that can reveal two group interfacial area transport, a systematic database for adiabatic, air-water, vertically downward two-phase flow in a round pipe with inner diameter of 25.4 mm was collected to gain an insight of interfacial structure and provide benchmarking data for two-group interfacial area transport models. A four-sensor conductivity probe was used to measure the local two phase flow parameters and data was collected with data sampling frequency much higher than conventional data sampling frequency to ensure the accuracy. Axial development of local flow parameter profiles including void fraction, interfacial area concentration, and Sauter mean diameter were presented. Drastic inter-group transfer of void fraction and interfacial area was observed at bubbly to slug transition flow. And the wall peaked interfacial area concentration profiles were observed in churn-turbulent flow. The importance of local data about these phenomenon on flow structure prediction and interfacial area transport equation benchmark was analyzed. Bedsides, in order to investigate the effect of inlet conditions, all experiments were repeated after installing the flow straightening facility, and the results were briefly analyzed. In order to check the accuracy of current data, the experiment results were cross-checked with rotameter measurement as well as drift-flux model prediction, the averaged error is less than 15%. Current models for two-group interfacial area transport equation were evaluated using these data. The results show that two-group interfacial area transport equations with current models can predict most flow conditions with error less than 20%, except some bubbly to slug transition flow conditions and some churn-turbulent flow conditions. The disagreement between models and experiments could result from underestimate of inter-group void transfer.

Elementary Hemodynamic Principles Based on Modified Bernoulli's Equation.

ERIC Educational Resources Information Center

Badeer, Henry S.

1985-01-01

Develops and expands basic concepts of Bernoulli's equation as it applies to vascular hemodynamics. Simple models are used to illustrate gravitational potential energy, steady nonturbulent flow, pump-driven streamline flow, and other areas. Relationships to the circulatory system are also discussed. (DH)

A theoretical study of the acoustic impedance of orifices in the presence of a steady grazing flow

NASA Technical Reports Server (NTRS)

Rice, E. J.

1976-01-01

An analysis of the oscillatory fluid flow in the vicinity of a circular orifice with a steady grazing flow is presented. The study is similar to that of Hersh and Rogers but with the addition of the grazing flow. Starting from the momentum and continuity equations, a considerably simplified system of partial differential equations is developed with the assumption that the flow can be described by an oscillatory motion superimposed upon the known steady flow. The equations are seen to be linear in the region where the grazing flow effects are dominant, and a solution and the resulting orifice impedance are presented for this region. The nonlinearity appears to be unimportant for the usual conditions found in aircraft noise suppressors. Some preliminary conclusions of the study are that orifice resistance is directly proportional to grazing flow velocity (known previously from experimental data) and that the orifice inductive (mass reactance) end correction is not a function of grazing flow. This latter conclusion is contrary to the widely held notion that grazing flow removes the effect of the orifice inductive end correction. This conclusion also implies that the experimentally observed total inductance reduction with grazing flow might be in the flow within the orifice rather than in the end correction.

A unified gas-kinetic scheme for continuum and rarefied flows IV: Full Boltzmann and model equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Chang, E-mail: cliuaa@ust.hk; Xu, Kun, E-mail: makxu@ust.hk; Sun, Quanhua, E-mail: qsun@imech.ac.cn

Fluid dynamic equations are valid in their respective modeling scales, such as the particle mean free path scale of the Boltzmann equation and the hydrodynamic scale of the Navier–Stokes (NS) equations. With a variation of the modeling scales, theoretically there should have a continuous spectrum of fluid dynamic equations. Even though the Boltzmann equation is claimed to be valid in all scales, many Boltzmann solvers, including direct simulation Monte Carlo method, require the cell resolution to the order of particle mean free path scale. Therefore, they are still single scale methods. In order to study multiscale flow evolution efficiently, themore » dynamics in the computational fluid has to be changed with the scales. A direct modeling of flow physics with a changeable scale may become an appropriate approach. The unified gas-kinetic scheme (UGKS) is a direct modeling method in the mesh size scale, and its underlying flow physics depends on the resolution of the cell size relative to the particle mean free path. The cell size of UGKS is not limited by the particle mean free path. With the variation of the ratio between the numerical cell size and local particle mean free path, the UGKS recovers the flow dynamics from the particle transport and collision in the kinetic scale to the wave propagation in the hydrodynamic scale. The previous UGKS is mostly constructed from the evolution solution of kinetic model equations. Even though the UGKS is very accurate and effective in the low transition and continuum flow regimes with the time step being much larger than the particle mean free time, it still has space to develop more accurate flow solver in the region, where the time step is comparable with the local particle mean free time. In such a scale, there is dynamic difference from the full Boltzmann collision term and the model equations. This work is about the further development of the UGKS with the implementation of the full Boltzmann collision term in the region where it is needed. The central ingredient of the UGKS is the coupled treatment of particle transport and collision in the flux evaluation across a cell interface, where a continuous flow dynamics from kinetic to hydrodynamic scales is modeled. The newly developed UGKS has the asymptotic preserving (AP) property of recovering the NS solutions in the continuum flow regime, and the full Boltzmann solution in the rarefied regime. In the mostly unexplored transition regime, the UGKS itself provides a valuable tool for the non-equilibrium flow study. The mathematical properties of the scheme, such as stability, accuracy, and the asymptotic preserving, will be analyzed in this paper as well.« less

Effectiveness of the New Hampshire stream-gaging network in providing regional streamflow information

USGS Publications Warehouse

Olson, Scott A.

2003-01-01

The stream-gaging network in New Hampshire was analyzed for its effectiveness in providing regional information on peak-flood flow, mean-flow, and low-flow frequency. The data available for analysis were from stream-gaging stations in New Hampshire and selected stations in adjacent States. The principles of generalized-least-squares regression analysis were applied to develop regional regression equations that relate streamflow-frequency characteristics to watershed characteristics. Regression equations were developed for (1) the instantaneous peak flow with a 100-year recurrence interval, (2) the mean-annual flow, and (3) the 7-day, 10-year low flow. Active and discontinued stream-gaging stations with 10 or more years of flow data were used to develop the regression equations. Each stream-gaging station in the network was evaluated and ranked on the basis of how much the data from that station contributed to the cost-weighted sampling-error component of the regression equation. The potential effect of data from proposed and new stream-gaging stations on the sampling error also was evaluated. The stream-gaging network was evaluated for conditions in water year 2000 and for estimated conditions under various network strategies if an additional 5 years and 20 years of streamflow data were collected. The effectiveness of the stream-gaging network in providing regional streamflow information could be improved for all three flow characteristics with the collection of additional flow data, both temporally and spatially. With additional years of data collection, the greatest reduction in the average sampling error of the regional regression equations was found for the peak- and low-flow characteristics. In general, additional data collection at stream-gaging stations with unregulated flow, relatively short-term record (less than 20 years), and drainage areas smaller than 45 square miles contributed the largest cost-weighted reduction to the average sampling error of the regional estimating equations. The results of the network analyses can be used to prioritize the continued operation of active stations, the reactivation of discontinued stations, or the activation of new stations to maximize the regional information content provided by the stream-gaging network. Final decisions regarding altering the New Hampshire stream-gaging network would require the consideration of the many uses of the streamflow data serving local, State, and Federal interests.

Numerical Simulation of Combustion and Rotor-Stator Interaction in a Turbine Combustor

DOE PAGES

Isvoranu, Dragos D.; Cizmas, Paul G. A.

2003-01-01

This article presents the development of a numerical algorithm for the computation of flow and combustion in a turbine combustor. The flow and combustion are modeled by the Reynolds-averaged Navier-Stokes equations coupled with the species-conservation equations. The chemistry model used herein is a two-step, global, finite-rate combustion model for methane and combustion gases. The governing equations are written in the strong conservation form and solved using a fully implicit, finite-difference approximation. The gas dynamics and chemistry equations are fully decoupled. A correction technique has been developed to enforce the conservation of mass fractions. The numerical algorithm developed herein has beenmore » used to investigate the flow and combustion in a one-stage turbine combustor.« less

Linear and nonlinear stability criteria for compressible MHD flows in a gravitational field

NASA Astrophysics Data System (ADS)

Moawad, S. M.; Moawad

2013-10-01

The equilibrium and stability properties of ideal magnetohydrodynamics (MHD) of compressible flow in a gravitational field with a translational symmetry are investigated. Variational principles for the steady-state equations are formulated. The MHD equilibrium equations are obtained as critical points of a conserved Lyapunov functional. This functional consists of the sum of the total energy, the mass, the circulation along field lines (cross helicity), the momentum, and the magnetic helicity. In the unperturbed case, the equilibrium states satisfy a nonlinear second-order partial differential equation (PDE) associated with hydrodynamic Bernoulli law. The PDE can be an elliptic or a parabolic equation depending on increasing the poloidal flow speed. Linear and nonlinear Lyapunov stability conditions under translational symmetric perturbations are established for the equilibrium states.

Transonic flow solutions using a composite velocity procedure for potential, Euler and RNS equations

NASA Technical Reports Server (NTRS)

Gordnier, R. E.; Rubin, S. G.

1986-01-01

Solutions for transonic viscous and inviscid flows using a composite velocity procedure are presented. The velocity components of the compressible flow equations are written in terms of a multiplicative composite consisting of a viscous or rotational velocity and an inviscid, irrotational, potential-like function. This provides for an efficient solution procedure that is locally representative of both asymptotic inviscid and boundary layer theories. A modified conservative form of the axial momentum equation that is required to obtain rotational solutions in the inviscid region is presented and a combined conservation/nonconservation form is applied for evaluation of the reduced Navier-Stokes (RNS), Euler and potential equations. A variety of results is presented and the effects of the approximations on entropy production, shock capturing, and viscous interaction are discussed.

Selected topics of fluid mechanics

USGS Publications Warehouse

Kindsvater, Carl E.

1958-01-01

The fundamental equations of fluid mechanics are specific expressions of the principles of motion which are ascribed to Isaac Newton. Thus, the equations which form the framework of applied fluid mechanics or hydraulics are, in addition to the equation of continuity, the Newtonian equations of energy and momentum. These basic relationships are also the foundations of river hydraulics. The fundamental equations are developed in this report with sufficient rigor to support critical examinations of their applicability to most problems met by hydraulic engineers of the Water Resources Division of the United States Geological Survey. Physical concepts are emphasized, and mathematical procedures are the simplest consistent with the specific requirements of the derivations. In lieu of numerical examples, analogies, and alternative procedures, this treatment stresses a brief methodical exposition of the essential principles. An important objective of this report is to prepare the user to read the literature of the science. Thus, it begins With a basic vocabulary of technical symbols, terms, and concepts. Throughout, emphasis is placed on the language of modern fluid mechanics as it pertains to hydraulic engineering. The basic differential and integral equations of simple fluid motion are derived, and these equations are, in turn, used to describe the essential characteristics of hydrostatics and piezometry. The one-dimensional equations of continuity and motion are defined and are used to derive the general discharge equation. The flow net is described as a means of demonstrating significant characteristics of two-dimensional irrotational flow patterns. A typical flow net is examined in detail. The influence of fluid viscosity is described as an obstacle to the derivation of general, integral equations of motion. It is observed that the part played by viscosity is one which is usually dependent on experimental evaluation. It follows that the dimensionless ratios known as the Euler, Froude, Reynolds, Weber, and Cauchy numbers are defined as essential tools for interpreting and using experimental data. The derivations of the energy and momentum equations are treated in detail. One-dimensional equations for steady nonuniform flow are developed, and the restrictions applicable to the equations are emphasized. Conditions of uniform and gradually varied flow are discussed, and the origin of the Chezy equation is examined in relation to both the energy and the momentum equations. The inadequacy of all uniform-flow equations as a means of describing gradually varied flow is explained. Thus, one of the definitive problems of river hydraulics is analyzed in the light of present knowledge. This report is the outgrowth of a series of short schools conducted during the spring and summer of 1953 for engineers of the Surface Water Branch, Water Resources Division, U. S. Geological Survey. The topics considered are essentially the same as the topics selected for inclusion in the schools. However, in order that they might serve better as a guide and outline for informal study, the arrangement of the writer's original lecture notes has been considerably altered. The purpose of the report, like the purpose of the schools which inspired it, is to build a simple but strong framework of the fundamentals of fluid mechanics. It is believed that this framework is capable of supporting a detailed analysis of most of the practical problems met by the engineers of the Geological Survey. It is hoped that the least accomplishment of this work will be to inspire the reader with the confidence and desire to read more of the recent and current technical literature of modern fluid mechanics.

Modelling vortex-induced fluid-structure interaction.

PubMed

Benaroya, Haym; Gabbai, Rene D

2008-04-13

The principal goal of this research is developing physics-based, reduced-order, analytical models of nonlinear fluid-structure interactions associated with offshore structures. Our primary focus is to generalize the Hamilton's variational framework so that systems of flow-oscillator equations can be derived from first principles. This is an extension of earlier work that led to a single energy equation describing the fluid-structure interaction. It is demonstrated here that flow-oscillator models are a subclass of the general, physical-based framework. A flow-oscillator model is a reduced-order mechanical model, generally comprising two mechanical oscillators, one modelling the structural oscillation and the other a nonlinear oscillator representing the fluid behaviour coupled to the structural motion.Reduced-order analytical model development continues to be carried out using a Hamilton's principle-based variational approach. This provides flexibility in the long run for generalizing the modelling paradigm to complex, three-dimensional problems with multiple degrees of freedom, although such extension is very difficult. As both experimental and analytical capabilities advance, the critical research path to developing and implementing fluid-structure interaction models entails-formulating generalized equations of motion, as a superset of the flow-oscillator models; and-developing experimentally derived, semi-analytical functions to describe key terms in the governing equations of motion. The developed variational approach yields a system of governing equations. This will allow modelling of multiple d.f. systems. The extensions derived generalize the Hamilton's variational formulation for such problems. The Navier-Stokes equations are derived and coupled to the structural oscillator. This general model has been shown to be a superset of the flow-oscillator model. Based on different assumptions, one can derive a variety of flow-oscillator models.

Development of a nonlinear unsteady transonic flow theory

NASA Technical Reports Server (NTRS)

Stahara, S. S.; Spreiter, J. R.

1973-01-01

A nonlinear, unsteady, small-disturbance theory capable of predicting inviscid transonic flows about aerodynamic configurations undergoing both rigid body and elastic oscillations was developed. The theory is based on the concept of dividing the flow into steady and unsteady components and then solving, by method of local linearization, the coupled differential equation for unsteady surface pressure distribution. The equations, valid at all frequencies, were derived for two-dimensional flows, numerical results, were obtained for two classses of airfoils and two types of oscillatory motions.

Mathematical modelling of surface water-groundwater flow and salinity interactions in the coastal zone

NASA Astrophysics Data System (ADS)

Spanoudaki, Katerina; Kampanis, Nikolaos A.

2014-05-01

Coastal areas are the most densely-populated areas in the world. Consequently water demand is high, posing great pressure on fresh water resources. Climatic change and its direct impacts on meteorological variables (e.g. precipitation) and indirect impact on sea level rise, as well as anthropogenic pressures (e.g. groundwater abstraction), are strong drivers causing groundwater salinisation and subsequently affecting coastal wetlands salinity with adverse effects on the corresponding ecosystems. Coastal zones are a difficult hydrologic environment to represent with a mathematical model due to the large number of contributing hydrologic processes and variable-density flow conditions. Simulation of sea level rise and tidal effects on aquifer salinisation and accurate prediction of interactions between coastal waters, groundwater and neighbouring wetlands requires the use of integrated surface water-groundwater models. In the past few decades several computer codes have been developed to simulate coupled surface and groundwater flow. In these numerical models surface water flow is usually described by the 1-D Saint Venant equations (e.g. Swain and Wexler, 1996) or the 2D shallow water equations (e.g. Liang et al., 2007). Further simplified equations, such as the diffusion and kinematic wave approximations to the Saint Venant equations, are also employed for the description of 2D overland flow and 1D stream flow (e.g. Gunduz and Aral, 2005). However, for coastal bays, estuaries and wetlands it is often desirable to solve the 3D shallow water equations to simulate surface water flow. This is the case e.g. for wind-driven flows or density-stratified flows. Furthermore, most integrated models are based on the assumption of constant fluid density and therefore their applicability to coastal regions is questionable. Thus, most of the existing codes are not well-suited to represent surface water-groundwater interactions in coastal areas. To this end, the 3D integrated surface water-groundwater model IRENE (Spanoudaki et al., 2009; Spanoudaki, 2010) has been modified in order to simulate surface water-groundwater flow and salinity interactions in the coastal zone. IRENE, in its original form, couples the 3D, non-steady state Navier-Stokes equations, after Reynolds averaging and with the assumption of hydrostatic pressure distribution, to the equations describing 3D saturated groundwater flow of constant density. A semi-implicit finite difference scheme is used to solve the surface water flow equations, while a fully implicit finite difference scheme is used for the groundwater equations. Pollution interactions are simulated by coupling the advection-diffusion equation describing the fate and transport of contaminants introduced in a 3D turbulent flow field to the partial differential equation describing the fate and transport of contaminants in 3D transient groundwater flow systems. The model has been further developed to include the effects of density variations on surface water and groundwater flow, while the already built-in solute transport capabilities are used to simulate salinity interactions. Initial results show that IRENE can accurately predict surface water-groundwater flow and salinity interactions in coastal areas. Important research issues that can be investigated using IRENE include: (a) sea level rise and tidal effects on aquifer salinisation and the configuration of the saltwater wedge, (b) the effects of surface water-groundwater interaction on salinity increase of coastal wetlands and (c) the estimation of the location and magnitude of groundwater discharge to coasts. Acknowledgement The work presented in this paper has been funded by the Greek State Scholarships Foundation (IKY), Fellowships of Excellence for Postdoctoral Studies (Siemens Program), 'A simulation-optimization model for assessing the best practices for the protection of surface water and groundwater in the coastal zone', (2013 - 2015). References Gunduz, O. and Aral, M.M. (2005). River networks and groundwater flow: a simultaneous solution of a coupled system. Journal of Hydrology 301 (1-4), 216-234. Liang, D., Falconer, R.A. and Lin, B. (2007). Coupling surface and subsurface flows in a depth-averaged flood wave model. Journal of Hydrology 337, 147-158. Spanoudaki, K., Stamou, A.I. and Nanou-Giannarou, A. (2009). Development and verification of a 3-D integrated surface water-groundwater model. Journal of Hydrology, 375 (3-4), 410-427. Spanoudaki, K. (2010). Integrated numerical modelling of surface water groundwater systems (in Greek). Ph.D. Thesis, National Technical University of Athens, Greece. Swain, E.D. and Wexler, E.J. (1996). A coupled surface water and groundwater flow model (Modbranch) for simulation of stream-aquifer interaction. United States Geological Survey, Techniques of Water Resources Investigations (Book 6, Chapter A6).

Development of linear projecting in studies of non-linear flow. Acoustic heating induced by non-periodic sound

NASA Astrophysics Data System (ADS)

Perelomova, Anna

2006-08-01

The equation of energy balance is subdivided into two dynamics equations, one describing evolution of the dominative sound, and the second one responsible for acoustic heating. The first one is the famous KZK equation, and the second one is a novel equation governing acoustic heating. The novel dynamic equation considers both periodic and non-periodic sound. Quasi-plane geometry of flow is supposed. Subdividing is provided on the base of specific links of every mode. Media with arbitrary thermic T(p,ρ) and caloric e(p,ρ) equations of state are considered. Individual roles of thermal conductivity and viscosity in the heating induced by aperiodic sound in the ideal gases and media different from ideal gases are discussed.

Regional regression equations for the estimation of selected monthly low-flow duration and frequency statistics at ungaged sites on streams in New Jersey

USGS Publications Warehouse

Watson, Kara M.; McHugh, Amy R.

2014-01-01

Regional regression equations were developed for estimating monthly flow-duration and monthly low-flow frequency statistics for ungaged streams in Coastal Plain and non-coastal regions of New Jersey for baseline and current land- and water-use conditions. The equations were developed to estimate 87 different streamflow statistics, which include the monthly 99-, 90-, 85-, 75-, 50-, and 25-percentile flow-durations of the minimum 1-day daily flow; the August–September 99-, 90-, and 75-percentile minimum 1-day daily flow; and the monthly 7-day, 10-year (M7D10Y) low-flow frequency. These 87 streamflow statistics were computed for 41 continuous-record streamflow-gaging stations (streamgages) with 20 or more years of record and 167 low-flow partial-record stations in New Jersey with 10 or more streamflow measurements. The regression analyses used to develop equations to estimate selected streamflow statistics were performed by testing the relation between flow-duration statistics and low-flow frequency statistics for 32 basin characteristics (physical characteristics, land use, surficial geology, and climate) at the 41 streamgages and 167 low-flow partial-record stations. The regression analyses determined drainage area, soil permeability, average April precipitation, average June precipitation, and percent storage (water bodies and wetlands) were the significant explanatory variables for estimating the selected flow-duration and low-flow frequency statistics. Streamflow estimates were computed for two land- and water-use conditions in New Jersey—land- and water-use during the baseline period of record (defined as the years a streamgage had little to no change in development and water use) and current land- and water-use conditions (1989–2008)—for each selected station using data collected through water year 2008. The baseline period of record is representative of a period when the basin was unaffected by change in development. The current period is representative of the increased development of the last 20 years (1989–2008). The two different land- and water-use conditions were used as surrogates for development to determine whether there have been changes in low-flow statistics as a result of changes in development over time. The State was divided into two low-flow regression regions, the Coastal Plain and the non-coastal region, in order to improve the accuracy of the regression equations. The left-censored parametric survival regression method was used for the analyses to account for streamgages and partial-record stations that had zero flow values for some of the statistics. The average standard error of estimate for the 348 regression equations ranged from 16 to 340 percent. These regression equations and basin characteristics are presented in the U.S. Geological Survey (USGS) StreamStats Web-based geographic information system application. This tool allows users to click on an ungaged site on a stream in New Jersey and get the estimated flow-duration and low-flow frequency statistics. Additionally, the user can click on a streamgage or partial-record station and get the “at-site” streamflow statistics. The low-flow characteristics of a stream ultimately affect the use of the stream by humans. Specific information on the low-flow characteristics of streams is essential to water managers who deal with problems related to municipal and industrial water supply, fish and wildlife conservation, and dilution of wastewater.

Techniques for Estimating the Magnitude and Frequency of Peak Flows on Small Streams in Minnesota Based on Data through Water Year 2005

USGS Publications Warehouse

Lorenz, David L.; Sanocki, Chris A.; Kocian, Matthew J.

2010-01-01

Knowledge of the peak flow of floods of a given recurrence interval is essential for regulation and planning of water resources and for design of bridges, culverts, and dams along Minnesota's rivers and streams. Statistical techniques are needed to estimate peak flow at ungaged sites because long-term streamflow records are available at relatively few places. Because of the need to have up-to-date peak-flow frequency information in order to estimate peak flows at ungaged sites, the U.S. Geological Survey (USGS) conducted a peak-flow frequency study in cooperation with the Minnesota Department of Transportation and the Minnesota Pollution Control Agency. Estimates of peak-flow magnitudes for 1.5-, 2-, 5-, 10-, 25-, 50-, 100-, and 500-year recurrence intervals are presented for 330 streamflow-gaging stations in Minnesota and adjacent areas in Iowa and South Dakota based on data through water year 2005. The peak-flow frequency information was subsequently used in regression analyses to develop equations relating peak flows for selected recurrence intervals to various basin and climatic characteristics. Two statistically derived techniques-regional regression equation and region of influence regression-can be used to estimate peak flow on ungaged streams smaller than 3,000 square miles in Minnesota. Regional regression equations were developed for selected recurrence intervals in each of six regions in Minnesota: A (northwestern), B (north central and east central), C (northeastern), D (west central and south central), E (southwestern), and F (southeastern). The regression equations can be used to estimate peak flows at ungaged sites. The region of influence regression technique dynamically selects streamflow-gaging stations with characteristics similar to a site of interest. Thus, the region of influence regression technique allows use of a potentially unique set of gaging stations for estimating peak flow at each site of interest. Two methods of selecting streamflow-gaging stations, similarity and proximity, can be used for the region of influence regression technique. The regional regression equation technique is the preferred technique as an estimate of peak flow in all six regions for ungaged sites. The region of influence regression technique is not appropriate for regions C, E, and F because the interrelations of some characteristics of those regions do not agree with the interrelations throughout the rest of the State. Both the similarity and proximity methods for the region of influence technique can be used in the other regions (A, B, and D) to provide additional estimates of peak flow. The peak-flow-frequency estimates and basin characteristics for selected streamflow-gaging stations and regional peak-flow regression equations are included in this report.

HST3D; a computer code for simulation of heat and solute transport in three-dimensional ground-water flow systems

USGS Publications Warehouse

Kipp, K.L.

1987-01-01

The Heat- and Soil-Transport Program (HST3D) simulates groundwater flow and associated heat and solute transport in three dimensions. The three governing equations are coupled through the interstitial pore velocity, the dependence of the fluid density on pressure, temperature, the solute-mass fraction , and the dependence of the fluid viscosity on temperature and solute-mass fraction. The solute transport equation is for only a single, solute species with possible linear equilibrium sorption and linear decay. Finite difference techniques are used to discretize the governing equations using a point-distributed grid. The flow-, heat- and solute-transport equations are solved , in turn, after a particle Gauss-reduction scheme is used to modify them. The modified equations are more tightly coupled and have better stability for the numerical solutions. The basic source-sink term represents wells. A complex well flow model may be used to simulate specified flow rate and pressure conditions at the land surface or within the aquifer, with or without pressure and flow rate constraints. Boundary condition types offered include specified value, specified flux, leakage, heat conduction, and approximate free surface, and two types of aquifer influence functions. All boundary conditions can be functions of time. Two techniques are available for solution of the finite difference matrix equations. One technique is a direct-elimination solver, using equations reordered by alternating diagonal planes. The other technique is an iterative solver, using two-line successive over-relaxation. A restart option is available for storing intermediate results and restarting the simulation at an intermediate time with modified boundary conditions. This feature also can be used as protection against computer system failure. Data input and output may be in metric (SI) units or inch-pound units. Output may include tables of dependent variables and parameters, zoned-contour maps, and plots of the dependent variables versus time. (Lantz-PTT)

Adapting HYDRUS-1D to Simulate Overland Flow and Reactive Transport During Sheet Flow Deviations

NASA Astrophysics Data System (ADS)

Liang, J.; Bradford, S. A.; Simunek, J.; Hartmann, A.

2017-12-01

The HYDRUS-1D code is a popular numerical model for solving the Richards equation for variably-saturated water flow and solute transport in porous media. This code was adapted to solve rather than the Richards equation for subsurface flow the diffusion wave equation for overland flow at the soil surface. The numerical results obtained by the new model produced an excellent agreement with the analytical solution of the kinematic wave equation. Model tests demonstrated its applicability to simulate the transport and fate of many different solutes, such as non-adsorbing tracers, nutrients, pesticides, and microbes. However, the diffusion wave or kinematic wave equations describe surface runoff as sheet flow with a uniform depth and velocity across the slope. In reality, overland water flow and transport processes are rarely uniform. Local soil topography, vegetation, and spatial soil heterogeneity control directions and magnitudes of water fluxes, and strongly influence runoff characteristics. There is increasing evidence that variations in soil surface characteristics influence the distribution of overland flow and transport of pollutants. These spatially varying surface characteristics are likely to generate non-equilibrium flow and transport processes. HYDRUS-1D includes a hierarchical series of models of increasing complexity to account for both physical equilibrium and non-equilibrium, e.g., dual-porosity and dual-permeability models, up to a dual-permeability model with immobile water. The same conceptualization as used for the subsurface was implemented to simulate non-equilibrium overland flow and transport at the soil surface. The developed model improves our ability to describe non-equilibrium overland flow and transport processes and to improves our understanding of factors that cause this behavior. The HYDRUS-1D overland flow and transport model was additionally also extended to simulate soil erosion. The HYDRUS-1D Soil Erosion Model has been verified by comparing with other soil erosion models. The model performed well when the average soil particle size is relatively large. The performance of the soil erosion model has been further validated by comparing with selected experimental datasets from the literature.

Numberical Solution to Transient Heat Flow Problems

ERIC Educational Resources Information Center

Kobiske, Ronald A.; Hock, Jeffrey L.

1973-01-01

Discusses the reduction of the one- and three-dimensional diffusion equation to the difference equation and its stability, convergence, and heat-flow applications under different boundary conditions. Indicates the usefulness of this presentation for beginning students of physics and engineering as well as college teachers. (CC)

Flow model for open-channel reach or network

USGS Publications Warehouse

Schaffranek, R.W.

1987-01-01

Formulation of a one-dimensional model for simulating unsteady flow in a single open-channel reach or in a network of interconnected channels is presented. The model is both general and flexible in that it can be used to simulate a wide range of flow conditions for various channel configurations. It is based on a four-point (box), implicit, finite-difference approximation of the governing nonlinear flow equations with user-definable weighting coefficients to permit varying the solution scheme from box-centered to fully forward. Unique transformation equations are formulated that permit correlation of the unknowns at the extremities of the channels, thereby reducing coefficient matrix and execution time requirements. Discharges and water-surface elevations computed at intermediate locations within a channel are determined following solution of the transformation equations. The matrix of transformation and boundary-condition equations is solved by Gauss elimination using maximum pivot strategy. Two diverse applications of the model are presented to illustrate its broad utility. (USGS)

Anisotropic hydrodynamics for conformal Gubser flow

NASA Astrophysics Data System (ADS)

Nopoush, Mohammad; Ryblewski, Radoslaw; Strickland, Michael

2015-02-01

We derive the equations of motion for a system undergoing boost-invariant longitudinal and azimuthally symmetric transverse "Gubser flow" using leading-order anisotropic hydrodynamics. This is accomplished by assuming that the one-particle distribution function is ellipsoidally symmetric in the momenta conjugate to the de Sitter coordinates used to parametrize the Gubser flow. We then demonstrate that the S O (3 )q symmetry in de Sitter space further constrains the anisotropy tensor to be of spheroidal form. The resulting system of two coupled ordinary differential equations for the de Sitter-space momentum scale and anisotropy parameter are solved numerically and compared to a recently obtained exact solution of the relaxation-time-approximation Boltzmann equation subject to the same flow. We show that anisotropic hydrodynamics describes the spatiotemporal evolution of the system better than all currently known dissipative hydrodynamics approaches. In addition, we prove that anisotropic hydrodynamics gives the exact solution of the relaxation-time approximation Boltzmann equation in the ideal, η /s →0 , and free-streaming, η /s →∞, limits.

Diffuse-Interface Modelling of Flow in Porous Media

NASA Astrophysics Data System (ADS)

Addy, Doug; Pradas, Marc; Schmuck, Marcus; Kalliadasis, Serafim

2016-11-01

Multiphase flows are ubiquitous in a wide spectrum of scientific and engineering applications, and their computational modelling often poses many challenges associated with the presence of free boundaries and interfaces. Interfacial flows in porous media encounter additional challenges and complexities due to their inherently multiscale behaviour. Here we investigate the dynamics of interfaces in porous media using an effective convective Cahn-Hilliard (CH) equation recently developed in from a Stokes-CH equation for microscopic heterogeneous domains by means of a homogenization methodology, where the microscopic details are taken into account as effective tensor coefficients which are given by a Poisson equation. The equations are decoupled under appropriate assumptions and solved in series using a classic finite-element formulation with the open-source software FEniCS. We investigate the effects of different microscopic geometries, including periodic and non-periodic, at the bulk fluid flow, and find that our model is able to describe the effective macroscopic behaviour without the need to resolve the microscopic details.

Test of a new heat-flow equation for dense-fluid shock waves.

PubMed

Holian, Brad Lee; Mareschal, Michel; Ravelo, Ramon

2010-09-21

Using a recently proposed equation for the heat-flux vector that goes beyond Fourier's Law of heat conduction, we model shockwave propagation in the dense Lennard-Jones fluid. Disequilibrium among the three components of temperature, namely, the difference between the kinetic temperature in the direction of a planar shock wave and those in the transverse directions, particularly in the region near the shock front, gives rise to a new transport (equilibration) mechanism not seen in usual one-dimensional heat-flow situations. The modification of the heat-flow equation was tested earlier for the case of strong shock waves in the ideal gas, which had been studied in the past and compared to Navier-Stokes-Fourier solutions. Now, the Lennard-Jones fluid, whose equation of state and transport properties have been determined from independent calculations, allows us to study the case where potential, as well as kinetic contributions are important. The new heat-flow treatment improves the agreement with nonequilibrium molecular-dynamics simulations under strong shock wave conditions, compared to Navier-Stokes.

Inflow performance relationship for perforated wells producing from solution gas drive reservoir

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sukarno, P.; Tobing, E.L.

1995-10-01

The IPR curve equations, which are available today, are developed for open hole wells. In the application of Nodal System Analysis in perforated wells, an accurate calculation of pressure loss in the perforation is very important. Nowadays, the equation which is widely used is Blount, Jones and Glaze equation, to estimate pressure loss across perforation. This equation is derived for single phase flow, either oil or gas, therefore it is not suitable for two-phase production wells. In this paper, an IPR curve equation for perforated wells, producing from solution gas drive reservoir, is introduced. The equation has been developed usingmore » two phase single well simulator combine to two phase flow in perforation equation, derived by Perez and Kelkar. A wide range of reservoir rock and fluid properties and perforation geometry are used to develop the equation statistically.« less

Modeling of nonequilibrium space plasma flows

NASA Technical Reports Server (NTRS)

Gombosi, Tamas

1995-01-01

Godunov-type numerical solution of the 20 moment plasma transport equations. One of the centerpieces of our proposal was the development of a higher order Godunov-type numerical scheme to solve the gyration dominated 20 moment transport equations. In the first step we explored some fundamental analytic properties of the 20 moment transport equations for a low b plasma, including the eigenvectors and eigenvalues of propagating disturbances. The eigenvalues correspond to wave speeds, while the eigenvectors characterize the transported physical quantities. In this paper we also explored the physically meaningful parameter range of the normalized heat flow components. In the second step a new Godunov scheme type numerical method was developed to solve the coupled set of 20 moment transport equations for a quasineutral single-ion plasma. The numerical method and the first results were presented at several national and international meetings and a paper describing the method has been published in the Journal of Computational Physics. To our knowledge this is the first numerical method which is capable of producing stable time-dependent solutions to the full 20 (or 16) moment set of transport equations, including the full heat flow equation. Previous attempts resulted in unstable (oscillating) solutions of the heat flow equations. Our group invested over two man-years into the development and implementation of the new method. The present model solves the 20 moment transport equations for an ion species and thermal electrons in 8 domain extending from a collision dominated to a collisionless region (200 km to 12,000 km). This model has been applied to study O+ acceleration due to Joule heating in the lower ionosphere.

Gradient flow of O(N) nonlinear sigma model at large N

DOE PAGES

Aoki, Sinya; Kikuchi, Kengo; Onogi, Tetsuya

2015-04-28

Here, we study the gradient flow equation for the O(N) nonlinear sigma model in two dimensions at large N. We parameterize solution of the field at flow time t in powers of bare fields by introducing the coefficient function X n for the n-th power term (n = 1, 3, ··· ). Reducing the flow equation by keeping only the contributions at leading order in large N, we obtain a set of equations for X n ’s, which can be solved iteratively starting from n = 1. For n = 1 case, we find an explicit form of the exactmore » solution. Using this solution, we show that the two point function at finite flow time t is finite. As an application, we obtain the non-perturbative running coupling defined from the energy density. We also discuss the solution for n = 3 case.« less

Vortex equations: Singularities, numerical solution, and axisymmetric vortex breakdown

NASA Technical Reports Server (NTRS)

Bossel, H. H.

1972-01-01

A method of weighted residuals for the computation of rotationally symmetric quasi-cylindrical viscous incompressible vortex flow is presented and used to compute a wide variety of vortex flows. The method approximates the axial velocity and circulation profiles by series of exponentials having (N + 1) and N free parameters, respectively. Formal integration results in a set of (2N + 1) ordinary differential equations for the free parameters. The governing equations are shown to have an infinite number of discrete singularities corresponding to critical values of the swirl parameters. The computations point to the controlling influence of the inner core flow on vortex behavior. They also confirm the existence of two particular critical swirl parameter values: one separates vortex flow which decays smoothly from vortex flow which eventually breaks down, and the second is the first singularity of the quasi-cylindrical system, at which point physical vortex breakdown is thought to occur.

Numerical study of unsteady Williamson fluid flow and heat transfer in the presence of MHD through a permeable stretching surface

NASA Astrophysics Data System (ADS)

Bibi, Madiha; Khalil-Ur-Rehman; Malik, M. Y.; Tahir, M.

2018-04-01

In the present article, unsteady flow field characteristics of the Williamson fluid model are explored. The nanosized particles are suspended in the flow regime having the interaction of a magnetic field. The fluid flow is induced due to a stretching permeable surface. The flow model is controlled through coupled partial differential equations to the used shooting method for a numerical solution. The obtained partial differential equations are converted into ordinary differential equations as an initial value problem. The shooting method is used to find a numerical solution. The mathematical modeling yields physical parameters, namely the Weissenberg number, the Prandtl number, the unsteadiness parameter, the magnetic parameter, the mass transfer parameter, the Lewis number, the thermophoresis parameter and Brownian parameters. It is found that the Williamson fluid velocity, temperature and nanoparticles concentration are a decreasing function of the unsteadiness parameter.

Quantification of uncertainty for fluid flow in heterogeneous petroleum reservoirs

NASA Astrophysics Data System (ADS)

Zhang, Dongxiao

Detailed description of the heterogeneity of oil/gas reservoirs is needed to make performance predictions of oil/gas recovery. However, only limited measurements at a few locations are usually available. This combination of significant spatial heterogeneity with incomplete information about it leads to uncertainty about the values of reservoir properties and thus, to uncertainty in estimates of production potential. The theory of stochastic processes provides a natural method for evaluating these uncertainties. In this study, we present a stochastic analysis of transient, single phase flow in heterogeneous reservoirs. We derive general equations governing the statistical moments of flow quantities by perturbation expansions. These moments can be used to construct confidence intervals for the flow quantities (e.g., pressure and flow rate). The moment equations are deterministic and can be solved numerically with existing solvers. The proposed moment equation approach has certain advantages over the commonly used Monte Carlo approach.

Numerical Simulation and Quantitative Uncertainty Assessment of Microchannel Flow

NASA Astrophysics Data System (ADS)

Debusschere, Bert; Najm, Habib; Knio, Omar; Matta, Alain; Ghanem, Roger; Le Maitre, Olivier

2002-11-01

This study investigates the effect of uncertainty in physical model parameters on computed electrokinetic flow of proteins in a microchannel with a potassium phosphate buffer. The coupled momentum, species transport, and electrostatic field equations give a detailed representation of electroosmotic and pressure-driven flow, including sample dispersion mechanisms. The chemistry model accounts for pH-dependent protein labeling reactions as well as detailed buffer electrochemistry in a mixed finite-rate/equilibrium formulation. To quantify uncertainty, the governing equations are reformulated using a pseudo-spectral stochastic methodology, which uses polynomial chaos expansions to describe uncertain/stochastic model parameters, boundary conditions, and flow quantities. Integration of the resulting equations for the spectral mode strengths gives the evolution of all stochastic modes for all variables. Results show the spatiotemporal evolution of uncertainties in predicted quantities and highlight the dominant parameters contributing to these uncertainties during various flow phases. This work is supported by DARPA.

Mahdi S. Hantush 1921”1984

NASA Astrophysics Data System (ADS)

Ahmad, M. U.; Gross, G. W.; Marino, M. A.; Papadopulos, S. S.; Saleem, Z. A.

1984-04-01

Mahdi Salih Hantush, Professor of Hydrology at the University of Kuwait, died on January 14, 1984 from complications following heart surgery.A hydrologist, scientist, and great teacher, Mantush specialized in the application of mathematics to the solution of transient groundwater flow problems. His particular expertise in the development of well-flow equations led the late R.W. Stallman of the U.S. Geological Survey to refer to him as “The Master of Radial Flow.” Hantush's numerous scientific publications contributed greatly to the present theories of flow in leaky aquifers, unconfined aquifers, and anisotropic aquifers. He derived the mathematical equations of flow to fully and/or partially penetrating wells in such aquifer systems, and devised methods for the analysis of pumpingtest data to determine their hydraulic properties. He was not only a researcher, but also a practicing hydrologist, deriving the equations he needed to solve practical problems.

Regional regression equations to estimate peak-flow frequency at sites in North Dakota using data through 2009

USGS Publications Warehouse

Williams-Sether, Tara

2015-08-06

Annual peak-flow frequency data from 231 U.S. Geological Survey streamflow-gaging stations in North Dakota and parts of Montana, South Dakota, and Minnesota, with 10 or more years of unregulated peak-flow record, were used to develop regional regression equations for exceedance probabilities of 0.5, 0.20, 0.10, 0.04, 0.02, 0.01, and 0.002 using generalized least-squares techniques. Updated peak-flow frequency estimates for 262 streamflow-gaging stations were developed using data through 2009 and log-Pearson Type III procedures outlined by the Hydrology Subcommittee of the Interagency Advisory Committee on Water Data. An average generalized skew coefficient was determined for three hydrologic zones in North Dakota. A StreamStats web application was developed to estimate basin characteristics for the regional regression equation analysis. Methods for estimating a weighted peak-flow frequency for gaged sites and ungaged sites are presented.

Numerical calculation of flow fields about rectangular wings of finite thickness in supersonic flow. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Vogel, J. M.

1973-01-01

The calculation of the outer inviscid flow about a rectangular wing moving at supersonic speeds is reported. The inviscid equations of motion governing the flow generated by the wing form a set of hyperbolic differential equations. The flow field about the rectangular wing is separated into three regions consisting of the forebody, the afterbody, and the wing wake. Solutions for the forebody are obtained using conical flow techniques while the afterbody and the wing wake regions are treated as initial value problems. The numerical solutions are compared in the two dimensional regions with known exact solutions.

On a solution of the nonlinear differential equation for transonic flow past a wave-shaped wall

NASA Technical Reports Server (NTRS)

Kaplan, Carl

1952-01-01

The Prandtl-Busemann small-perturbation method is utilized to obtain the flow of a compressible fluid past an infinitely long wave-shaped wall. When the essential assumption for transonic flow (that all Mach numbers in the region of flow are nearly unity) is introduced, the expression for the velocity potential takes the form of a power series in the transonic similarity parameter. On the basis of this form of the solution, an attempt is made to solve the nonlinear differential equation for transonic flow past the wavy wall. The analysis utilized exhibits clearly the difficulties inherent in nonlinear-flow problems.

A Model to Couple Flow, Thermal and Reactive Chemical Transport, and Geo-mechanics in Variably Saturated Media

NASA Astrophysics Data System (ADS)

Yeh, G. T.; Tsai, C. H.

2015-12-01

This paper presents the development of a THMC (thermal-hydrology-mechanics-chemistry) process model in variably saturated media. The governing equations for variably saturated flow and reactive chemical transport are obtained based on the mass conservation principle of species transport supplemented with Darcy's law, constraint of species concentration, equation of states, and constitutive law of K-S-P (Conductivity-Degree of Saturation-Capillary Pressure). The thermal transport equation is obtained based on the conservation of energy. The geo-mechanic displacement is obtained based on the assumption of equilibrium. Conventionally, these equations have been implicitly coupled via the calculations of secondary variables based on primary variables. The mechanisms of coupling have not been obvious. In this paper, governing equations are explicitly coupled for all primary variables. The coupling is accomplished via the storage coefficients, transporting velocities, and conduction-dispersion-diffusion coefficient tensor; one set each for every primary variable. With this new system of equations, the coupling mechanisms become clear. Physical interpretations of every term in the coupled equations will be discussed. Examples will be employed to demonstrate the intuition and superiority of these explicit coupling approaches. Keywords: Variably Saturated Flow, Thermal Transport, Geo-mechanics, Reactive Transport.

Calculation Of Pneumatic Attenuation In Pressure Sensors

NASA Technical Reports Server (NTRS)

Whitmore, Stephen A.

1991-01-01

Errors caused by attenuation of air-pressure waves in narrow tubes calculated by method based on fundamental equations of flow. Changes in ambient pressure transmitted along narrow tube to sensor. Attenuation of high-frequency components of pressure wave calculated from wave equation derived from Navier-Stokes equations of viscous flow in tube. Developed to understand and compensate for frictional attenuation in narrow tubes used to connect aircraft pressure sensors with pressure taps on affected surfaces.

Finite element methods and Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Cuvelier, C.; Segal, A.; van Steenhoven, A. A.

This book is devoted to two and three-dimensional FEM analysis of the Navier-Stokes (NS) equations describing one flow of a viscous incompressible fluid. Three different approaches to the NS equations are described: a direct method, a penalty method, and a method that constructs discrete solenoidal vector fields. Subjects of current research which are important from the industrial/technological viewpoint are considered, including capillary-free boundaries, nonisothermal flows, turbulence, and non-Newtonian fluids.

Computing Flow through Well Screens Using an Embedded Well Technique

DTIC Science & Technology

2015-08-01

average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed...necessary to solve the continuity equation and the momentum equation using small time - steps . With the assumption that the well flow reaches...well system so that much greater time - steps can be used for computation. The 1D steady- state well equation can be written as well well well well well

Smoothed Particle Hydrodynamics and its applications for multiphase flow and reactive transport in porous media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tartakovsky, Alexandre M.; Trask, Nathaniel; Pan, K.

2016-03-11

Smoothed Particle Hydrodynamics (SPH) is a Lagrangian method based on a meshless discretization of partial differential equations. In this review, we present SPH discretization of the Navier-Stokes and Advection-Diffusion-Reaction equations, implementation of various boundary conditions, and time integration of the SPH equations, and we discuss applications of the SPH method for modeling pore-scale multiphase flows and reactive transport in porous and fractured media.

On the Flow of a Compressible Fluid by the Hodograph Method. II - Fundamental Set of Particular Flow Solutions of the Chaplygin Differential Equation

NASA Technical Reports Server (NTRS)

Garrick, I. E.; Kaplan, Carl

1944-01-01

The differential equation of Chaplygin's jet problem is utilized to give a systematic development of particular solutions of the hodograph flow equations, which extends the treatment of Chaplygin into the supersonic range and completes the set of particular solutions. The particular solutions serve to place on a reasonable basis the use of velocity correction formulas for the comparison of incompressible and compressible flows. It is shown that the geometric-mean type of velocity correction formula introduced in part I has significance as an over-all type of approximation in the subsonic range. A brief review of general conditions limiting the potential flow of an adiabatic compressible fluid is given and application is made to the particular solutions, yielding conditions for the existence of singular loci in the supersonic range. The combining of particular solutions in accordance with prescribed boundary flow conditions is not treated in the present paper.

Comparison of NACA 0012 Laminar Flow Solutions: Structured and Unstructured Grid Methods

NASA Technical Reports Server (NTRS)

Swanson, R. C.; Langer, S.

2016-01-01

In this paper we consider the solution of the compressible Navier-Stokes equations for a class of laminar airfoil flows. The principal objective of this paper is to demonstrate that members of this class of laminar flows have steady-state solutions. These laminar airfoil flow cases are often used to evaluate accuracy, stability and convergence of numerical solution algorithms for the Navier-Stokes equations. In recent years, such flows have also been used as test cases for high-order numerical schemes. While generally consistent steady-state solutions have been obtained for these flows using higher order schemes, a number of results have been published with various solutions, including unsteady ones. We demonstrate with two different numerical methods and a range of meshes with a maximum density that exceeds 8 × 106 grid points that steady-state solutions are obtained. Furthermore, numerical evidence is presented that even when solving the equations with an unsteady algorithm, one obtains steady-state solutions.

Analysis of atmospheric flow over a surface protrusion using the turbulence kinetic energy equation with reference to aeronautical operating systems

NASA Technical Reports Server (NTRS)

Frost, W.; Harper, W. L.

1975-01-01

Flow over surface obstructions can produce significantly large wind shears such that adverse flying conditions can occur for aeronautical systems (helicopters, STOL vehicles, etc.). Atmospheric flow fields resulting from a semi-elliptical surface obstruction in an otherwise horizontally homogeneous statistically stationary flow are modelled with the boundary-layer/Boussinesq-approximation of the governing equation of fluid mechanics. The turbulence kinetic energy equation is used to determine the dissipative effects of turbulent shear on the mean flow. Iso-lines of turbulence kinetic energy and turbulence intensity are plotted in the plane of the flow and highlight regions of high turbulence intensity in the stagnation zone and sharp gradients in intensity along the transition from adverse to favourable pressure gradient. Discussion of the effects of the disturbed wind field in CTOL and STOL aircraft flight path and obstruction clearance standards is given. The results indicate that closer inspection of these presently recommended standards as influenced by wind over irregular terrains is required.

Development of numerical techniques for simulation of magnetogasdynamics and hypersonic chemistry

NASA Astrophysics Data System (ADS)

Damevin, Henri-Marie

Magnetogasdynamics, the science concerned with the mutual interaction between electromagnetic field and flow of electrically conducting gas, offers promising advances in flow control and propulsion of future hypersonic vehicles. Numerical simulations are essential for understanding phenomena, and for research and development. The current dissertation is devoted to the development and validation of numerical algorithms for the solution of multidimensional magnetogasdynamic equations and the simulation of hypersonic high-temperature effects. Governing equations are derived, based on classical magnetogasdynamic assumptions. Two sets of equations are considered, namely the full equations and equations in the low magnetic Reynolds number approximation. Equations are expressed in a suitable formulation for discretization by finite differences in a computational space. For the full equations, Gauss law for magnetism is enforced using Powell's methodology. The time integration method is a four-stage modified Runge-Kutta scheme, amended with a Total Variation Diminishing model in a postprocessing stage. The eigensystem, required for the Total Variation Diminishing scheme, is derived in generalized three-dimensional coordinate system. For the simulation of hypersonic high-temperature effects, two chemical models are utilized, namely a nonequilibrium model and an equilibrium model. A loosely coupled approach is implemented to communicate between the magnetogasdynamic equations and the chemical models. The nonequilibrium model is a one-temperature, five-species, seventeen-reaction model solved by an implicit flux-vector splitting scheme. The chemical equilibrium model computes thermodynamics properties using curve fit procedures. Selected results are provided, which explore the different features of the numerical algorithms. The shock-capturing properties are validated for shock-tube simulations using numerical solutions reported in the literature. The computations of superfast flows over corners and in convergent channels demonstrate the performances of the algorithm in multiple dimensions. The implementation of diffusion terms is validated by solving the magnetic Rayleigh problem and Hartmann problem, for which analytical solutions are available. Prediction of blunt-body type flow are investigated and compared with numerical solutions reported in the literature. The effectiveness of the chemical models for hypersonic flow over blunt body is examined in various flow conditions. It is shown that the proposed schemes perform well in a variety of test cases, though some limitations have been identified.

Application of discontinuous Galerkin method for solving a compressible five-equation two-phase flow model

NASA Astrophysics Data System (ADS)

Saleem, M. Rehan; Ali, Ishtiaq; Qamar, Shamsul

2018-03-01

In this article, a reduced five-equation two-phase flow model is numerically investigated. The formulation of the model is based on the conservation and energy exchange laws. The model is non-conservative and the governing equations contain two equations for the mass conservation, one for the over all momentum and one for the total energy. The fifth equation is the energy equation for one of the two phases that includes a source term on the right hand side for incorporating energy exchange between the two fluids in the form of mechanical and thermodynamical works. A Runge-Kutta discontinuous Galerkin finite element method is applied to solve the model equations. The main attractive features of the proposed method include its formal higher order accuracy, its nonlinear stability, its ability to handle complicated geometries, and its ability to capture sharp discontinuities or strong gradients in the solutions without producing spurious oscillations. The proposed method is robust and well suited for large-scale time-dependent computational problems. Several case studies of two-phase flows are presented. For validation and comparison of the results, the same model equations are also solved by using a staggered central scheme. It was found that discontinuous Galerkin scheme produces better results as compared to the staggered central scheme.

Computation of steady and unsteady quasi-one-dimensional viscous/inviscid interacting internal flows at subsonic, transonic, and supersonic Mach numbers

NASA Technical Reports Server (NTRS)

Swafford, Timothy W.; Huddleston, David H.; Busby, Judy A.; Chesser, B. Lawrence

1992-01-01

Computations of viscous-inviscid interacting internal flowfields are presented for steady and unsteady quasi-one-dimensional (Q1D) test cases. The unsteady Q1D Euler equations are coupled with integral boundary-layer equations for unsteady, two-dimensional (planar or axisymmetric), turbulent flow over impermeable, adiabatic walls. The coupling methodology differs from that used in most techniques reported previously in that the above mentioned equation sets are written as a complete system and solved simultaneously; that is, the coupling is carried out directly through the equations as opposed to coupling the solutions of the different equation sets. Solutions to the coupled system of equations are obtained using both explicit and implicit numerical schemes for steady subsonic, steady transonic, and both steady and unsteady supersonic internal flowfields. Computed solutions are compared with measurements as well as Navier-Stokes and inverse boundary-layer methods. An analysis of the eigenvalues of the coefficient matrix associated with the quasi-linear form of the coupled system of equations indicates the presence of complex eigenvalues for certain flow conditions. It is concluded that although reasonable solutions can be obtained numerically, these complex eigenvalues contribute to the overall difficulty in obtaining numerical solutions to the coupled system of equations.

Assessments of a Turbulence Model Based on Menter's Modification to Rotta's Two-Equation Model

NASA Technical Reports Server (NTRS)

Abdol-Hamid, Khaled S.

2013-01-01

The main objective of this paper is to construct a turbulence model with a more reliable second equation simulating length scale. In the present paper, we assess the length scale equation based on Menter s modification to Rotta s two-equation model. Rotta shows that a reliable second equation can be formed in an exact transport equation from the turbulent length scale L and kinetic energy. Rotta s equation is well suited for a term-by-term modeling and shows some interesting features compared to other approaches. The most important difference is that the formulation leads to a natural inclusion of higher order velocity derivatives into the source terms of the scale equation, which has the potential to enhance the capability of Reynolds-averaged Navier-Stokes (RANS) to simulate unsteady flows. The model is implemented in the PAB3D solver with complete formulation, usage methodology, and validation examples to demonstrate its capabilities. The detailed studies include grid convergence. Near-wall and shear flows cases are documented and compared with experimental and Large Eddy Simulation (LES) data. The results from this formulation are as good or better than the well-known SST turbulence model and much better than k-epsilon results. Overall, the study provides useful insights into the model capability in predicting attached and separated flows.

General Equation Set Solver for Compressible and Incompressible Turbomachinery Flows

NASA Technical Reports Server (NTRS)

Sondak, Douglas L.; Dorney, Daniel J.

2002-01-01

Turbomachines for propulsion applications operate with many different working fluids and flow conditions. The flow may be incompressible, such as in the liquid hydrogen pump in a rocket engine, or supersonic, such as in the turbine which may drive the hydrogen pump. Separate codes have traditionally been used for incompressible and compressible flow solvers. The General Equation Set (GES) method can be used to solve both incompressible and compressible flows, and it is not restricted to perfect gases, as are many compressible-flow turbomachinery solvers. An unsteady GES turbomachinery flow solver has been developed and applied to both air and water flows through turbines. It has been shown to be an excellent alternative to maintaining two separate codes.

Development of monitoring system of helium leakage from canister

DOE Office of Scientific and Technical Information (OSTI.GOV)

Toriu, D.; Ushijima, S.; Takeda, H.

2013-07-01

This paper presents a computational method for the helium leakage from a canister. The governing equations for compressible fluids consist of mass conservation equation in Eulerian description, momentum equations and energy equation. The numerical procedures are divided into three phases, advection, diffusion and acoustic phases, and the equations of compressible fluids are discretized with a finite volume method. Thus, the mass conservation law is sufficiently satisfied in the calculation region. In particular, our computational method enables us to predict the change of the temperature distributions around the canister boundaries by calculating the governing equations for the compressible gas flows, whichmore » are leaked out from a slight crack on the canister boundary. In order to confirm the validity of our method, it was applied to the basic problem, 2-dimensional natural convection flows in a rectangular cavity. As a result, it was shown that the naturally convected flows can be reasonably simulated by our method. Furthermore, numerical experiments were conducted for the helium leakage from canister and we derived a close relationship between the inner pressure and the boundary temperature distributions.« less

Direct computation of stochastic flow in reservoirs with uncertain parameters

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dainton, M.P.; Nichols, N.K.; Goldwater, M.H.

1997-01-15

A direct method is presented for determining the uncertainty in reservoir pressure, flow, and net present value (NPV) using the time-dependent, one phase, two- or three-dimensional equations of flow through a porous medium. The uncertainty in the solution is modelled as a probability distribution function and is computed from given statistical data for input parameters such as permeability. The method generates an expansion for the mean of the pressure about a deterministic solution to the system equations using a perturbation to the mean of the input parameters. Hierarchical equations that define approximations to the mean solution at each point andmore » to the field convariance of the pressure are developed and solved numerically. The procedure is then used to find the statistics of the flow and the risked value of the field, defined by the NPV, for a given development scenario. This method involves only one (albeit complicated) solution of the equations and contrasts with the more usual Monte-Carlo approach where many such solutions are required. The procedure is applied easily to other physical systems modelled by linear or nonlinear partial differential equations with uncertain data. 14 refs., 14 figs., 3 tabs.« less

Rapid Aeroelastic Analysis of Blade Flutter in Turbomachines

NASA Technical Reports Server (NTRS)

Trudell, J. J.; Mehmed, O.; Stefko, G. L.; Bakhle, M. A.; Reddy, T. S. R.; Montgomery, M.; Verdon, J.

2006-01-01

The LINFLUX-AE computer code predicts flutter and forced responses of blades and vanes in turbomachines under subsonic, transonic, and supersonic flow conditions. The code solves the Euler equations of unsteady flow in a blade passage under the assumption that the blades vibrate harmonically at small amplitudes. The steady-state nonlinear Euler equations are solved by a separate program, then equations for unsteady flow components are obtained through linearization around the steady-state solution. A structural-dynamics analysis (see figure) is performed to determine the frequencies and mode shapes of blade vibrations, a preprocessor interpolates mode shapes from the structural-dynamics mesh onto the LINFLUX computational-fluid-dynamics mesh, and an interface code is used to convert the steady-state flow solution to a form required by LINFLUX. Then LINFLUX solves the linearized equations in the frequency domain to calculate the unsteady aerodynamic pressure distribution for a given vibration mode, frequency, and interblade phase angle. A post-processor uses the unsteady pressures to calculate generalized aerodynamic forces, response amplitudes, and eigenvalues (which determine the flutter frequency and damping). In comparison with the TURBO-AE aeroelastic-analysis code, which solves the equations in the time domain, LINFLUX-AE is 6 to 7 times faster.

Investigation of culvert hydraulics related to juvenile fish passage. Final research report

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barber, M.E.; Downs, R.C.

1996-01-01

Culverts often create barriers to the upstream migration of juvenile fish. The objective of this study was to determine hydraulic characteristics of culverts with different flow conditions. Methods of predicting flow profiles were developed by both Chiu and Mountjoy. Two equations were compared to experimental results. An area of flow corresponding to a predetermined allowable velocity can be calculated using Mountjoy equation. This can then be used in the design of culverts as fish passage guidelines. The report contains a summary of background information, experimental methodology, the results of experimental tests, and an analysis of both the Chiu and Mountjoymore » equations.« less

Extension of the Gladstone-Dale equation for flame flow field diagnosis by optical computerized tomography

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen Yunyun; Li Zhenhua; Song Yang

2009-05-01

An extended model of the original Gladstone-Dale (G-D) equation is proposed for optical computerized tomography (OCT) diagnosis of flame flow fields. For the purpose of verifying the newly established model, propane combustion is used as a practical example for experiment, and moire deflection tomography is introduced with the probe wavelength 808 nm. The results indicate that the temperature based on the extended model is more accurate than that based on the original G-D equation. In a word, the extended model can be suitable for all kinds of flame flow fields whatever the components, temperature, and ionization are.

Numerical solution of the hypersonic viscous-shock-layer equations for laminar, transitional, and turbulent flows of a perfect gas over blunt axially symmetric bodies

NASA Technical Reports Server (NTRS)

Anderson, E. C.; Moss, J. N.

1975-01-01

The viscous shock layer equations applicable to hypersonic laminar, transitional, and turbulent flows of a perfect gas over two-dimensional plane or axially symmetric blunt bodies are presented. The equations are solved by means of an implicit finite difference scheme, and the results are compared with a turbulent boundary layer analysis. The agreement between the two solution procedures is satisfactory for the region of flow where streamline swallowing effects are negligible. For the downstream regions, where streamline swallowing effects are present, the expected differences in the two solution procedures are evident.

Group solution for unsteady free-convection flow from a vertical moving plate subjected to constant heat flux

NASA Astrophysics Data System (ADS)

Kassem, M.

2006-03-01

The problem of heat and mass transfer in an unsteady free-convection flow over a continuous moving vertical sheet in an ambient fluid is investigated for constant heat flux using the group theoretical method. The nonlinear coupled partial differential equation governing the flow and the boundary conditions are transformed to a system of ordinary differential equations with appropriate boundary conditions. The obtained ordinary differential equations are solved numerically using the shooting method. The effect of Prandlt number on the velocity and temperature of the boundary-layer is plotted in curves. A comparison with previous work is presented.

Analysis and control of supersonic vortex breakdown flows

NASA Technical Reports Server (NTRS)

Kandil, Osama A.

1990-01-01

Analysis and computation of steady, compressible, quasi-axisymmetric flow of an isolated, slender vortex are considered. The compressible, Navier-Stokes equations are reduced to a simpler set by using the slenderness and quasi-axisymmetry assumptions. The resulting set along with a compatibility equation are transformed from the diverging physical domain to a rectangular computational domain. Solving for a compatible set of initial profiles and specifying a compatible set of boundary conditions, the equations are solved using a type-differencing scheme. Vortex breakdown locations are detected by the failure of the scheme to converge. Computational examples include isolated vortex flows at different Mach numbers, external axial-pressure gradients and swirl ratios.

Dynamic sealing principles

NASA Technical Reports Server (NTRS)

Zuk, J.

1976-01-01

The fundamental principles governing dynamic sealing operation are discussed. Different seals are described in terms of these principles. Despite the large variety of detailed construction, there appear to be some basic principles, or combinations of basic principles, by which all seals function, these are presented and discussed. Theoretical and practical considerations in the application of these principles are discussed. Advantages, disadvantages, limitations, and application examples of various conventional and special seals are presented. Fundamental equations governing liquid and gas flows in thin film seals, which enable leakage calculations to be made, are also presented. Concept of flow functions, application of Reynolds lubrication equation, and nonlubrication equation flow, friction and wear; and seal lubrication regimes are explained.

Preconditioned conjugate gradient methods for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Ajmani, Kumud; Ng, Wing-Fai; Liou, Meng-Sing

1994-01-01

A preconditioned Krylov subspace method (GMRES) is used to solve the linear systems of equations formed at each time-integration step of the unsteady, two-dimensional, compressible Navier-Stokes equations of fluid flow. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux-split formulation. Several preconditioning techniques are investigated to enhance the efficiency and convergence rate of the implicit solver based on the GMRES algorithm. The superiority of the new solver is established by comparisons with a conventional implicit solver, namely line Gauss-Seidel relaxation (LGSR). Computational test results for low-speed (incompressible flow over a backward-facing step at Mach 0.1), transonic flow (trailing edge flow in a transonic turbine cascade), and hypersonic flow (shock-on-shock interactions on a cylindrical leading edge at Mach 6.0) are presented. For the Mach 0.1 case, overall speedup factors of up to 17 (in terms of time-steps) and 15 (in terms of CPU time on a CRAY-YMP/8) are found in favor of the preconditioned GMRES solver, when compared with the LGSR solver. The corresponding speedup factors for the transonic flow case are 17 and 23, respectively. The hypersonic flow case shows slightly lower speedup factors of 9 and 13, respectively. The study of preconditioners conducted in this research reveals that a new LUSGS-type preconditioner is much more efficient than a conventional incomplete LU-type preconditioner.

Computer code for predicting coolant flow and heat transfer in turbomachinery

NASA Technical Reports Server (NTRS)

Meitner, Peter L.

1990-01-01

A computer code was developed to analyze any turbomachinery coolant flow path geometry that consist of a single flow passage with a unique inlet and exit. Flow can be bled off for tip-cap impingement cooling, and a flow bypass can be specified in which coolant flow is taken off at one point in the flow channel and reintroduced at a point farther downstream in the same channel. The user may either choose the coolant flow rate or let the program determine the flow rate from specified inlet and exit conditions. The computer code integrates the 1-D momentum and energy equations along a defined flow path and calculates the coolant's flow rate, temperature, pressure, and velocity and the heat transfer coefficients along the passage. The equations account for area change, mass addition or subtraction, pumping, friction, and heat transfer.

Viscous flow computations using a second-order upwind differencing scheme

NASA Technical Reports Server (NTRS)

Chen, Y. S.

1988-01-01

In the present computations of a wide range of fluid flow problems by means of the primitive variables-incorporating Navier-Stokes equations, a mixed second-order upwinding scheme approximates the convective terms of the transport equations and the scheme's accuracy is verified for convection-dominated high Re number flow problems. An adaptive dissipation scheme is used as a monotonic supersonic shock flow capture mechanism. Many benchmark fluid flow problems, including the compressible and incompressible, laminar and turbulent, over a wide range of M and Re numbers, are presently studied to verify the accuracy and robustness of this numerical method.

A Study of Flow Separation in Transonic Flow Using Inviscid and Viscous Computational Fluid Dynamics (CFD) Schemes

NASA Technical Reports Server (NTRS)

Rhodes, J. A.; Tiwari, S. N.; Vonlavante, E.

1988-01-01

A comparison of flow separation in transonic flows is made using various computational schemes which solve the Euler and the Navier-Stokes equations of fluid mechanics. The flows examined are computed using several simple two-dimensional configurations including a backward facing step and a bump in a channel. Comparison of the results obtained using shock fitting and flux vector splitting methods are presented and the results obtained using the Euler codes are compared to results on the same configurations using a code which solves the Navier-Stokes equations.

Turbulence model sensitivity and scour gap effect of unsteady flow around pipe: a CFD study.

PubMed

Ali, Abbod; Sharma, R K; Ganesan, P; Akib, Shatirah

2014-01-01

A numerical investigation of incompressible and transient flow around circular pipe has been carried out at different five gap phases. Flow equations such as Navier-Stokes and continuity equations have been solved using finite volume method. Unsteady horizontal velocity and kinetic energy square root profiles are plotted using different turbulence models and their sensitivity is checked against published experimental results. Flow parameters such as horizontal velocity under pipe, pressure coefficient, wall shear stress, drag coefficient, and lift coefficient are studied and presented graphically to investigate the flow behavior around an immovable pipe and scoured bed.

Surge dynamics coupled to pore-pressure evolution in debris flows

USGS Publications Warehouse

Savage, S.B.; Iverson, R.M.; ,

2003-01-01

Temporally and spatially varying pore-fluid pressures exert strong controls on debris-flow motion by mediating internal and basal friction at grain contacts. We analyze these effects by deriving a one-dimensional model of pore-pressure diffusion explicitly coupled to changes in debris-flow thickness. The new pore-pressure equation is combined with Iverson's (1997) extension of the depth-averaged Savage-Hutter (1989, 1991) granular avalanche equations to predict motion of unsteady debris-flow surges with evolving pore-pressure distributions. Computational results illustrate the profound effects of pore-pressure diffusivities on debris-flow surge depths and velocities. ?? 2003 Millpress,.

Theoretical Prediction of Pressure Distributions on Nonlifting Airfoils at High Subsonic Speeds

NASA Technical Reports Server (NTRS)

Spreiter, John R; Alksne, Alberta

1955-01-01

Theoretical pressure distributions on nonlifting circular-arc airfoils in two-dimensional flows with high subsonic free-stream velocity are found by determining approximate solutions, through an iteration process, of an integral equation for transonic flow proposed by Oswatitsch. The integral equation stems directly from the small-disturbance theory for transonic flow. This method of analysis possesses the advantage of remaining in the physical, rather than the hodograph, variable and can be applied in airfoils having curved surfaces. After discussion of the derivation of the integral equation and qualitative aspects of the solution, results of calculations carried out for circular-arc airfoils in flows with free-stream Mach numbers up to unity are described. These results indicate most of the principal phenomena observed in experimental studies.

Determination of the turbulence integral model parameters for a case of a coolant angular flow in regular rod-bundle

NASA Astrophysics Data System (ADS)

Bayaskhalanov, M. V.; Vlasov, M. N.; Korsun, A. S.; Merinov, I. G.; Philippov, M. Ph

2017-11-01

Research results of “k-ε” turbulence integral model (TIM) parameters dependence on the angle of a coolant flow in regular smooth cylindrical rod-bundle are presented. TIM is intended for the definition of efficient impulse and heat transport coefficients in the averaged equations of a heat and mass transfer in the regular rod structures in an anisotropic porous media approximation. The TIM equations are received by volume-averaging of the “k-ε” turbulence model equations on periodic cell of rod-bundle. The water flow across rod-bundle under angles from 15 to 75 degrees was simulated by means of an ANSYS CFX code. Dependence of the TIM parameters on flow angle was as a result received.

A frequency domain linearized Navier-Stokes equations approach to acoustic propagation in flow ducts with sharp edges.

PubMed

Kierkegaard, Axel; Boij, Susann; Efraimsson, Gunilla

2010-02-01

Acoustic wave propagation in flow ducts is commonly modeled with time-domain non-linear Navier-Stokes equation methodologies. To reduce computational effort, investigations of a linearized approach in frequency domain are carried out. Calculations of sound wave propagation in a straight duct are presented with an orifice plate and a mean flow present. Results of transmission and reflections at the orifice are presented on a two-port scattering matrix form and are compared to measurements with good agreement. The wave propagation is modeled with a frequency domain linearized Navier-Stokes equation methodology. This methodology is found to be efficient for cases where the acoustic field does not alter the mean flow field, i.e., when whistling does not occur.

An assessment and application of turbulence models for hypersonic flows

NASA Technical Reports Server (NTRS)

Coakley, T. J.; Viegas, J. R.; Huang, P. G.; Rubesin, M. W.

1990-01-01

The current approach to the Accurate Computation of Complex high-speed flows is to solve the Reynolds averaged Navier-Stokes equations using finite difference methods. An integral part of this approach consists of development and applications of mathematical turbulence models which are necessary in predicting the aerothermodynamic loads on the vehicle and the performance of the propulsion plant. Computations of several high speed turbulent flows using various turbulence models are described and the models are evaluated by comparing computations with the results of experimental measurements. The cases investigated include flows over insulated and cooled flat plates with Mach numbers ranging from 2 to 8 and wall temperature ratios ranging from 0.2 to 1.0. The turbulence models investigated include zero-equation, two-equation, and Reynolds-stress transport models.

A New Constitutive Model for the Plastic Flow of Metals at Elevated Temperatures

NASA Astrophysics Data System (ADS)

Spigarelli, S.; El Mehtedi, M.

2014-02-01

A new constitutive model based on the combination of the Garofalo and Hensel-Spittel equations has been used to describe the plastic flow behavior of an AA6005 aluminum alloy tested in torsion. The analysis of the experimental data by the constitutive model resulted in an excellent description of the flow curves. The model equation was then rewritten to explicitly include the Arrhenius term describing the temperature dependence of plastic deformation. The calculation indicated that the activation energy for hot working slowly decreased with increasing strain, leading to thermally activated flow softening. The combined use of the new equation and torsion testing led to the development of a constitutive model which can be safely adopted in a computer code to simulate forging or extrusion.

A Note on the Wave Action Density of a Viscous Instability Mode on a Laminar Free-shear Flow

NASA Technical Reports Server (NTRS)

Balsa, Thomas F.

1994-01-01

Using the assumptions of an incompressible and viscous flow at large Reynolds number, we derive the evolution equation for the wave action density of an instability wave traveling on top of a laminar free-shear flow. The instability is considered to be viscous; the purpose of the present work is to include the cumulative effect of the (locally) small viscous correction to the wave, over length and time scales on which the underlying base flow appears inhomogeneous owing to its viscous diffusion. As such, we generalize our previous work for inviscid waves. This generalization appears as an additional (but usually non-negligible) term in the equation for the wave action. The basic structure of the equation remains unaltered.

Numerical Simulation of Subsonic and Transonic Propeller Flow. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Snyder, Aaron

1988-01-01

The numerical simulation of 3-D transonic flow about a system of propeller blades is investigated. In particular, it is shown that the use of helical coordinates significantly simplifies the form of the governing equation when the propeller system is assumed to be surrounded by an irrotational flow field of an inviscid fluid. The unsteady small disturbance equation, valid for lightly loaded blades and expressed in helical coordinates, is derived from the general blade-fixed potential equation, given for an arbitrary coordinate system. The use of a coordinate system which inherently adapts to the mean flow results in a disturbance equation requiring relatively few terms to accurately model the physics of the flow. Furthermore, the helical coordinate system presented here is novel in that it is periodic in the circumferential direction while, simultaneously, maintaining orthogonal properties at the mean blade locations. The periodic characteristic allows a complete cascade of blades to be treated, and the orthogonality property affords straightforward treatment of blade boundary conditions. An ADI numerical scheme is used to compute the solution of the steady flow as an asymptotic limit of an unsteady flow. As an example of the method, solutions are presented for subsonic and transonic flow about a 5 percent thick bicircular arc blade of an 8-bladed cascade. Both high and low advance ratio cases are computed and include a lifting as well as nonlifting cases. The nonlifting solutions obtained are compared to solutions from a Euler code.

Prognostic residual mean flow in an ocean general circulation model and its relation to prognostic Eulerian mean flow

DOE PAGES

Saenz, Juan A.; Chen, Qingshan; Ringler, Todd

2015-05-19

Recent work has shown that taking the thickness-weighted average (TWA) of the Boussinesq equations in buoyancy coordinates results in exact equations governing the prognostic residual mean flow where eddy–mean flow interactions appear in the horizontal momentum equations as the divergence of the Eliassen–Palm flux tensor (EPFT). It has been proposed that, given the mathematical tractability of the TWA equations, the physical interpretation of the EPFT, and its relation to potential vorticity fluxes, the TWA is an appropriate framework for modeling ocean circulation with parameterized eddies. The authors test the feasibility of this proposition and investigate the connections between the TWAmore » framework and the conventional framework used in models, where Eulerian mean flow prognostic variables are solved for. Using the TWA framework as a starting point, this study explores the well-known connections between vertical transfer of horizontal momentum by eddy form drag and eddy overturning by the bolus velocity, used by Greatbatch and Lamb and Gent and McWilliams to parameterize eddies. After implementing the TWA framework in an ocean general circulation model, we verify our analysis by comparing the flows in an idealized Southern Ocean configuration simulated using the TWA and conventional frameworks with the same mesoscale eddy parameterization.« less

Investigation of micromixing by acoustically oscillated sharp-edges

PubMed Central

Nama, Nitesh; Huang, Po-Hsun; Huang, Tony Jun; Costanzo, Francesco

2016-01-01

Recently, acoustically oscillated sharp-edges have been utilized to achieve rapid and homogeneous mixing in microchannels. Here, we present a numerical model to investigate acoustic mixing inside a sharp-edge-based micromixer in the presence of a background flow. We extend our previously reported numerical model to include the mixing phenomena by using perturbation analysis and the Generalized Lagrangian Mean (GLM) theory in conjunction with the convection-diffusion equation. We divide the flow variables into zeroth-order, first-order, and second-order variables. This results in three sets of equations representing the background flow, acoustic response, and the time-averaged streaming flow, respectively. These equations are then solved successively to obtain the mean Lagrangian velocity which is combined with the convection-diffusion equation to predict the concentration profile. We validate our numerical model via a comparison of the numerical results with the experimentally obtained values of the mixing index for different flow rates. Further, we employ our model to study the effect of the applied input power and the background flow on the mixing performance of the sharp-edge-based micromixer. We also suggest potential design changes to the previously reported sharp-edge-based micromixer to improve its performance. Finally, we investigate the generation of a tunable concentration gradient by a linear arrangement of the sharp-edge structures inside the microchannel. PMID:27158292

Liquid hydrogen mass flow through a multiple orifice Joule-Thomson device

NASA Astrophysics Data System (ADS)

Papell, S. Stephen; Nyland, Ted W.; Saiyed, Naseem H.

Liquid hydrogen mass flow rate, pressure drop, and temperature drop data were obtained for a number of multiple orifice Joule-Thomas devices known as visco jets. The present investigation continues a study to develop an equation for predicting two phase flow of cryogens through these devices. The test apparatus design allowed isenthalpic expansion of the cryogen through the visco jets. The data covered a range of inlet and outlet operating conditions. The mass flow rate range single phase or two phase was 0.015 to 0.98 lbm/hr. The manufacturer's equation was found to overpredict the single phase hydrogen data by 10 percent and the two phase data by as much as 27 percent. Two modifications of the equation resulted in a data correlation that predicts both the single and two phase flow across the visco jet. The first modification was of a theoretical nature, and the second strictly empirical. The former reduced the spread in the two phase data. It was a multiplication factor of 1 - X applied to the manufacturer's equation. The parameter X is the flow quality downstream of the visco jet based on isenthalpic expansion across the device. The latter modification was a 10 percent correction term that correlated 90 percent of the single and two phase data to within +/- 10 percent scatter band.

Liquid hydrogen mass flow through a multiple orifice Joule-Thomson device

NASA Technical Reports Server (NTRS)

Papell, S. S.; Nyland, Ted W.; Saiyed, Naseem H.

1992-01-01

Liquid hydrogen mass flow rate, pressure drop, and temperature drop data were obtained for a number of multiple orifice Joule-Thomson devices known as visco jets. The present investigation continues a study to develop an equation for predicting two phase flow of cryogens through these devices. The test apparatus design allowed isenthalpic expansion of the cryogen through the visco jets. The data covered a range of inlet and outlet operating conditions. The mass flow rate range single phase or two phase was 0.015 to 0.98 lbm/hr. The manufacturer's equation was found to overpredict the single phase hydrogen data by 10 percent and the two phase data by as much as 27 percent. Two modifications of the equation resulted in a data correlation that predicts both the single and two phase flow across the visco jet. The first modification was of a theoretical nature, and the second strictly empirical. The former reduced the spread in the two phase data. It was a multiplication factor of 1-X applied to the manufacturer's equation. The parameter X is the flow quality downstream of the visco jet based on isenthalpic expansion across the device. The latter modification was a 10 percent correction term that correlated 90 percent of the single and two phase data to within +/- 10 percent scatter band.

Liquid hydrogen mass flow through a multiple orifice Joule-Thomson device

NASA Technical Reports Server (NTRS)

Papell, S. Stephen; Nyland, Ted W.; Saiyed, Naseem H.

1992-01-01

Liquid hydrogen mass flow rate, pressure drop, and temperature drop data were obtained for a number of multiple orifice Joule-Thomas devices known as visco jets. The present investigation continues a study to develop an equation for predicting two phase flow of cryogens through these devices. The test apparatus design allowed isenthalpic expansion of the cryogen through the visco jets. The data covered a range of inlet and outlet operating conditions. The mass flow rate range single phase or two phase was 0.015 to 0.98 lbm/hr. The manufacturer's equation was found to overpredict the single phase hydrogen data by 10 percent and the two phase data by as much as 27 percent. Two modifications of the equation resulted in a data correlation that predicts both the single and two phase flow across the visco jet. The first modification was of a theoretical nature, and the second strictly empirical. The former reduced the spread in the two phase data. It was a multiplication factor of 1 - X applied to the manufacturer's equation. The parameter X is the flow quality downstream of the visco jet based on isenthalpic expansion across the device. The latter modification was a 10 percent correction term that correlated 90 percent of the single and two phase data to within +/- 10 percent scatter band.

Liquid hydrogen mass flow through a multiple orifice Joule-Thomson device

NASA Astrophysics Data System (ADS)

Papell, S. S.; Nyland, Ted W.; Saiyed, Naseem H.

1992-07-01

Liquid hydrogen mass flow rate, pressure drop, and temperature drop data were obtained for a number of multiple orifice Joule-Thomson devices known as visco jets. The present investigation continues a study to develop an equation for predicting two phase flow of cryogens through these devices. The test apparatus design allowed isenthalpic expansion of the cryogen through the visco jets. The data covered a range of inlet and outlet operating conditions. The mass flow rate range single phase or two phase was 0.015 to 0.98 lbm/hr. The manufacturer's equation was found to overpredict the single phase hydrogen data by 10 percent and the two phase data by as much as 27 percent. Two modifications of the equation resulted in a data correlation that predicts both the single and two phase flow across the visco jet. The first modification was of a theoretical nature, and the second strictly empirical. The former reduced the spread in the two phase data. It was a multiplication factor of 1-X applied to the manufacturer's equation. The parameter X is the flow quality downstream of the visco jet based on isenthalpic expansion across the device. The latter modification was a 10 percent correction term that correlated 90 percent of the single and two phase data to within +/- 10 percent scatter band.

Influence of Lorentz force, Cattaneo-Christov heat flux and viscous dissipation on the flow of micropolar fluid past a nonlinear convective stretching vertical surface

NASA Astrophysics Data System (ADS)

Gnaneswara Reddy, Machireddy

2017-12-01

The problem of micropolar fluid flow over a nonlinear stretching convective vertical surface in the presence of Lorentz force and viscous dissipation is investigated. Due to the nature of heat transfer in the flow past vertical surface, Cattaneo-Christov heat flux model effect is properly accommodated in the energy equation. The governing partial differential equations for the flow and heat transfer are converted into a set of ordinary differential equations by employing the acceptable similarity transformations. Runge-Kutta and Newton's methods are utilized to resolve the altered governing nonlinear equations. Obtained numerical results are compared with the available literature and found to be an excellent agreement. The impacts of dimensionless governing flow pertinent parameters on velocity, micropolar velocity and temperature profiles are presented graphically for two cases (linear and nonlinear) and analyzed in detail. Further, the variations of skin friction coefficient and local Nusselt number are reported with the aid of plots for the sundry flow parameters. The temperature and the related boundary enhances enhances with the boosting values of M. It is found that fluid temperature declines for larger thermal relaxation parameter. Also, it is revealed that the Nusselt number declines for the hike values of Bi.

Investigation of micromixing by acoustically oscillated sharp-edges.

PubMed

Nama, Nitesh; Huang, Po-Hsun; Huang, Tony Jun; Costanzo, Francesco

2016-03-01

Recently, acoustically oscillated sharp-edges have been utilized to achieve rapid and homogeneous mixing in microchannels. Here, we present a numerical model to investigate acoustic mixing inside a sharp-edge-based micromixer in the presence of a background flow. We extend our previously reported numerical model to include the mixing phenomena by using perturbation analysis and the Generalized Lagrangian Mean (GLM) theory in conjunction with the convection-diffusion equation. We divide the flow variables into zeroth-order, first-order, and second-order variables. This results in three sets of equations representing the background flow, acoustic response, and the time-averaged streaming flow, respectively. These equations are then solved successively to obtain the mean Lagrangian velocity which is combined with the convection-diffusion equation to predict the concentration profile. We validate our numerical model via a comparison of the numerical results with the experimentally obtained values of the mixing index for different flow rates. Further, we employ our model to study the effect of the applied input power and the background flow on the mixing performance of the sharp-edge-based micromixer. We also suggest potential design changes to the previously reported sharp-edge-based micromixer to improve its performance. Finally, we investigate the generation of a tunable concentration gradient by a linear arrangement of the sharp-edge structures inside the microchannel.

Effects of mean flow on transmission loss of orthogonally rib-stiffened aeroelastic plates.

PubMed

Xin, F X; Lu, T J

2013-06-01

This paper investigates the sound transmission loss (STL) of aeroelastic plates reinforced by two sets of orthogonal rib-stiffeners in the presence of external mean flow. Built upon the periodicity of the structure, a comprehensive theoretical model is developed by considering the convection effect of mean flow. The rib-stiffeners are modeled by employing the Bernoulli-Euler beam theory and the torsional wave equation. While the solution for the transmission loss of the structure based on plate displacement and acoustic pressures is given in the form of space-harmonic series, the corresponding coefficients are obtained from the solution of a system of linear equations derived from the plate-beam coupling vibration governing equation and Helmholtz equation. The model predictions are validated by comparing with existing theoretical and experimental results in the absence of mean flow. A parametric study is subsequently performed to quantify the effects of mean flow as well as structure geometrical parameters upon the transmission loss. It is demonstrated that the transmission loss of periodically rib-stiffened structure is increased significantly with increasing Mach number of mean flow over a wide frequency range. The STL value for the case of sound wave incident downstream is pronouncedly larger than that associated with sound wave incident upstream.

On the Lagrangian description of unsteady boundary-layer separation. I - General theory

NASA Technical Reports Server (NTRS)

Van Dommelen, Leon L.; Cowley, Stephen J.

1990-01-01

Although unsteady, high-Reynolds number, laminar boundary layers have conventionally been studied in terms of Eulerian coordinates, a Lagrangian approach may have significant analytical and computational advantages. In Lagrangian coordinates the classical boundary layer equations decouple into a momentum equation for the motion parallel to the boundary, and a hyperbolic continuity equation (essentially a conserved Jacobian) for the motion normal to the boundary. The momentum equations, plus the energy equation if the flow is compressible, can be solved independently of the continuity equation. Unsteady separation occurs when the continuity equation becomes singular as a result of touching characteristics, the condition for which can be expressed in terms of the solution of the momentum equations. The solutions to the momentum and energy equations remain regular. Asymptotic structures for a number of unsteady 3-D separating flows follow and depend on the symmetry properties of the flow. In the absence of any symmetry, the singularity structure just prior to separation is found to be quasi 2-D with a displacement thickness in the form of a crescent shaped ridge. Physically the singularities can be understood in terms of the behavior of a fluid element inside the boundary layer which contracts in a direction parallel to the boundary and expands normal to it, thus forcing the fluid above it to be ejected from the boundary layer.

On the Lagrangian description of unsteady boundary layer separation. Part 1: General theory

NASA Technical Reports Server (NTRS)

Vandommelen, Leon L.; Cowley, Stephen J.

1989-01-01

Although unsteady, high-Reynolds number, laminar boundary layers have conventionally been studied in terms of Eulerian coordinates, a Lagrangian approach may have significant analytical and computational advantages. In Lagrangian coordinates the classical boundary layer equations decouple into a momentum equation for the motion parallel to the boundary, and a hyperbolic continuity equation (essentially a conserved Jacobian) for the motion normal to the boundary. The momentum equations, plus the energy equation if the flow is compressible, can be solved independently of the continuity equation. Unsteady separation occurs when the continuity equation becomes singular as a result of touching characteristics, the condition for which can be expressed in terms of the solution of the momentum equations. The solutions to the momentum and energy equations remain regular. Asymptotic structures for a number of unsteady 3-D separating flows follow and depend on the symmetry properties of the flow. In the absence of any symmetry, the singularity structure just prior to separation is found to be quasi 2-D with a displacement thickness in the form of a crescent shaped ridge. Physically the singularities can be understood in terms of the behavior of a fluid element inside the boundary layer which contracts in a direction parallel to the boundary and expands normal to it, thus forcing the fluid above it to be ejected from the boundary layer.

Large-Amplitude, High-Rate Roll Oscillations of a 65 deg Delta Wing at High Incidence

NASA Technical Reports Server (NTRS)

Chaderjian, Neal M.; Schiff, Lewis B.

2000-01-01

The IAR/WL 65 deg delta wing experimental results provide both detail pressure measurements and a wide range of flow conditions covering from simple attached flow, through fully developed vortex and vortex burst flow, up to fully-stalled flow at very high incidence. Thus, the Computational Unsteady Aerodynamics researchers can use it at different level of validating the corresponding code. In this section a range of CFD results are provided for the 65 deg delta wing at selected flow conditions. The time-dependent, three-dimensional, Reynolds-averaged, Navier-Stokes (RANS) equations are used to numerically simulate the unsteady vertical flow. Two sting angles and two large- amplitude, high-rate, forced-roll motions and a damped free-to-roll motion are presented. The free-to-roll motion is computed by coupling the time-dependent RANS equations to the flight dynamic equation of motion. The computed results are compared with experimental pressures, forces, moments and roll angle time history. In addition, surface and off-surface flow particle streaks are also presented.

Smoothed particle hydrodynamics method for simulating waterfall flow

NASA Astrophysics Data System (ADS)

Suwardi, M. G.; Jondri; Tarwidi, D.

2018-03-01

The existence of waterfall in many nations, such as Indonesia has a potential to develop and to fulfill the electricity demand in the nation. By utilizing mechanical flow energy of the waterfall, it would be able to generate electricity. The study of mechanical energy could be done by simulating waterfall flow using 2-D smoothed particle hydrodynamics (SPH) method. The SPH method is suitable to simulate the flow of the waterfall, because it has an advantage which could form particles movement that mimic the characteristics of fluid. In this paper, the SPH method is used to solve Navier-Stokes and continuity equation which are the main cores of fluid motion. The governing equations of fluid flow are used to obtain the acceleration, velocity, density, and position of the SPH particles as well as the completion of Leapfrog time-stepping method. With these equations, simulating a waterfall flow would be more attractive and able to complete the analysis of mechanical energy as desired. The mechanical energy that generated from the waterfall flow is calculated and analyzed based on the mass, height, and velocity of each SPH particle.

Travelling-wave solutions of a weakly nonlinear two-dimensional higher-order Kadomtsev-Petviashvili dynamical equation for dispersive shallow-water waves

NASA Astrophysics Data System (ADS)

Seadawy, Aly R.

2017-01-01

The propagation of three-dimensional nonlinear irrotational flow of an inviscid and incompressible fluid of the long waves in dispersive shallow-water approximation is analyzed. The problem formulation of the long waves in dispersive shallow-water approximation lead to fifth-order Kadomtsev-Petviashvili (KP) dynamical equation by applying the reductive perturbation theory. By using an extended auxiliary equation method, the solitary travelling-wave solutions of the two-dimensional nonlinear fifth-order KP dynamical equation are derived. An analytical as well as a numerical solution of the two-dimensional nonlinear KP equation are obtained and analyzed with the effects of external pressure flow.

Calculation of the recirculating compressible flow downstream a sudden axisymmetric expansion

NASA Technical Reports Server (NTRS)

Vandromme, D.; Haminh, H.; Brunet, H.

1988-01-01

Significant progress has been made during the last five years to adapt conventional Navier-Stokes solver for handling nonconservative equations. A primary type of application is to use transport equation turbulence models, but the extension is also possible for describing the transport of nonpassive scalars, such as in reactive media. Among others, combustion and gas dissociation phenomena are topics needing a considerable research effort. An implicit two step scheme based on the well-known MacCormack scheme has been modified to treat compressible turbulent flows on complex geometries. Implicit treatment of nonconservative equations (in the present case a two-equation turbulence model) opens the way to the coupled solution of thermochemical transport equations.

Personal computer study of finite-difference methods for the transonic small disturbance equation

NASA Technical Reports Server (NTRS)

Bland, Samuel R.

1989-01-01

Calculation of unsteady flow phenomena requires careful attention to the numerical treatment of the governing partial differential equations. The personal computer provides a convenient and useful tool for the development of meshes, algorithms, and boundary conditions needed to provide time accurate solution of these equations. The one-dimensional equation considered provides a suitable model for the study of wave propagation in the equations of transonic small disturbance potential flow. Numerical results for effects of mesh size, extent, and stretching, time step size, and choice of far-field boundary conditions are presented. Analysis of the discretized model problem supports these numerical results. Guidelines for suitable mesh and time step choices are given.

Gas-kinetic unified algorithm for hypersonic flows covering various flow regimes solving Boltzmann model equation in nonequilibrium effect

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Zhihui; Ma, Qiang; Wu, Junlin

2014-12-09

Based on the Gas-Kinetic Unified Algorithm (GKUA) directly solving the Boltzmann model equation, the effect of rotational non-equilibrium is investigated recurring to the kinetic Rykov model with relaxation property of rotational degrees of freedom. The spin movement of diatomic molecule is described by moment of inertia, and the conservation of total angle momentum is taken as a new Boltzmann collision invariant. The molecular velocity distribution function is integrated by the weight factor on the internal energy, and the closed system of two kinetic controlling equations is obtained with inelastic and elastic collisions. The optimization selection technique of discrete velocity ordinatemore » points and numerical quadrature rules for macroscopic flow variables with dynamic updating evolvement are developed to simulate hypersonic flows, and the gas-kinetic numerical scheme is constructed to capture the time evolution of the discretized velocity distribution functions. The gas-kinetic boundary conditions in thermodynamic non-equilibrium and numerical procedures are studied and implemented by directly acting on the velocity distribution function, and then the unified algorithm of Boltzmann model equation involving non-equilibrium effect is presented for the whole range of flow regimes. The hypersonic flows involving non-equilibrium effect are numerically simulated including the inner flows of shock wave structures in nitrogen with different Mach numbers of 1.5-Ma-25, the planar ramp flow with the whole range of Knudsen numbers of 0.0009-Kn-10 and the three-dimensional re-entering flows around tine double-cone body.« less

Analysis, Verification, and Application of Equations and Procedures for Design of Exhaust-pipe Shrouds

NASA Technical Reports Server (NTRS)

Ellerbrock, Herman H.; Wcislo, Chester R.; Dexter, Howard E.

1947-01-01

Investigations were made to develop a simplified method for designing exhaust-pipe shrouds to provide desired or maximum cooling of exhaust installations. Analysis of heat exchange and pressure drop of an adequate exhaust-pipe shroud system requires equations for predicting design temperatures and pressure drop on cooling air side of system. Present experiments derive such equations for usual straight annular exhaust-pipe shroud systems for both parallel flow and counter flow. Equations and methods presented are believed to be applicable under certain conditions to the design of shrouds for tail pipes of jet engines.

On a modified form of navier-stokes equations for three-dimensional flows.

PubMed

Venetis, J

2015-01-01

A rephrased form of Navier-Stokes equations is performed for incompressible, three-dimensional, unsteady flows according to Eulerian formalism for the fluid motion. In particular, we propose a geometrical method for the elimination of the nonlinear terms of these fundamental equations, which are expressed in true vector form, and finally arrive at an equivalent system of three semilinear first order PDEs, which hold for a three-dimensional rectangular Cartesian coordinate system. Next, we present the related variational formulation of these modified equations as well as a general type of weak solutions which mainly concern Sobolev spaces.

On a Modified Form of Navier-Stokes Equations for Three-Dimensional Flows

PubMed Central

Venetis, J.

2015-01-01

A rephrased form of Navier-Stokes equations is performed for incompressible, three-dimensional, unsteady flows according to Eulerian formalism for the fluid motion. In particular, we propose a geometrical method for the elimination of the nonlinear terms of these fundamental equations, which are expressed in true vector form, and finally arrive at an equivalent system of three semilinear first order PDEs, which hold for a three-dimensional rectangular Cartesian coordinate system. Next, we present the related variational formulation of these modified equations as well as a general type of weak solutions which mainly concern Sobolev spaces. PMID:25918743

A new Eulerian model for viscous and heat conducting compressible flows

NASA Astrophysics Data System (ADS)

Svärd, Magnus

2018-09-01

In this article, a suite of physically inconsistent properties of the Navier-Stokes equations, associated with the lack of mass diffusion and the definition of velocity, is presented. We show that these inconsistencies are consequences of the Lagrangian derivation that models viscous stresses rather than diffusion. A new model for compressible and diffusive (viscous and heat conducting) flows of an ideal gas, is derived in a purely Eulerian framework. We propose that these equations supersede the Navier-Stokes equations. A few numerical experiments demonstrate some differences and similarities between the new system and the Navier-Stokes equations.

The solution of three-variable duct-flow equations

NASA Technical Reports Server (NTRS)

Stuart, A. R.; Hetherington, R.

1974-01-01

This paper establishes a numerical method for the solution of three-variable problems and is applied here to rotational flows through ducts of various cross sections. An iterative scheme is developed, the main feature of which is the addition of a duplicate variable to the forward component of velocity. Two forward components of velocity result from integrating two sets of first order ordinary differential equations for the streamline curvatures, in intersecting directions across the duct. Two pseudo-continuity equations are introduced with source/sink terms, whose strengths are dependent on the difference between the forward components of velocity. When convergence is obtained, the two forward components of velocity are identical, the source/sink terms are zero, and the original equations are satisfied. A computer program solves the exact equations and boundary conditions numerically. The method is economical and compares successfully with experiments on bent ducts of circular and rectangular cross section where secondary flows are caused by gradients of total pressure upstream.

The study of the Boltzmann equation of solid-gas two-phase flow with three-dimensional BGK model

NASA Astrophysics Data System (ADS)

Liu, Chang-jiang; Pang, Song; Xu, Qiang; He, Ling; Yang, Shao-peng; Qing, Yun-jie

2018-06-01

The motion of many solid-gas two-phase flows can be described by the Boltzmann equation. In order to simplify the Boltzmann equation, the convective-diffusion term is reserved and the collision term is replaced by the three-dimensional Bharnagar-Gross-Krook (BGK) model. Then the simplified Boltzmann equation is solved by homotopy perturbation method (HPM), and its approximate analytical solution is obtained. Through the analyzing, it is proved that the analytical solution satisfies all the constraint conditions, and its formation is in accord with the formation of the solution that is obtained by traditional Chapman-Enskog method, and the solving process of HPM is much more simple and convenient. This preliminarily shows the effectiveness and rapidness of HPM to solve the Boltzmann equation. The results obtained herein provide some theoretical basis for the further study of dynamic model of solid-gas two-phase flows, such as the sturzstrom of high-speed distant landslide caused by microseism and the sand storm caused by strong breeze.

Numerical simulations of incompressible laminar flows using viscous-inviscid interaction procedures

NASA Astrophysics Data System (ADS)

Shatalov, Alexander V.

The present method is based on Helmholtz velocity decomposition where velocity is written as a sum of irrotational (gradient of a potential) and rotational (correction due to vorticity) components. Substitution of the velocity decomposition into the continuity equation yields an equation for the potential, while substitution into the momentum equations yields equations for the velocity corrections. A continuation approach is used to relate the pressure to the gradient of the potential through a modified Bernoulli's law, which allows the elimination of the pressure variable from the momentum equations. The present work considers steady and unsteady two-dimensional incompressible flows over an infinite cylinder and NACA 0012 airfoil shape. The numerical results are compared against standard methods (stream function-vorticity and SMAC methods) and data available in literature. The results demonstrate that the proposed formulation leads to a good approximation with some possible benefits compared to the available formulations. The method is not restricted to two-dimensional flows and can be used for viscous-inviscid domain decomposition calculations.

A Modified Double Multiple Nonlinear Regression Constitutive Equation for Modeling and Prediction of High Temperature Flow Behavior of BFe10-1-2 Alloy

NASA Astrophysics Data System (ADS)

Cai, Jun; Wang, Kuaishe; Shi, Jiamin; Wang, Wen; Liu, Yingying

2018-01-01

Constitutive analysis for hot working of BFe10-1-2 alloy was carried out by using experimental stress-strain data from isothermal hot compression tests, in a wide range of temperature of 1,023 1,273 K, and strain rate range of 0.001 10 s-1. A constitutive equation based on modified double multiple nonlinear regression was proposed considering the independent effects of strain, strain rate, temperature and their interrelation. The predicted flow stress data calculated from the developed equation was compared with the experimental data. Correlation coefficient (R), average absolute relative error (AARE) and relative errors were introduced to verify the validity of the developed constitutive equation. Subsequently, a comparative study was made on the capability of strain-compensated Arrhenius-type constitutive model. The results showed that the developed constitutive equation based on modified double multiple nonlinear regression could predict flow stress of BFe10-1-2 alloy with good correlation and generalization.

A rain splash transport equation assimilating field and laboratory measurements

USGS Publications Warehouse

Dunne, T.; Malmon, D.V.; Mudd, S.M.

2010-01-01

Process-based models of hillslope evolution require transport equations relating sediment flux to its major controls. An equation for rain splash transport in the absence of overland flow was constructed by modifying an approach developed by Reeve (1982) and parameterizing it with measurements from single-drop laboratory experiments and simulated rainfall on a grassland in East Africa. The equation relates rain splash to hillslope gradient, the median raindrop diameter of a storm, and ground cover density; the effect of soil texture on detachability can be incorporated from other published results. The spatial and temporal applicability of such an equation for rain splash transport in the absence of overland flow on uncultivated hillslopes can be estimated from hydrological calculations. The predicted transport is lower than landscape-averaged geologic erosion rates from Kenya but is large enough to modify short, slowly eroding natural hillslopes as well as microtopographic interrill surfaces between which overland flow transports the mobilized sediment. Copyright 2010 by the American Geophysical Union. Copyright 2010 by the American Geophysical Union.

Ill-posedness of Dynamic Equations of Compressible Granular Flow

NASA Astrophysics Data System (ADS)

Shearer, Michael; Gray, Nico

2017-11-01

We introduce models for 2-dimensional time-dependent compressible flow of granular materials and suspensions, based on the rheology of Pouliquen and Forterre. The models include density dependence through a constitutive equation in which the density or volume fraction of solid particles with material density ρ* is taken as a function of an inertial number I: ρ = ρ * Φ(I), in which Φ(I) is a decreasing function of I. This modelling has different implications from models relying on critical state soil mechanics, in which ρ is treated as a variable in the equations, contributing to a flow rule. The analysis of the system of equations builds on recent work of Barker et al in the incompressible case. The main result is the identification of a criterion for well-posedness of the equations. We additionally analyze a modification that applies to suspensions, for which the rheology takes a different form and the inertial number reflects the role of the fluid viscosity.

The Boundary Integral Equation Method for Porous Media Flow

NASA Astrophysics Data System (ADS)

Anderson, Mary P.

Just as groundwater hydrologists are breathing sighs of relief after the exertions of learning the finite element method, a new technique has reared its nodes—the boundary integral equation method (BIEM) or the boundary equation method (BEM), as it is sometimes called. As Liggett and Liu put it in the preface to The Boundary Integral Equation Method for Porous Media Flow, “Lately, the Boundary Integral Equation Method (BIEM) has emerged as a contender in the computation Derby.” In fact, in July 1984, the 6th International Conference on Boundary Element Methods in Engineering will be held aboard the Queen Elizabeth II, en route from Southampton to New York. These conferences are sponsored by the Department of Civil Engineering at Southampton College (UK), whose members are proponents of BIEM. The conferences have featured papers on applications of BIEM to all aspects of engineering, including flow through porous media. Published proceedings are available, as are textbooks on application of BIEM to engineering problems. There is even a 10-minute film on the subject.

Central Upwind Scheme for a Compressible Two-Phase Flow Model

PubMed Central

Ahmed, Munshoor; Saleem, M. Rehan; Zia, Saqib; Qamar, Shamsul

2015-01-01

In this article, a compressible two-phase reduced five-equation flow model is numerically investigated. The model is non-conservative and the governing equations consist of two equations describing the conservation of mass, one for overall momentum and one for total energy. The fifth equation is the energy equation for one of the two phases and it includes source term on the right-hand side which represents the energy exchange between two fluids in the form of mechanical and thermodynamical work. For the numerical approximation of the model a high resolution central upwind scheme is implemented. This is a non-oscillatory upwind biased finite volume scheme which does not require a Riemann solver at each time step. Few numerical case studies of two-phase flows are presented. For validation and comparison, the same model is also solved by using kinetic flux-vector splitting (KFVS) and staggered central schemes. It was found that central upwind scheme produces comparable results to the KFVS scheme. PMID:26039242

Central upwind scheme for a compressible two-phase flow model.

PubMed

Ahmed, Munshoor; Saleem, M Rehan; Zia, Saqib; Qamar, Shamsul

2015-01-01

In this article, a compressible two-phase reduced five-equation flow model is numerically investigated. The model is non-conservative and the governing equations consist of two equations describing the conservation of mass, one for overall momentum and one for total energy. The fifth equation is the energy equation for one of the two phases and it includes source term on the right-hand side which represents the energy exchange between two fluids in the form of mechanical and thermodynamical work. For the numerical approximation of the model a high resolution central upwind scheme is implemented. This is a non-oscillatory upwind biased finite volume scheme which does not require a Riemann solver at each time step. Few numerical case studies of two-phase flows are presented. For validation and comparison, the same model is also solved by using kinetic flux-vector splitting (KFVS) and staggered central schemes. It was found that central upwind scheme produces comparable results to the KFVS scheme.

Particle flows to shape and voltage surface discontinuities in the electron sheath surrounding a high voltage solar array in LEO

NASA Technical Reports Server (NTRS)

Metz, Roger N.

1991-01-01

This paper discusses the numerical modeling of electron flows from the sheath surrounding high positively biased objects in LEO (Low Earth Orbit) to regions of voltage or shape discontinuity on the biased surfaces. The sheath equations are derived from the Two-fluid, Warm Plasma Model. An equipotential corner and a plane containing strips of alternating voltage bias are treated in two dimensions. A self-consistent field solution of the sheath equations is outlined and is pursued through one cycle. The electron density field is determined by numerical solution of Poisson's equation for the electrostatic potential in the sheath using the NASCAP-LEO relation between electrostatic potential and charge density. Electron flows are calculated numerically from the electron continuity equation. Magnetic field effects are not treated.

Exact Solutions for Stokes' Flow of a Non-Newtonian Nanofluid Model: A Lie Similarity Approach

NASA Astrophysics Data System (ADS)

Aziz, Taha; Aziz, A.; Khalique, C. M.

2016-07-01

The fully developed time-dependent flow of an incompressible, thermodynamically compatible non-Newtonian third-grade nanofluid is investigated. The classical Stokes model is considered in which the flow is generated due to the motion of the plate in its own plane with an impulsive velocity. The Lie symmetry approach is utilised to convert the governing nonlinear partial differential equation into different linear and nonlinear ordinary differential equations. The reduced ordinary differential equations are then solved by using the compatibility and generalised group method. Exact solutions for the model equation are deduced in the form of closed-form exponential functions which are not available in the literature before. In addition, we also derived the conservation laws associated with the governing model. Finally, the physical features of the pertinent parameters are discussed in detail through several graphs.

Tollmien-Schlichting/vortex interactions in compressible boundary layer flows

NASA Technical Reports Server (NTRS)

Blackaby, Nicholas D.

1993-01-01

The weakly nonlinear interaction of oblique Tollmien-Schlichting waves and longitudinal vortices in compressible, high Reynolds number, boundary-layer flow over a flat plate is considered for all ranges of the Mach number. The interaction equations comprise of equations for the vortex which is indirectly forced by the waves via a boundary condition, whereas a vortex term appears in the amplitude equation for the wave pressure. The downstream solution properties of interaction equations are found to depend on the sign of an interaction coefficient. Compressibility is found to have a significant effect on the interaction properties; principally through its impact on the waves and their governing mechanism, the triple-deck structure. It is found that, in general, the flow quantities will grow slowly with increasing downstream co-ordinate; i.e. in general, solutions do not terminate in abrupt, finite-distance 'break-ups'.

Numerical study of supersonic combustion using a finite rate chemistry model

NASA Technical Reports Server (NTRS)

Chitsomboon, T.; Tiwari, S. N.; Kumar, A.; Drummond, J. P.

1986-01-01

The governing equations of two-dimensional chemically reacting flows are presented together with a global two-step chemistry model for H2-air combustion. The explicit unsplit MacCormack finite difference algorithm is used to advance the discrete system of the governing equations in time until convergence is attained. The source terms in the species equations are evaluated implicitly to alleviate stiffness associated with fast reactions. With implicit source terms, the species equations give rise to a block-diagonal system which can be solved very efficiently on vector-processing computers. A supersonic reacting flow in an inlet-combustor configuration is calculated for the case where H2 is injected into the flow from the side walls and the strut. Results of the calculation are compared against the results obtained by using a complete reaction model.

Recent Turbulence Model Advances Applied to Multielement Airfoil Computations

NASA Technical Reports Server (NTRS)

Rumsey, Christopher L.; Gatski, Thomas B.

2000-01-01

A one-equation linear turbulence model and a two-equation nonlinear explicit algebraic stress model (EASM) are applied to the flow over a multielement airfoil. The effect of the K-epsilon and K-omega forms of the two-equation model are explored, and the K-epsilon form is shown to be deficient in the wall-bounded regions of adverse pressure gradient flows. A new K-omega form of EASM is introduced. Nonlinear terms present in EASM are shown to improve predictions of turbulent shear stress behind the trailing edge of the main element and near midflap. Curvature corrections are applied to both the one- and two-equation turbulence models and yield only relatively small local differences in the flap region, where the flow field undergoes the greatest curvature. Predictions of maximum lift are essentially unaffected by the turbulence model variations studied.

Thermochemical nonequilibrium in atomic hydrogen at elevated temperatures

NASA Technical Reports Server (NTRS)

Scott, R. K.

1972-01-01

A numerical study of the nonequilibrium flow of atomic hydrogen in a cascade arc was performed to obtain insight into the physics of the hydrogen cascade arc. A rigorous mathematical model of the flow problem was formulated, incorporating the important nonequilibrium transport phenomena and atomic processes which occur in atomic hydrogen. Realistic boundary conditions, including consideration of the wall electrostatic sheath phenomenon, were included in the model. The governing equations of the asymptotic region of the cascade arc were obtained by writing conservation of mass and energy equations for the electron subgas, an energy conservation equation for heavy particles and an equation of state. Finite-difference operators for variable grid spacing were applied to the governing equations and the resulting system of strongly coupled, stiff equations were solved numerically by the Newton-Raphson method.

Nonlinear Solver Approaches for the Diffusive Wave Approximation to the Shallow Water Equations

NASA Astrophysics Data System (ADS)

Collier, N.; Knepley, M.

2015-12-01

The diffusive wave approximation to the shallow water equations (DSW) is a doubly-degenerate, nonlinear, parabolic partial differential equation used to model overland flows. Despite its challenges, the DSW equation has been extensively used to model the overland flow component of various integrated surface/subsurface models. The equation's complications become increasingly problematic when ponding occurs, a feature which becomes pervasive when solving on large domains with realistic terrain. In this talk I discuss the various forms and regularizations of the DSW equation and highlight their effect on the solvability of the nonlinear system. In addition to this analysis, I present results of a numerical study which tests the applicability of a class of composable nonlinear algebraic solvers recently added to the Portable, Extensible, Toolkit for Scientific Computation (PETSc).

Numerical modeling of the interaction of liquid drops and jets with shock waves and gas jets

NASA Astrophysics Data System (ADS)

Surov, V. S.

1993-02-01

The motion of a liquid drop (jet) and of the ambient gas is described, in the general case, by Navier-Stokes equations. An approximate solution to the interaction of a plane shock wave with a single liquid drop is presented. Based on the analysis, the general system of Navier-Stokes equations is reduced to two groups of equations, Euler equations for gas and Navier-Stokes equations for liquid; solutions to these equations are presented. The discussion also covers the modeling of the interaction of a shock wave with a drop screen, interaction of a liquid jet with a counterpropagating supersonic gas flow, and modeling of processes in a shock layer during the impact of a drop against an obstacle in gas flow.

Variational method enabling simplified solutions to the linearized Boltzmann equation for oscillatory gas flows

NASA Astrophysics Data System (ADS)

Ladiges, Daniel R.; Sader, John E.

2018-05-01

Nanomechanical resonators and sensors, operated in ambient conditions, often generate low-Mach-number oscillating rarefied gas flows. Cercignani [C. Cercignani, J. Stat. Phys. 1, 297 (1969), 10.1007/BF01007482] proposed a variational principle for the linearized Boltzmann equation, which can be used to derive approximate analytical solutions of steady (time-independent) flows. Here we extend and generalize this principle to unsteady oscillatory rarefied flows and thus accommodate resonating nanomechanical devices. This includes a mathematical approach that facilitates its general use and allows for systematic improvements in accuracy. This formulation is demonstrated for two canonical flow problems: oscillatory Couette flow and Stokes' second problem. Approximate analytical formulas giving the bulk velocity and shear stress, valid for arbitrary oscillation frequency, are obtained for Couette flow. For Stokes' second problem, a simple system of ordinary differential equations is derived which may be solved to obtain the desired flow fields. Using this framework, a simple and accurate formula is provided for the shear stress at the oscillating boundary, again for arbitrary frequency, which may prove useful in application. These solutions are easily implemented on any symbolic or numerical package, such as Mathematica or matlab, facilitating the characterization of flows produced by nanomechanical devices and providing insight into the underlying flow physics.

The use of numerical programs in research and academic institutions

NASA Astrophysics Data System (ADS)

Scupi, A. A.

2016-08-01

This paper is conceived on the idea that numerical programs using computer models of physical processes can be used both for scientific research and academic teaching to study different phenomena. Computational Fluid Dynamics (CFD) is used today on a large scale in research and academic institutions. CFD development is not limited to computer simulations of fluid flow phenomena. Analytical solutions for most fluid dynamics problems are already available for ideal or simplified situations for different situations. CFD is based on the Navier- Stokes (N-S) equations characterizing the flow of a single phase of any liquid. For multiphase flows the integrated N-S equations are complemented with equations of the Volume of Fluid Model (VOF) and with energy equations. Different turbulent models were used in the paper, each one of them with practical engineering applications: the flow around aerodynamic surfaces used as unconventional propulsion system, multiphase flows in a settling chamber and pneumatic transport systems, heat transfer in a heat exchanger etc. Some of them numerical results were validated by experimental results. Numerical programs are also used in academic institutions where certain aspects of various phenomena are presented to students (Bachelor, Master and PhD) for a better understanding of the phenomenon itself.

Stability analysis of rimming flow inside a horizontally rotating cylinder in the presence of an insoluble surfactant

NASA Astrophysics Data System (ADS)

Kumawat, Tara Chand; Tiwari, Naveen

2017-12-01

Two-dimensional base state solutions for rimming flows and their stability analysis to small axial perturbations are analyzed numerically. A thin liquid film which is uniformly covered with an insoluble surfactant flows inside a counterclockwise rotating horizontal cylinder. In the present work, a mathematical model is obtained which consists of coupled thin film thickness and surfactant concentration evolution equations. The governing equations are obtained by simplifying the momentum and species transport equations using the thin-film approximation. The model equations include the effect of gravity, viscosity, capillarity, inertia, and Marangoni stress. The concentration gradients generated due to flow result in the surface tension gradient that generates the Marangoni stress near the interface region. The oscillations in the flow due to inertia are damped out by the Marangoni stress. It is observed that the Marangoni stress has stabilizing effect, whereas inertia and surface tension enhance the instability growth rate. In the presence of low diffusion of the surfactant or large value of the Péclet number, the Marangoni stress becomes more effective. The analytically obtained eigenvalues match well with the numerically computed eigenvalues in the absence of gravity.

Longitudinal vibration and stability analysis of carbon nanotubes conveying viscous fluid

NASA Astrophysics Data System (ADS)

Oveissi, Soheil; Toghraie, Davood; Eftekhari, Seyyed Ali

2016-09-01

Nowadays, carbon nanotubes (CNT) play an important role in practical applications in fluidic devices. To this end, researchers have studied various aspects of vibration analysis of a behavior of CNT conveying fluid. In this paper, based on nonlocal elasticity theory, single-walled carbon nanotube (SWCNT) is simulated. To investigate and analyze the effect of internal fluid flow on the longitudinal vibration and stability of SWCNT, the equation of motion for longitudinal vibration is obtained by using Navier-Stokes equations. In the governing equation of motion, the interaction of fluid-structure, dynamic and fluid flow velocity along the axial coordinate of the nanotube and the nano-scale effect of the structure are considered. To solve the nonlocal longitudinal vibration equation, the approximate Galerkin method is employed and appropriate simply supported boundary conditions are applied. The results show that the axial vibrations of the nanotubesstrongly depend on the small-size effect. In addition, the fluid flowing in nanotube causes a decrease in the natural frequency of the system. It is obvious that the system natural frequencies reach zero at lower critical flow velocities as the wave number increases. Moreover, the critical flow velocity decreases as the nonlocal parameter increases.

A research on wave equation on inclined channel and observation for intermittent debris flow

NASA Astrophysics Data System (ADS)

Arai, Muneyuki

2014-05-01

Phenomenon of intermittent surges is known a debris flow called viscous debris flow in China, and recently is observed in the European Alps and other mountains region. A purpose of this research is to obtain a wave equation for wave motion of intermittent surges with sediment on inclined channel, especially to evaluate influence of momentum correction factor on flow mechanism. Using non-dimensional basic equations as Laplace equation, δ2φ'/δx'2 + δ2φ'/δy'2 = 0 , boundary condition at bottom of flow, δφ'/δy' = 0, (y' = -1; at bottom of mean depth h0 ), surface condition ( conservation condition of flow surface ), ' ' ' ' - δφ-+ δη- + δφ-δη-= 0 (y' = 0;atsurfaceofmean depth h0 ), δy' δt' δt'δx' and momentum equation, ' ( ')2 '2 δφ-+ 1 (2β - 1) δφ- - c0'2 tanθx ' +c0'2 (1+ η')+ tan θ c0-φ' δt' 2 δx' u0' δ« ( δφ')2 δη' ' ' u0 ' c0 + (β - 1) δx' δx'dx = 0, here,u0 = v-, c0 = v- p0 p0 where, x : coordinate axis of flow direction, x' = x/h0, y : coordinate axis of depth direction, y' = y/h0, h : depth of flow, h0 : mean depth, t : time, t' = tvp0/h0, u0 : mean velocity, vp0 : velocity parameter in G-M transfer, φ = φ(x,y,t) : potential function, φ' = φ/(h0 vp0), g : acceleration due to gravity, θ : slope angle of the channel, c0 = ---- gh0cosθ. From these basic equation, a wave equation is obtained as follow by perturbation method, here neglecting the term of φ' with tanθ ≪ 1, δη' 1 '2 ' δη' 1 c0'2 δ2η' 1( 1 ) δ3η' δτ' + 2 (2β + 1) c0 η δξ' - 2 tanθ u-'-δξ'2-+ 2 c-'2- 1-δξ'3 = 0, 0 0 where η : deflection from h0 (h = h0 + η), η' = η/h0, ξ = ɛ1/2(x - vp0t), ξ' = ξ/h0, τ = ɛ3/2t, τ' = tvp0/h0, ɛ: parameter of perturbation method. In this equation, second term of left side is non-linear term which generates waves of various periods, third is dissipation term which disappear high frequency wave and forth is dispersion term which has a characteristic of a soliton on KdV equation. In a case using vp0 = c0, above equation is expressed as δη' 1 ' δη' 1tanθ-δ2η' δτ' + 2 (2β + 1) η δξ' - 2 u0' δξ'2 = 0. Usually β varies from 1 to 1.2, then it is expected that the influence of β for wave formation η' is small by above equation. For observation on wave characteristic of intermittent surges, it is indicated to measure phase velocity of wave, mean velocity of the flow, depth fluctuation and other usual terms.

Flow stress equations for type 304 stainless and AISI 1055 steels

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dadras, P.

A model for stress-strain behavior under hot working conditions has been proposed. Based on experimental data, equations for the dependence of flow stress on strain, strain rate, and temperature have been developed. Application to type 304 stainless steel and AISI 1055 steel has been demonstrated.

A Critical Technical Review of Six Hazard Assessment Models

DTIC Science & Technology

1975-12-01

temperature is 3000K. Vi The equation describing flame length is taken from a paper of Hawthorne, Weddell, and Hottel [3] who obtained the equation by...should be noted that the flame length given by equation (6.1) in AMSHAH is independent of the flow rate; flame length independence of flow rate does not...experiments and analyses upon which the formula for flame length is based are for jets issuing from circular orifices. Substantial departures from this

A method for the automated construction of the joint system of equations to solve the problem of the flow distribution in hydraulic networks

NASA Astrophysics Data System (ADS)

Novikov, A. E.

1993-10-01

There are several methods of solving the problem of the flow distribution in hydraulic networks. But all these methods have no mathematical tools for forming joint systems of equations to solve this problem. This paper suggests a method of constructing joint systems of equations to calculate hydraulic circuits of the arbitrary form. The graph concept, according to Kirchhoff, has been introduced.

An electrical analogy relating the Atlantic multidecadal oscillation to the Atlantic meridional overturning circulation.

PubMed

Kurtz, Bruce E

2014-01-01

The Atlantic meridional overturning circulation (AMOC) is the northward flow of surface water to subpolar latitudes where deepwater is formed, balanced by southward abyssal flow and upwelling in the vicinity of the Southern Ocean. It is generally accepted that AMOC flow oscillates with a period of 60-80 years, creating a regular variation in North Atlantic sea surface temperature known as the Atlantic multidecadal oscillation (AMO). This article attempts to answer two questions: how is the AMOC driven and why does it oscillate? Using methods commonly employed by chemical engineers for analyzing processes involving flowing liquids, apparently not previously applied to trying to understand the AMOC, an equation is developed for AMOC flow as a function of the meridional density gradient or the corresponding temperature gradient. The equation is based on the similarity between the AMOC and an industrial thermosyphon loop cooler, which circulates a heat transfer liquid without using a mechanical pump. Extending this equation with an analogy between the flow of heat and electricity explains why the AMOC flow oscillates and what determines its period. Calculated values for AMOC flow and AMO oscillation period are in good agreement with measured values.

An Electrical Analogy Relating the Atlantic Multidecadal Oscillation to the Atlantic Meridional Overturning Circulation

PubMed Central

Kurtz, Bruce E.

2014-01-01

The Atlantic meridional overturning circulation (AMOC) is the northward flow of surface water to subpolar latitudes where deepwater is formed, balanced by southward abyssal flow and upwelling in the vicinity of the Southern Ocean. It is generally accepted that AMOC flow oscillates with a period of 60–80 years, creating a regular variation in North Atlantic sea surface temperature known as the Atlantic multidecadal oscillation (AMO). This article attempts to answer two questions: how is the AMOC driven and why does it oscillate? Using methods commonly employed by chemical engineers for analyzing processes involving flowing liquids, apparently not previously applied to trying to understand the AMOC, an equation is developed for AMOC flow as a function of the meridional density gradient or the corresponding temperature gradient. The equation is based on the similarity between the AMOC and an industrial thermosyphon loop cooler, which circulates a heat transfer liquid without using a mechanical pump. Extending this equation with an analogy between the flow of heat and electricity explains why the AMOC flow oscillates and what determines its period. Calculated values for AMOC flow and AMO oscillation period are in good agreement with measured values. PMID:24940739

Interactive calculation procedure for supersonic flows. Ph.D. Thesis - Case Western Reserve Univ., 1976. Final Report

NASA Technical Reports Server (NTRS)

Tassa, Y.; Anderson, B. H.; Reshotko, E.

1977-01-01

An interactive procedure was developed for supersonic viscous flows that can be used for either two-dimensional or axisymmetric configurations. The procedure is directed to supersonic internal flows as well as those supersonic external flows that require consideration of mutual interaction between the outer flow and the boundary layer flow. The flow field is divided into two regions: an inner region which is highly viscous and mostly subsonic and an outer region where the flow is supersonic and in which viscous effects are small but not negligible. For the outer region a numerical solution is obtained by applying the method of characteristics to a system of equations which includes viscous and conduction transport terms only normal to the streamlines. The inner region is treated by a system of equations of the boundary layer type that includes higher order effects such as longitudinal and transverse curvature and normal pressure gradients. These equations are coupled and solved simultaneously in the physical coordinates by using an implicit finite difference scheme. This system can also be used to calculate laminar and turbulent boundary layers using a scalar eddy viscosity concept.

Influence of the Haizhou Open Pit Coal Mine on the atmospheric flow over Fuxin, China.

PubMed

Chen, He; Yang, Zhi-Feng; Wang, Xuan

2004-01-01

The influence of the Haizhou Open Pit Mine on the atmospheric flow in nearby Fuxin City in China was analyzed with the aid of the steady-state Navier-Stokes equations. The finite element method was used to obtain numerical solutions to these equations. The results showed that the Haizhou Open Pit Coal Mine contributes to the turbulent flow in the Fuxin City and its surroundings. However, when compared with the climatic effects, the open pit mine has a relatively small impact on the atmospheric flow over Fuxin.

Numerical simulation study on the distribution law of smoke flow velocity in horizontal tunnel fire

NASA Astrophysics Data System (ADS)

Liu, Yejiao; Tian, Zhichao; Xue, Junhua; Wang, Wencai

2018-02-01

According to the fluid similarity theory, the simulation experiment system of mining tunnel fire is established. The grid division of experimental model roadway is carried on by GAMBIT software. By setting the boundary and initial conditions of smoke flow during fire period in FLUENT software, using RNG k-Ɛ two-equation turbulence model, energy equation and SIMPLE algorithm, the steady state numerical simulation of smoke flow velocity in mining tunnel is done to obtain the distribution law of smoke flow velocity in tunnel during fire period.

A numerical study of the 2- and 3-dimensional unsteady Navier-Stokes equations in velocity-vorticity variables using compact difference schemes

NASA Technical Reports Server (NTRS)

Gatski, T. B.; Grosch, C. E.

1984-01-01

A compact finite-difference approximation to the unsteady Navier-Stokes equations in velocity-vorticity variables is used to numerically simulate a number of flows. These include two-dimensional laminar flow of a vortex evolving over a flat plate with an embedded cavity, the unsteady flow over an elliptic cylinder, and aspects of the transient dynamics of the flow over a rearward facing step. The methodology required to extend the two-dimensional formulation to three-dimensions is presented.

Transonic small disturbances equation applied to the solution of two-dimensional nonsteady flows

NASA Technical Reports Server (NTRS)

Couston, M.; Angelini, J. J.; Mulak, P.

1980-01-01

Transonic nonsteady flows are of large practical interest. Aeroelastic instability prediction, control figured vehicle techniques or rotary wings in forward flight are some examples justifying the effort undertaken to improve knowledge of these problems is described. The numerical solution of these problems under the potential flow hypothesis is described. The use of an alternating direction implicit scheme allows the efficient resolution of the two dimensional transonic small perturbations equation.

A Unified View of Global Instabilities of Compressible Flow Over Open Cavities

DTIC Science & Technology

2005-06-30

the early work of Rossiter [3], have treated the shear-layer emanating from the upstream comer of the cavity in isolation ( using parallel flow... using a domain-decomposition method. The code has optional equation sets to solve either (i) nonlinear Navier-Stokes, (ii) Navier-Stokes equations...early experments of Maull and East [15]. They used oil flow visualization of surface streamlines on the cavity bottom to show the existence, under certain

The Development of a Factorizable Multigrid Algorithm for Subsonic and Transonic Flow

NASA Technical Reports Server (NTRS)

Roberts, Thomas W.

2001-01-01

The factorizable discretization of Sidilkover for the compressible Euler equations previously demonstrated for channel flows has been extended to external flows.The dissipation of the original scheme has been modified to maintain stability for moderately stretched grids. The discrete equations are solved by symmetric collective Gauss-Seidel relaxation and FAS multigrid. Unlike the earlier work ordering the grid vertices in the flow direction has been found to be unnecessary. Solutions for essential incompressible flow (Mach 0.01) and supercritical flows have obtained for a Karman-Trefftz airfoil with it conformally mapped grid,as well as a NACA 0012 on an algebraically generated grid. The current work demonstrates nearly 0(n) convergence for subsonic and slightly transonic flows.

A New Reynolds Stress Algebraic Equation Model

NASA Technical Reports Server (NTRS)

Shih, Tsan-Hsing; Zhu, Jiang; Lumley, John L.

1994-01-01

A general turbulent constitutive relation is directly applied to propose a new Reynolds stress algebraic equation model. In the development of this model, the constraints based on rapid distortion theory and realizability (i.e. the positivity of the normal Reynolds stresses and the Schwarz' inequality between turbulent velocity correlations) are imposed. Model coefficients are calibrated using well-studied basic flows such as homogeneous shear flow and the surface flow in the inertial sublayer. The performance of this model is then tested in complex turbulent flows including the separated flow over a backward-facing step and the flow in a confined jet. The calculation results are encouraging and point to the success of the present model in modeling turbulent flows with complex geometries.

On the coupled evolution of oceanic internal waves and quasi-geostrophic flow

NASA Astrophysics Data System (ADS)

Wagner, Gregory LeClaire

Oceanic motion outside thin boundary layers is primarily a mixture of quasi-geostrophic flow and internal waves with either near-inertial frequencies or the frequency of the semidiurnal lunar tide. This dissertation seeks a deeper understanding of waves and flow through reduced models that isolate their nonlinear and coupled evolution from the Boussinesq equations. Three physical-space models are developed: an equation that describes quasi-geostrophic evolution in an arbitrary and prescribed field of hydrostatic internal waves; a three-component model that couples quasi-geostrophic flow to both near-inertial waves and the near-inertial second harmonic; and a model for the slow evolution of hydrostatic internal tides in quasi-geostrophic flow of near-arbitrary scale. This slow internal tide equation opens the path to a coupled model for the energetic interaction of quasi-geostrophic flow and oceanic internal tides. Four results emerge. First, the wave-averaged quasi-geostrophic equation reveals that finite-amplitude waves give rise to a mean flow that advects quasi-geostrophic potential vorticity. Second is the definition of a new material invariant: Available Potential Vorticity, or APV. APV isolates the part of Ertel potential vorticity available for balanced-flow evolution in Eulerian frames and proves necessary in the separating waves and quasi-geostrophic flow. The third result, hashed out for near-inertial waves and quasi-geostrophic flow, is that wave-flow interaction leads to energy exchange even under conditions of weak nonlinearity. For storm-forced oceanic near-inertial waves the interaction often energizes waves at the expense of flow. We call this extraction of balanced quasi-geostrophic energy 'stimulated generation' since it requires externally-forced rather than spontaneously-generated waves. The fourth result is that quasi-geostrophic flow can encourage or 'catalyze' a nonlinear interaction between a near-inertial wave field and its second harmonic that transfers energy to the small near-inertial vertical scales of wave breaking and mixing.

A time-accurate algorithm for chemical non-equilibrium viscous flows at all speeds

NASA Technical Reports Server (NTRS)

Shuen, J.-S.; Chen, K.-H.; Choi, Y.

1992-01-01

A time-accurate, coupled solution procedure is described for the chemical nonequilibrium Navier-Stokes equations over a wide range of Mach numbers. This method employs the strong conservation form of the governing equations, but uses primitive variables as unknowns. Real gas properties and equilibrium chemistry are considered. Numerical tests include steady convergent-divergent nozzle flows with air dissociation/recombination chemistry, dump combustor flows with n-pentane-air chemistry, nonreacting flow in a model double annular combustor, and nonreacting unsteady driven cavity flows. Numerical results for both the steady and unsteady flows demonstrate the efficiency and robustness of the present algorithm for Mach numbers ranging from the incompressible limit to supersonic speeds.

REVIEWS OF TOPICAL PROBLEMS: Axisymmetric stationary flows in compact astrophysical objects

NASA Astrophysics Data System (ADS)

Beskin, Vasilii S.

1997-07-01

A review is presented of the analytical results available for a large class of axisymmetric stationary flows in the vicinity of compact astrophysical objects. The determination of the two-dimensional structure of the poloidal magnetic field (hydrodynamic flow field) faces severe difficulties, due to the complexity of the trans-field equation for stationary axisymmetric flows. However, an approach exists which enables direct problems to be solved even within the balance law framework. This possibility arises when an exact solution to the equation is available and flows close to it are investigated. As a result, with the use of simple model problems, the basic features of supersonic flows past real compact objects are determined.

Low flow of streams in the Susquehanna River basin of New York

USGS Publications Warehouse

Randall, Allan D.

2011-01-01

The principal source of streamflow during periods of low flow in the Susquehanna River basin of New York is the discharge of groundwater from sand-and-gravel deposits. Spatial variation in low flow is mostly a function of differences in three watershed properties: the amount of water that is introduced to the watershed and available for runoff, the extent of surficial sand and gravel relative to till-mantled bedrock, and the extent of wetlands. These three properties were consistently significant in regression equations that were developed to estimate several indices of low flow expressed in cubic feet per second or in cubic feet per second per square mile. The equations explain 90 to 99 percent of the spatial variation in low flow. A few equations indicate that underflow that bypasses streamflow-measurement sites through permeable sand and gravel can significantly decrease low flows. Analytical and numerical groundwater-flow models indicate that spatial extent, hydraulic conductivity and thickness, storage capacity, and topography of stratified sandand- gravel deposits affect low-flow yields from those deposits. Model-simulated discharge of groundwater to streams at low flow reaches a maximum where hydraulic-conductivity values are about 15 feet per day (in valleys 0.5 mile wide) to 60 feet per day (in valleys 1 mile wide). These hydraulic-conductivity values are much larger than those that are considered typical of till and bedrock, but smaller than values reported for productive sand-and-gravel aquifers in some valley reaches in New York. Differences in the properties of till and bedrock and in land-surface slope or relief within the Susquehanna River basin of New York apparently have little effect on low flow. Three regression equations were selected for practical application in estimating 7-day mean low flows in cubic feet per second with 10-year and 2-year recurrence intervals, and 90-percent flow duration, at ungaged sites draining more than 30 square miles; standard errors were 0.88, 1.40, and 1.95 cubic feet per second, respectively. Equations that express low flows in cubic feet per second per square mile were selected for estimating these three indices at ungaged sites draining less than 30 square miles; standard errors were 0.012, 0.018, and 0.022 cubic feet per second per square mile, respectively.

Development of comprehensive numerical schemes for predicting evaporating gas-droplets flow processes of a liquid-fueled combustor

NASA Technical Reports Server (NTRS)

Chen, C. P.

1990-01-01

An existing Computational Fluid Dynamics code for simulating complex turbulent flows inside a liquid rocket combustion chamber was validated and further developed. The Advanced Rocket Injector/Combustor Code (ARICC) is simplified and validated against benchmark flow situations for laminar and turbulent flows. The numerical method used in ARICC Code is re-examined for incompressible flow calculations. For turbulent flows, both the subgrid and the two equation k-epsilon turbulence models are studied. Cases tested include idealized Burger's equation in complex geometries and boundaries, a laminar pipe flow, a high Reynolds number turbulent flow, and a confined coaxial jet with recirculations. The accuracy of the algorithm is examined by comparing the numerical results with the analytical solutions as well as experimented data with different grid sizes.

Numerical methods for the weakly compressible Generalized Langevin Model in Eulerian reference frame

DOE Office of Scientific and Technical Information (OSTI.GOV)

Azarnykh, Dmitrii, E-mail: d.azarnykh@tum.de; Litvinov, Sergey; Adams, Nikolaus A.

2016-06-01

A well established approach for the computation of turbulent flow without resolving all turbulent flow scales is to solve a filtered or averaged set of equations, and to model non-resolved scales by closures derived from transported probability density functions (PDF) for velocity fluctuations. Effective numerical methods for PDF transport employ the equivalence between the Fokker–Planck equation for the PDF and a Generalized Langevin Model (GLM), and compute the PDF by transporting a set of sampling particles by GLM (Pope (1985) [1]). The natural representation of GLM is a system of stochastic differential equations in a Lagrangian reference frame, typically solvedmore » by particle methods. A representation in a Eulerian reference frame, however, has the potential to significantly reduce computational effort and to allow for the seamless integration into a Eulerian-frame numerical flow solver. GLM in a Eulerian frame (GLMEF) formally corresponds to the nonlinear fluctuating hydrodynamic equations derived by Nakamura and Yoshimori (2009) [12]. Unlike the more common Landau–Lifshitz Navier–Stokes (LLNS) equations these equations are derived from the underdamped Langevin equation and are not based on a local equilibrium assumption. Similarly to LLNS equations the numerical solution of GLMEF requires special considerations. In this paper we investigate different numerical approaches to solving GLMEF with respect to the correct representation of stochastic properties of the solution. We find that a discretely conservative staggered finite-difference scheme, adapted from a scheme originally proposed for turbulent incompressible flow, in conjunction with a strongly stable (for non-stochastic PDE) Runge–Kutta method performs better for GLMEF than schemes adopted from those proposed previously for the LLNS. We show that equilibrium stochastic fluctuations are correctly reproduced.« less

Manning’s equation and two-dimensional flow analogs

NASA Astrophysics Data System (ADS)

Hromadka, T. V., II; Whitley, R. J.; Jordan, N.; Meyer, T.

2010-07-01

SummaryTwo-dimensional (2D) flow models based on the well-known governing 2D flow equations are applied to floodplain analysis purposes. These 2D models numerically solve the governing flow equations simultaneously or explicitly on a discretization of the floodplain using grid tiles or similar tile cell geometry, called "elements". By use of automated information systems such as digital terrain modeling, digital elevation models, and GIS, large-scale topographic floodplain maps can be readily discretized into thousands of elements that densely cover the floodplain in an edge-to-edge form. However, the assumed principal flow directions of the flow model analog, as applied across an array of elements, typically do not align with the floodplain flow streamlines. This paper examines the mathematical underpinnings of a four-direction flow analog using an array of square elements with respect to floodplain flow streamlines that are not in alignment with the analog's principal flow directions. It is determined that application of Manning's equation to estimate the friction slope terms of the governing flow equations, in directions that are not coincident with the flow streamlines, may introduce a bias in modeling results, in the form of slight underestimation of flow depths. It is also determined that the maximum theoretical bias, occurs when a single square element is rotated by about 13°, and not 45° as would be intuitively thought. The bias as a function of rotation angle for an array of square elements follows approximately the bias for a single square element. For both the theoretical single square element and an array of square elements, the bias as a function of alignment angle follows a relatively constant value from about 5° to about 85°, centered at about 45°. This bias was first noted about a decade prior to the present paper, and the magnitude of this bias was estimated then to be about 20% at about 10° misalignment. An adjustment of Manning's n is investigated based on a considered steady state uniform flow problem, but the magnitude of the adjustment (about 20%) is on the order of the magnitude of the accepted ranges of friction factors. For usual cases where random streamline trajectory variability within the floodplain flow is greater than a few degrees from perfect alignment, the apparent bias appears to be implicitly included in the Manning's n values. It can be concluded that the array of square elements may be applied over the digital terrain model without respect to topographic flow directions.

Mathematical Model of Two Phase Flow in Natural Draft Wet-Cooling Tower Including Flue Gas Injection

NASA Astrophysics Data System (ADS)

Hyhlík, Tomáš

2016-03-01

The previously developed model of natural draft wet-cooling tower flow, heat and mass transfer is extended to be able to take into account the flow of supersaturated moist air. The two phase flow model is based on void fraction of gas phase which is included in the governing equations. Homogeneous equilibrium model, where the two phases are well mixed and have the same velocity, is used. The effect of flue gas injection is included into the developed mathematical model by using source terms in governing equations and by using momentum flux coefficient and kinetic energy flux coefficient. Heat and mass transfer in the fill zone is described by the system of ordinary differential equations, where the mass transfer is represented by measured fill Merkel number and heat transfer is calculated using prescribed Lewis factor.

Numerical investigations of passive scalar transport in Taylor-Couette flows: Counter-rotation effect

NASA Astrophysics Data System (ADS)

Ouazib, Nabila; Salhi, Yacine; Si-Ahmed, El-Khider; Legrand, Jack; Degrez, G.

2017-07-01

Numerical methods for solving convection-diffusion-reaction (CDR) scalar transport equation in three-dimensional flow are used in the present investigation. The flow is confined between two concentric cylinders both the inner cylinder and the outer one are allowed to rotate. Direct numerical simulations (DNS) have been achieved to study the effects of the gravitational and the centrifugal potentials on the stability of incompressible Taylor-Couette flow. The Navier-Stokes equations and the uncoupled convection-diffusion-reaction equation are solved using a spectral development in one direction combined together with a finite element discretization in the two remaining directions. The complexity of the patterns is highlighted. Since, it increases as the rotation rates of the cylinders increase. In addition, the effect of the counter-rotation of the cylinders on the mass transfer is pointed out.

The four fixed points of scale invariant single field cosmological models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xue, BingKan, E-mail: bxue@princeton.edu

2012-10-01

We introduce a new set of flow parameters to describe the time dependence of the equation of state and the speed of sound in single field cosmological models. A scale invariant power spectrum is produced if these flow parameters satisfy specific dynamical equations. We analyze the flow of these parameters and find four types of fixed points that encompass all known single field models. Moreover, near each fixed point we uncover new models where the scale invariance of the power spectrum relies on having simultaneously time varying speed of sound and equation of state. We describe several distinctive new modelsmore » and discuss constraints from strong coupling and superluminality.« less

Brine flow in heated geologic salt.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kuhlman, Kristopher L.; Malama, Bwalya

This report is a summary of the physical processes, primary governing equations, solution approaches, and historic testing related to brine migration in geologic salt. Although most information presented in this report is not new, we synthesize a large amount of material scattered across dozens of laboratory reports, journal papers, conference proceedings, and textbooks. We present a mathematical description of the governing brine flow mechanisms in geologic salt. We outline the general coupled thermal, multi-phase hydrologic, and mechanical processes. We derive these processes governing equations, which can be used to predict brine flow. These equations are valid under a wide varietymore » of conditions applicable to radioactive waste disposal in rooms and boreholes excavated into geologic salt.« less

Solving Navier-Stokes Equations with Advanced Turbulence Models on Three-Dimensional Unstructured Grids

NASA Technical Reports Server (NTRS)

Wang, Qun-Zhen; Massey, Steven J.; Abdol-Hamid, Khaled S.; Frink, Neal T.

1999-01-01

USM3D is a widely-used unstructured flow solver for simulating inviscid and viscous flows over complex geometries. The current version (version 5.0) of USM3D, however, does not have advanced turbulence models to accurately simulate complicated flows. We have implemented two modified versions of the original Jones and Launder k-epsilon two-equation turbulence model and the Girimaji algebraic Reynolds stress model in USM3D. Tests have been conducted for two flat plate boundary layer cases, a RAE2822 airfoil and an ONERA M6 wing. The results are compared with those of empirical formulae, theoretical results and the existing Spalart-Allmaras one-equation model.

Radiation Transport Around Axisymmetric Blunt Body Vehicles Using a Modified Differential Approximation

NASA Technical Reports Server (NTRS)

Hartung, Lin C.; Hassan, H. A.

1992-01-01

A moment method for computing 3-D radiative transport is applied to axisymmetric flows in thermochemical nonequilibrium. Such flows are representative of proposed aerobrake missions. The method uses the P-1 approximation to reduce the governing system of integro-di erential equations to a coupled set of partial di erential equations. A numerical solution method for these equations given actual variations of the radiation properties in thermochemical nonequilibrium blunt body flows is developed. Initial results from the method are shown and compared to tangent slab calculations. The agreement between the transport methods is found to be about 10 percent in the stagnation region, with the difference increasing along the flank of the vehicle.

The electromagnetic force field, fluid flow field and temperature profiles in levitated metal droplets

NASA Technical Reports Server (NTRS)

El-Kaddah, N.; Szekely, J.

1982-01-01

A mathematical representation was developed for the electromagnetic force field, the flow field, the temperature field (and for transport controlled kinetics), in a levitation melted metal droplet. The technique of mutual inductances was employed for the calculation of the electromagnetic force field, while the turbulent Navier - Stokes equations and the turbulent convective transport equations were used to represent the fluid flow field, the temperature field and the concentration field. The governing differential equations, written in spherical coordinates, were solved numerically. The computed results were in good agreement with measurements, regarding the lifting force, and the average temperature of the specimen and carburization rates, which were transport controlled.

Interpretation of Bernoulli's Equation.

ERIC Educational Resources Information Center

Bauman, Robert P.; Schwaneberg, Rolf

1994-01-01

Discusses Bernoulli's equation with regards to: horizontal flow of incompressible fluids, change of height of incompressible fluids, gases, liquids and gases, and viscous fluids. Provides an interpretation, properties, terminology, and applications of Bernoulli's equation. (MVL)

Documentation of a Conduit Flow Process (CFP) for MODFLOW-2005

USGS Publications Warehouse

Shoemaker, W. Barclay; Kuniansky, Eve L.; Birk, Steffen; Bauer, Sebastian; Swain, Eric D.

2007-01-01

This report documents the Conduit Flow Process (CFP) for the modular finite-difference ground-water flow model, MODFLOW-2005. The CFP has the ability to simulate turbulent ground-water flow conditions by: (1) coupling the traditional ground-water flow equation with formulations for a discrete network of cylindrical pipes (Mode 1), (2) inserting a high-conductivity flow layer that can switch between laminar and turbulent flow (Mode 2), or (3) simultaneously coupling a discrete pipe network while inserting a high-conductivity flow layer that can switch between laminar and turbulent flow (Mode 3). Conduit flow pipes (Mode 1) may represent dissolution or biological burrowing features in carbonate aquifers, voids in fractured rock, and (or) lava tubes in basaltic aquifers and can be fully or partially saturated under laminar or turbulent flow conditions. Preferential flow layers (Mode 2) may represent: (1) a porous media where turbulent flow is suspected to occur under the observed hydraulic gradients; (2) a single secondary porosity subsurface feature, such as a well-defined laterally extensive underground cave; or (3) a horizontal preferential flow layer consisting of many interconnected voids. In this second case, the input data are effective parameters, such as a very high hydraulic conductivity, representing multiple features. Data preparation is more complex for CFP Mode 1 (CFPM1) than for CFP Mode 2 (CFPM2). Specifically for CFPM1, conduit pipe locations, lengths, diameters, tortuosity, internal roughness, critical Reynolds numbers (NRe), and exchange conductances are required. CFPM1, however, solves the pipe network equations in a matrix that is independent of the porous media equation matrix, which may mitigate numerical instability associated with solution of dual flow components within the same matrix. CFPM2 requires less hydraulic information and knowledge about the specific location and hydraulic properties of conduits, and turbulent flow is approximated by modifying horizontal conductances assembled by the Block-Centered Flow (BCF), Layer-Property Flow (LPF), or Hydrogeologic-Unit Flow Packages (HUF) of MODFLOW-2005. For both conduit flow pipes (CFPM1) and preferential flow layers (CFPM2), critical Reynolds numbers are used to determine if flow is laminar or turbulent. Due to conservation of momentum, flow in a laminar state tends to remain laminar and flow in a turbulent state tends to remain turbulent. This delayed transition between laminar and turbulent flow is introduced in the CFP, which provides an additional benefit of facilitating convergence of the computer algorithm during iterations of transient simulations. Specifically, the user can specify a higher critical Reynolds number to determine when laminar flow within a pipe converts to turbulent flow, and a lower critical Reynolds number for determining when a pipe with turbulent flow switches to laminar flow. With CFPM1, the Hagen-Poiseuille equation is used for laminar flow conditions and the Darcy-Weisbach equation is applied to turbulent flow conditions. With CFPM2, turbulent flow is approximated by reducing the laminar hydraulic conductivity by a nonlinear function of the Reynolds number, once the critical head difference is exceeded. This adjustment approximates the reductions in mean velocity under turbulent ground-water flow conditions.

Turbulence Model Sensitivity and Scour Gap Effect of Unsteady Flow around Pipe: A CFD Study

PubMed Central

Ali, Abbod; Sharma, R. K.; Ganesan, P.

2014-01-01

A numerical investigation of incompressible and transient flow around circular pipe has been carried out at different five gap phases. Flow equations such as Navier-Stokes and continuity equations have been solved using finite volume method. Unsteady horizontal velocity and kinetic energy square root profiles are plotted using different turbulence models and their sensitivity is checked against published experimental results. Flow parameters such as horizontal velocity under pipe, pressure coefficient, wall shear stress, drag coefficient, and lift coefficient are studied and presented graphically to investigate the flow behavior around an immovable pipe and scoured bed. PMID:25136666

Singular flow dynamics in three space dimensions driven by advection

NASA Astrophysics Data System (ADS)

Karimov, A. R.; Schamel, H.

2002-03-01

The initial value problem of an ideal, compressible fluid is investigated in three space dimensions (3D). Starting from a situation where the inertia terms dominate over the force terms in Euler's equation we explore by means of the Lagrangian flow description the basic flow properties. Special attention is drawn to the appearance of singularities in the flow pattern at finite time. Classes of initial velocity profiles giving rise to collapses of density and vorticity are found. This paper, hence, furnishes evidence of focused singularities for coherent structures obeying the 3D Euler equation and applies to potential as well as vortex flows.

Viscous-shock-layer analysis of hypersonic flows over long slender vehicles. Ph.D. Thesis, 1988

NASA Technical Reports Server (NTRS)

Lee, Kam-Pui; Gupta, Roop N.

1992-01-01

An efficient and accurate method for solving the viscous shock layer equations for hypersonic flows over long slender bodies is presented. The two first order equations, continuity and normal momentum, are solved simultaneously as a coupled set. The flow conditions included are from high Reynolds numbers at low altitudes to low Reynolds numbers at high altitudes. For high Reynolds number flows, both chemical nonequilibrium and perfect gas cases are analyzed with surface catalytic effects and different turbulence models, respectively. At low Reynolds number flow conditions, corrected slip models are implemented with perfect gas case. Detailed comparisons are included with other predictions and experimental data.

Flow Rate Through Pigtail Catheter Used for Left Heart Decompression in an Artificial Model of Extracorporeal Membrane Oxygenation Circuit.

PubMed

Kim, Won Ho; Hong, Tae Hee; Byun, Joung Hun; Kim, Jong Woo; Kim, Sung Hwan; Moon, Sung Ho; Park, Hyun Oh; Choi, Jun Young; Yang, Jun Ho; Jang, In Seok; Lee, Chung Eun; Yun, Jeong Hee

In refractory cardiogenic shock, veno-arterial extracorporeal membrane oxygenation (ECMO) can be initiated. Although left heart decompression can be accomplished by insertion of a left atrial (LA) or left ventricular (LV) cannula using a percutaneous pigtail catheter, the venting flow rate according to catheter size and ECMO flow rate is unknown. We developed an artificial ECMO circuit. One liter saline bag with its pressure set to 20 mm Hg was connected to ECMO to mimic LV failure. A pigtail catheter was inserted into the 1 L saline bag to simulate LV unloading. For each pigtail catheter size (5-8 Fr) and ECMO flow rate (2.0-4.0 L/min), the moving distance of an air bubble that was injected through a three-way stopcock was measured in the arterial pressure line between the pigtail catheter and ECMO inflow limb. The flow rate was then calculated. We obtained the following equation to estimate the pigtail catheter flow rate.Pigtail vent catheter flow rate (ml/min) = 8×ECMOflow rate(L /min)+9×pigtail catheter size(Fr)- 57This equation would aid in designing of a further study to determine optimal venting flow rate. To achieve optimal venting flow, our equation would enable selection of an adequate catheter size.

Regionalization of winter low-flow characteristics of Tennessee streams

USGS Publications Warehouse

Bingham, R.H.

1986-01-01

Procedures were developed for estimating winter (December-April) low flows at ungaged stream sites in Tennessee based on surface geology and drainage area size. One set of equations applies to West Tennessee streams, and another set applies to Middle and East Tennessee streams. The equations do not apply to streams where flow is significantly altered by the activities of man. Standard errors of estimate of equations for West Tennessee are 22% - 35% and for middle and East Tennessee 31% - 36%. Statistical analyses indicate that summer low-flow characteristics are the same as annual low-flow characteristics, and that winter low flows are larger than annual low flows. Streamflow-recession indexes, in days per log cycle of decrease in discharge, were used to account for effects of geology on low flow of streams. The indexes in Tennessee range from 32 days/log cycle for clay and shale to 350 days/log cycle for gravel and sand, indicating different aquifer characteristics of the geologic units that contribute to streamflows during periods of no surface runoff. Streamflow-recession rate depends primarily on transmissivity and storage characteristics of the aquifers, and the average distance from stream channels to basin divides. Geology and drainage basin size are the most significant variables affecting low flow in Tennessee streams according to regression analyses. (Author 's abstract)

Regression method for estimating long-term mean annual ground-water recharge rates from base flow in Pennsylvania

USGS Publications Warehouse

Risser, Dennis W.; Thompson, Ronald E.; Stuckey, Marla H.

2008-01-01

A method was developed for making estimates of long-term, mean annual ground-water recharge from streamflow data at 80 streamflow-gaging stations in Pennsylvania. The method relates mean annual base-flow yield derived from the streamflow data (as a proxy for recharge) to the climatic, geologic, hydrologic, and physiographic characteristics of the basins (basin characteristics) by use of a regression equation. Base-flow yield is the base flow of a stream divided by the drainage area of the basin, expressed in inches of water basinwide. Mean annual base-flow yield was computed for the period of available streamflow record at continuous streamflow-gaging stations by use of the computer program PART, which separates base flow from direct runoff on the streamflow hydrograph. Base flow provides a reasonable estimate of recharge for basins where streamflow is mostly unaffected by upstream regulation, diversion, or mining. Twenty-eight basin characteristics were included in the exploratory regression analysis as possible predictors of base-flow yield. Basin characteristics found to be statistically significant predictors of mean annual base-flow yield during 1971-2000 at the 95-percent confidence level were (1) mean annual precipitation, (2) average maximum daily temperature, (3) percentage of sand in the soil, (4) percentage of carbonate bedrock in the basin, and (5) stream channel slope. The equation for predicting recharge was developed using ordinary least-squares regression. The standard error of prediction for the equation on log-transformed data was 9.7 percent, and the coefficient of determination was 0.80. The equation can be used to predict long-term, mean annual recharge rates for ungaged basins, providing that the explanatory basin characteristics can be determined and that the underlying assumption is accepted that base-flow yield derived from PART is a reasonable estimate of ground-water recharge rates. For example, application of the equation for 370 hydrologic units in Pennsylvania predicted a range of ground-water recharge from about 6.0 to 22 inches per year. A map of the predicted recharge illustrates the general magnitude and variability of recharge throughout Pennsylvania.

Weak solutions of the three-dimensional vorticity equation with vortex singularities

NASA Technical Reports Server (NTRS)

Winckelmans, G.; Leonard, A.

1988-01-01

The extension of the concept of vortex singularities, developed by Saffman and Meiron (1986) for the case of two-dimensional point vortices in an incompressible vortical flow, to the three-dimensional case of vortex sticks (vortons) is investigated analytically. The derivation of the governing equations is explained, and it is demonstrated that the formulation obtained conserves total vorticity and is a weak solution of the vorticity equation, making it an appropriate means for representing three-dimensional vortical flows with limited numbers of vortex singularities.

Analytic Approximate Solutions to the Boundary Layer Flow Equation over a Stretching Wall with Partial Slip at the Boundary.

PubMed

Ene, Remus-Daniel; Marinca, Vasile; Marinca, Bogdan

2016-01-01

Analytic approximate solutions using Optimal Homotopy Perturbation Method (OHPM) are given for steady boundary layer flow over a nonlinearly stretching wall in presence of partial slip at the boundary. The governing equations are reduced to nonlinear ordinary differential equation by means of similarity transformations. Some examples are considered and the effects of different parameters are shown. OHPM is a very efficient procedure, ensuring a very rapid convergence of the solutions after only two iterations.

Perfect gas effects in compressible rapid distortion theory

NASA Technical Reports Server (NTRS)

Kerschen, E. J.; Myers, M. R.

1987-01-01

The governing equations presented for small amplitude unsteady disturbances imposed on steady, compressible mean flows that are two-dimensional and nearly uniform have their basis in the perfect gas equations of state, and therefore generalize previous results based on tangent gas theory. While these equations are more complex, this complexity is required for adequate treatment of high frequency disturbances, especially when the base flow Mach number is large; under such circumstances, the simplifying assumptions of tangent gas theory are not applicable.

BRIEF COMMUNICATION: On the drift kinetic equation driven by plasma flows

NASA Astrophysics Data System (ADS)

Shaing, K. C.

2010-07-01

A drift kinetic equation that is driven by plasma flows has previously been derived by Shaing and Spong 1990 (Phys. Fluids B 2 1190). The terms that are driven by particle speed that is parallel to the magnetic field B have been neglected. Here, such terms are discussed to examine their importance to the equation and to show that these terms do not contribute to the calculations of plasma viscosity in large aspect ratio toroidal plasmas, e.g. tokamaks and stellarators.

Analytic Approximate Solutions to the Boundary Layer Flow Equation over a Stretching Wall with Partial Slip at the Boundary

PubMed Central

Ene, Remus-Daniel; Marinca, Vasile; Marinca, Bogdan

2016-01-01

Analytic approximate solutions using Optimal Homotopy Perturbation Method (OHPM) are given for steady boundary layer flow over a nonlinearly stretching wall in presence of partial slip at the boundary. The governing equations are reduced to nonlinear ordinary differential equation by means of similarity transformations. Some examples are considered and the effects of different parameters are shown. OHPM is a very efficient procedure, ensuring a very rapid convergence of the solutions after only two iterations. PMID:27031232

A theory of post-stall transients in axial compression systems. I - Development of equations

NASA Technical Reports Server (NTRS)

Moore, F. K.; Greitzer, E. M.

1985-01-01

An approximate theory is presented for post-stall transients in multistage axial compression systems. The theory leads to a set of three simultaneous nonlinear third-order partial differential equations for pressure rise, and average and disturbed values of flow coefficient, as functions of time and angle around the compressor. By a Galerkin procedure, angular dependence is averaged, and the equations become first order in time. These final equations are capable of describing the growth and possible decay of a rotating-stall cell during a compressor mass-flow transient. It is shown how rotating-stall-like and surgelike motions are coupled through these equations, and also how the instantaneous compressor pumping characteristic changes during the transient stall process.

A new stream function formulation for the Euler equations

NASA Technical Reports Server (NTRS)

Atkins, H. L.; Hassan, H. A.

1983-01-01

A new stream function formulation is developed for the solution of Euler's equations in the transonic flow region. The stream function and the density are the dependent variables in this method, while the governing equations for adiabatic flow are the momentum equations which are solved in the strong conservation law form. The application of this method does not require a knowledge of the vorticity. The algorithm is combined with the automatic grid solver (GRAPE) of Steger and Sorenson (1979) in order to study arbitrary geometries. Results of the application of this method are presented for the NACA 0012 airfoil at various Mach numbers and angles of attack, and cylinders. In addition, detailed comparisons are made with other solutions of the Euler equations.