Accurate solutions for transonic viscous flow over finite wings
NASA Technical Reports Server (NTRS)
Vatsa, V. N.
1986-01-01
An explicit multistage Runge-Kutta type time-stepping scheme is used for solving the three-dimensional, compressible, thin-layer Navier-Stokes equations. A finite-volume formulation is employed to facilitate treatment of complex grid topologies encountered in three-dimensional calculations. Convergence to steady state is expedited through usage of acceleration techniques. Further numerical efficiency is achieved through vectorization of the computer code. The accuracy of the overall scheme is evaluated by comparing the computed solutions with the experimental data for a finite wing under different test conditions in the transonic regime. A grid refinement study ir conducted to estimate the grid requirements for adequate resolution of salient features of such flows.
Accurate solutions, parameter studies and comparisons for the Euler and potential flow equations
NASA Technical Reports Server (NTRS)
Anderson, W. Kyle; Batina, John T.
1988-01-01
Parameter studies are conducted using the Euler and potential flow equation models for steady and unsteady flows in both two and three dimensions. The Euler code is an implicit, upwind, finite volume code which uses the Van Leer method of flux vector splitting which has been recently extended for use on dynamic meshes and maintain all the properties of the original splitting. The potential flow code is an implicit, finite difference method for solving the transonic small disturbance equations and incorporates both entropy and vorticity corrections into the solution procedures thereby extending its applicability into regimes where shock strength normally precludes its use. Parameter studies resulting in benchmark type calculations include the effects of spatial and temporal refinement, spatial order of accuracy, far field boundary conditions for steady flow, frequency of oscillation, and the use of subiterations at each time step to reduce linearization and factorization errors. Comparisons between Euler and potential flow results are made, as well as with experimental data where available.
Accurate solutions, parameter studies and comparisons for the Euler and potential flow equations
NASA Technical Reports Server (NTRS)
Anderson, W. Kyle; Batina, John T.
1988-01-01
Parameter studies are conducted using the Euler and potential flow equation models for unsteady and steady flows in both two and three dimensions. The Euler code is an implicit, upwind, finite volume code which uses the Van Leer method of flux-vector-splitting which has been recently extended for use on dynamic meshes and maintain all the properties of the original splitting. The potential flow code is an implicit, finite difference method for solving the transonic small disturbance equations and incorporates both entropy and vorticity corrections into the solution procedures thereby extending its applicability into regimes where shock strength normally precludes its use. Parameter studies resulting in benchmark type calculations include the effects of spatial and temporal refinement, spatial order of accuracy, far field boundary conditions for steady flow, frequency of oscillation, and the use of subiterations at each time step to reduce linearization and factorization errors. Comparisons between Euler and potential flows results are made as well as with experimental data where available.
NASA Astrophysics Data System (ADS)
Jiang, Shidong; Luo, Li-Shi
2016-07-01
The integral equation for the flow velocity u (x ; k) in the steady Couette flow derived from the linearized Bhatnagar-Gross-Krook-Welander kinetic equation is studied in detail both theoretically and numerically in a wide range of the Knudsen number k between 0.003 and 100.0. First, it is shown that the integral equation is a Fredholm equation of the second kind in which the norm of the compact integral operator is less than 1 on Lp for any 1 ≤ p ≤ ∞ and thus there exists a unique solution to the integral equation via the Neumann series. Second, it is shown that the solution is logarithmically singular at the endpoints. More precisely, if x = 0 is an endpoint, then the solution can be expanded as a double power series of the form ∑n=0∞∑m=0∞cn,mxn(xln x) m about x = 0 on a small interval x ∈ (0 , a) for some a > 0. And third, a high-order adaptive numerical algorithm is designed to compute the solution numerically to high precision. The solutions for the flow velocity u (x ; k), the stress Pxy (k), and the half-channel mass flow rate Q (k) are obtained in a wide range of the Knudsen number 0.003 ≤ k ≤ 100.0; and these solutions are accurate for at least twelve significant digits or better, thus they can be used as benchmark solutions.
NASA Astrophysics Data System (ADS)
Stukel, Michael R.; Landry, Michael R.; Ohman, Mark D.; Goericke, Ralf; Samo, Ty; Benitez-Nelson, Claudia R.
2012-03-01
Despite the increasing use of linear inverse modeling techniques to elucidate fluxes in undersampled marine ecosystems, the accuracy with which they estimate food web flows has not been resolved. New Markov Chain Monte Carlo (MCMC) solution methods have also called into question the biases of the commonly used L2 minimum norm (L 2MN) solution technique. Here, we test the abilities of MCMC and L 2MN methods to recover field-measured ecosystem rates that are sequentially excluded from the model input. For data, we use experimental measurements from process cruises of the California Current Ecosystem (CCE-LTER) Program that include rate estimates of phytoplankton and bacterial production, micro- and mesozooplankton grazing, and carbon export from eight study sites varying from rich coastal upwelling to offshore oligotrophic conditions. Both the MCMC and L 2MN methods predicted well-constrained rates of protozoan and mesozooplankton grazing with reasonable accuracy, but the MCMC method overestimated primary production. The MCMC method more accurately predicted the poorly constrained rate of vertical carbon export than the L 2MN method, which consistently overestimated export. Results involving DOC and bacterial production were equivocal. Overall, when primary production is provided as model input, the MCMC method gives a robust depiction of ecosystem processes. Uncertainty in inverse ecosystem models is large and arises primarily from solution under-determinacy. We thus suggest that experimental programs focusing on food web fluxes expand the range of experimental measurements to include the nature and fate of detrital pools, which play large roles in the model.
Predict amine solution properties accurately
Cheng, S.; Meisen, A.; Chakma, A.
1996-02-01
Improved process design begins with using accurate physical property data. Especially in the preliminary design stage, physical property data such as density viscosity, thermal conductivity and specific heat can affect the overall performance of absorbers, heat exchangers, reboilers and pump. These properties can also influence temperature profiles in heat transfer equipment and thus control or affect the rate of amine breakdown. Aqueous-amine solution physical property data are available in graphical form. However, it is not convenient to use with computer-based calculations. Developed equations allow improved correlations of derived physical property estimates with published data. Expressions are given which can be used to estimate physical properties of methyldiethanolamine (MDEA), monoethanolamine (MEA) and diglycolamine (DGA) solutions.
High order accurate solutions of viscous problems
NASA Technical Reports Server (NTRS)
Hayder, M. E.; Turkel, Eli
1993-01-01
We consider a fourth order extension to MacCormack's scheme. The original extension was fourth order only for the inviscid terms but was second order for the viscous terms. We show how to modify the viscous terms so that the scheme is uniformly fourth order in the spatial derivatives. Applications are given to some boundary layer flows. In addition, for applications to shear flows the effect of the outflow boundary conditions are very important. We compare the accuracy of several of these different boundary conditions for both boundary layer and shear flows. Stretching at the outflow usually increases the oscillations in the numerical solution but the addition of a filtered sponge layer (with or without stretching) reduces such oscillations. The oscillations are generated by insufficient resolution of the shear layer. When the shear layer is sufficiently resolved then oscillations are not generated and there is less of a need for a nonreflecting boundary condition.
Accurate numerical solutions of conservative nonlinear oscillators
NASA Astrophysics Data System (ADS)
Khan, Najeeb Alam; Nasir Uddin, Khan; Nadeem Alam, Khan
2014-12-01
The objective of this paper is to present an investigation to analyze the vibration of a conservative nonlinear oscillator in the form u" + lambda u + u^(2n-1) + (1 + epsilon^2 u^(4m))^(1/2) = 0 for any arbitrary power of n and m. This method converts the differential equation to sets of algebraic equations and solve numerically. We have presented for three different cases: a higher order Duffing equation, an equation with irrational restoring force and a plasma physics equation. It is also found that the method is valid for any arbitrary order of n and m. Comparisons have been made with the results found in the literature the method gives accurate results.
Accurate numerical solution of compressible, linear stability equations
NASA Technical Reports Server (NTRS)
Malik, M. R.; Chuang, S.; Hussaini, M. Y.
1982-01-01
The present investigation is concerned with a fourth order accurate finite difference method and its application to the study of the temporal and spatial stability of the three-dimensional compressible boundary layer flow on a swept wing. This method belongs to the class of compact two-point difference schemes discussed by White (1974) and Keller (1974). The method was apparently first used for solving the two-dimensional boundary layer equations. Attention is given to the governing equations, the solution technique, and the search for eigenvalues. A general purpose subroutine is employed for solving a block tridiagonal system of equations. The computer time can be reduced significantly by exploiting the special structure of two matrices.
Time accurate simulations of compressible shear flows
NASA Technical Reports Server (NTRS)
Givi, Peyman; Steinberger, Craig J.; Vidoni, Thomas J.; Madnia, Cyrus K.
1993-01-01
The objectives of this research are to employ direct numerical simulation (DNS) to study the phenomenon of mixing (or lack thereof) in compressible free shear flows and to suggest new means of enhancing mixing in such flows. The shear flow configurations under investigation are those of parallel mixing layers and planar jets under both non-reacting and reacting nonpremixed conditions. During the three-years of this research program, several important issues regarding mixing and chemical reactions in compressible shear flows were investigated.
More-Accurate Model of Flows in Rocket Injectors
NASA Technical Reports Server (NTRS)
Hosangadi, Ashvin; Chenoweth, James; Brinckman, Kevin; Dash, Sanford
2011-01-01
An improved computational model for simulating flows in liquid-propellant injectors in rocket engines has been developed. Models like this one are needed for predicting fluxes of heat in, and performances of, the engines. An important part of predicting performance is predicting fluctuations of temperature, fluctuations of concentrations of chemical species, and effects of turbulence on diffusion of heat and chemical species. Customarily, diffusion effects are represented by parameters known in the art as the Prandtl and Schmidt numbers. Prior formulations include ad hoc assumptions of constant values of these parameters, but these assumptions and, hence, the formulations, are inaccurate for complex flows. In the improved model, these parameters are neither constant nor specified in advance: instead, they are variables obtained as part of the solution. Consequently, this model represents the effects of turbulence on diffusion of heat and chemical species more accurately than prior formulations do, and may enable more-accurate prediction of mixing and flows of heat in rocket-engine combustion chambers. The model has been implemented within CRUNCH CFD, a proprietary computational fluid dynamics (CFD) computer program, and has been tested within that program. The model could also be implemented within other CFD programs.
A third-order-accurate upwind scheme for Navier-Stokes solutions at high Reynolds numbers
NASA Astrophysics Data System (ADS)
Agarwal, R. K.
1981-01-01
A third-order-accurate upwind scheme is presented for solution of the steady two-dimensional Navier-Stokes equations in stream-function/vorticity form. The scheme is found to be accurate and stable at high Reynolds numbers. A series of test computations is performed on flows with large recirculating regions. In particular, highly accurate solutions are obtained for flow in a driven square cavity up to Reynolds numbers of 10,000. These computations are used to critically evaluate the accuracy of other existing first- and second-order-accurate upwind schemes. In addition, computations are carried out for flow in a channel with symmetric sudden expansion, flow in a channel with a symmetrically placed blunt base, and the flowfield of an impinging jet. Good agreement is obtained with the computations of other investigators as well as with the available experimental data.
Device accurately measures and records low gas-flow rates
NASA Technical Reports Server (NTRS)
Branum, L. W.
1966-01-01
Free-floating piston in a vertical column accurately measures and records low gas-flow rates. The system may be calibrated, using an adjustable flow-rate gas supply, a low pressure gage, and a sequence recorder. From the calibration rates, a nomograph may be made for easy reduction. Temperature correction may be added for further accuracy.
Vibration of clamped right triangular thin plates: Accurate simplified solutions
NASA Astrophysics Data System (ADS)
Saliba, H. T.
1994-12-01
Use of the superposition techniques in the free-vibration analyses of thin plates, as they were first introduced by Gorman, has provided simple and effective solutions to a vast number of rectangular plate problems. A modified superposition method is presented that is a noticeable improvement over existing techniques. It deals only with simple support conditions, leading to a simple, highly accurate, and very economical solution to the free-vibration problem of simply-supported right angle triangular plates. The modified method is also applicable to clamped-edge conditions.
Electroosmotic Flow Hysteresis for Dissimilar Anionic Solutions.
Lim, An Eng; Lim, Chun Yee; Lam, Yee Cheong
2016-08-16
Electroosmotic flow (EOF) with two or more fluids is often encountered in various microfluidic applications. However, no investigation has hitherto been conducted to investigate the hysteretic or flow direction-dependent behavior during displacement flow of solutions with dissimilar anion species. In this investigation, EOF of dissimilar anionic solutions was studied experimentally through the current monitoring method and numerically through finite element simulations. As opposed to other conventional displacement flows, EOF involving dissimilar anionic solutions exhibits counterintuitive behavior, whereby the current-time curve does not reach the steady-state value of the displacing electrolyte. Two distinct mechanics have been identified as the causes for this observation: (a) ion concentration adjustment when the displacing anions migrate upstream against EOF due to competition between the gradients of electromigrative and convective fluxes and (b) ion concentration readjustment induced by the static diffusive interfacial region between the dissimilar fluids which can only be propagated throughout the entire microchannel with the presence of EOF. The resultant ion distributions lead to the flow rate to be directional-dependent, indicating that the flow conditions are asymmetric between these two different flow directions. The outcomes of this investigation contribute to the in-depth understanding of flow behavior in microfluidic systems involving inhomogeneous fluids, particularly dissimilar anionic solutions. The understanding of EOF hysteresis is fundamentally important for the accurate prediction of analytes transport in microfluidic devices under EOF. PMID:27426052
Accurate modelling of flow induced stresses in rigid colloidal aggregates
NASA Astrophysics Data System (ADS)
Vanni, Marco
2015-07-01
A method has been developed to estimate the motion and the internal stresses induced by a fluid flow on a rigid aggregate. The approach couples Stokesian dynamics and structural mechanics in order to take into account accurately the effect of the complex geometry of the aggregates on hydrodynamic forces and the internal redistribution of stresses. The intrinsic error of the method, due to the low-order truncation of the multipole expansion of the Stokes solution, has been assessed by comparison with the analytical solution for the case of a doublet in a shear flow. In addition, it has been shown that the error becomes smaller as the number of primary particles in the aggregate increases and hence it is expected to be negligible for realistic reproductions of large aggregates. The evaluation of internal forces is performed by an adaptation of the matrix methods of structural mechanics to the geometric features of the aggregates and to the particular stress-strain relationship that occurs at intermonomer contacts. A preliminary investigation on the stress distribution in rigid aggregates and their mode of breakup has been performed by studying the response to an elongational flow of both realistic reproductions of colloidal aggregates (made of several hundreds monomers) and highly simplified structures. A very different behaviour has been evidenced between low-density aggregates with isostatic or weakly hyperstatic structures and compact aggregates with highly hyperstatic configuration. In low-density clusters breakup is caused directly by the failure of the most stressed intermonomer contact, which is typically located in the inner region of the aggregate and hence originates the birth of fragments of similar size. On the contrary, breakup of compact and highly cross-linked clusters is seldom caused by the failure of a single bond. When this happens, it proceeds through the removal of a tiny fragment from the external part of the structure. More commonly, however
Vibration of clamped right triangular thin plates: Accurate simplified solutions
NASA Astrophysics Data System (ADS)
Saliba, H. T.
1994-12-01
Use of the superposition techniques in the free-vibration analyses of thin plates, as they were first introduced by Gorman, has provided simple and effective solutions to a vast number of rectangular plate problems. The method has also been extended to nonrectangular plates such as triangular and trapezoidal plates. However, serious difficulties were encountered in some of these analyses. These difficulties were discussed and obviated in Salibra, 1990. This reference, however, dealt only with simple support conditions, leading to a simple, highly accurate, and very economical solution to the free-vibration problem of simply supported right angle triangular plates. The purpose of this Note is to show that the modified superposition method of Salibra, 1990 is also applicable to clamped-edge conditions. This is accomplished through the application of this method to the title problem.
A time-accurate implicit method for chemical non-equilibrium flows at all speeds
NASA Technical Reports Server (NTRS)
Shuen, Jian-Shun
1992-01-01
A new time accurate coupled solution procedure for solving the chemical non-equilibrium Navier-Stokes equations over a wide range of Mach numbers is described. The scheme is shown to be very efficient and robust for flows with velocities ranging from M less than or equal to 10(exp -10) to supersonic speeds.
A spectrally accurate method for overlapping grid solution of incompressible Navier-Stokes equations
NASA Astrophysics Data System (ADS)
Merrill, Brandon E.; Peet, Yulia T.; Fischer, Paul F.; Lottes, James W.
2016-02-01
An overlapping mesh methodology that is spectrally accurate in space and up to third-order accurate in time is developed for solution of unsteady incompressible flow equations in three-dimensional domains. The ability to decompose a global domain into separate, but overlapping, subdomains eases mesh generation procedures and increases flexibility of modeling flows with complex geometries. The methodology employs implicit spectral element discretization of equations in each subdomain and explicit treatment of subdomain interfaces with spectrally-accurate spatial interpolation and high-order accurate temporal extrapolation, and requires few, if any, iterations, yet maintains the global accuracy and stability of the underlying flow solver. The overlapping mesh methodology is thoroughly validated using two-dimensional and three-dimensional benchmark problems in laminar and turbulent flows. The spatial and temporal convergence is documented and is in agreement with the nominal order of accuracy of the solver. The influence of long integration times, as well as inflow-outflow global boundary conditions on the performance of the overlapping grid solver is assessed. In a turbulent benchmark of fully-developed turbulent pipe flow, the turbulent statistics with the overlapping grids is validated against published available experimental and other computation data. Scaling tests are presented that show near linear strong scaling, even for moderately large processor counts.
Accurate Navier-Stokes results for the hypersonic flow over a spherical nosetip
Blottner, F.G.
1989-01-01
The unsteady thin-layer Navier-Stokes equations for a perfect gas are solved with a linearized block Alternating Direction Implicit finite-difference solution procedure. Solution errors due to numerical dissipation added to the governing equations are evaluated. Errors in the numerical predictions on three different grids are determined where Richardson extrapolation is used to estimate the exact solution. Accurate computational results are tabulated for the hypersonic laminar flow over a spherical body which can be used as a benchmark test case. Predictions obtained from the code are in good agreement with inviscid numerical results and experimental data. 9 refs., 11 figs., 3 tabs.
Accurate deterministic solutions for the classic Boltzmann shock profile
NASA Astrophysics Data System (ADS)
Yue, Yubei
The Boltzmann equation or Boltzmann transport equation is a classical kinetic equation devised by Ludwig Boltzmann in 1872. It is regarded as a fundamental law in rarefied gas dynamics. Rather than using macroscopic quantities such as density, temperature, and pressure to describe the underlying physics, the Boltzmann equation uses a distribution function in phase space to describe the physical system, and all the macroscopic quantities are weighted averages of the distribution function. The information contained in the Boltzmann equation is surprisingly rich, and the Euler and Navier-Stokes equations of fluid dynamics can be derived from it using series expansions. Moreover, the Boltzmann equation can reach regimes far from the capabilities of fluid dynamical equations, such as the realm of rarefied gases---the topic of this thesis. Although the Boltzmann equation is very powerful, it is extremely difficult to solve in most situations. Thus the only hope is to solve it numerically. But soon one finds that even a numerical simulation of the equation is extremely difficult, due to both the complex and high-dimensional integral in the collision operator, and the hyperbolic phase-space advection terms. For this reason, until few years ago most numerical simulations had to rely on Monte Carlo techniques. In this thesis I will present a new and robust numerical scheme to compute direct deterministic solutions of the Boltzmann equation, and I will use it to explore some classical gas-dynamical problems. In particular, I will study in detail one of the most famous and intrinsically nonlinear problems in rarefied gas dynamics, namely the accurate determination of the Boltzmann shock profile for a gas of hard spheres.
Accurate analysis of multicomponent fuel spray evaporation in turbulent flow
NASA Astrophysics Data System (ADS)
Rauch, Bastian; Calabria, Raffaela; Chiariello, Fabio; Le Clercq, Patrick; Massoli, Patrizio; Rachner, Michael
2012-04-01
The aim of this paper is to perform an accurate analysis of the evaporation of single component and binary mixture fuels sprays in a hot weakly turbulent pipe flow by means of experimental measurement and numerical simulation. This gives a deeper insight into the relationship between fuel composition and spray evaporation. The turbulence intensity in the test section is equal to 10%, and the integral length scale is three orders of magnitude larger than the droplet size while the turbulence microscale (Kolmogorov scales) is of same order as the droplet diameter. The spray produced by means of a calibrated droplet generator was injected in a gas flow electrically preheated. N-nonane, isopropanol, and their mixtures were used in the tests. The generalized scattering imaging technique was applied to simultaneously determine size, velocity, and spatial location of the droplets carried by the turbulent flow in the quartz tube. The spray evaporation was computed using a Lagrangian particle solver coupled to a gas-phase solver. Computations of spray mean diameter and droplet size distributions at different locations along the pipe compare very favorably with the measurement results. This combined research tool enabled further investigation concerning the influencing parameters upon the evaporation process such as the turbulence, droplet internal mixing, and liquid-phase thermophysical properties.
Accurate measurement of streamwise vortices in low speed aerodynamic flows
NASA Astrophysics Data System (ADS)
Waldman, Rye M.; Kudo, Jun; Breuer, Kenneth S.
2010-11-01
Low Reynolds number experiments with flapping animals (such as bats and small birds) are of current interest in understanding biological flight mechanics, and due to their application to Micro Air Vehicles (MAVs) which operate in a similar parameter space. Previous PIV wake measurements have described the structures left by bats and birds, and provided insight to the time history of their aerodynamic force generation; however, these studies have faced difficulty drawing quantitative conclusions due to significant experimental challenges associated with the highly three-dimensional and unsteady nature of the flows, and the low wake velocities associated with lifting bodies that only weigh a few grams. This requires the high-speed resolution of small flow features in a large field of view using limited laser energy and finite camera resolution. Cross-stream measurements are further complicated by the high out-of-plane flow which requires thick laser sheets and short interframe times. To quantify and address these challenges we present data from a model study on the wake behind a fixed wing at conditions comparable to those found in biological flight. We present a detailed analysis of the PIV wake measurements, discuss the criteria necessary for accurate measurements, and present a new dual-plane PIV configuration to resolve these issues.
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.
Turbulence Models for Accurate Aerothermal Prediction in Hypersonic Flows
NASA Astrophysics Data System (ADS)
Zhang, Xiang-Hong; Wu, Yi-Zao; Wang, Jiang-Feng
Accurate description of the aerodynamic and aerothermal environment is crucial to the integrated design and optimization for high performance hypersonic vehicles. In the simulation of aerothermal environment, the effect of viscosity is crucial. The turbulence modeling remains a major source of uncertainty in the computational prediction of aerodynamic forces and heating. In this paper, three turbulent models were studied: the one-equation eddy viscosity transport model of Spalart-Allmaras, the Wilcox k-ω model and the Menter SST model. For the k-ω model and SST model, the compressibility correction, press dilatation and low Reynolds number correction were considered. The influence of these corrections for flow properties were discussed by comparing with the results without corrections. In this paper the emphasis is on the assessment and evaluation of the turbulence models in prediction of heat transfer as applied to a range of hypersonic flows with comparison to experimental data. This will enable establishing factor of safety for the design of thermal protection systems of hypersonic vehicle.
Cartesian Off-Body Grid Adaption for Viscous Time- Accurate Flow Simulation
NASA Technical Reports Server (NTRS)
Buning, Pieter G.; Pulliam, Thomas H.
2011-01-01
An improved solution adaption capability has been implemented in the OVERFLOW overset grid CFD code. Building on the Cartesian off-body approach inherent in OVERFLOW and the original adaptive refinement method developed by Meakin, the new scheme provides for automated creation of multiple levels of finer Cartesian grids. Refinement can be based on the undivided second-difference of the flow solution variables, or on a specific flow quantity such as vorticity. Coupled with load-balancing and an inmemory solution interpolation procedure, the adaption process provides very good performance for time-accurate simulations on parallel compute platforms. A method of using refined, thin body-fitted grids combined with adaption in the off-body grids is presented, which maximizes the part of the domain subject to adaption. Two- and three-dimensional examples are used to illustrate the effectiveness and performance of the adaption scheme.
A high order accurate finite element algorithm for high Reynolds number flow prediction
NASA Technical Reports Server (NTRS)
Baker, A. J.
1978-01-01
A Galerkin-weighted residuals formulation is employed to establish an implicit finite element solution algorithm for generally nonlinear initial-boundary value problems. Solution accuracy, and convergence rate with discretization refinement, are quantized in several error norms, by a systematic study of numerical solutions to several nonlinear parabolic and a hyperbolic partial differential equation characteristic of the equations governing fluid flows. Solutions are generated using selective linear, quadratic and cubic basis functions. Richardson extrapolation is employed to generate a higher-order accurate solution to facilitate isolation of truncation error in all norms. Extension of the mathematical theory underlying accuracy and convergence concepts for linear elliptic equations is predicted for equations characteristic of laminar and turbulent fluid flows at nonmodest Reynolds number. The nondiagonal initial-value matrix structure introduced by the finite element theory is determined intrinsic to improved solution accuracy and convergence. A factored Jacobian iteration algorithm is derived and evaluated to yield a consequential reduction in both computer storage and execution CPU requirements while retaining solution accuracy.
Highly accurate boronimeter assay of concentrated boric acid solutions
Ball, R.M. )
1992-01-01
The Random-Walk Boronimeter has successfully been used as an on-line indicator of boric acid concentration in an operating commercial pressurized water reactor. The principle has been adapted for measurement of discrete samples to high accuracy and to concentrations up to 6000 ppm natural boron in light water. Boric acid concentration in an aqueous solution is a necessary measurement in many nuclear power plants, particularly those that use boric acid dissolved in the reactor coolant as a reactivity control system. Other nuclear plants use a high-concentration boric acid solution as a backup shutdown system. Such a shutdown system depends on rapid injection of the solution and frequent surveillance of the fluid to ensure the presence of the neutron absorber. The two methods typically used to measure boric acid are the chemical and the physical methods. The chemical method uses titration to determine the ionic concentration of the BO[sub 3] ions and infers the boron concentration. The physical method uses the attenuation of neutrons by the solution and infers the boron concentration from the neutron absorption properties. This paper describes the Random-Walk Boronimeter configured to measure discrete samples to high accuracy and high concentration.
Accurate computation of Stokes flow driven by an open immersed interface
NASA Astrophysics Data System (ADS)
Li, Yi; Layton, Anita T.
2012-06-01
We present numerical methods for computing two-dimensional Stokes flow driven by forces singularly supported along an open, immersed interface. Two second-order accurate methods are developed: one for accurately evaluating boundary integral solutions at a point, and another for computing Stokes solution values on a rectangular mesh. We first describe a method for computing singular or nearly singular integrals, such as a double layer potential due to sources on a curve in the plane, evaluated at a point on or near the curve. To improve accuracy of the numerical quadrature, we add corrections for the errors arising from discretization, which are found by asymptotic analysis. When used to solve the Stokes equations with sources on an open, immersed interface, the method generates second-order approximations, for both the pressure and the velocity, and preserves the jumps in the solutions and their derivatives across the boundary. We then combine the method with a mesh-based solver to yield a hybrid method for computing Stokes solutions at N2 grid points on a rectangular grid. Numerical results are presented which exhibit second-order accuracy. To demonstrate the applicability of the method, we use the method to simulate fluid dynamics induced by the beating motion of a cilium. The method preserves the sharp jumps in the Stokes solution and their derivatives across the immersed boundary. Model results illustrate the distinct hydrodynamic effects generated by the effective stroke and by the recovery stroke of the ciliary beat cycle.
Electroosmotic flow hysteresis for dissimilar ionic solutions.
Lim, An Eng; Lim, Chun Yee; Lam, Yee Cheong
2015-03-01
Electroosmotic flow (EOF) with two or more fluids is commonly encountered in various microfluidics applications. However, no investigation has hitherto been conducted to investigate the hysteretic or flow direction-dependent behavior during the displacement flow of solutions with dissimilar ionic species. In this investigation, electroosmotic displacement flow involving dissimilar ionic solutions was studied experimentally through a current monitoring method and numerically through finite element simulations. The flow hysteresis can be characterized by the turning and displacement times; turning time refers to the abrupt gradient change of current-time curve while displacement time is the time for one solution to completely displace the other solution. Both experimental and simulation results illustrate that the turning and displacement times for a particular solution pair can be directional-dependent, indicating that the flow conditions in the microchannel are not the same in the two different flow directions. The mechanics of EOF hysteresis was elucidated through the theoretical model which includes the ionic mobility of each species, a major governing parameter. Two distinct mechanics have been identified as the causes for the EOF hysteresis involving dissimilar ionic solutions: the widening/sharpening effect of interfacial region between the two solutions and the difference in ion concentration distributions (and thus average zeta potentials) in different flow directions. The outcome of this investigation contributes to the fundamental understanding of flow behavior in microfluidic systems involving solution pair with dissimilar ionic species. PMID:25945139
Electroosmotic flow hysteresis for dissimilar ionic solutions
Lim, An Eng; Lam, Yee Cheong
2015-01-01
Electroosmotic flow (EOF) with two or more fluids is commonly encountered in various microfluidics applications. However, no investigation has hitherto been conducted to investigate the hysteretic or flow direction-dependent behavior during the displacement flow of solutions with dissimilar ionic species. In this investigation, electroosmotic displacement flow involving dissimilar ionic solutions was studied experimentally through a current monitoring method and numerically through finite element simulations. The flow hysteresis can be characterized by the turning and displacement times; turning time refers to the abrupt gradient change of current-time curve while displacement time is the time for one solution to completely displace the other solution. Both experimental and simulation results illustrate that the turning and displacement times for a particular solution pair can be directional-dependent, indicating that the flow conditions in the microchannel are not the same in the two different flow directions. The mechanics of EOF hysteresis was elucidated through the theoretical model which includes the ionic mobility of each species, a major governing parameter. Two distinct mechanics have been identified as the causes for the EOF hysteresis involving dissimilar ionic solutions: the widening/sharpening effect of interfacial region between the two solutions and the difference in ion concentration distributions (and thus average zeta potentials) in different flow directions. The outcome of this investigation contributes to the fundamental understanding of flow behavior in microfluidic systems involving solution pair with dissimilar ionic species. PMID:25945139
Accurate, reliable control of process gases by mass flow controllers
Hardy, J.; McKnight, T.
1997-02-01
The thermal mass flow controller, or MFC, has become an instrument of choice for the monitoring and controlling of process gas flow throughout the materials processing industry. These MFCs are used on CVD processes, etching tools, and furnaces and, within the semiconductor industry, are used on 70% of the processing tools. Reliability and accuracy are major concerns for the users of the MFCs. Calibration and characterization technologies for the development and implementation of mass flow devices are described. A test facility is available to industry and universities to test and develop gas floe sensors and controllers and evaluate their performance related to environmental effects, reliability, reproducibility, and accuracy. Additional work has been conducted in the area of accuracy. A gravimetric calibrator was invented that allows flow sensors to be calibrated in corrosive, reactive gases to an accuracy of 0.3% of reading, at least an order of magnitude better than previously possible. Although MFCs are typically specified with accuracies of 1% of full scale, MFCs may often be implemented with unwarranted confidence due to the conventional use of surrogate gas factors. Surrogate gas factors are corrections applied to process flow indications when an MFC has been calibrated on a laboratory-safe surrogate gas, but is actually used on a toxic, or corrosive process gas. Previous studies have indicated that the use of these factors may cause process flow errors of typically 10%, but possibly as great as 40% of full scale. This paper will present possible sources of error in MFC process gas flow monitoring and control, and will present an overview of corrective measures which may be implemented with MFC use to significantly reduce these sources of error.
Fluid flow in nanopores: Accurate boundary conditions for carbon nanotubes
NASA Astrophysics Data System (ADS)
Sokhan, Vladimir P.; Nicholson, David; Quirke, Nicholas
2002-11-01
Steady-state Poiseuille flow of a simple fluid in carbon nanopores under a gravitylike force is simulated using a realistic empirical many-body potential model for carbon. Building on our previous study of slit carbon nanopores we show that fluid flow in a nanotube is also characterized by a large slip length. By analyzing temporal profiles of the velocity components of particles colliding with the wall we obtain values of the Maxwell coefficient defining the fraction of molecules thermalized by the wall and, for the first time, propose slip boundary conditions for smooth continuum surfaces such that they are equivalent in adsorption, diffusion, and fluid flow properties to fully dynamic atomistic models.
Multigrid solution of internal flows using unstructured solution adaptive meshes
NASA Astrophysics Data System (ADS)
Smith, Wayne A.; Blake, Kenneth R.
1992-11-01
This is the final report of the NASA Lewis SBIR Phase 2 Contract Number NAS3-25785, Multigrid Solution of Internal Flows Using Unstructured Solution Adaptive Meshes. The objective of this project, as described in the Statement of Work, is to develop and deliver to NASA a general three-dimensional Navier-Stokes code using unstructured solution-adaptive meshes for accuracy and multigrid techniques for convergence acceleration. The code will primarily be applied, but not necessarily limited, to high speed internal flows in turbomachinery.
Accurate Effective Hamiltonians via Unitary Flow in Floquet Space
NASA Astrophysics Data System (ADS)
Verdeny, Albert; Mielke, Andreas; Mintert, Florian
2013-10-01
We present a systematic construction of effective Hamiltonians of periodically driven quantum systems. Because of an equivalence between the time dependence of a Hamiltonian and an interaction in its Floquet operator, flow equations, that permit us to decouple interacting quantum systems, allow us to identify time-independent Hamiltonians for driven systems. With this approach, we explain the experimentally observed deviation of expected suppression of tunneling in ultracold atoms.
Device for accurately measuring mass flow of gases
Hylton, James O.; Remenyik, Carl J.
1994-01-01
A device for measuring mass flow of gases which utilizes a substantially buoyant pressure vessel suspended within a fluid/liquid in an enclosure. The pressure vessel is connected to a weighing device for continuously determining weight change of the vessel as a function of the amount of gas within the pressure vessel. In the preferred embodiment, this pressure vessel is formed from inner and outer right circular cylindrical hulls, with a volume between the hulls being vented to the atmosphere external the enclosure. The fluid/liquid, normally in the form of water typically with an added detergent, is contained within an enclosure with the fluid/liquid being at a level such that the pressure vessel is suspended beneath this level but above a bottom of the enclosure. The buoyant pressure vessel can be interconnected with selected valves to an auxiliary pressure vessel so that initial flow can be established to or from the auxiliary pressure vessel prior to flow to or from the buoyant pressure vessel.
Device for accurately measuring mass flow of gases
Hylton, J.O.; Remenyik, C.J.
1994-08-09
A device for measuring mass flow of gases which utilizes a substantially buoyant pressure vessel suspended within a fluid/liquid in an enclosure is disclosed. The pressure vessel is connected to a weighing device for continuously determining weight change of the vessel as a function of the amount of gas within the pressure vessel. In the preferred embodiment, this pressure vessel is formed from inner and outer right circular cylindrical hulls, with a volume between the hulls being vented to the atmosphere external the enclosure. The fluid/liquid, normally in the form of water typically with an added detergent, is contained within an enclosure with the fluid/liquid being at a level such that the pressure vessel is suspended beneath this level but above a bottom of the enclosure. The buoyant pressure vessel can be interconnected with selected valves to an auxiliary pressure vessel so that initial flow can be established to or from the auxiliary pressure vessel prior to flow to or from the buoyant pressure vessel. 5 figs.
NASA Technical Reports Server (NTRS)
Venkatachari, Balaji Shankar; Streett, Craig L.; Chang, Chau-Lyan; Friedlander, David J.; Wang, Xiao-Yen; Chang, Sin-Chung
2016-01-01
Despite decades of development of unstructured mesh methods, high-fidelity time-accurate simulations are still predominantly carried out on structured, or unstructured hexahedral meshes by using high-order finite-difference, weighted essentially non-oscillatory (WENO), or hybrid schemes formed by their combinations. In this work, the space-time conservation element solution element (CESE) method is used to simulate several flow problems including supersonic jet/shock interaction and its impact on launch vehicle acoustics, and direct numerical simulations of turbulent flows using tetrahedral meshes. This paper provides a status report for the continuing development of the space-time conservation element solution element (CESE) numerical and software framework under the Revolutionary Computational Aerosciences (RCA) project. Solution accuracy and large-scale parallel performance of the numerical framework is assessed with the goal of providing a viable paradigm for future high-fidelity flow physics simulations.
Approximate Solution for Choked Flow in Gas Seal Pads
NASA Technical Reports Server (NTRS)
Fleming, David P.
2004-01-01
Previous analyses of high pressure seals have considered adiabatic flow with friction but neglected effects of seal rotation. Most of this work analyzed a one-dimensional flow field. This works well to calculate stiffness and leakage of full circular seals, either face seals or annular ring seals. However, it cannot provide accurate results for a rectangular seal pad with its strongly two-dimensional flow field and its reliance on hydrodynamic forces to maintain a full fluid film. On the other hand, solutions of Reynolds lubrication equation have been obtained for the two-dimensional flow in a seal pad. But these solutions do not account for choking which occurs at high seal pressure ratios, nor do they consider the pressure loss that occurs in the entrance region of the flow field. The aim of the present work is to build on the Reynolds equation solution by use of an approximate choked flow analysis. This will account for the pressure losses in the flow entrance region, ensure that fluid velocities remain subsonic, and enable fluid inertial effects within the pad film to be accounted for. Results show that, in general, fluid inertia acts to decrease pad film load capacity and leakage, and increase film stiffness.
Fullerton, G D; Keener, C R; Cameron, I L
1994-12-01
The authors describe empirical corrections to ideally dilute expressions for freezing point depression of aqueous solutions to arrive at new expressions accurate up to three molal concentration. The method assumes non-ideality is due primarily to solute/solvent interactions such that the correct free water mass Mwc is the mass of water in solution Mw minus I.M(s) where M(s) is the mass of solute and I an empirical solute/solvent interaction coefficient. The interaction coefficient is easily derived from the constant in the linear regression fit to the experimental plot of Mw/M(s) as a function of 1/delta T (inverse freezing point depression). The I-value, when substituted into the new thermodynamic expressions derived from the assumption of equivalent activity of water in solution and ice, provides accurate predictions of freezing point depression (+/- 0.05 degrees C) up to 2.5 molal concentration for all the test molecules evaluated; glucose, sucrose, glycerol and ethylene glycol. The concentration limit is the approximate monolayer water coverage limit for the solutes which suggests that direct solute/solute interactions are negligible below this limit. This is contrary to the view of many authors due to the common practice of including hydration forces (a soft potential added to the hard core atomic potential) in the interaction potential between solute particles. When this is recognized the two viewpoints are in fundamental agreement. PMID:7699200
Workshop on electrodes for flowing solution batteries
NASA Astrophysics Data System (ADS)
Nanis, L.
1981-02-01
The electrochemical technology of aqueous secondary cells with flowing electrolyte solutions was addressed. Emphasis was placed on the significant parameters believed to govern the performance of the two basic types of electrodes now in use: a porous flow through electrode (PFTE), and an impervious flow by electrode. Progress, problems, and prospects were informally discussed. Key topics included: (current distribution in FTPE; conversion efficiency, segmented FTPE studies; general discussion on FTPE parameters; surface activation; application of FTPE to waste recovery; Exxon zinc bromine flow by system, FTPE in NASA redox energy storage; and application of FTPE in Lockheed zinc ferricyanide redox system). In generally comparing flow through to flow by electrodes, there were some surprising differences arising from experimental results that did not fit conventional thinking.
Solution of steady and unsteady transonic-vortex flows using Euler and full-potential equations
NASA Technical Reports Server (NTRS)
Kandil, Osama A.; Chuang, Andrew H.; Hu, Hong
1989-01-01
Two methods are presented for inviscid transonic flows: unsteady Euler equations in a rotating frame of reference for transonic-vortex flows and integral solution of full-potential equation with and without embedded Euler domains for transonic airfoil flows. The computational results covered: steady and unsteady conical vortex flows; 3-D steady transonic vortex flow; and transonic airfoil flows. The results are in good agreement with other computational results and experimental data. The rotating frame of reference solution is potentially efficient as compared with the space fixed reference formulation with dynamic gridding. The integral equation solution with embedded Euler domain is computationally efficient and as accurate as the Euler equations.
Finite element solutions of free surface flows
NASA Technical Reports Server (NTRS)
Zarda, P. R.; Marcus, M. S.
1977-01-01
A procedure is presented for using NASTRAN to determine the flow field about arbitrarily shaped bodies in the presence of a free surface. The fundamental unknown of the problem is the velocity potential which must satisfy Laplace's equation in the fluid region. Boundary conditions on the free surface may involve second order derivatives in space and time. In cases involving infinite domains either a tractable radiation condition is applied at a truncated boundary or a series expansion is used and matched to the local finite elements. Solutions are presented for harmonic, transient, and steady state problems and compared to either exact solutions or other numerical solutions.
An Accurate Upper Bound Solution for Plane Strain Extrusion through a Wedge-Shaped Die
Mustafa, Yusof; Lyamina, Elena
2014-01-01
An upper bound method for the process of plane strain extrusion through a wedge-shaped die is derived. A technique for constructing a kinematically admissible velocity field satisfying the exact asymptotic singular behavior of real velocity fields in the vicinity of maximum friction surfaces (the friction stress at sliding is equal to the shear yield stress on such surfaces) is described. Two specific upper bound solutions are found using the method derived. The solutions are compared to an accurate slip-line solution and it is shown that the accuracy of the new method is very high. PMID:25101311
Accurate on-line mass flow measurements in supercritical fluid chromatography.
Tarafder, Abhijit; Vajda, Péter; Guiochon, Georges
2013-12-13
This work demonstrates the possible advantages and the challenges of accurate on-line measurements of the CO2 mass flow rate during supercritical fluid chromatography (SFC) operations. Only the mass flow rate is constant along the column in SFC. The volume flow rate is not. The critical importance of accurate measurements of mass flow rates for the achievement of reproducible data and the serious difficulties encountered in supercritical fluid chromatography for its assessment were discussed earlier based on the physical properties of carbon dioxide. In this report, we experimentally demonstrate the problems encountered when performing mass flow rate measurements and the gain that can possibly be achieved by acquiring reproducible data using a Coriolis flow meter. The results obtained show how the use of a highly accurate mass flow meter permits, besides the determination of accurate values of the mass flow rate, a systematic, constant diagnosis of the correct operation of the instrument and the monitoring of the condition of the carbon dioxide pump. PMID:24210558
A novel numerical technique to obtain an accurate solution to the Thomas-Fermi equation
NASA Astrophysics Data System (ADS)
Parand, Kourosh; Yousefi, Hossein; Delkhosh, Mehdi; Ghaderi, Amin
2016-07-01
In this paper, a new algorithm based on the fractional order of rational Euler functions (FRE) is introduced to study the Thomas-Fermi (TF) model which is a nonlinear singular ordinary differential equation on a semi-infinite interval. This problem, using the quasilinearization method (QLM), converts to the sequence of linear ordinary differential equations to obtain the solution. For the first time, the rational Euler (RE) and the FRE have been made based on Euler polynomials. In addition, the equation will be solved on a semi-infinite domain without truncating it to a finite domain by taking FRE as basic functions for the collocation method. This method reduces the solution of this problem to the solution of a system of algebraic equations. We demonstrated that the new proposed algorithm is efficient for obtaining the value of y'(0) , y(x) and y'(x) . Comparison with some numerical and analytical solutions shows that the present solution is highly accurate.
Influence of surfactants on unsaturated water flow and solute transport
NASA Astrophysics Data System (ADS)
Karagunduz, Ahmet; Young, Michael H.; Pennell, Kurt D.
2015-04-01
Surfactants can reduce soil water retention by changing the surface tension of water and the contact angle between the liquid and solid phases. As a result, water flow and solute transport in unsaturated soil may be altered in the presence of surfactants. In this study, the effects of a representative nonionic surfactant, Triton X-100, on coupled water flow and nonreactive solute transport during unsaturated flow conditions were evaluated. Batch reactor experiments were conducted to measure the surfactant sorption characteristics, while unsaturated transport experiments were performed in columns packed with 40-270 mesh Ottawa sand at five initial water contents. Following the introduction of surfactant solution, the rate of water percolation through the sand increased; however, this period of rapid water drainage was followed by decreased water percolation due to the reduction in soil water content and the corresponding decrease in unsaturated hydraulic conductivity behind the surfactant front. The observed changes in water percolation occurred sequentially, and resulted in faster nonreactive solute transport than was observed in the absence of surfactant. A one-dimensional mathematical model accurately described coupled water flow, surfactant, and solute transport under most experimental conditions. Differences between model predictions and experimental data were observed in the column study performed at the lowest water content (0.115 cm3/cm3), which was attributed to surfactant adsorption at the air-water interface. These findings demonstrate the potential influence of surfactants additives on unsaturated water flow and solute transport in soils, and demonstrate a methodology to couple these processes in a predictive modeling tool.
NASA Astrophysics Data System (ADS)
Gregg, T. K. P.; Sakimoto, S. E. H.
1999-03-01
3-D analytic lava channel flow solutions provide more accurate and realistic viscosity and flow rate extimates. This study compares model with data for laboratory channel simulations, active Pu'u O'o and Mauna Loa channels, and MOLA topography of a Mars Elysium channel.
Accurate solution of the proton-hydrogen three-body scattering problem
NASA Astrophysics Data System (ADS)
Abdurakhmanov, I. B.; Kadyrov, A. S.; Bray, I.
2016-02-01
An accurate solution to the fundamental three-body problem of proton-hydrogen scattering including direct scattering and ionization, electron capture and electron capture into the continuum (ECC) is presented. The problem has been addressed using a quantum-mechanical two-center convergent close-coupling approach. At each energy the internal consistency of the solution is demonstrated with the help of single-center calculations, with both approaches converging independently to the same electron-loss cross section. This is the sum of the electron capture, ECC and direct ionization cross sections, which are only obtainable separately in the solution of the problem using the two-center expansion. Agreement with experiment for the electron-capture cross section is excellent. However, for the ionization cross sections some discrepancy exists. Given the demonstrated internal consistency we remain confident in the provided theoretical solution.
ASYMPTOTICALLY OPTIMAL HIGH-ORDER ACCURATE ALGORITHMS FOR THE SOLUTION OF CERTAIN ELLIPTIC PDEs
Leonid Kunyansky, PhD
2008-11-26
The main goal of the project, "Asymptotically Optimal, High-Order Accurate Algorithms for the Solution of Certain Elliptic PDE's" (DE-FG02-03ER25577) was to develop fast, high-order algorithms for the solution of scattering problems and spectral problems of photonic crystals theory. The results we obtained lie in three areas: (1) asymptotically fast, high-order algorithms for the solution of eigenvalue problems of photonics, (2) fast, high-order algorithms for the solution of acoustic and electromagnetic scattering problems in the inhomogeneous media, and (3) inversion formulas and fast algorithms for the inverse source problem for the acoustic wave equation, with applications to thermo- and opto- acoustic tomography.
Accurate ω-ψ Spectral Solution of the Singular Driven Cavity Problem
NASA Astrophysics Data System (ADS)
Auteri, F.; Quartapelle, L.; Vigevano, L.
2002-08-01
This article provides accurate spectral solutions of the driven cavity problem, calculated in the vorticity-stream function representation without smoothing the corner singularities—a prima facie impossible task. As in a recent benchmark spectral calculation by primitive variables of Botella and Peyret, closed-form contributions of the singular solution for both zero and finite Reynolds numbers are subtracted from the unknown of the problem tackled here numerically in biharmonic form. The method employed is based on a split approach to the vorticity and stream function equations, a Galerkin-Legendre approximation of the problem for the perturbation, and an evaluation of the nonlinear terms by Gauss-Legendre numerical integration. Results computed for Re=0, 100, and 1000 compare well with the benchmark steady solutions provided by the aforementioned collocation-Chebyshev projection method. The validity of the proposed singularity subtraction scheme for computing time-dependent solutions is also established.
GENERAL SOLUTIONS FOR VISCOPLASTIC DEBRIS FLOW.
Chen, Cheng-lung
1988-01-01
Theoretical velocity profile and theoretical pressure and concentration distributions for (steady) uniform debris flow in wide channels are derived from a generalized viscoplastic fluid (GVF) model without imposing R. A. Bagnold's assumption of constant grain concentration. Good agreement between the theoretical velocity profile and the experimental data of Japanese scientists strongly supports the validity of both the GVF model and the proposed method of solution from the model. It is shown that both E. C. Bingham and Bagnold versions (or submodels) of the GVF model can be used to simulate debris flow at the dynamic state. Although Bagnold's dilatant submodel appears to fit the Japanese data better than the Bingham submodel for flow of noncohesive grains, the choice between them is by no means clear-cut.
Exact solutions to magnetized plasma flow
Wang, Zhehui; Barnes, Cris W.
2001-03-01
Exact analytic solutions for steady-state magnetized plasma flow (MPF) using ideal magnetohydrodynamics formalism are presented. Several cases are considered. When plasma flow is included, a finite plasma pressure gradient {nabla}p can be maintained in a force-free state JxB=0 by the velocity gradient. Both incompressible and compressible MPF examples are discussed for a Taylor-state spheromak B field. A new magnetized nozzle solution is given for compressible plasma when U{parallel}B. Transition from a magnetized nozzle to a magnetic nozzle is possible when the B field is strong enough. No physical nozzle would be needed in the magnetic nozzle case. Diverging-, drum- and nozzle-shaped MPF solutions when U{perpendicular}B are also given. The electric field is needed to balance the UxB term in Ohm's law. The electric field can be generated in the laboratory with the proposed conducting electrodes. If such electric fields also exist in stars and galaxies, such as through a dynamo process, then these solutions can be candidates to explain single and double jets.
Estimation of deviation angle for axial-flow compressor blade sections using inviscid-flow solutions
NASA Technical Reports Server (NTRS)
Miller, M. J.
1974-01-01
Development of a method of estimating deviation angles by analytical procedures was begun. Solutions for inviscid, irrotational flow in the blade-to-blade plane were obtained with a finite-difference calculation method. Deviation angles for a plane cascade with a rounded trailing edge were estimated by using the inviscid-flow solutions and three trailing-edge hypotheses. The estimated deviation angles were compared with existing experimental data over a range of incidence angles at inlet flow angles of 30 deg and 60 deg. The results indicate that deviation angles can be estimated accurately (within 1 deg) by using one of the three trailing-edge hypotheses, but only when pressure losses are low. A new trailing-edge hypotheses is presented which is suitable (for the cascade considered) for both low- and high-loss operating points.
NASA Technical Reports Server (NTRS)
Liu, Yen; Vinokur, Marcel
1989-01-01
This paper treats the accurate and efficient calculation of thermodynamic properties of arbitrary gas mixtures for equilibrium flow computations. New improvements in the Stupochenko-Jaffe model for the calculation of thermodynamic properties of diatomic molecules are presented. A unified formulation of equilibrium calculations for gas mixtures in terms of irreversible entropy is given. Using a highly accurate thermo-chemical data base, a new, efficient and vectorizable search algorithm is used to construct piecewise interpolation procedures with generate accurate thermodynamic variable and their derivatives required by modern computational algorithms. Results are presented for equilibrium air, and compared with those given by the Srinivasan program.
NASA Technical Reports Server (NTRS)
Stahara, S. S.; Elliott, J. P.; Spreiter, J. R.
1981-01-01
Perturbation procedures and associated computational codes for determining nonlinear flow solutions were developed to establish a method for minimizing computational requirements associated with parametric studies of transonic flows in turbomachines. The procedure that was developed and evaluated was found to be capable of determining highly accurate approximations to families of strongly nonlinear solutions which are either continuous or discontinuous, and which represent variations in some arbitrary parameter. Coordinate straining is employed to account for the movement of discontinuities and maxima of high gradient regions due to the perturbation. The development and results reported are for the single parameter perturbation problem. Flows past both isolated airfoils and compressor cascades involving a wide variety of flow and geometry parameter changes are reported. Attention is focused in particular on transonic flows which are strongly supercritical and exhibit large surface shock movement over the parametric range studied; and on subsonic flows which display large pressure variations in the stagnation and peak suction pressure regions. Comparisons with the corresponding 'exact' nonlinear solutions indicate a remarkable accuracy and range of validity of such a procedure.
Free Vibration of Simply Supported General Triangular Thin Plates: AN Accurate Simplified Solution
NASA Astrophysics Data System (ADS)
Saliba, H. T.
1996-09-01
In this paper, a highly accurate, simplified, and economical solution is provided for the free vibration problem of simply supported thin general triangular plates. The method is applicable to thin plates with linear boundaries regardless of there geometrical shapes. Results are compared with previously published reliable data for both the isosceles as well as the general triangles. Excellent agreements are reported. Eigenvalues are provided for a wide range of place aspect ratios. The first five mode shapes for some isosceles triangles are also provided for illustrative purposes. The advantages of the solution presented in the paper over previously published solutions are briefly discussed. Although the paper deals only with simple support conditions, it is mentioned that any combination of classical boundary conditions, with or without complicating factors, can easily be handled.
MONA: An accurate two-phase well flow model based on phase slippage
Asheim, H.
1984-10-01
In two phase flow, holdup and pressure loss are related to interfacial slippage. A model based on the slippage concept has been developed and tested using production well data from Forties, the Ekofisk area, and flowline data from Prudhoe Bay. The model developed turned out considerably more accurate than the standard models used for comparison.
Direct Coupling Method for Time-Accurate Solution of Incompressible Navier-Stokes Equations
NASA Technical Reports Server (NTRS)
Soh, Woo Y.
1992-01-01
A noniterative finite difference numerical method is presented for the solution of the incompressible Navier-Stokes equations with second order accuracy in time and space. Explicit treatment of convection and diffusion terms and implicit treatment of the pressure gradient give a single pressure Poisson equation when the discretized momentum and continuity equations are combined. A pressure boundary condition is not needed on solid boundaries in the staggered mesh system. The solution of the pressure Poisson equation is obtained directly by Gaussian elimination. This method is tested on flow problems in a driven cavity and a curved duct.
Unique solution for accurate in-situ infrared profiling in reheat furnaces
NASA Astrophysics Data System (ADS)
Primhak, David; Wileman, Ben; Drögmöller, Peter
2010-05-01
As thermal imaging becomes a more accepted technology in industrial environments it can provide exciting new solutions to applications that have been previously dominated by single point pyrometers. The new development of an uncooled focal plane array thermal imager with a narrow band 3.9μm filter and background compensation processing enables measurements in industrial furnaces to provide temperature profiling of the product. This paper will show why the use of a 3.9μm camera with a borescope optic is the most accurate noncontact method for in-furnace temperature measurement. This will be done using the example of a reheat furnace where in a controlled trial using an instrumented billet the measurement from the IR device was shown to accurately track the thermocouple temperature during a variety of furnace operating conditions.
NASA Technical Reports Server (NTRS)
Constantinescu, G.S.; Lele, S. K.
2000-01-01
The motivation of this work is the ongoing effort at the Center for Turbulence Research (CTR) to use large eddy simulation (LES) techniques to calculate the noise radiated by jet engines. The focus on engine exhaust noise reduction is motivated by the fact that a significant reduction has been achieved over the last decade on the other main sources of acoustic emissions of jet engines, such as the fan and turbomachinery noise, which gives increased priority to jet noise. To be able to propose methods to reduce the jet noise based on results of numerical simulations, one first has to be able to accurately predict the spatio-temporal distribution of the noise sources in the jet. Though a great deal of understanding of the fundamental turbulence mechanisms in high-speed jets was obtained from direct numerical simulations (DNS) at low Reynolds numbers, LES seems to be the only realistic available tool to obtain the necessary near-field information that is required to estimate the acoustic radiation of the turbulent compressible engine exhaust jets. The quality of jet-noise predictions is determined by the accuracy of the numerical method that has to capture the wide range of pressure fluctuations associated with the turbulence in the jet and with the resulting radiated noise, and by the boundary condition treatment and the quality of the mesh. Higher Reynolds numbers and coarser grids put in turn a higher burden on the robustness and accuracy of the numerical method used in this kind of jet LES simulations. As these calculations are often done in cylindrical coordinates, one of the most important requirements for the numerical method is to provide a flow solution that is not contaminated by numerical artifacts. The coordinate singularity is known to be a source of such artifacts. In the present work we use 6th order Pade schemes in the non-periodic directions to discretize the full compressible flow equations. It turns out that the quality of jet-noise predictions
Adjustable flow rate controller for polymer solutions
Jackson, Kenneth M.
1981-01-01
An adjustable device for controlling the flow rate of polymer solutions which results in only little shearing of the polymer molecules, said device comprising an inlet manifold, an outlet manifold, a plurality of tubes capable of providing communication between said inlet and outlet manifolds, said tubes each having an internal diameter that is smaller than that of the inlet manifold and large enough to insure that viscosity of the polymer solution passing through each said tube will not be reduced more than about 25 percent, and a valve associated with each tube, said valve being capable of opening or closing communication in that tube between the inlet and outlet manifolds, each said valve when fully open having a diameter that is substantially at least as great as that of the tube with which it is associated.
A new algorithm for generating highly accurate benchmark solutions to transport test problems
Azmy, Y.Y.
1997-06-01
We present a new algorithm for solving the neutron transport equation in its discrete-variable form. The new algorithm is based on computing the full matrix relating the scalar flux spatial moments in all cells to the fixed neutron source spatial moments, foregoing the need to compute the angular flux spatial moments, and thereby eliminating the need for sweeping the spatial mesh in each discrete-angular direction. The matrix equation is solved exactly in test cases, producing a solution vector that is free from iteration convergence error, and subject only to truncation and roundoff errors. Our algorithm is designed to provide method developers with a quick and simple solution scheme to test their new methods on difficult test problems without the need to develop sophisticated solution techniques, e.g. acceleration, before establishing the worthiness of their innovation. We demonstrate the utility of the new algorithm by applying it to the Arbitrarily High Order Transport Nodal (AHOT-N) method, and using it to solve two of Burre`s Suite of Test Problems (BSTP). Our results provide highly accurate benchmark solutions, that can be distributed electronically and used to verify the pointwise accuracy of other solution methods and algorithms.
Toward Accurate Modeling of the Effect of Ion-Pair Formation on Solute Redox Potential.
Qu, Xiaohui; Persson, Kristin A
2016-09-13
A scheme to model the dependence of a solute redox potential on the supporting electrolyte is proposed, and the results are compared to experimental observations and other reported theoretical models. An improved agreement with experiment is exhibited if the effect of the supporting electrolyte on the redox potential is modeled through a concentration change induced via ion pair formation with the salt, rather than by only considering the direct impact on the redox potential of the solute itself. To exemplify the approach, the scheme is applied to the concentration-dependent redox potential of select molecules proposed for nonaqueous flow batteries. However, the methodology is general and enables rational computational electrolyte design through tuning of the operating window of electrochemical systems by shifting the redox potential of its solutes; including potentially both salts as well as redox active molecules. PMID:27500744
Solution of plane cascade flow using improved surface singularity methods
NASA Technical Reports Server (NTRS)
Mcfarland, E. R.
1981-01-01
A solution method has been developed for calculating compressible inviscid flow through a linear cascade of arbitrary blade shapes. The method uses advanced surface singularity formulations which were adapted from those found in current external flow analyses. The resulting solution technique provides a fast flexible calculation for flows through turbomachinery blade rows. The solution method and some examples of the method's capabilities are presented.
Accurate integral equation theory for the central force model of liquid water and ionic solutions
NASA Astrophysics Data System (ADS)
Ichiye, Toshiko; Haymet, A. D. J.
1988-10-01
The atom-atom pair correlation functions and thermodynamics of the central force model of water, introduced by Lemberg, Stillinger, and Rahman, have been calculated accurately by an integral equation method which incorporates two new developments. First, a rapid new scheme has been used to solve the Ornstein-Zernike equation. This scheme combines the renormalization methods of Allnatt, and Rossky and Friedman with an extension of the trigonometric basis-set solution of Labik and co-workers. Second, by adding approximate ``bridge'' functions to the hypernetted-chain (HNC) integral equation, we have obtained predictions for liquid water in which the hydrogen bond length and number are in good agreement with ``exact'' computer simulations of the same model force laws. In addition, for dilute ionic solutions, the ion-oxygen and ion-hydrogen coordination numbers display both the physically correct stoichiometry and good agreement with earlier simulations. These results represent a measurable improvement over both a previous HNC solution of the central force model and the ex-RISM integral equation solutions for the TIPS and other rigid molecule models of water.
Accurate and robust methods for variable density incompressible flows with discontinuities
Rider, W.J.; Kothe, D.B.; Puckett, E.G.
1996-09-01
We are interested in the solution of incompressible flows which are characterized by large density variations, interfacial physics, arbitrary material topologies and strong vortical content. The issues present in constant density incompressible flow are exacerbated by the presence of density discontinuities. A much greater premium requirement is placed the positivity of computed quantities The mechanism of baroclinc vorticity generation exists ({gradient}p x {gradient}p) to further complicate the physics.
NASA Technical Reports Server (NTRS)
Loh, Ching Y.; Jorgenson, Philip C. E.
2007-01-01
A time-accurate, upwind, finite volume method for computing compressible flows on unstructured grids is presented. The method is second order accurate in space and time and yields high resolution in the presence of discontinuities. For efficiency, the Roe approximate Riemann solver with an entropy correction is employed. In the basic Euler/Navier-Stokes scheme, many concepts of high order upwind schemes are adopted: the surface flux integrals are carefully treated, a Cauchy-Kowalewski time-stepping scheme is used in the time-marching stage, and a multidimensional limiter is applied in the reconstruction stage. However even with these up-to-date improvements, the basic upwind scheme is still plagued by the so-called "pathological behaviors," e.g., the carbuncle phenomenon, the expansion shock, etc. A solution to these limitations is presented which uses a very simple dissipation model while still preserving second order accuracy. This scheme is referred to as the enhanced time-accurate upwind (ETAU) scheme in this paper. The unstructured grid capability renders flexibility for use in complex geometry; and the present ETAU Euler/Navier-Stokes scheme is capable of handling a broad spectrum of flow regimes from high supersonic to subsonic at very low Mach number, appropriate for both CFD (computational fluid dynamics) and CAA (computational aeroacoustics). Numerous examples are included to demonstrate the robustness of the methods.
Implicit solution of three-dimensional internal turbulent flows
NASA Technical Reports Server (NTRS)
Michelassi, V.; Liou, M.-S.; Povinelli, Louis A.; Martelli, F.
1991-01-01
The scalar form of the approximate factorization method was used to develop a new code for the solution of three dimensional internal laminar and turbulent compressible flows. The Navier-Stokes equations in their Reynolds-averaged form were iterated in time until a steady solution was reached. Evidence was given to the implicit and explicit artificial damping schemes that proved to be particularly efficient in speeding up convergence and enhancing the algorithm robustness. A conservative treatment of these terms at the domain boundaries was proposed in order to avoid undesired mass and/or momentum artificial fluxes. Turbulence effects were accounted for by the zero-equation Baldwin-Lomax turbulence model and the q-omega two-equation model. The flow in a developing S-duct was then solved in the laminar regime in a Reynolds number (Re) of 790 and in the turbulent regime at Re equals 40,000 by using the Baldwin-Lomax model. The Stanitz elbow was then solved by using an invicid version of the same code at M sub inlet equals 0.4. Grid dependence and convergence rate were investigated, showing that for this solver the implicit damping scheme may play a critical role for convergence characteristics. The same flow at Re equals 2.5 times 10(exp 6) was solved with the Baldwin-Lomax and the q-omega models. Both approaches show satisfactory agreement with experiments, although the q-omega model was slightly more accurate.
Li, Chunyan; Wu, Pei-ming; Wu, Zhizhen; Limnuson, Kanokwan; Mehan, Neal; Mozayan, Cameron; Golanov, Eugene V; Ahn, Chong H; Hartings, Jed A; Narayan, Raj K
2015-10-01
Cerebral blood flow (CBF) plays a critical role in the exchange of nutrients and metabolites at the capillary level and is tightly regulated to meet the metabolic demands of the brain. After major brain injuries, CBF normally decreases and supporting the injured brain with adequate CBF is a mainstay of therapy after traumatic brain injury. Quantitative and localized measurement of CBF is therefore critically important for evaluation of treatment efficacy and also for understanding of cerebral pathophysiology. We present here an improved thermal flow microsensor and its operation which provides higher accuracy compared to existing devices. The flow microsensor consists of three components, two stacked-up thin film resistive elements serving as composite heater/temperature sensor and one remote resistive element for environmental temperature compensation. It operates in constant-temperature mode (~2 °C above the medium temperature) providing 20 ms temporal resolution. Compared to previous thermal flow microsensor based on self-heating and self-sensing design, the sensor presented provides at least two-fold improvement in accuracy in the range from 0 to 200 ml/100 g/min. This is mainly achieved by using the stacked-up structure, where the heating and sensing are separated to improve the temperature measurement accuracy by minimization of errors introduced by self-heating. PMID:26256480
A vectorized solution for incompressible flow
NASA Technical Reports Server (NTRS)
Patel, N. R.; Thompson, J. F.
1984-01-01
An algorithm is developed to obtain solutions to the unsteady Reynolds-averaged incompressible Navier-Stokes equations in general curvilinear coordinates on a vector processor. The governing equations are in nonconservative form with the velocity and pressure as dependent variables. Two momentum equations and the Poisson equation for pressure form a set of three governing equations for three flow field unknowns: u, v, and p. The governing equations and boundary conditions are expressed in terms of boundary-conforming curvilinear coordinates, and a checkerboard SOR iteration is used to solve the governing equations. Several possible sequences for a checkerboard SOR iteration are investigated for finding the best overall convergence rate. The efficiency and capability of the present algorithm was assessed using the example of an 18 percent thick NACA 66(3)018 airfoil at zero degree angle of attack for chord Reynolds number range 1000-40,000.
Accurate and molecular-size-tolerant NMR quantitation of diverse components in solution
Okamura, Hideyasu; Nishimura, Hiroshi; Nagata, Takashi; Kigawa, Takanori; Watanabe, Takashi; Katahira, Masato
2016-01-01
Determining the amount of each component of interest in a mixture is a fundamental first step in characterizing the nature of the solution and to develop possible means of utilization of its components. Similarly, determining the composition of units in complex polymers, or polymer mixtures, is crucial. Although NMR is recognized as one of the most powerful methods to achieve this and is widely used in many fields, variation in the molecular sizes or the relative mobilities of components skews quantitation due to the size-dependent decay of magnetization. Here, a method to accurately determine the amount of each component by NMR was developed. This method was validated using a solution that contains biomass-related components in which the molecular sizes greatly differ. The method is also tolerant of other factors that skew quantitation such as variation in the one-bond C–H coupling constant. The developed method is the first and only way to reliably overcome the skewed quantitation caused by several different factors to provide basic information on the correct amount of each component in a solution. PMID:26883279
Invited Article: Time accurate mass flow measurements of solid-fueled systems
NASA Astrophysics Data System (ADS)
Olliges, Jordan D.; Lilly, Taylor C.; Joslyn, Thomas B.; Ketsdever, Andrew D.
2008-10-01
A novel diagnostic method is described that utilizes a thrust stand mass balance (TSMB) to directly measure time-accurate mass flow from a solid-fuel thruster. The accuracy of the TSMB mass flow measurement technique was demonstrated in three ways including the use of an idealized numerical simulation, verifying a fluid mass calibration with high-speed digital photography, and by measuring mass loss in more than 30 hybrid rocket motor firings. Dynamic response of the mass balance was assessed through weight calibration and used to derive spring, damping, and mass moment of inertia coefficients for the TSMB. These dynamic coefficients were used to determine the mass flow rate and total mass loss within an acrylic and gaseous oxygen hybrid rocket motor firing. Intentional variations in the oxygen flow rate resulted in corresponding variations in the total propellant mass flow as expected. The TSMB was optimized to determine mass losses of up to 2.5 g and measured total mass loss to within 2.5% of that calculated by a NIST-calibrated digital scale. Using this method, a mass flow resolution of 0.0011 g/s or 2% of the average mass flow in this study has been achieved.
Invited article: Time accurate mass flow measurements of solid-fueled systems.
Olliges, Jordan D; Lilly, Taylor C; Joslyn, Thomas B; Ketsdever, Andrew D
2008-10-01
A novel diagnostic method is described that utilizes a thrust stand mass balance (TSMB) to directly measure time-accurate mass flow from a solid-fuel thruster. The accuracy of the TSMB mass flow measurement technique was demonstrated in three ways including the use of an idealized numerical simulation, verifying a fluid mass calibration with high-speed digital photography, and by measuring mass loss in more than 30 hybrid rocket motor firings. Dynamic response of the mass balance was assessed through weight calibration and used to derive spring, damping, and mass moment of inertia coefficients for the TSMB. These dynamic coefficients were used to determine the mass flow rate and total mass loss within an acrylic and gaseous oxygen hybrid rocket motor firing. Intentional variations in the oxygen flow rate resulted in corresponding variations in the total propellant mass flow as expected. The TSMB was optimized to determine mass losses of up to 2.5 g and measured total mass loss to within 2.5% of that calculated by a NIST-calibrated digital scale. Using this method, a mass flow resolution of 0.0011 g/s or 2% of the average mass flow in this study has been achieved. PMID:19044695
NASA Technical Reports Server (NTRS)
VanZante, Dale E.; Strazisar, Anthony J.; Wood, Jerry R,; Hathaway, Michael D.; Okiishi, Theodore H.
2000-01-01
The tip clearance flows of transonic compressor rotors are important because they have a significant impact on rotor and stage performance. While numerical simulations of these flows are quite sophisticated. they are seldom verified through rigorous comparisons of numerical and measured data because these kinds of measurements are rare in the detail necessary to be useful in high-speed machines. In this paper we compare measured tip clearance flow details (e.g. trajectory and radial extent) with corresponding data obtained from a numerical simulation. Recommendations for achieving accurate numerical simulation of tip clearance flows are presented based on this comparison. Laser Doppler Velocimeter (LDV) measurements acquired in a transonic compressor rotor, NASA Rotor 35, are used. The tip clearance flow field of this transonic rotor was simulated using a Navier-Stokes turbomachinery solver that incorporates an advanced k-epsilon turbulence model derived for flows that are not in local equilibrium. Comparison between measured and simulated results indicates that simulation accuracy is primarily dependent upon the ability of the numerical code to resolve important details of a wall-bounded shear layer formed by the relative motion between the over-tip leakage flow and the shroud wall. A simple method is presented for determining the strength of this shear layer.
Approximate Solutions for Flow with a Stretching Boundary due to Partial Slip
Filobello-Nino, U.; Vazquez-Leal, H.; Sarmiento-Reyes, A.; Benhammouda, B.; Jimenez-Fernandez, V. M.; Pereyra-Diaz, D.; Perez-Sesma, A.; Cervantes-Perez, J.; Huerta-Chua, J.; Sanchez-Orea, J.; Contreras-Hernandez, A. D.
2014-01-01
The homotopy perturbation method (HPM) is coupled with versions of Laplace-Padé and Padé methods to provide an approximate solution to the nonlinear differential equation that describes the behaviour of a flow with a stretching flat boundary due to partial slip. Comparing results between approximate and numerical solutions, we concluded that our results are capable of providing an accurate solution and are extremely efficient. PMID:27433526
Approximate Analytical Solutions for Hypersonic Flow Over Slender Power Law Bodies
NASA Technical Reports Server (NTRS)
Mirels, Harold
1959-01-01
Approximate analytical solutions are presented for two-dimensional and axisymmetric hypersonic flow over slender power law bodies. Both zero order (M approaches infinity) and first order (small but nonvanishing values of 1/(M(Delta)(sup 2) solutions are presented, where M is free-stream Mach number and Delta is a characteristic slope. These solutions are compared with exact numerical integration of the equations of motion and appear to be accurate particularly when the shock is relatively close to the body.
Chang, Chih-Hao . E-mail: chchang@engineering.ucsb.edu; Liou, Meng-Sing . E-mail: meng-sing.liou@grc.nasa.gov
2007-07-01
In this paper, we propose a new approach to compute compressible multifluid equations. Firstly, a single-pressure compressible multifluid model based on the stratified flow model is proposed. The stratified flow model, which defines different fluids in separated regions, is shown to be amenable to the finite volume method. We can apply the conservation law to each subregion and obtain a set of balance equations. Secondly, the AUSM{sup +} scheme, which is originally designed for the compressible gas flow, is extended to solve compressible liquid flows. By introducing additional dissipation terms into the numerical flux, the new scheme, called AUSM{sup +}-up, can be applied to both liquid and gas flows. Thirdly, the contribution to the numerical flux due to interactions between different phases is taken into account and solved by the exact Riemann solver. We will show that the proposed approach yields an accurate and robust method for computing compressible multiphase flows involving discontinuities, such as shock waves and fluid interfaces. Several one-dimensional test problems are used to demonstrate the capability of our method, including the Ransom's water faucet problem and the air-water shock tube problem. Finally, several two dimensional problems will show the capability to capture enormous details and complicated wave patterns in flows having large disparities in the fluid density and velocities, such as interactions between water shock wave and air bubble, between air shock wave and water column(s), and underwater explosion.
Ohyanagi, Toshio; Sengoku, Yasuhito
2010-02-01
This article presents a new solution for measuring accurate reaction time (SMART) to visual stimuli. The SMART is a USB device realized with a Cypress Programmable System-on-Chip (PSoC) mixed-signal array programmable microcontroller. A brief overview of the hardware and firmware of the PSoC is provided, together with the results of three experiments. In Experiment 1, we investigated the timing accuracy of the SMART in measuring reaction time (RT) under different conditions of operating systems (OSs; Windows XP or Vista) and monitor displays (a CRT or an LCD). The results indicated that the timing error in measuring RT by the SMART was less than 2 msec, on average, under all combinations of OS and display and that the SMART was tolerant to jitter and noise. In Experiment 2, we tested the SMART with 8 participants. The results indicated that there was no significant difference among RTs obtained with the SMART under the different conditions of OS and display. In Experiment 3, we used Microsoft (MS) PowerPoint to present visual stimuli on the display. We found no significant difference in RTs obtained using MS DirectX technology versus using the PowerPoint file with the SMART. We are certain that the SMART is a simple and practical solution for measuring RTs accurately. Although there are some restrictions in using the SMART with RT paradigms, the SMART is capable of providing both researchers and health professionals working in clinical settings with new ways of using RT paradigms in their work. PMID:20160303
Consisitent and Accurate Finite Volume Methods for Coupled Flow and Geomechanics
NASA Astrophysics Data System (ADS)
Nordbotten, J. M.
2014-12-01
We introduce a new class of cell-centered finite volume methods for elasticity and poro-elasticity. As compared to lowest-order finite element discretizations, the new discretization has no additional degrees of freedom, and yet gives more accurate stress and flow fields. This finite volume discretization methods has furthermore the advantage that the mechanical discretization is fully compatible (in terms of grid and variables) with the standard cell-centered finite volume discretizations that are prevailing for commercial simulation of multi-phase flows in porous media. Theoretical analysis proves the convergence of the method. We give results showing that so-called numerical locking is avoided for a large class of structured and unstructured grids. The results are valid in both two and three spatial dimensions. The talk concludes with applications to problems with coupled multi-phase flow, transport and deformation, together with fractured porous media.
A fast and accurate method to predict 2D and 3D aerodynamic boundary layer flows
NASA Astrophysics Data System (ADS)
Bijleveld, H. A.; Veldman, A. E. P.
2014-12-01
A quasi-simultaneous interaction method is applied to predict 2D and 3D aerodynamic flows. This method is suitable for offshore wind turbine design software as it is a very accurate and computationally reasonably cheap method. This study shows the results for a NACA 0012 airfoil. The two applied solvers converge to the experimental values when the grid is refined. We also show that in separation the eigenvalues remain positive thus avoiding the Goldstein singularity at separation. In 3D we show a flow over a dent in which separation occurs. A rotating flat plat is used to show the applicability of the method for rotating flows. The shown capabilities of the method indicate that the quasi-simultaneous interaction method is suitable for design methods for offshore wind turbine blades.
An accurate and comprehensive model of thin fluid flows with inertia on curved substrates
NASA Astrophysics Data System (ADS)
Roberts, A. J.; Li, Zhenquan
2006-04-01
Consider the three-dimensional flow of a viscous Newtonian fluid upon a curved two-dimensional substrate when the fluid film is thin, as occurs in many draining, coating and biological flows. We derive a comprehensive model of the dynamics of the film, the model being expressed in terms of the film thickness eta and the average lateral velocity bar{bm u}. Centre manifold theory assures us that the model accurately and systematically includes the effects of the curvature of substrate, gravitational body force, fluid inertia and dissipation. The model resolves wavelike phenomena in the dynamics of viscous fluid flows over arbitrarily curved substrates such as cylinders, tubes and spheres. We briefly illustrate its use in simulating drop formation on cylindrical fibres, wave transitions, three-dimensional instabilities, Faraday waves, viscous hydraulic jumps, flow vortices in a compound channel and flow down and up a step. These models are the most complete models for thin-film flow of a Newtonian fluid; many other thin-film models can be obtained by different restrictions and truncations of the model derived here.
ANALYTICAL SOLUTION TO SATURATED FLOW IN A FINITE STRATIFIED AQUIFER
An analytical solution for the flow of water in a saturated-stratified aquitard-aquifer-aquitard system of finite length is presented. The analytical solution assumes one-dimensional horizontal flow in the aquifer and two-dimensional flow in the aquitards. Several examples are gi...
A quasilinear model for solute transport under unsaturated flow
Houseworth, J.E.; Leem, J.
2009-05-15
We developed an analytical solution for solute transport under steady-state, two-dimensional, unsaturated flow and transport conditions for the investigation of high-level radioactive waste disposal. The two-dimensional, unsaturated flow problem is treated using the quasilinear flow method for a system with homogeneous material properties. Dispersion is modeled as isotropic and is proportional to the effective hydraulic conductivity. This leads to a quasilinear form for the transport problem in terms of a scalar potential that is analogous to the Kirchhoff potential for quasilinear flow. The solutions for both flow and transport scalar potentials take the form of Fourier series. The particular solution given here is for two sources of flow, with one source containing a dissolved solute. The solution method may easily be extended, however, for any combination of flow and solute sources under steady-state conditions. The analytical results for multidimensional solute transport problems, which previously could only be solved numerically, also offer an additional way to benchmark numerical solutions. An analytical solution for two-dimensional, steady-state solute transport under unsaturated flow conditions is presented. A specific case with two sources is solved but may be generalized to any combination of sources. The analytical results complement numerical solutions, which were previously required to solve this class of problems.
A new general 1-D vadose zone flow solution method
NASA Astrophysics Data System (ADS)
Ogden, Fred L.; Lai, Wencong; Steinke, Robert C.; Zhu, Jianting; Talbot, Cary A.; Wilson, John L.
2015-06-01
We have developed an alternative to the one-dimensional partial differential equation (PDE) attributed to Richards (1931) that describes unsaturated porous media flow in homogeneous soil layers. Our solution is a set of three ordinary differential equations (ODEs) derived from unsaturated flux and mass conservation principles. We used a hodograph transformation, the Method of Lines, and a finite water-content discretization to produce ODEs that accurately simulate infiltration, falling slugs, and groundwater table dynamic effects on vadose zone fluxes. This formulation, which we refer to as "finite water-content", simulates sharp fronts and is guaranteed to conserve mass using a finite-volume solution. Our ODE solution method is explicitly integrable, does not require iterations and therefore has no convergence limits and is computationally efficient. The method accepts boundary fluxes including arbitrary precipitation, bare soil evaporation, and evapotranspiration. The method can simulate heterogeneous soils using layers. Results are presented in terms of fluxes and water content profiles. Comparing our method against analytical solutions, laboratory data, and the Hydrus-1D solver, we find that predictive performance of our finite water-content ODE method is comparable to or in some cases exceeds that of the solution of Richards' equation, with or without a shallow water table. The presented ODE method is transformative in that it offers accuracy comparable to the Richards (1931) PDE numerical solution, without the numerical complexity, in a form that is robust, continuous, and suitable for use in large watershed and land-atmosphere simulation models, including regional-scale models of coupled climate and hydrology.
NASA Astrophysics Data System (ADS)
Dougherty, N. S.; Burnette, D. W.; Holt, J. B.; Matienzo, Jose
1993-07-01
Time-accurate unsteady flow simulations are being performed supporting the SRM T+68sec pressure 'spike' anomaly investigation. The anomaly occurred in the RH SRM during the STS-54 flight (STS-54B) but not in the LH SRM (STS-54A) causing a momentary thrust mismatch approaching the allowable limit at that time into the flight. Full-motor internal flow simulations using the USA-2D axisymmetric code are in progress for the nominal propellant burn-back geometry and flow conditions at T+68-sec--Pc = 630 psi, gamma = 1.1381, T(sub c) = 6200 R, perfect gas without aluminum particulate. In a cooperative effort with other investigation team members, CFD-derived pressure loading on the NBR and castable inhibitors was used iteratively to obtain nominal deformed geometry of each inhibitor, and the deformed (bent back) inhibitor geometry was entered into this model. Deformed geometry was computed using structural finite-element models. A solution for the unsteady flow has been obtained for the nominal flow conditions (existing prior to the occurrence of the anomaly) showing sustained standing pressure oscillations at nominally 14.5 Hz in the motor IL acoustic mode that flight and static test data confirm to be normally present at this time. Average mass flow discharged from the nozzle was confirmed to be the nominal expected (9550 lbm/sec). The local inlet boundary condition is being perturbed at the location of the presumed reconstructed anomaly as identified by interior ballistics performance specialist team members. A time variation in local mass flow is used to simulate sudden increase in burning area due to localized propellant grain cracks. The solution will proceed to develop a pressure rise (proportional to total mass flow rate change squared). The volume-filling time constant (equivalent to 0.5 Hz) comes into play in shaping the rise rate of the developing pressure 'spike' as it propagates at the speed of sound in both directions to the motor head end and nozzle. The
NASA Technical Reports Server (NTRS)
Dougherty, N. S.; Burnette, D. W.; Holt, J. B.; Matienzo, Jose
1993-01-01
Time-accurate unsteady flow simulations are being performed supporting the SRM T+68sec pressure 'spike' anomaly investigation. The anomaly occurred in the RH SRM during the STS-54 flight (STS-54B) but not in the LH SRM (STS-54A) causing a momentary thrust mismatch approaching the allowable limit at that time into the flight. Full-motor internal flow simulations using the USA-2D axisymmetric code are in progress for the nominal propellant burn-back geometry and flow conditions at T+68-sec--Pc = 630 psi, gamma = 1.1381, T(sub c) = 6200 R, perfect gas without aluminum particulate. In a cooperative effort with other investigation team members, CFD-derived pressure loading on the NBR and castable inhibitors was used iteratively to obtain nominal deformed geometry of each inhibitor, and the deformed (bent back) inhibitor geometry was entered into this model. Deformed geometry was computed using structural finite-element models. A solution for the unsteady flow has been obtained for the nominal flow conditions (existing prior to the occurrence of the anomaly) showing sustained standing pressure oscillations at nominally 14.5 Hz in the motor IL acoustic mode that flight and static test data confirm to be normally present at this time. Average mass flow discharged from the nozzle was confirmed to be the nominal expected (9550 lbm/sec). The local inlet boundary condition is being perturbed at the location of the presumed reconstructed anomaly as identified by interior ballistics performance specialist team members. A time variation in local mass flow is used to simulate sudden increase in burning area due to localized propellant grain cracks. The solution will proceed to develop a pressure rise (proportional to total mass flow rate change squared). The volume-filling time constant (equivalent to 0.5 Hz) comes into play in shaping the rise rate of the developing pressure 'spike' as it propagates at the speed of sound in both directions to the motor head end and nozzle. The
Second-order accurate finite volume method for well-driven flows
NASA Astrophysics Data System (ADS)
Dotlić, M.; Vidović, D.; Pokorni, B.; Pušić, M.; Dimkić, M.
2016-02-01
We consider a finite volume method for a well-driven fluid flow in a porous medium. Due to the singularity of the well, modeling in the near-well region with standard numerical schemes results in a completely wrong total well flux and an inaccurate hydraulic head. Local grid refinement can help, but it comes at computational cost. In this article we propose two methods to address the well singularity. In the first method the flux through well faces is corrected using a logarithmic function, in a way related to the Peaceman model. Coupling this correction with a non-linear second-order accurate two-point scheme gives a greatly improved total well flux, but the resulting scheme is still inconsistent. In the second method fluxes in the near-well region are corrected by representing the hydraulic head as a sum of a logarithmic and a linear function. This scheme is second-order accurate.
NASA Astrophysics Data System (ADS)
Diwakar, S. V.; Das, Sarit K.; Sundararajan, T.
2009-12-01
A new Quadratic Spline based Interface (QUASI) reconstruction algorithm is presented which provides an accurate and continuous representation of the interface in a multiphase domain and facilitates the direct estimation of local interfacial curvature. The fluid interface in each of the mixed cells is represented by piecewise parabolic curves and an initial discontinuous PLIC approximation of the interface is progressively converted into a smooth quadratic spline made of these parabolic curves. The conversion is achieved by a sequence of predictor-corrector operations enforcing function ( C0) and derivative ( C1) continuity at the cell boundaries using simple analytical expressions for the continuity requirements. The efficacy and accuracy of the current algorithm has been demonstrated using standard test cases involving reconstruction of known static interface shapes and dynamically evolving interfaces in prescribed flow situations. These benchmark studies illustrate that the present algorithm performs excellently as compared to the other interface reconstruction methods available in literature. Quadratic rate of error reduction with respect to grid size has been observed in all the cases with curved interface shapes; only in situations where the interface geometry is primarily flat, the rate of convergence becomes linear with the mesh size. The flow algorithm implemented in the current work is designed to accurately balance the pressure gradients with the surface tension force at any location. As a consequence, it is able to minimize spurious flow currents arising from imperfect normal stress balance at the interface. This has been demonstrated through the standard test problem of an inviscid droplet placed in a quiescent medium. Finally, the direct curvature estimation ability of the current algorithm is illustrated through the coupled multiphase flow problem of a deformable air bubble rising through a column of water.
A Weight-Averaged Interpolation Method for Coupling Time-Accurate Rarefied and Continuum Flows
NASA Astrophysics Data System (ADS)
Diaz, Steven William
A novel approach to coupling rarefied and continuum flow regimes as a single, hybrid model is introduced. The method borrows from techniques used in the simulation of spray flows to interpolate Lagrangian point-particles onto an Eulerian grid in a weight-averaged sense. A brief overview of traditional methods for modeling both rarefied and continuum domains is given, and a review of the literature regarding rarefied/continuum flow coupling is presented. Details of the theoretical development of the method of weighted interpolation are then described. The method evaluates macroscopic properties at the nodes of a CFD grid via the weighted interpolation of all simulated molecules in a set surrounding the node. The weight factor applied to each simulated molecule is the inverse of the linear distance between it and the given node. During development, the method was applied to several preliminary cases, including supersonic flow over an airfoil, subsonic flow over tandem airfoils, and supersonic flow over a backward facing step; all at low Knudsen numbers. The main thrust of the research centered on the time-accurate expansion of a rocket plume into a near-vacuum. The method proves flexible enough to be used with various flow solvers, demonstrated by the use of Fluent as the continuum solver for the preliminary cases and a NASA-developed Large Eddy Simulation research code, WRLES, for the full lunar model. The method is applicable to a wide range of Mach numbers and is completely grid independent, allowing the rarefied and continuum solvers to be optimized for their respective domains without consideration of the other. The work presented demonstrates the validity, and flexibility of the method of weighted interpolation as a novel concept in the field of hybrid flow coupling. The method marks a significant divergence from current practices in the coupling of rarefied and continuum flow domains and offers a kernel on which to base an ongoing field of research. It has the
Implicit solution of three-dimensional internal turbulent flows
NASA Technical Reports Server (NTRS)
Michelassi, V.; Liou, M.-S.; Povinelli, L. A.
1990-01-01
The scalar form of the approximate factorization method was used to develop a new code for the solution of three-dimensional internal laminar and turbulent compressible flows. The Navier-Stokes equations in their Reynolds-averaged form are iterated in time until a steady solution is reached. Evidence is given to the implicit and explicit artificial damping schemes that proved to be particularly efficient in speeding up convergence and enhancing the algorithm robustness. A conservative treatment of these terms at domain boundaries is proposed in order to avoid undesired mass and/or momentum artificial fluxes. Turbulence effects are accounted for by the zero-equation Baldwin-Lomax turbulence model and the q-omega two-equation model. For the first, an investigation on the model behavior in case of multiple boundaries is performed. The flow in a developing S-duct is then solved in the laminar regime at Reynolds number (Re) 790 and in the turbulent regime at Re=40,000 using the Baldwin-Lomax model . The Stanitz elbow is then solved using an inviscid version of the same code at M(sub inlet)=0.4. Grid dependence and convergence rate are investigated showing that for this solver the implicit damping scheme may play a critical role for convergence characteristics. The same flow at Re=2.5x10(exp 6) is solved with the Baldwin-Lomax and the q-omega models. Both approaches showed satisfactory agreement with experiments, although the q-omega model is slightly more accurate.
Cao, Youfang; Terebus, Anna; Liang, Jie
2016-04-01
truncation and error analysis methods developed here can be used to ensure accurate direct solutions to the dCME for a large number of stochastic networks. PMID:27105653
Cao, Youfang; Terebus, Anna; Liang, Jie
2016-01-01
truncation and error analysis methods developed here can be used to ensure accurate direct solutions to the dCME for a large number of stochastic networks. PMID:27105653
Boraldi, Federica; Bartolomeo, Angelica; De Biasi, Sara; Orlando, Stefania; Costa, Sonia; Cossarizza, Andrea; Quaglino, Daniela
2016-01-01
Introduction Although rare, circulating endothelial and progenitor cells could be considered as markers of endothelial damage and repair potential, possibly predicting the severity of cardiovascular manifestations. A number of studies highlighted the role of these cells in age-related diseases, including those characterized by ectopic calcification. Nevertheless, their use in clinical practice is still controversial, mainly due to difficulties in finding reproducible and accurate methods for their determination. Methods Circulating mature cells (CMC, CD45-, CD34+, CD133-) and circulating progenitor cells (CPC, CD45dim, CD34bright, CD133+) were investigated by polychromatic high-speed flow cytometry to detect the expression of endothelial (CD309+) or osteogenic (BAP+) differentiation markers in healthy subjects and in patients affected by peripheral vascular manifestations associated with ectopic calcification. Results This study shows that: 1) polychromatic flow cytometry represents a valuable tool to accurately identify rare cells; 2) the balance of CD309+ on CMC/CD309+ on CPC is altered in patients affected by peripheral vascular manifestations, suggesting the occurrence of vascular damage and low repair potential; 3) the increase of circulating cells exhibiting a shift towards an osteoblast-like phenotype (BAP+) is observed in the presence of ectopic calcification. Conclusion Differences between healthy subjects and patients with ectopic calcification indicate that this approach may be useful to better evaluate endothelial dysfunction in a clinical context. PMID:27560136
Hong Xinguo; Hao Quan
2009-01-15
In this paper, we report a method of precise in situ x-ray scattering measurements on protein solutions using small stationary sample cells. Although reduction in the radiation damage induced by intense synchrotron radiation sources is indispensable for the correct interpretation of scattering data, there is still a lack of effective methods to overcome radiation-induced aggregation and extract scattering profiles free from chemical or structural damage. It is found that radiation-induced aggregation mainly begins on the surface of the sample cell and grows along the beam path; the diameter of the damaged region is comparable to the x-ray beam size. Radiation-induced aggregation can be effectively avoided by using a two-dimensional scan (2D mode), with an interval as small as 1.5 times the beam size, at low temperature (e.g., 4 deg. C). A radiation sensitive protein, bovine hemoglobin, was used to test the method. A standard deviation of less than 5% in the small angle region was observed from a series of nine spectra recorded in 2D mode, in contrast to the intensity variation seen using the conventional stationary technique, which can exceed 100%. Wide-angle x-ray scattering data were collected at a standard macromolecular diffraction station using the same data collection protocol and showed a good signal/noise ratio (better than the reported data on the same protein using a flow cell). The results indicate that this method is an effective approach for obtaining precise measurements of protein solution scattering.
Unfitted Two-Phase Flow Simulations in Pore-Geometries with Accurate
NASA Astrophysics Data System (ADS)
Heimann, Felix; Engwer, Christian; Ippisch, Olaf; Bastian, Peter
2013-04-01
The development of better macro scale models for multi-phase flow in porous media is still impeded by the lack of suitable methods for the simulation of such flow regimes on the pore scale. The highly complicated geometry of natural porous media imposes requirements with regard to stability and computational efficiency which current numerical methods fail to meet. Therefore, current simulation environments are still unable to provide a thorough understanding of porous media in multi-phase regimes and still fail to reproduce well known effects like hysteresis or the more peculiar dynamics of the capillary fringe with satisfying accuracy. Although flow simulations in pore geometries were initially the domain of Lattice-Boltzmann and other particle methods, the development of Galerkin methods for such applications is important as they complement the range of feasible flow and parameter regimes. In the recent past, it has been shown that unfitted Galerkin methods can be applied efficiently to topologically demanding geometries. However, in the context of two-phase flows, the interface of the two immiscible fluids effectively separates the domain in two sub-domains. The exact representation of such setups with multiple independent and time depending geometries exceeds the functionality of common unfitted methods. We present a new approach to pore scale simulations with an unfitted discontinuous Galerkin (UDG) method. Utilizing a recursive sub-triangulation algorithm, we extent the UDG method to setups with multiple independent geometries. This approach allows an accurate representation of the moving contact line and the interface conditions, i.e. the pressure jump across the interface. Example simulations in two and three dimensions illustrate and verify the stability and accuracy of this approach.
NASA Astrophysics Data System (ADS)
Shukla, Ratnesh K.
2014-11-01
Single fluid schemes that rely on an interface function for phase identification in multicomponent compressible flows are widely used to study hydrodynamic flow phenomena in several diverse applications. Simulations based on standard numerical implementation of these schemes suffer from an artificial increase in the width of the interface function owing to the numerical dissipation introduced by an upwind discretization of the governing equations. In addition, monotonicity requirements which ensure that the sharp interface function remains bounded at all times necessitate use of low-order accurate discretization strategies. This results in a significant reduction in accuracy along with a loss of intricate flow features. In this paper we develop a nonlinear transformation based interface capturing method which achieves superior accuracy without compromising the simplicity, computational efficiency and robustness of the original flow solver. A nonlinear map from the signed distance function to the sigmoid type interface function is used to effectively couple a standard single fluid shock and interface capturing scheme with a high-order accurate constrained level set reinitialization method in a way that allows for oscillation-free transport of the sharp material interface. Imposition of a maximum principle, which ensures that the multidimensional preconditioned interface capturing method does not produce new maxima or minima even in the extreme events of interface merger or breakup, allows for an explicit determination of the interface thickness in terms of the grid spacing. A narrow band method is formulated in order to localize computations pertinent to the preconditioned interface capturing method. Numerical tests in one dimension reveal a significant improvement in accuracy and convergence; in stark contrast to the conventional scheme, the proposed method retains its accuracy and convergence characteristics in a shifted reference frame. Results from the test
Orbital Advection by Interpolation: A Fast and Accurate Numerical Scheme for Super-Fast MHD Flows
Johnson, B M; Guan, X; Gammie, F
2008-04-11
In numerical models of thin astrophysical disks that use an Eulerian scheme, gas orbits supersonically through a fixed grid. As a result the timestep is sharply limited by the Courant condition. Also, because the mean flow speed with respect to the grid varies with position, the truncation error varies systematically with position. For hydrodynamic (unmagnetized) disks an algorithm called FARGO has been developed that advects the gas along its mean orbit using a separate interpolation substep. This relaxes the constraint imposed by the Courant condition, which now depends only on the peculiar velocity of the gas, and results in a truncation error that is more nearly independent of position. This paper describes a FARGO-like algorithm suitable for evolving magnetized disks. Our method is second order accurate on a smooth flow and preserves {del} {center_dot} B = 0 to machine precision. The main restriction is that B must be discretized on a staggered mesh. We give a detailed description of an implementation of the code and demonstrate that it produces the expected results on linear and nonlinear problems. We also point out how the scheme might be generalized to make the integration of other supersonic/super-fast flows more efficient. Although our scheme reduces the variation of truncation error with position, it does not eliminate it. We show that the residual position dependence leads to characteristic radial variations in the density over long integrations.
Analytical solutions of moisture flow equations and their numerical evaluation
Gibbs, A.G.
1981-04-01
The role of analytical solutions of idealized moisture flow problems is discussed. Some different formulations of the moisture flow problem are reviewed. A number of different analytical solutions are summarized, including the case of idealized coupled moisture and heat flow. The evaluation of special functions which commonly arise in analytical solutions is discussed, including some pitfalls in the evaluation of expressions involving combinations of special functions. Finally, perturbation theory methods are summarized which can be used to obtain good approximate analytical solutions to problems which are too complicated to solve exactly, but which are close to an analytically solvable problem.
Accurate burner air flow measurement for low NO{sub x} burners
Earley, D.; Penterson, C.
1998-07-01
In 1990, Congress enacted an amendment to the Clean Air Act that required reductions in NO{sub x} emissions through the application of low NO{sub x} burner systems on fossil fueled utility steam generators. For most of the existing steam generator population, the original burning equipment incorporated highly turbulent burners that created significant in-furnace flame interaction. Thus, the measurement and control of air flow to the individual burners was much less critical than in recent years with low NO{sub x} combustion systems. With low NO{sub x} systems, the reduction of NO{sub x} emissions, as well as minimizing flyash unburned carbon levels, is very much dependent on the ability to control the relative ratios of air and fuel on a per-burner basis and their rate of mixing, particularly in the near burner zones. Air Monitor Corporation (AMC) and DB Riley, Inc. (DBR), and a large Midwestern electric utility have successfully developed and applied AMC's equipment to low NO{sub x} coal burners in order to enhance NO{sub x} control combustion systems. The results have improved burner optimization and provided real time continuous air flow balancing capability and the control of individual burner stoichiometries. To date, these enhancements have been applied to wall-fired low NO{sub x} systems for balancing individual burner air flows in a common windbox and to staged combustion systems. Most recently, calibration testing in a wind tunnel facility of AMC's individual burner air measurement (IBAM{trademark}) probes installed in DB Riley's low NO{sub x} CCV{reg{underscore}sign} burners has demonstrated the ability to produce reproducible and consistent air flow measurement accurate to within 5%. This paper will summarize this product development and quantify the benefits of its application to low NO{sub x} combustion systems.
Modeling flow and solute transport in irrigation furrows
Technology Transfer Automated Retrieval System (TEKTRAN)
This paper presents an internally coupled flow and solute transport model for free-draining irrigation furrows. Furrow hydraulics is simulated with a numerical zero-inertia model and solute transport is computed with a model based on a numerical solution of the cross-section averaged advection-dispe...
NASA Astrophysics Data System (ADS)
Park, Jong Ho; Park, Jung Jin; Park, O. Ok; Jin, Chang-Soo; Yang, Jung Hoon
2016-04-01
Because of the rise in renewable energy use, the redox flow battery (RFB) has attracted extensive attention as an energy storage system. Thus, many studies have focused on improving the performance of the felt electrodes used in RFBs. However, existing analysis cells are unsuitable for characterizing felt electrodes because of their complex 3-dimensional structure. Analysis is also greatly affected by the measurement conditions, viz. compression ratio, contact area, and contact strength between the felt and current collector. To address the growing need for practical analytical apparatus, we report a new analysis cell for accurate electrochemical characterization of felt electrodes under various conditions, and compare it with previous ones. In this cell, the measurement conditions can be exhaustively controlled with a compression supporter. The cell showed excellent reproducibility in cyclic voltammetry analysis and the results agreed well with actual RFB charge-discharge performance.
NASA Astrophysics Data System (ADS)
Wosnik, M.; Bachant, P.
2014-12-01
Cross-flow turbines, often referred to as vertical-axis turbines, show potential for success in marine hydrokinetic (MHK) and wind energy applications, ranging from small- to utility-scale installations in tidal/ocean currents and offshore wind. As turbine designs mature, the research focus is shifting from individual devices to the optimization of turbine arrays. It would be expensive and time-consuming to conduct physical model studies of large arrays at large model scales (to achieve sufficiently high Reynolds numbers), and hence numerical techniques are generally better suited to explore the array design parameter space. However, since the computing power available today is not sufficient to conduct simulations of the flow in and around large arrays of turbines with fully resolved turbine geometries (e.g., grid resolution into the viscous sublayer on turbine blades), the turbines' interaction with the energy resource (water current or wind) needs to be parameterized, or modeled. Models used today--a common model is the actuator disk concept--are not able to predict the unique wake structure generated by cross-flow turbines. This wake structure has been shown to create "constructive" interference in some cases, improving turbine performance in array configurations, in contrast with axial-flow, or horizontal axis devices. Towards a more accurate parameterization of cross-flow turbines, an extensive experimental study was carried out using a high-resolution turbine test bed with wake measurement capability in a large cross-section tow tank. The experimental results were then "interpolated" using high-fidelity Navier--Stokes simulations, to gain insight into the turbine's near-wake. The study was designed to achieve sufficiently high Reynolds numbers for the results to be Reynolds number independent with respect to turbine performance and wake statistics, such that they can be reliably extrapolated to full scale and used for model validation. The end product of
Calculations of steady and transient channel flows with a time-accurate L-U factorization scheme
NASA Technical Reports Server (NTRS)
Kim, S.-W.
1991-01-01
Calculations of steady and unsteady, transonic, turbulent channel flows with a time accurate, lower-upper (L-U) factorization scheme are presented. The L-U factorization scheme is formally second-order accurate in time and space, and it is an extension of the steady state flow solver (RPLUS) used extensively to solve compressible flows. A time discretization method and the implementation of a consistent boundary condition specific to the L-U factorization scheme are also presented. The turbulence is described by the Baldwin-Lomax algebraic turbulence model. The present L-U scheme yields stable numerical results with the use of much smaller artificial dissipations than those used in the previous steady flow solver for steady and unsteady channel flows. The capability to solve time dependent flows is shown by solving very weakly excited and strongly excited, forced oscillatory, channel flows.
Drag enhancement of aqueous electrolyte solutions in turbulent pipe flow.
Doherty, Andrew P; Spedding, Peter L; Chen, John J J
2010-04-22
Detailed experimental results are presented for both laminar and turbulent flow of aqueous solutions in pipes of different diameters. Nonelectrolytes, such as sugar solutions followed the normal Moody pressure loss curves. Drag enhancement was demonstrated for turbulent flow of aqueous electrolyte solutions but not for laminar flow. The increased pressure drop for turbulent electrolyte flow was attributed to an electroviscous effect and a theory was developed to explain the drag enhancement. The increased pressure drop for the turbulent region of flow was shown to depend on the Debye length in the laminar sublayer on the pipe wall. Reasonable predictions of the increasing drag were obtained for both 1:1 and 2:1 electrolyte solutions. PMID:20337452
A comparative study of computational solutions to flow over a backward-facing step
NASA Technical Reports Server (NTRS)
Mizukami, M.; Georgiadis, N. J.; Cannon, M. R.
1993-01-01
A comparative study was conducted for computational fluid dynamic solutions to flow over a backward-facing step. This flow is a benchmark problem, with a simple geometry, but involves complicated flow physics such as free shear layers, reattaching flow, recirculation, and high turbulence intensities. Three Reynolds-averaged Navier-Stokes flow solvers with k-epsilon turbulence models were used, each using a different solution algorithm: finite difference, finite element, and hybrid finite element - finite difference. Comparisons were made with existing experimental data. Results showed that velocity profiles and reattachment lengths were predicted reasonably well by all three methods, while the skin friction coefficients were more difficult to predict accurately. It was noted that, in general, selecting an appropriate solver for each problem to be considered is important.
A coupled Eulerian/Lagrangian method for the solution of three-dimensional vortical flows
NASA Technical Reports Server (NTRS)
Felici, Helene Marie
1992-01-01
A coupled Eulerian/Lagrangian method is presented for the reduction of numerical diffusion observed in solutions of three-dimensional rotational flows using standard Eulerian finite-volume time-marching procedures. A Lagrangian particle tracking method using particle markers is added to the Eulerian time-marching procedure and provides a correction of the Eulerian solution. In turn, the Eulerian solutions is used to integrate the Lagrangian state-vector along the particles trajectories. The Lagrangian correction technique does not require any a-priori information on the structure or position of the vortical regions. While the Eulerian solution ensures the conservation of mass and sets the pressure field, the particle markers, used as 'accuracy boosters,' take advantage of the accurate convection description of the Lagrangian solution and enhance the vorticity and entropy capturing capabilities of standard Eulerian finite-volume methods. The combined solution procedures is tested in several applications. The convection of a Lamb vortex in a straight channel is used as an unsteady compressible flow preservation test case. The other test cases concern steady incompressible flow calculations and include the preservation of turbulent inlet velocity profile, the swirling flow in a pipe, and the constant stagnation pressure flow and secondary flow calculations in bends. The last application deals with the external flow past a wing with emphasis on the trailing vortex solution. The improvement due to the addition of the Lagrangian correction technique is measured by comparison with analytical solutions when available or with Eulerian solutions on finer grids. The use of the combined Eulerian/Lagrangian scheme results in substantially lower grid resolution requirements than the standard Eulerian scheme for a given solution accuracy.
Aeroacoustic Flow Phenomena Accurately Captured by New Computational Fluid Dynamics Method
NASA Technical Reports Server (NTRS)
Blech, Richard A.
2002-01-01
One of the challenges in the computational fluid dynamics area is the accurate calculation of aeroacoustic phenomena, especially in the presence of shock waves. One such phenomenon is "transonic resonance," where an unsteady shock wave at the throat of a convergent-divergent nozzle results in the emission of acoustic tones. The space-time Conservation-Element and Solution-Element (CE/SE) method developed at the NASA Glenn Research Center can faithfully capture the shock waves, their unsteady motion, and the generated acoustic tones. The CE/SE method is a revolutionary new approach to the numerical modeling of physical phenomena where features with steep gradients (e.g., shock waves, phase transition, etc.) must coexist with those having weaker variations. The CE/SE method does not require the complex interpolation procedures (that allow for the possibility of a shock between grid cells) used by many other methods to transfer information between grid cells. These interpolation procedures can add too much numerical dissipation to the solution process. Thus, while shocks are resolved, weaker waves, such as acoustic waves, are washed out.
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)
Techniques for correcting approximate finite difference solutions. [considering transonic flow
NASA Technical Reports Server (NTRS)
Nixon, D.
1978-01-01
A method of correcting finite-difference solutions for the effect of truncation error or the use of an approximate basic equation is presented. Applications to transonic flow problems are described and examples are given.
Flow Battery Solution for Smart Grid Applications
none,
2014-11-30
To address future grid requirements, a U.S. Department of Energy ARRA Storage Demonstration program was launched in 2009 to commercialize promising technologies needed for stronger and more renewables-intensive grids. Raytheon Ktech and EnerVault received a cost-share grant award from the U.S. Department of Energy to develop a grid-scale storage system based on EnerVault’s iron-chromium redox flow battery technology.
Material combustion in oxidant flows: Self-similar solutions
NASA Astrophysics Data System (ADS)
Tyurenkova, V. V.; Smirnova, M. N.
2016-03-01
The paper presents exact solution for the problem of condensed material surface burning in a flow of oxidant in the case of steady flame over fuel layer. The solution is obtained within the frame of assumption of fuel gasification and gas phase chemical reacting in a diffusion flame. The regression rate of the material surface in the turbulent and laminar flow regimes is studied. The zones corresponding to kinetic and diffusion regime are determined.
Superposition flows of entangled polymeric solutions
NASA Astrophysics Data System (ADS)
Ianniruberto, Giovanni; Unidad, Herwin Jerome
2015-12-01
Parallel and orthogonal superposition experiments by Vermant et al. (1998) on a polydisperse, entangled polymeric solution are here analyzed by using a simple, multi-mode differential constitutive equation based on the tube model, and also accounting for convective constraint release effects. Model predictions are in very good qualitative and quantitative agreement with parallel superposition data, while some discrepancies are found with orthogonal data, thus suggesting that orthogonal superposition experiments represent a more severe test for molecularly-based constitutive equations.
Numerical solution of the three-dimensional fluid flow in a rotating heterogeneous porous channel
NASA Astrophysics Data System (ADS)
Havstad, Mark A.; Vadasz, Peter
1999-09-01
A numerical solution to the problem of the three-dimensional fluid flow in a long rotating heterogeneous porous channel is presented. A co-ordinate transformation technique is employed to obtain accurate solutions over a wide range of porous media Ekman number values and consequent boundary layer thicknesses. Comparisons with an approximate asymptotic solution (for large values of Ekman number) and with theoretical predictions on the validity of Taylor-Proudman theorem in porous media for small values of Ekman number show good qualitative agreement. An evaluation of the boundary layer thickness is presented and a power-law correlation to Ekman number is shown to well-represent the results for small values of Ekman number. The different three-dimensional fluid flow regimes are presented graphically, demonstrating the distinct variation of the flow field over the wide range of Ekman numbers used. Copyright
Are 0. 1%-accurate gamma-ray assays possible for /sup 235/U solutions
Parker, J.L.
1983-01-01
The factors influencing the accuracy of passive gamma-ray assay of uniform, homogeneous solution samples have been studied in some detail, particularly for the assay of /sup 235/U in uranium solutions. Factors considered are the overall long-term electronic stability, the information losses caused by the rate-related electronic processes of pulse pileup and dead-time, and the self-attenuation of gamma rays within the samples. Both experimental and computational studies indicate that gamma-ray assay procedures for solution samples of moderate size (from approx. 10 to perhaps a few hundred milliliters) are now capable of accuracies approaching 0.1% in many practical cases.
Limiting Step Bunch Height During Crystal Growth from Flowing Solutions
NASA Technical Reports Server (NTRS)
Booth, N. A.; Chernov, A. A.; Vekilov, P. G.
2003-01-01
High precision interferometric studies of step bunching on KDP crystal surface growing from solution moving at rates up to 1 d s . It is shown that the bunch height is limited as the bunch propagates over the surface. An hypothesis is put forward describing why the bunch height decreases as the solution flow rate increases.
Lagrangian solution of supersonic real gas flows
NASA Technical Reports Server (NTRS)
Loh, Ching-Yuen; Liou, Meng-Sing
1993-01-01
The present extention of a Lagrangian approach of the Riemann solution procedure, which was originally proposed for perfect gases, to real gases, is nontrivial and requires the development of an exact real-gas Riemann solver for the Lagrangian form of the conservation laws. Calculations including complex wave interactions of various types were conducted to test the accuracy and robustness of the approach. Attention is given to the case of 2D oblique waves' capture, where a slip line is clearly in evidence; the real gas effect is demonstrated in the case of a generic engine nozzle.
An accurate two-phase approximate solution to the acute viral infection model
Perelson, Alan S
2009-01-01
During an acute viral infection, virus levels rise, reach a peak and then decline. Data and numerical solutions suggest the growth and decay phases are linear on a log scale. While viral dynamic models are typically nonlinear with analytical solutions difficult to obtain, the exponential nature of the solutions suggests approximations can be found. We derive a two-phase approximate solution to the target cell limited influenza model and illustrate the accuracy using data and previously established parameter values of six patients infected with influenza A. For one patient, the subsequent fall in virus concentration was not consistent with our predictions during the decay phase and an alternate approximation is derived. We find expressions for the rate and length of initial viral growth in terms of the parameters, the extent each parameter is involved in viral peaks, and the single parameter responsible for virus decay. We discuss applications of this analysis in antiviral treatments and investigating host and virus heterogeneities.
NASA Technical Reports Server (NTRS)
Hamilton, H. H., II; Spall, J. R.
1986-01-01
A time-asymptotic method has been used to obtain steady-flow solutions for axisymmetric inviscid flow over several blunt bodies including spheres, paraboloids, ellipsoids, and spherically blunted cones. Comparisons with experimental data and results of other computational methods have demonstrated that accurate solutions can be obtained using this approach. The method should prove useful as an analysis tool for comparing with experimental data and for making engineering calculations for blunt reentry vehicles.
Numerical solution of inviscid and viscous flow around the profile
NASA Astrophysics Data System (ADS)
Slouka, Martin; Kozel, Karel; Prihoda, Jaromir
2015-05-01
This work deals with the 2D numerical solution of inviscid compressible flow and viscous compressible laminar and turbulent flow around the profile. In a case of turbulent flow algebraic Baldwin-Lomax model is used and compared with Wilcox's k-ω model. Calculations are done in GAMM channel computational domain with 10% DCA profile and in turbine cascade computational domain with 8% DCA profile. Numerical methods are based on a finite volume solution and compared with experimental measurements for 8% DCA profile.
An analytical solution for flow in a manifold
NASA Astrophysics Data System (ADS)
Warrick, A. W.; Yitayew, M.
An analytical solution is developed for flow in a manifold. The interest is primarily for trickle irrigation laterals, but the solution has broader applications including those for which pressure increases in the direction of flow and for intake manifolds. Both velocity head losses and variable discharge along the manifold are considered in the fundamental analysis. The appropriate second order, nonlinear equation is solved for two flow regimes, laminar and fully turbulent. Results indicate that for most trickle irrigation laterals the velocity head loss is negligible, but for an example from a chemical processing system the effect is important.
Lewis, E.R.; Schwartz, S.
2010-03-15
Light scattering by aerosols plays an important role in Earth’s radiative balance, and quantification of this phenomenon is important in understanding and accounting for anthropogenic influences on Earth’s climate. Light scattering by an aerosol particle is determined by its radius and index of refraction, and for aerosol particles that are hygroscopic, both of these quantities vary with relative humidity RH. Here exact expressions are derived for the dependences of the radius ratio (relative to the volume-equivalent dry radius) and index of refraction on RH for aqueous solutions of single solutes. Both of these quantities depend on the apparent molal volume of the solute in solution and on the practical osmotic coefficient of the solution, which in turn depend on concentration and thus implicitly on RH. Simple but accurate approximations are also presented for the RH dependences of both radius ratio and index of refraction for several atmospherically important inorganic solutes over the entire range of RH values for which these substances can exist as solution drops. For all substances considered, the radius ratio is accurate to within a few percent, and the index of refraction to within ~0.02, over this range of RH. Such parameterizations will be useful in radiation transfer models and climate models.
Wind-US Unstructured Flow Solutions for a Transonic Diffuser
NASA Technical Reports Server (NTRS)
Mohler, Stanley R., Jr.
2005-01-01
The Wind-US Computational Fluid Dynamics flow solver computed flow solutions for a transonic diffusing duct. The calculations used an unstructured (hexahedral) grid. The Spalart-Allmaras turbulence model was used. Static pressures along the upper and lower wall agreed well with experiment, as did velocity profiles. The effect of the smoothing input parameters on convergence and solution accuracy was investigated. The meaning and proper use of these parameters are discussed for the benefit of Wind-US users. Finally, the unstructured solver is compared to the structured solver in terms of run times and solution accuracy.
NASA Astrophysics Data System (ADS)
Dwyer, G. S.; Vengosh, A.
2008-12-01
The negative thermal ionization mass spectrometry technique has become the major tool for investigating boron isotopes in the environment. The high sensitivity of BO2- ionization enables measurements of ng levels of boron. However, B isotope measurement by this technique suffers from two fundamental problems (1) fractionation induced by selective ionization of B isotopes in the mass spectrometer; and (2) CNO- interference on mass 42 that is often present in some load solutions (such as B-free seawater processed through ion-exchange resin). Here we report a potentially improved methodology using an alternative filament loading solution with a recently-installed Thermo Scientific TRITON thermal ionization mass spectrometer. Our initial results suggest that this solution -- prepared by combining high-purity single- element standard solutions of Ca, Mg, Na, and K in proportions similar to those in seawater in a 5% HCl matrix -- may offer significant improvement over some other commonly used load solutions. Total loading blank is around 15pg as determined by isotope dilution (NIST952). Replicate analyses of NIST SRM951 and modern seawater thus far have yielded 11B/10B ratios of 4.0057 (±0.0008, n=14) and 4.1645 (±0.0017, n=7; δ11B=39.6 permil), respectively. Replicate analyses of samples and SRM951 yield an average standard deviation (1 σ) of approximately 0.001 (0.25 permil). Fractionation during analysis (60-90 minutes) has thus far typically been less than 0.002 (0.5 permil). The load solution delivers ionization efficiency similar to directly-loaded seawater and has negligible signal at mass 26 (CN-), a proxy for the common interfering molecular ion (CNO-) on mass 42. Standards and samples loaded with the solution behave fairly predictably during filament heating and analysis, thus allowing for the possibility of fully automated data collection.
Lagrangian solution of supersonic real gas flows
Loh, Chingyuen; Liou, Mengsing )
1993-01-01
This paper details the procedure of the real gas Riemann solution in the Lagrangian approach originally proposed by Loh and Hui for perfect gases. The extension to real gases is nontrivial and requires substantial development of an exact real-gas Riemann solver for the Lagrangian form of conservation laws. The first-order Gudonov scheme is enhanced for accuracy by adding limited anti-diffusive terms according to Sweby. Extensive calculations were made to test the accuracy and robustness of the present real gas Lagrangian approach, including complex wave interactions of different types. The accuracy for capturing 2D oblique waves and slip line is clearly demonstrated. In addition, we also show the real gas effect in a generic engine nozzle.
NASA Astrophysics Data System (ADS)
Kafri, H. Q.; Khuri, S. A.; Sayfy, A.
2016-03-01
In this paper, a novel approach is introduced for the solution of the non-linear Troesch's boundary value problem. The underlying strategy is based on Green's functions and fixed-point iterations, including Picard's and Krasnoselskii-Mann's schemes. The resulting numerical solutions are compared with both the analytical solutions and numerical solutions that exist in the literature. Convergence of the iterative schemes is proved via manipulation of the contraction principle. It is observed that the method handles the boundary layer very efficiently, reduces lengthy calculations, provides rapid convergence, and yields accurate results particularly for large eigenvalues. Indeed, to our knowledge, this is the first time that this problem is solved successfully for very large eigenvalues, actually the rate of convergence increases as the magnitude of the eigenvalues increases.
Accurate and inexpensive prediction of the color optical properties of anthocyanins in solution.
Ge, Xiaochuan; Timrov, Iurii; Binnie, Simon; Biancardi, Alessandro; Calzolari, Arrigo; Baroni, Stefano
2015-04-23
The simulation of the color optical properties of molecular dyes in liquid solution requires the calculation of time evolution of the solute absorption spectra fluctuating in the solvent at finite temperature. Time-averaged spectra can be directly evaluated by combining ab initio Car-Parrinello molecular dynamics and time-dependent density functional theory calculations. The inclusion of hybrid exchange-correlation functionals, necessary for the prediction of the correct transition frequencies, prevents one from using these techniques for the simulation of the optical properties of large realistic systems. Here we present an alternative approach for the prediction of the color of natural dyes in solution with a low computational cost. We applied this approach to representative anthocyanin dyes: the excellent agreement between the simulated and the experimental colors makes this method a straightforward and inexpensive tool for the high-throughput prediction of colors of molecules in liquid solvents. PMID:25830823
Free-Flowing Solutions for CFD
NASA Technical Reports Server (NTRS)
2003-01-01
Licensed to over 1,500 customers worldwide, an advanced computational fluid dynamics (CFD) post-processor with a quick learning curve is consistently providing engineering solutions, with just the right balance of visual insight and hard data. FIELDVIEW is the premier product of JMSI, Inc., d.b.a. Intelligent Light, a woman-owned, small business founded in 1994 and located in Lyndhurst, New Jersey. In the early 1990s, Intelligent Light entered into a joint development contract with a research based company to commercialize the post-processing FIELDVIEW code. As Intelligent Light established itself, it purchased the exclusive rights to the code, and structured its business solely around the software technology. As a result, it is enjoying profits and growing at a rate of 25 to 30 percent per year. Advancements made from the earliest commercial launch of FIELDVIEW, all the way up to the recently released versions 8 and 8.2 of the program, have been backed by research collaboration with NASA's Langley Research Center, where some of the world's most progressive work in transient (also known as time-varying) CFD takes place.
Solid rocket booster internal flow analysis by highly accurate adaptive computational methods
NASA Technical Reports Server (NTRS)
Huang, C. Y.; Tworzydlo, W.; Oden, J. T.; Bass, J. M.; Cullen, C.; Vadaketh, S.
1991-01-01
The primary objective of this project was to develop an adaptive finite element flow solver for simulating internal flows in the solid rocket booster. Described here is a unique flow simulator code for analyzing highly complex flow phenomena in the solid rocket booster. New methodologies and features incorporated into this analysis tool are described.
Redox flow batteries based on supporting solutions containing chloride
Li, Liyu; Kim, Soowhan; Yang, Zhenguo; Wang, Wei; Nie, Zimin; Chen, Baowei; Zhang, Jianlu; Xia, Guanguang
2015-09-01
Redox flow battery systems having a supporting solution that contains Cl.sup.- ions can exhibit improved performance and characteristics. Furthermore, a supporting solution having mixed SO.sub.4.sup.2- and Cl.sup.- ions can provide increased energy density and improved stability and solubility of one or more of the ionic species in the catholyte and/or anolyte. According to one example, a vanadium-based redox flow battery system is characterized by an anolyte having V.sup.2+ and V.sup.3+ in a supporting solution and a catholyte having V.sup.4+ and V.sup.5+ in a supporting solution. The supporting solution can contain Cl.sup.- ions or a mixture of SO.sub.4.sup.2- and Cl.sup.- ions.
Redox flow batteries based on supporting solutions containing chloride
Li, Liyu; Kim, Soowhan; Yang, Zhenguo; Wang, Wei; Nie, Zimin; Chen, Baowei; Zhang, Jianlu; Xia, Guanguang
2015-07-07
Redox flow battery systems having a supporting solution that contains Cl.sup.- ions can exhibit improved performance and characteristics. Furthermore, a supporting solution having mixed SO.sub.4.sup.2- and Cl.sup.- ions can provide increased energy density and improved stability and solubility of one or more of the ionic species in the catholyte and/or anolyte. According to one example, a vanadium-based redox flow battery system is characterized by an anolyte having V.sup.2+ and V.sup.3+ in a supporting solution and a catholyte having V.sup.4+ and V.sup.5+ in a supporting solution. The supporting solution can contain Cl.sup.- ions or a mixture of SO.sub.4.sup.2- and Cl.sup.- ions.
Redox flow batteries based on supporting solutions containing chloride
Li, Liyu; Kim, Soowhan; Yang, Zhenguo; Wang, Wei; Zhang, Jianlu; Chen, Baowei; Nie, Zimin; Xia, Guanguang
2014-01-14
Redox flow battery systems having a supporting solution that contains Cl.sup.- ions can exhibit improved performance and characteristics. Furthermore, a supporting solution having mixed SO.sub.4.sup.2- and Cl.sup.- ions can provide increased energy density and improved stability and solubility of one or more of the ionic species in the catholyte and/or anolyte. According to one example, a vanadium-based redox flow battery system is characterized by an anolyte having V.sup.2+ and V.sup.3+ in a supporting solution and a catholyte having V.sup.4+ and V.sup.5+ in a supporting solution. The supporting solution can contain Cl.sup.- ions or a mixture of SO.sub.4.sup.2- and Cl.sup.- ions.
Highly Accurate Beam Torsion Solutions Using the p-Version Finite Element Method
NASA Technical Reports Server (NTRS)
Smith, James P.
1996-01-01
A new treatment of the classical beam torsion boundary value problem is applied. Using the p-version finite element method with shape functions based on Legendre polynomials, torsion solutions for generic cross-sections comprised of isotropic materials are developed. Element shape functions for quadrilateral and triangular elements are discussed, and numerical examples are provided.
Numerical solutions for heat flow in adhesive lap joints
NASA Technical Reports Server (NTRS)
Howell, P. A.; Winfree, William P.
1992-01-01
The present formulation for the modeling of heat transfer in thin, adhesively bonded lap joints precludes difficulties associated with large aspect ratio grids required by standard FEM formulations. This quasi-static formulation also reduces the problem dimensionality (by one), thereby minimizing computational requirements. The solutions obtained are found to be in good agreement with both analytical solutions and solutions from standard FEM programs. The approach is noted to yield a more accurate representation of heat-flux changes between layers due to a disbond.
Multiple Solutions of Transonic Flow over NACA0012 Airfoil
NASA Astrophysics Data System (ADS)
Xiong, Juntao; Liu, Ya; Liu, Feng; Luo, Shijun; Zhao, Zijie; Ren, Xudong; Gao, Chao
2012-11-01
Multiple solutions of the small-disturbance potential equation and full potential equation were known for the NACA0012 airfoil in a certain range of transonic Mach numbers and at zero angle of attack. However the multiple solutions for this airfoil were not observed using Euler or Navier-Stokes equations under the above flow conditions. In the present work, both the Unsteady Reynolds-Averaged Navier-Stokes (URANS) computations and transonic wind tunnel experiments are performed under certain Reynolds numbers to further study the problem. The results of the two methods reveal that buffet appears in a narrow Mach number range where the potential flow methods predict multiple solutions. Boundary layer displacement thickness computed from URANS at the same flow condition is used to modify the geometry of the airfoil. Euler equations are then solved for the modified geometry. The results show that the addition of the boundary layer displacement thickness creates multiple solutions for the NACA0012 airfoil. Global linear stability analysis is also performed on the original and the modified airfoils. This shows a close relationship between the viscous unsteady shock buffet phenomenon of transonic airfoil flow and the existence of multiple solutions of the external inviscid flow. Postdoctoral Research Assistant.
Extensional flow of blood analog solutions in microfluidic devices
Sousa, P. C.; Pinho, F. T.; Oliveira, M. S. N.; Alves, M. A.
2011-01-01
In this study, we show the importance of extensional rheology, in addition to the shear rheology, in the choice of blood analog solutions intended to be used in vitro for mimicking the microcirculatory system. For this purpose, we compare the flow of a Newtonian fluid and two well-established viscoelastic blood analog polymer solutions through microfluidic channels containing both hyperbolic and abrupt contractions∕expansions. The hyperbolic shape was selected in order to impose a nearly constant strain rate at the centerline of the microchannels and achieve a quasihomogeneous and strong extensional flow often found in features of the human microcirculatory system such as stenoses. The two blood analog fluids used are aqueous solutions of a polyacrylamide (125 ppm w∕w) and of a xanthan gum (500 ppm w∕w), which were characterized rheologically in steady-shear flow using a rotational rheometer and in extension using a capillary breakup extensional rheometer (CaBER). Both blood analogs exhibit a shear-thinning behavior similar to that of whole human blood, but their relaxation times, obtained from CaBER experiments, are substantially different (by one order of magnitude). Visualizations of the flow patterns using streak photography, measurements of the velocity field using microparticle image velocimetry, and pressure-drop measurements were carried out experimentally for a wide range of flow rates. The experimental results were also compared with the numerical simulations of the flow of a Newtonian fluid and a generalized Newtonian fluid with shear-thinning behavior. Our results show that the flow patterns of the two blood analog solutions are considerably different, despite their similar shear rheology. Furthermore, we demonstrate that the elastic properties of the fluid have a major impact on the flow characteristics, with the polyacrylamide solution exhibiting a much stronger elastic character. As such, these properties must be taken into account in the
Solute transport along preferential flow paths in unsaturated fractures
Su, G.W.; Geller, J.T.; Pruess, K.; Hunt, J.R.
2001-01-01
Laboratory experiments were conducted to study solute transport along preferential flow paths in unsaturated, inclined fractures. Qualitative aspects of solute transport were identified in a miscible dye tracer experiment conducted in a transparent replica of a natural granite fracture. Additional experiments were conducted to measure the breakthrough curves of a conservative tracer introduced into an established preferential flow path in two different fracture replicas and a rock-replica combination. The influence of gravity was investigated by varying fracture inclination. The relationship between the travel times of the solute and the relative influence of gravity was substantially affected by two modes of intermittent flow that occurred: the snapping rivulet and the pulsating blob modes. The measured travel times of the solute were evaluated with three transfer function models: the axial dispersion, the reactors-in-series, and the lognormal models. The three models described the solute travel times nearly equally well. A mechanistic model was also formulated to describe transport when the pulsating blob mode occurred which assumed blobs of water containing solute mixed with residual pools of water along the flow path.
Elastic turbulence in curvilinear flows of polymer solutions
NASA Astrophysics Data System (ADS)
Groisman, Alexander; Steinberg, Victor
2004-03-01
Following our first report (A Groisman and V Steinberg 2000 Nature 405 53), we present an extended account of experimental observations of elasticity-induced turbulence in three different systems: a swirling flow between two plates, a Couette-Taylor (CT) flow between two cylinders, and a flow in a curvilinear channel (Dean flow). All three set-ups had a high ratio of the width of the region available for flow to the radius of curvature of the streamlines. The experiments were carried out with dilute solutions of high-molecular-weight polyacrylamide in concentrated sugar syrups. High polymer relaxation time and solution viscosity ensured prevalence of non-linear elastic effects over inertial non-linearity, and development of purely elastic instabilities at low Reynolds number (Re) in all three flows. Above the elastic instability threshold, flows in all three systems exhibit features of developed turbulence. They include: (i) randomly fluctuating fluid motion excited in a broad range of spatial and temporal scales and (ii) significant increase in the rates of momentum and mass transfer (compared with those expected for a steady flow with a smooth velocity profile). Phenomenology, driving mechanisms and parameter dependence of the elastic turbulence are compared with those of the conventional high-Re hydrodynamic turbulence in Newtonian fluids. Some similarities as well as multiple principal differences were found. In two out of three systems (swirling flow between two plates and flow in the curvilinear channel), power spectra of velocity fluctuations decayed rather quickly, following power laws with exponents of about -3.5. It suggests that, being random in time, the flow is rather smooth in space, in the sense that the main contribution to deformation and mixing (and, possibly, elastic energy) is coming from flow at the largest scale of the system. This situation, random in time and smooth in space, is analogous to flows at small scales (below the Kolmogorov
The accurate solution of Poisson's equation by expansion in Chebyshev polynomials
NASA Technical Reports Server (NTRS)
Haidvogel, D. B.; Zang, T.
1979-01-01
A Chebyshev expansion technique is applied to Poisson's equation on a square with homogeneous Dirichlet boundary conditions. The spectral equations are solved in two ways - by alternating direction and by matrix diagonalization methods. Solutions are sought to both oscillatory and mildly singular problems. The accuracy and efficiency of the Chebyshev approach compare favorably with those of standard second- and fourth-order finite-difference methods.
Flow of DNA solutions in a microfluidic gradual contraction
Gulati, Shelly; Muller, Susan J.; Liepmann, Dorian
2015-01-01
The flow of λ-DNA solutions in a gradual micro-contraction was investigated using direct measurement techniques. The effects on DNA transport in microscale flows are significant because the flow behavior is influenced by macromolecular conformations, both viscous and elastic forces dominate inertial forces at this length scale, and the fully extended length of the molecule approaches the characteristic channel length wc (L/wc ∼ 0.13). This study examines the flow of semi-dilute and entangled DNA solutions in a gradual planar micro-contraction for low Reynolds numbers (3.7 × 10−6 < Re < 3.1 × 10−1) and high Weissenberg numbers (0.4 < Wi < 446). The semi-dilute DNA solutions have modest elasticity number, El = Wi/Re = 55, and do not exhibit viscoelastic behavior. For the entangled DNA solutions, we access high elasticity numbers (7.9 × 103 < El < 6.0 × 105). Video microscopy and streak images of entangled DNA solution flow reveal highly elastic behavior evidenced by the presence of large, stable vortices symmetric about the centerline and upstream of the channel entrance. Micro-particle image velocimetry measurements are used to obtain high resolution, quantitative velocity measurements of the vortex growth in this micro-contraction flow. These direct measurements provide a deeper understanding of the underlying physics of macromolecular transport in microfluidic flow, which will enable the realization of enhanced designs of lab-on-a-chip systems. PMID:26392834
Dual Solutions for Nonlinear Flow Using Lie Group Analysis
Awais, Muhammad; Hayat, Tasawar; Irum, Sania; Saleem, Salman
2015-01-01
`The aim of this analysis is to investigate the existence of the dual solutions for magnetohydrodynamic (MHD) flow of an upper-convected Maxwell (UCM) fluid over a porous shrinking wall. We have employed the Lie group analysis for the simplification of the nonlinear differential system and computed the absolute invariants explicitly. An efficient numerical technique namely the shooting method has been employed for the constructions of solutions. Dual solutions are computed for velocity profile of an upper-convected Maxwell (UCM) fluid flow. Plots reflecting the impact of dual solutions for the variations of Deborah number, Hartman number, wall mass transfer are presented and analyzed. Streamlines are also plotted for the wall mass transfer effects when suction and blowing situations are considered. PMID:26575996
High-Order Accurate Solutions to the Helmholtz Equation in the Presence of Boundary Singularities
NASA Astrophysics Data System (ADS)
Britt, Darrell Steven, Jr.
Problems of time-harmonic wave propagation arise in important fields of study such as geological surveying, radar detection/evasion, and aircraft design. These often involve highfrequency waves, which demand high-order methods to mitigate the dispersion error. We propose a high-order method for computing solutions to the variable-coefficient inhomogeneous Helmholtz equation in two dimensions on domains bounded by piecewise smooth curves of arbitrary shape with a finite number of boundary singularities at known locations. We utilize compact finite difference (FD) schemes on regular structured grids to achieve highorder accuracy due to their efficiency and simplicity, as well as the capability to approximate variable-coefficient differential operators. In this work, a 4th-order compact FD scheme for the variable-coefficient Helmholtz equation on a Cartesian grid in 2D is derived and tested. The well known limitation of finite differences is that they lose accuracy when the boundary curve does not coincide with the discretization grid, which is a severe restriction on the geometry of the computational domain. Therefore, the algorithm presented in this work combines high-order FD schemes with the method of difference potentials (DP), which retains the efficiency of FD while allowing for boundary shapes that are not aligned with the grid without sacrificing the accuracy of the FD scheme. Additionally, the theory of DP allows for the universal treatment of the boundary conditions. One of the significant contributions of this work is the development of an implementation that accommodates general boundary conditions (BCs). In particular, Robin BCs with discontinuous coefficients are studied, for which we introduce a piecewise parameterization of the boundary curve. Problems with discontinuities in the boundary data itself are also studied. We observe that the design convergence rate suffers whenever the solution loses regularity due to the boundary conditions. This is
Instabilities in stagnation point flows of polymer solutions
NASA Astrophysics Data System (ADS)
Haward, S. J.; McKinley, G. H.
2013-08-01
A recently developed microfluidic device, the optimized shape cross-slot extensional rheometer or OSCER [S. J. Haward, M. S. N. Oliveira, M. A. Alves, and G. H. McKinley, "Optimized cross-slot flow geometry for microfluidic extensional rheometry," Phys. Rev. Lett. 109, 128301 (2012), 10.1103/PhysRevLett.109.128301], is used to investigate the stability of viscoelastic polymer solutions in an idealized planar stagnation point flow. Aqueous polymer solutions, consisting of poly(ethylene oxide) and of hyaluronic acid with various molecular weights and concentrations, are formulated in order to provide fluids with a wide range of rheological properties. Semi-dilute solutions of high molecular weight polymers provide highly viscoelastic fluids with long relaxation times, which achieve a high Weissenberg number (Wi) at flow rates for which the Reynolds number (Re) remains low; hence the elasticity number El = Wi/Re is high. Lower concentration solutions of moderate molecular weight polymers provide only weakly viscoelastic fluids in which inertia remains important and El is relatively low. Flow birefringence observations are used to visualize the nature of flow instabilities in the fluids as the volumetric flow rate through the OSCER device is steadily incremented. At low Wi and Re, all of the fluids display a steady, symmetric, and uniform "birefringent strand" of highly oriented polymer molecules aligned along the outflowing symmetry axis of the test geometry, indicating the stability of the flow field under such conditions. In fluids of El > 1, we observe steady elastic flow asymmetries beyond a critical Weissenberg number,Wicrit, that are similar in character to those already reported in standard cross-slot geometries [e.g., P. E. Arratia, C. C. Thomas, J. Diorio, and J. P. Gollub, "Elastic instabilities of polymer solutions in cross-channel flow," Phys. Rev. Lett. 96, 144502 (2006), 10.1103/PhysRevLett.96.144502]. However, in fluids with El < 1 we observe a sequence
Design and Construction Solutions in the Accurate Realization of NCSX Magnetic Fields
Heitzenroeder, P.; Dudek, Lawrence E.; Brooks, Arthur W.; Viola, Michael E.; Brown, Thomas; Neilson, George H.; Zarnstorff, Michael C.; Rej, Donald; Cole,Michael J.; Freudenberg, Kevin D.; Harris J. H.; McGinnis, Gary
2008-09-29
The National Compact Stellarator Experiment, NCSX, is being constructed at the Princeton Plasma Physics Laboratory (PPPL) in partnership with the Oak Ridge national Laboratory. The goal of NCSX is to provide the understanding necessary to develop an attractive, disruption free, steady state compact stellaratorbased reactor design. This paper describes the recently revised designs of the critical interfaces between the modular coils, the construction solutions developed to meet assembly tolerances, and the recently revised trim coil system that provides the required compensation to correct for the “as built” conditions and to allow flexibility in the disposition of as-built conditions. In May, 2008, the sponsor decided to terminate the NCSX project due to growth in the project’s cost and schedule estimates. However significant technical challenges in design and construction were overcome, greatly reducing the risk in the remaining work to complete the project.
Mutelet, Fabrice; Jaubert, Jean-Noël
2006-01-13
Activity coefficients at infinite dilution of 29 organic compounds in two room temperature ionic liquids were determined using inverse gas chromatography. The measurements were carried out at different temperatures between 323.15 and 343.15K. To establish the influence of concurrent retention mechanisms on the accuracy of activity coefficients at infinite dilution for 1-butyl-3-methylimidazolium octyl sulfate and 1-ethyl-3-methylimidazolium tosylate, phase loading studies of the net retention volume per gram of packing as a function of the percent phase loading were used. It is shown that most of the solutes are retained largely by partition with a small contribution from adsorption on 1-butyl-3-methylimidazolium octyl sulfate and that the n-alkanes are retained predominantly by interfacial adsorption on 1-ethyl-3-methylimidazolium tosylate. PMID:16310203
The fracture flow equation and its perturbation solution
NASA Astrophysics Data System (ADS)
Basha, H. A.; El-Asmar, W.
2003-12-01
This work derives the fracture flow equation from the two-dimensional steady form of the Navier-Stokes equation. Asymptotic solutions are obtained whereby the perturbation parameter is the ratio of the mean width over the length of the fracture segment. The perturbation expansion can handle arbitrary variation of the fracture walls as long as the dominant velocity is in the longitudinal direction. The effect of the matrix-fracture interaction is also taken into account by allowing leakage through the fracture walls. The perturbation solution is used to obtain an estimate of the flow rate and the fracture transmissivity as well as the velocity and the pressure distribution in fractures of various geometries. The analysis covers eight different configurations of fracture geometry including linear and curvilinear variation as well as sinusoidal variation in the top and bottom walls with varying horizontal alignment and roughness wavelengths. The zero-order solution yields the Reynolds lubrication approximation, and the higher-order equations provide a correction term to the flow rate in terms of the roughness frequency and the Reynolds number. For sinusoidal and linear walls, the mathematical analysis shows that the zero-order flow rate could be expressed in terms of the maximum to minimum width ratio. For equal widths at both ends of the fracture, the first-order correction is zero. For sinusoidal fractures, the flow rate decreases with increasing Reynolds number and with increasing roughness amplitude and frequency. The effect of leakage is to create a nonuniform flow distribution in the fracture that deviates significantly from the flow rate estimate for impermeable walls. The derived flow expressions can provide a more reliable tool for flow and transport predictions in fractured domain.
A fracture network model for water flow and solute transport
Robinson, B.A.
1989-01-01
This paper summarizes code development work and sample calculations for FRACNET, a two-dimensional steady state simulator of fluid flow and solute transport in fractured porous media. The model analyzes flow and transport by generating a fracture network based on statistical characteristics of fractures obtained from well logs and other data. After a network is generated, flow and tracer transport are computed for appropriate boundary conditions and wellbore source/sink terms. In addition, for a given realization, the code can be used to indicate whether the medium can be treated as an equivalent porous medium. 18 refs., 7 figs.
Fracture-Flow-Enhanced Solute Diffusion into Fractured Rock
Wu, Yu-Shu; Ye, Ming; Sudicky, E.A.
2007-12-15
We propose a new conceptual model of fracture-flow-enhanced matrix diffusion, which correlates with fracture-flow velocity, i.e., matrix diffusion enhancement induced by rapid fluid flow within fractures. According to the boundary-layer or film theory, fracture flow enhanced matrix diffusion may dominate mass-transfer processes at fracture-matrix interfaces, because rapid flow along fractures results in large velocity and concentration gradients at and near fracture-matrix interfaces, enhancing matrix diffusion at matrix surfaces. In this paper, we present a new formulation of the conceptual model for enhanced fracture-matrix diffusion, and its implementation is discussed using existing analytical solutions and numerical models. In addition, we use the enhanced matrix diffusion concept to analyze laboratory experimental results from nonreactive and reactive tracer breakthrough tests, in an effort to validate the new conceptual model.
A multilayer method of fundamental solutions for Stokes flow problems
NASA Astrophysics Data System (ADS)
Boselli, F.; Obrist, D.; Kleiser, L.
2012-07-01
The method of fundamental solutions (MFS) is a meshless method for the solution of boundary value problems and has recently been proposed as a simple and efficient method for the solution of Stokes flow problems. The MFS approximates the solution by an expansion of fundamental solutions whose singularities are located outside the flow domain. Typically, the source points (i.e. the singularities of the fundamental solutions) are confined to a smooth source layer embracing the flow domain. This monolayer implementation of the MFS (monolayer MFS) depends strongly on the location of the user-defined source points: On the one hand, increasing the distance of the source points from the boundary tends to increase the convergence rate. On the other hand, this may limit the achievable accuracy. This often results in an unfavorable compromise between the convergence rate and the achievable accuracy of the MFS. The idea behind the present work is that a multilayer implementation of the MFS (multilayer MFS) can improve the robustness of the MFS by efficiently resolving different scales of the solution by source layers at different distances from the boundary. We propose a block greedy-QR algorithm (BGQRa) which exploits this property in a multilevel fashion. The proposed multilayer MFS is much more robust than the monolayer MFS and can compute Stokes flows on general two- and three-dimensional domains. It converges rapidly and yields high levels of accuracy by combining the properties of distant and close source points. The block algorithm alleviates the overhead of multiple source layers and allows the multilayer MFS to outperform the monolayer MFS.
NASA Astrophysics Data System (ADS)
Lee, Dongwook
2013-06-01
In this paper, we extend the unsplit staggered mesh scheme (USM) for 2D magnetohydrodynamics (MHD) [D. Lee, A.E. Deane, An unsplit staggered mesh scheme for multidimensional magnetohydrodynamics, J. Comput. Phys. 228 (2009) 952-975] to a full 3D MHD scheme. The scheme is a finite-volume Godunov method consisting of a constrained transport (CT) method and an efficient and accurate single-step, directionally unsplit multidimensional data reconstruction-evolution algorithm, which extends Colella's original 2D corner transport upwind (CTU) method [P. Colella, Multidimensional upwind methods for hyperbolic conservation laws, J. Comput. Phys. 87 (1990) 446-466]. We present two types of data reconstruction-evolution algorithms for 3D: (1) a reduced CTU scheme and (2) a full CTU scheme. The reduced 3D CTU scheme is a variant of a simple 3D extension of Collela's 2D CTU method and is considered as a direct extension from the 2D USM scheme. The full 3D CTU scheme is our primary 3D solver which includes all multidimensional cross-derivative terms for stability. The latter method is logically analogous to the 3D unsplit CTU method by Saltzman [J. Saltzman, An unsplit 3D upwind method for hyperbolic conservation laws, J. Comput. Phys. 115 (1994) 153-168]. The major novelties in our algorithms are twofold. First, we extend the reduced CTU scheme to the full CTU scheme which is able to run with CFL numbers close to unity. Both methods utilize the transverse update technique developed in the 2D USM algorithm to account for transverse fluxes without solving intermediate Riemann problems, which in turn gives cost-effective 3D methods by reducing the total number of Riemann solves. The proposed algorithms are simple and efficient especially when including multidimensional MHD terms that maintain in-plane magnetic field dynamics. Second, we introduce a new CT scheme that makes use of proper upwind information in taking averages of electric fields. Our 3D USM schemes can be easily
Energy expenditure during level human walking: seeking a simple and accurate predictive solution.
Ludlow, Lindsay W; Weyand, Peter G
2016-03-01
Accurate prediction of the metabolic energy that walking requires can inform numerous health, bodily status, and fitness outcomes. We adopted a two-step approach to identifying a concise, generalized equation for predicting level human walking metabolism. Using literature-aggregated values we compared 1) the predictive accuracy of three literature equations: American College of Sports Medicine (ACSM), Pandolf et al., and Height-Weight-Speed (HWS); and 2) the goodness-of-fit possible from one- vs. two-component descriptions of walking metabolism. Literature metabolic rate values (n = 127; speed range = 0.4 to 1.9 m/s) were aggregated from 25 subject populations (n = 5-42) whose means spanned a 1.8-fold range of heights and a 4.2-fold range of weights. Population-specific resting metabolic rates (V̇o2 rest) were determined using standardized equations. Our first finding was that the ACSM and Pandolf et al. equations underpredicted nearly all 127 literature-aggregated values. Consequently, their standard errors of estimate (SEE) were nearly four times greater than those of the HWS equation (4.51 and 4.39 vs. 1.13 ml O2·kg(-1)·min(-1), respectively). For our second comparison, empirical best-fit relationships for walking metabolism were derived from the data set in one- and two-component forms for three V̇o2-speed model types: linear (∝V(1.0)), exponential (∝V(2.0)), and exponential/height (∝V(2.0)/Ht). We found that the proportion of variance (R(2)) accounted for, when averaged across the three model types, was substantially lower for one- vs. two-component versions (0.63 ± 0.1 vs. 0.90 ± 0.03) and the predictive errors were nearly twice as great (SEE = 2.22 vs. 1.21 ml O2·kg(-1)·min(-1)). Our final analysis identified the following concise, generalized equation for predicting level human walking metabolism: V̇o2 total = V̇o2 rest + 3.85 + 5.97·V(2)/Ht (where V is measured in m/s, Ht in meters, and V̇o2 in ml O2·kg(-1)·min(-1)). PMID:26679617
An Approximate Analytical Solution for Backward-Facing Step Flow
NASA Astrophysics Data System (ADS)
Celik, Ismail; Parsons, Don; Karaismail, Ertan; Nanduri, Jagannath
2007-11-01
Flow past a backward facing step is a classical bench mark for both laminar and turbulent flow calculations. Due to the near-singular behavior arising from the presence of the sharp step, it is very difficult to predict the size of the recirculation region and the reattachment length. This difficulty, in turn, manifests itself as a significant discrepancy between predicted and measured velocity profiles. The aim of the current work is to formulate an analytical solution to the 2D, steady flow in question that satisfies the Navier-Stokes equations with a source term. The proposed solution is a superposition of two stream functions, one being a semi-potential solution that satisfies all the boundary conditions for real incompressible fluids, and another composed of rotational vortices (e.g. Rankine vortices) which enable flow separation. The location and distribution of the vortices is selected to emulate the Reynolds number dependence of the re-attachment length, while other parameters in the model are used to minimize the additional source term that is needed. The proposed solution can be primarily used in code-verification, and quantification of discretization errors in CFD (Computational Fluid Dynamics). It can also be used to assess modeling errors, by adding additional source terms that represent the spatial variations in turbulent-eddy viscosity, the key quantity used in Boussinesq-type turbulence models.
Reference Solutions for Benchmark Turbulent Flows in Three Dimensions
NASA Technical Reports Server (NTRS)
Diskin, Boris; Thomas, James L.; Pandya, Mohagna J.; Rumsey, Christopher L.
2016-01-01
A grid convergence study is performed to establish benchmark solutions for turbulent flows in three dimensions (3D) in support of turbulence-model verification campaign at the Turbulence Modeling Resource (TMR) website. The three benchmark cases are subsonic flows around a 3D bump and a hemisphere-cylinder configuration and a supersonic internal flow through a square duct. Reference solutions are computed for Reynolds Averaged Navier Stokes equations with the Spalart-Allmaras turbulence model using a linear eddy-viscosity model for the external flows and a nonlinear eddy-viscosity model based on a quadratic constitutive relation for the internal flow. The study involves three widely-used practical computational fluid dynamics codes developed and supported at NASA Langley Research Center: FUN3D, USM3D, and CFL3D. Reference steady-state solutions computed with these three codes on families of consistently refined grids are presented. Grid-to-grid and code-to-code variations are described in detail.
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.
NASA Technical Reports Server (NTRS)
Hagstrom, Thomas; Hariharan, S. I.; Maccamy, R. C.
1993-01-01
We consider the solution of scattering problems for the wave equation using approximate boundary conditions at artificial boundaries. These conditions are explicitly viewed as approximations to an exact boundary condition satisfied by the solution on the unbounded domain. We study the short and long term behavior of the error. It is provided that, in two space dimensions, no local in time, constant coefficient boundary operator can lead to accurate results uniformly in time for the class of problems we consider. A variable coefficient operator is developed which attains better accuracy (uniformly in time) than is possible with constant coefficient approximations. The theory is illustrated by numerical examples. We also analyze the proposed boundary conditions using energy methods, leading to asymptotically correct error bounds.
Finite element solution theory for three-dimensional boundary flows
NASA Technical Reports Server (NTRS)
Baker, A. J.
1974-01-01
A finite element algorithm is derived for the numerical solution of a three-dimensional flow field described by a system of initial-valued, elliptic boundary value partial differential equations. The familiar three-dimensional boundary layer equations belong to this description when diffusional processes in only one coordinate direction are important. The finite element algorithm transforms the original description into large order systems of ordinary differential equations written for the dependent variables discretized at node points of an arbitrarily irregular computational lattice. The generalized elliptic boundary conditions is piecewise valid for each dependent variable on boundaries that need not explicitly coincide with coordinate surfaces. Solutions for sample problems in laminar and turbulent boundary flows illustrate favorable solution accuracy, convergence, and versatility.
NASA Astrophysics Data System (ADS)
Stecca, Guglielmo; Siviglia, Annunziato; Blom, Astrid
2016-07-01
We present an accurate numerical approximation to the Saint-Venant-Hirano model for mixed-sediment morphodynamics in one space dimension. Our solution procedure originates from the fully-unsteady matrix-vector formulation developed in [54]. The principal part of the problem is solved by an explicit Finite Volume upwind method of the path-conservative type, by which all the variables are updated simultaneously in a coupled fashion. The solution to the principal part is embedded into a splitting procedure for the treatment of frictional source terms. The numerical scheme is extended to second-order accuracy and includes a bookkeeping procedure for handling the evolution of size stratification in the substrate. We develop a concept of balancedness for the vertical mass flux between the substrate and active layer under bed degradation, which prevents the occurrence of non-physical oscillations in the grainsize distribution of the substrate. We suitably modify the numerical scheme to respect this principle. We finally verify the accuracy in our solution to the equations, and its ability to reproduce one-dimensional morphodynamics due to streamwise and vertical sorting, using three test cases. In detail, (i) we empirically assess the balancedness of vertical mass fluxes under degradation; (ii) we study the convergence to the analytical linearised solution for the propagation of infinitesimal-amplitude waves [54], which is here employed for the first time to assess a mixed-sediment model; (iii) we reproduce Ribberink's E8-E9 flume experiment [46].
Rapid, high-order accurate calculation of flows due to free source or vortex distributions
NASA Technical Reports Server (NTRS)
Halsey, D.
1981-01-01
Fast Fourier transform (FFT) techniques are applied to the problem of finding the flow due to source or vortex distributions in the field outside an airfoil or other two-dimensional body. Either the complex potential or the complex velocity may be obtained to a high order of accuracy, with computational effort similar to that required by second-order fast Poisson solvers. These techniques are applicable to general flow problems with compressibility and rotation. An example is given of their use for inviscid compressible flow.
The flow of dilute polymer solution in a narrow channel. II. Plane Poiseuille flow
NASA Astrophysics Data System (ADS)
Goh, C. J.; Atkinson, J. D.; Phan-Thien, N.
1985-04-01
As an extension of the previous paper, we derive a similar theory for the plane Poiseuille flow of a dilute polymer solution. The strict enforcement of reflective boundary conditions allows an approximate solution to the Fokker-Planck-Kolmogorov equation to be obtained which is found to be consistent with solutions obtained by Galerkin methods and Monte Carlo simulation. The approximate theory also allows us to derive analytical expressions for the slip velocity and the effective viscosity which are again consistent with the plane Couette flow results derived in the previous paper. The theory is also extended to the nonlinear Warner spring model via Monte Carlo simulation.
Efficient solutions of two-dimensional incompressible steady viscous flows
NASA Technical Reports Server (NTRS)
Morrison, J. H.; Napolitano, M.
1986-01-01
A simple, efficient, and robust numerical technique is provided for solving two dimensional incompressible steady viscous flows at moderate to high Reynolds numbers. The proposed approach employs an incremental multigrid method and an extrapolation procedure based on minimum residual concepts to accelerate the convergence rate of a robust block-line-Gauss-Seidel solver for the vorticity-stream function Navier-Stokes equations. Results are presented for the driven cavity flow problem using uniform and nonuniform grids and for the flow past a backward facing step in a channel. For this second problem, mesh refinement and Richardson extrapolation are used to obtain useful benchmark solutions in the full range of Reynolds numbers at which steady laminar flow is established.
Quiescent and flow-induced transitional behavior of hydroxypropylcellulose solutions
NASA Astrophysics Data System (ADS)
Grizzuti, Nino; Maffettone, Pier Luca
2003-03-01
The flow-induced transition of liquid crystalline polymers (LCPs) is studied by rheological techniques. Aqueous solutions of hydroxypropylcellulose (HPC) in water are adopted as a model LCP system. Nonisothermal oscillatory tests are first used to quantitatively determine the "rheological" phase diagram of the HPC/water system under quiescent conditions. The phase diagram compares well with those obtained by other, more conventional techniques. Superposition of oscillatory and steady shear flow is then used to describe the nonisothermal flow-induced transition. In this case, it is shown that a critical shear stress must be reached to effectively induce the isotropic/mesophase transition. Stress-loop experiments are also used to identify the isothermal flow-induced transition, and to provide information on the transition kinetics.
Tuning-free controller to accurately regulate flow rates in a microfluidic network
NASA Astrophysics Data System (ADS)
Heo, Young Jin; Kang, Junsu; Kim, Min Jun; Chung, Wan Kyun
2016-03-01
We describe a control algorithm that can improve accuracy and stability of flow regulation in a microfluidic network that uses a conventional pressure pump system. The algorithm enables simultaneous and independent control of fluid flows in multiple micro-channels of a microfluidic network, but does not require any model parameters or tuning process. We investigate robustness and optimality of the proposed control algorithm and those are verified by simulations and experiments. In addition, the control algorithm is compared with a conventional PID controller to show that the proposed control algorithm resolves critical problems induced by the PID control. The capability of the control algorithm can be used not only in high-precision flow regulation in the presence of disturbance, but in some useful functions for lab-on-a-chip devices such as regulation of volumetric flow rate, interface position control of two laminar flows, valveless flow switching, droplet generation and particle manipulation. We demonstrate those functions and also suggest further potential biological applications which can be accomplished by the proposed control framework.
Tuning-free controller to accurately regulate flow rates in a microfluidic network.
Heo, Young Jin; Kang, Junsu; Kim, Min Jun; Chung, Wan Kyun
2016-01-01
We describe a control algorithm that can improve accuracy and stability of flow regulation in a microfluidic network that uses a conventional pressure pump system. The algorithm enables simultaneous and independent control of fluid flows in multiple micro-channels of a microfluidic network, but does not require any model parameters or tuning process. We investigate robustness and optimality of the proposed control algorithm and those are verified by simulations and experiments. In addition, the control algorithm is compared with a conventional PID controller to show that the proposed control algorithm resolves critical problems induced by the PID control. The capability of the control algorithm can be used not only in high-precision flow regulation in the presence of disturbance, but in some useful functions for lab-on-a-chip devices such as regulation of volumetric flow rate, interface position control of two laminar flows, valveless flow switching, droplet generation and particle manipulation. We demonstrate those functions and also suggest further potential biological applications which can be accomplished by the proposed control framework. PMID:26987587
Tuning-free controller to accurately regulate flow rates in a microfluidic network
Heo, Young Jin; Kang, Junsu; Kim, Min Jun; Chung, Wan Kyun
2016-01-01
We describe a control algorithm that can improve accuracy and stability of flow regulation in a microfluidic network that uses a conventional pressure pump system. The algorithm enables simultaneous and independent control of fluid flows in multiple micro-channels of a microfluidic network, but does not require any model parameters or tuning process. We investigate robustness and optimality of the proposed control algorithm and those are verified by simulations and experiments. In addition, the control algorithm is compared with a conventional PID controller to show that the proposed control algorithm resolves critical problems induced by the PID control. The capability of the control algorithm can be used not only in high-precision flow regulation in the presence of disturbance, but in some useful functions for lab-on-a-chip devices such as regulation of volumetric flow rate, interface position control of two laminar flows, valveless flow switching, droplet generation and particle manipulation. We demonstrate those functions and also suggest further potential biological applications which can be accomplished by the proposed control framework. PMID:26987587
NASA Astrophysics Data System (ADS)
Brunker, J.; Beard, P.
2014-03-01
An assessment has been made of various experimental factors affecting the accuracy of flow velocities measured using a pulsed time correlation photoacoustic Doppler technique. In this method, Doppler time shifts are quantified via crosscorrelation of pairs of photoacoustic waveforms generated in moving absorbers using pairs of laser light pulses, and the photoacoustic waves are detected using an ultrasound transducer. The acoustic resolution mode is employed by using the transducer focal width, rather than the large illuminated volume, to define the lateral spatial resolution. This enables penetration depths of several millimetres or centimetres, unlike methods using the optical resolution mode, which limits the maximum penetration depth to approximately 1 mm. In the acoustic resolution mode, it is difficult to detect time shifts in highly concentrated suspensions of flowing absorbers, such as red blood cell suspensions and whole blood, and this challenge supposedly arises because of the lack of spatial heterogeneity. However, by assessing the effect of different absorption coefficients and tube diameters, we offer an alternative explanation relating to light attenuation and parabolic flow. We also demonstrate a new signal processing method that surmounts the previous problem of measurement under-reading. This method is a form of signal range gating and enables mapping of the flow velocity profile across the tube as well as measurement of the average flow velocity. We show that, using our signal processing scheme, it is possible to measure the flow of whole blood using a relatively low frequency detector. This important finding paves the way for application of the technique to measurements of blood flow several centimetres deep in living tissue.
Nonequilibrium thermodynamics of dilute polymer solutions in flow
Latinwo, Folarin; Hsiao, Kai-Wen; Schroeder, Charles M.
2014-11-07
Modern materials processing applications and technologies often occur far from equilibrium. To this end, the processing of complex materials such as polymer melts and nanocomposites generally occurs under strong deformations and flows, conditions under which equilibrium thermodynamics does not apply. As a result, the ability to determine the nonequilibrium thermodynamic properties of polymeric materials from measurable quantities such as heat and work is a major challenge in the field. Here, we use work relations to show that nonequilibrium thermodynamic quantities such as free energy and entropy can be determined for dilute polymer solutions in flow. In this way, we determine the thermodynamic properties of DNA molecules in strong flows using a combination of simulations, kinetic theory, and single molecule experiments. We show that it is possible to calculate polymer relaxation timescales purely from polymer stretching dynamics in flow. We further observe a thermodynamic equivalence between nonequilibrium and equilibrium steady-states for polymeric systems. In this way, our results provide an improved understanding of the energetics of flowing polymer solutions.
Time-Accurate Computation of Viscous Flow Around Deforming Bodies Using Overset Grids
Fast, P; Henshaw, W D
2001-04-02
Dynamically evolving boundaries and deforming bodies interacting with a flow are commonly encountered in fluid dynamics. However, the numerical simulation of flows with dynamic boundaries is difficult with current methods. We propose a new method for studying such problems. The key idea is to use the overset grid method with a thin, body-fitted grid near the deforming boundary, while using fixed Cartesian grids to cover most of the computational domain. Our approach combines the strengths of earlier moving overset grid methods for rigid body motion, and unstructured grid methods for Aow-structure interactions. Large scale deformation of the flow boundaries can be handled without a global regridding, and in a computationally efficient way. In terms of computational cost, even a full overset grid regridding is significantly cheaper than a full regridding of an unstructured grid for the same domain, especially in three dimensions. Numerical studies are used to verify accuracy and convergence of our flow solver. As a computational example, we consider two-dimensional incompressible flow past a flexible filament with prescribed dynamics.
Refined numerical solution of the transonic flow past a wedge
NASA Technical Reports Server (NTRS)
Liang, S.-M.; Fung, K.-Y.
1985-01-01
A numerical procedure combining the ideas of solving a modified difference equation and of adaptive mesh refinement is introduced. The numerical solution on a fixed grid is improved by using better approximations of the truncation error computed from local subdomain grid refinements. This technique is used to obtain refined solutions of steady, inviscid, transonic flow past a wedge. The effects of truncation error on the pressure distribution, wave drag, sonic line, and shock position are investigated. By comparing the pressure drag on the wedge and wave drag due to the shocks, a supersonic-to-supersonic shock originating from the wedge shoulder is confirmed.
Finite-amplitude solutions in rotating Hagen-Poiseuille flow
NASA Astrophysics Data System (ADS)
Pier, Benoît; Kumar, Abhishek; Govindarajan, Rama
2015-11-01
While the pipe Poiseuille base flow is linearly stable at all Reynolds numbers, a small amount of rotation of the pipe around its axis induces linear instability beyond a low critical Reynolds number Rc ~= 83 [Pedley, J. Fluid Mech. 1969]. More recently [Fernandez-Feria and del Pino, Phys. Fluids 2002], this configuration has been shown to become absolutely unstable at Reynolds numbers of the same order of magnitude. Using direct numerical simulations, we investigate here finite-amplitude solutions resulting from saturation of exponentially growing small-amplitude initial perturbations. The base flow depends on two dynamical parameters (axial Reynolds number and rotation rate) and the initial perturbation is characterized by its axial wavenumber and its azimuthal mode number. The range of nonlinear waves prevailing in this configuration, the associated nonlinear dispersion relation and the spatial structure of these solutions are systematically obtained by exploring the parameter space. Funding from CEFIPRA is gratefully acknowledged.
Towards Accurate Prediction of Turbulent, Three-Dimensional, Recirculating Flows with the NCC
NASA Technical Reports Server (NTRS)
Iannetti, A.; Tacina, R.; Jeng, S.-M.; Cai, J.
2001-01-01
The National Combustion Code (NCC) was used to calculate the steady state, nonreacting flow field of a prototype Lean Direct Injection (LDI) swirler. This configuration used nine groups of eight holes drilled at a thirty-five degree angle to induce swirl. These nine groups created swirl in the same direction, or a corotating pattern. The static pressure drop across the holes was fixed at approximately four percent. Computations were performed on one quarter of the geometry, because the geometry is considered rotationally periodic every ninety degrees. The final computational grid used was approximately 2.26 million tetrahedral cells, and a cubic nonlinear k - epsilon model was used to model turbulence. The NCC results were then compared to time averaged Laser Doppler Velocimetry (LDV) data. The LDV measurements were performed on the full geometry, but four ninths of the geometry was measured. One-, two-, and three-dimensional representations of both flow fields are presented. The NCC computations compare both qualitatively and quantitatively well to the LDV data, but differences exist downstream. The comparison is encouraging, and shows that NCC can be used for future injector design studies. To improve the flow prediction accuracy of turbulent, three-dimensional, recirculating flow fields with the NCC, recommendations are given.
Yu, Yang; Zhang, Fan; Gao, Ming-Xin; Li, Hai-Tao; Li, Jing-Xing; Song, Wei; Huang, Xin-Sheng; Gu, Cheng-Xiong
2013-01-01
OBJECTIVES Intraoperative transit time flow measurement (TTFM) is widely used to assess anastomotic quality in coronary artery bypass grafting (CABG). However, in sequential vein grafting, the flow characteristics collected by the conventional TTFM method are usually associated with total graft flow and might not accurately indicate the quality of every distal anastomosis in a sequential graft. The purpose of our study was to examine a new TTFM method that could assess the quality of each distal anastomosis in a sequential graft more reliably than the conventional TTFM approach. METHODS Two TTFM methods were tested in 84 patients who underwent sequential saphenous off-pump CABG in Beijing An Zhen Hospital between April and August 2012. In the conventional TTFM method, normal blood flow in the sequential graft was maintained during the measurement, and the flow probe was placed a few centimetres above the anastomosis to be evaluated. In the new method, blood flow in the sequential graft was temporarily reduced during the measurement by placing an atraumatic bulldog clamp at the graft a few centimetres distal to the anastomosis to be evaluated, while the position of the flow probe remained the same as in the conventional method. This new TTFM method was named the flow reduction TTFM. Graft flow parameters measured by both methods were compared. RESULTS Compared with the conventional TTFM, the flow reduction TTFM resulted in significantly lower mean graft blood flow (P < 0.05); in contrast, yielded significantly higher pulsatility index (P < 0.05). Diastolic filling was not significantly different between the two methods and was >50% in both cases. Interestingly, the flow reduction TTFM identified two defective middle distal anastomoses that the conventional TTFM failed to detect. Graft flows near the defective distal anastomoses were improved substantially after revision. CONCLUSIONS In this study, we found that temporary reduction of graft flow during TTFM seemed to
Fibrillization kinetics of insulin solution in an interfacial shearing flow
NASA Astrophysics Data System (ADS)
Balaraj, Vignesh; McBride, Samantha; Hirsa, Amir; Lopez, Juan
2015-11-01
Although the association of fibril plaques with neurodegenerative diseases like Alzheimer's and Parkinson's is well established, in-depth understanding of the roles played by various physical factors in seeding and growth of fibrils is far from well known. Of the numerous factors affecting this complex phenomenon, the effect of fluid flow and shear at interfaces is paramount as it is ubiquitous and the most varying factor in vivo. Many amyloidogenic proteins have been found to denature upon contact at hydrophobic interfaces due to the self-assembling nature of protein in its monomeric state. Here, fibrillization kinetics of insulin solution is studied in an interfacial shearing flow. The transient surface rheological response of the insulin solution to the flow and its effect on the bulk fibrillization process has been quantified. Minute differences in hydrophobic characteristics between two variants of insulin- Human recombinant and Bovine insulin are found to result in very different responses. Results presented will be in the form of fibrillization assays, images of fibril plaques formed, and changes in surface rheological properties of the insulin solution. The interfacial velocity field, measured from images (via Brewster Angle Microscopy), is compared with computations. Supported by NNX13AQ22G, National Aeronautics and Space Administration.
A second-order accurate immersed boundary-lattice Boltzmann method for particle-laden flows
NASA Astrophysics Data System (ADS)
Zhou, Qiang; Fan, Liang-Shih
2014-07-01
A new immersed boundary-lattice Boltzmann method (IB-LBM) is presented for fully resolved simulations of incompressible viscous flows laden with rigid particles. The immersed boundary method (IBM) recently developed by Breugem (2012) [19] is adopted in the present method, development including the retraction technique, the multi-direct forcing method and the direct account of the inertia of the fluid contained within the particles. The present IB-LBM is, however, formulated with further improvement with the implementation of the high-order Runge-Kutta schemes in the coupled fluid-particle interaction. The major challenge to implement high-order Runge-Kutta schemes in the LBM is that the flow information such as density and velocity cannot be directly obtained at a fractional time step from the LBM since the LBM only provides the flow information at an integer time step. This challenge can be, however, overcome as given in the present IB-LBM by extrapolating the flow field around particles from the known flow field at the previous integer time step. The newly calculated fluid-particle interactions from the previous fractional time steps of the current integer time step are also accounted for in the extrapolation. The IB-LBM with high-order Runge-Kutta schemes developed in this study is validated by several benchmark applications. It is demonstrated, for the first time, that the IB-LBM has the capacity to resolve the translational and rotational motion of particles with the second-order accuracy. The optimal retraction distances for spheres and tubes that help the method achieve the second-order accuracy are found to be around 0.30 and -0.47 times of the lattice spacing, respectively. Simulations of the Stokes flow through a simple cubic lattice of rotational spheres indicate that the lift force produced by the Magnus effect can be very significant in view of the magnitude of the drag force when the practical rotating speed of the spheres is encountered. This finding
Recommendations for accurate numerical blood flow simulations of stented intracranial aneurysms.
Janiga, Gábor; Berg, Philipp; Beuing, Oliver; Neugebauer, Mathias; Gasteiger, Rocco; Preim, Bernhard; Rose, Georg; Skalej, Martin; Thévenin, Dominique
2013-06-01
The number of scientific publications dealing with stented intracranial aneurysms is rapidly increasing. Powerful computational facilities are now available; an accurate computational modeling of hemodynamics in patient-specific configurations is, however, still being sought. Furthermore, there is still no general agreement on the quantities that should be computed and on the most adequate analysis for intervention support. In this article, the accurate representation of patient geometry is first discussed, involving successive improvements. Concerning the second step, the mesh required for the numerical simulation is especially challenging when deploying a stent with very fine wire structures. Third, the description of the fluid properties is a major challenge. Finally, a founded quantitative analysis of the simulation results is obviously needed to support interventional decisions. In the present work, an attempt has been made to review the most important steps for a high-quality computational fluid dynamics computation of virtually stented intracranial aneurysms. In consequence, this leads to concrete recommendations, whereby the obtained results are not discussed for their medical relevance but for the evaluation of their quality. This investigation might hopefully be helpful for further studies considering stent deployment in patient-specific geometries, in particular regarding the generation of the most appropriate computational model. PMID:23729530
NASA Technical Reports Server (NTRS)
Wong, T. C.; Liu, C. H.; Geer, J.
1984-01-01
Approximate solutions for potential flow past an axisymmetric slender body and past a thin airfoil are calculated using a uniform perturbation method and then compared with either the exact analytical solution or the solution obtained using a purely numerical method. The perturbation method is based upon a representation of the disturbance flow as the superposition of singularities distributed entirely within the body, while the numerical (panel) method is based upon a distribution of singularities on the surface of the body. It is found that the perturbation method provides very good results for small values of the slenderness ratio and for small angles of attack. Moreover, for comparable accuracy, the perturbation method is simpler to implement, requires less computer memory, and generally uses less computation time than the panel method. In particular, the uniform perturbation method yields good resolution near the regions of the leading and trailing edges where other methods fail or require special attention.
Cobb, J.W.
1995-02-01
There is an increasing need for more accurate numerical methods for large-scale nonlinear magneto-fluid turbulence calculations. These methods should not only increase the current state of the art in terms of accuracy, but should also continue to optimize other desired properties such as simplicity, minimized computation, minimized memory requirements, and robust stability. This includes the ability to stably solve stiff problems with long time-steps. This work discusses a general methodology for deriving higher-order numerical methods. It also discusses how the selection of various choices can affect the desired properties. The explicit discussion focuses on third-order Runge-Kutta methods, including general solutions and five examples. The study investigates the linear numerical analysis of these methods, including their accuracy, general stability, and stiff stability. Additional appendices discuss linear multistep methods, discuss directions for further work, and exhibit numerical analysis results for some other commonly used lower-order methods.
NASA Astrophysics Data System (ADS)
Zhang, Xiang; Vu-Quoc, Loc
2007-07-01
We present in this paper the displacement-driven version of a tangential force-displacement (TFD) model that accounts for both elastic and plastic deformations together with interfacial friction occurring in collisions of spherical particles. This elasto-plastic frictional TFD model, with its force-driven version presented in [L. Vu-Quoc, L. Lesburg, X. Zhang. An accurate tangential force-displacement model for granular-flow simulations: contacting spheres with plastic deformation, force-driven formulation, Journal of Computational Physics 196(1) (2004) 298-326], is consistent with the elasto-plastic frictional normal force-displacement (NFD) model presented in [L. Vu-Quoc, X. Zhang. An elasto-plastic contact force-displacement model in the normal direction: displacement-driven version, Proceedings of the Royal Society of London, Series A 455 (1991) 4013-4044]. Both the NFD model and the present TFD model are based on the concept of additive decomposition of the radius of contact area into an elastic part and a plastic part. The effect of permanent indentation after impact is represented by a correction to the radius of curvature. The effect of material softening due to plastic flow is represented by a correction to the elastic moduli. The proposed TFD model is accurate, and is validated against nonlinear finite element analyses involving plastic flows in both the loading and unloading conditions. The proposed consistent displacement-driven, elasto-plastic NFD and TFD models are designed for implementation in computer codes using the discrete-element method (DEM) for granular-flow simulations. The model is shown to be accurate and is validated against nonlinear elasto-plastic finite-element analysis.
NASA Technical Reports Server (NTRS)
Hasiuk, Jan; Hindman, Richard; Iversen, James
1988-01-01
The azimuthal-invariant, three-dimensional cylindrical, incompressible Navier-Stokes equations are solved to steady state for a finite-length, physically realistic model. The numerical method relies on an alternating-direction implicit scheme that is formally second-order accurate in space and first-order accurate in time. The equations are linearized and uncoupled by evaluating variable coefficients at the previous time iteration. Wall grid clustering is provided by a Roberts transformation in radial and axial directions. A vorticity-velocity formulation is found to be preferable to a vorticity-streamfunction approach. Subject to no-slip, Dirichlet boundary conditions, except for the inner cylinder rotation velocity (impulsive start-up) and zero-flow initial conditions, nonturbulent solutions are obtained for sub- and supercritical Reynolds numbers of 100 to 400 for a finite geometry where R(outer)/R(inner) = 1.5, H/R(inner) = 0.73, and H/Delta-R = 1.5. An axially-stretched model solution is shown to asymptotically approach the one-dimensional analytic Couette solution at the cylinder midheight. Flowfield change from laminar to Taylor-vortex flow is discussed as a function of Reynolds number. Three-dimensional velocities, vorticity, and streamfunction are presented via two-dimensional graphs and three-dimensional surface and contour plots.
Exact solutions and physical analogies for unidirectional flows
NASA Astrophysics Data System (ADS)
Bazant, Martin Z.
2016-06-01
Unidirectional flow is the simplest phenomenon of fluid mechanics. Its mathematical description, the Dirichlet problem for Poisson's equation in two dimensions with constant forcing, arises in many physical contexts, such as the torsion of elastic beams, first solved by de Saint-Venant for complex shapes. Here the literature is unified and extended by identifying 17 physical analogies for unidirectional flow and describing their common mathematical structure. Besides classical analogies in fluid and solid mechanics, applications are discussed in stochastic processes (first passage in two dimensions), pattern formation (river growth by erosion), and electrokinetics (ion transport in nanochannels), which also involve Poisson's equation with nonconstant forcing. Methods are given to construct approximate geometries that admit exact solutions, by adding harmonic functions to quadratic forms or by truncating eigenfunction expansions. Exact solutions for given geometries are also derived by conformal mapping. We prove that the remarkable geometrical interpretation of Poiseuille flow in an equilateral triangular pipe (the product of the distances from an interior point to the sides) is only shared by parallel plates and unbounded equilateral wedges (with the third side hidden behind the apex). We also prove Onsager reciprocity for linear electrokinetic phenomena in straight pores of arbitrary shape and surface charge, based on the mathematics of unidirectional flow.
Stability of Inviscid Flow over Airfoils Admitting Multiple Numerical Solutions
NASA Astrophysics Data System (ADS)
Liu, Ya; Xiong, Juntao; Liu, Feng; Luo, Shijun
2012-11-01
Multiple numerical solutions at the same flight condition are found of inviscid transonic flow over certain airfoils (Jameson et al., AIAA 2011-3509) within some Mach number range. Both symmetric and asymmetric solutions exist for a symmetric airfoil at zero angle of attack. Global linear stability analysis of the multiple solutions is conducted. Linear perturbation equations of the Euler equations around a steady-state solution are formed and discretized numerically. An eigenvalue problem is then constructed using the modal analysis approach. Only a small portion of the eigen spectrum is needed and thus can be found efficiently by using Arnoldi's algorithm. The least stable or unstable mode corresponds to the eigenvalue with the largest real part. Analysis of the NACA 0012 airfoil indicates stability of symmetric solutions of the Euler equations at conditions where buffet is found from unsteady Navier-Stokes equations. Euler solutions of the same airfoil but modified to include the displacement thickness of the boundary layer computed from the Navier-Stokes equations, however, exhibit instability based on the present linear stability analysis. Graduate Student.
Spectrally-accurate algorithm for the analysis of flows in two-dimensional vibrating channels
NASA Astrophysics Data System (ADS)
Zandi, S.; Mohammadi, A.; Floryan, J. M.
2015-11-01
A spectral algorithm based on the immersed boundary conditions (IBC) concept has been developed for the analysis of flows in channels bounded by vibrating walls. The vibrations take the form of travelling waves of arbitrary profile. The algorithm uses a fixed computational domain with the flow domain immersed in its interior. Boundary conditions enter the algorithm in the form of constraints. The spatial discretization uses a Fourier expansion in the stream-wise direction and a Chebyshev expansion in the wall-normal direction. Use of the Galileo transformation converts the unsteady problem into a steady one. An efficient solver which takes advantage of the structure of the coefficient matrix has been used. It is demonstrated that the method can be extended to more extreme geometries using the overdetermined formulation. Various tests confirm the spectral accuracy of the algorithm.
An Integrated Numerical Hydrodynamic Shallow Flow-Solute Transport Model for Urban Area
NASA Astrophysics Data System (ADS)
Alias, N. A.; Mohd Sidek, L.
2016-03-01
The rapidly changing on land profiles in the some urban areas in Malaysia led to the increasing of flood risk. Extensive developments on densely populated area and urbanization worsen the flood scenario. An early warning system is really important and the popular method is by numerically simulating the river and flood flows. There are lots of two-dimensional (2D) flood model predicting the flood level but in some circumstances, still it is difficult to resolve the river reach in a 2D manner. A systematic early warning system requires a precisely prediction of flow depth. Hence a reliable one-dimensional (1D) model that provides accurate description of the flow is essential. Research also aims to resolve some of raised issues such as the fate of pollutant in river reach by developing the integrated hydrodynamic shallow flow-solute transport model. Presented in this paper are results on flow prediction for Sungai Penchala and the convection-diffusion of solute transports simulated by the developed model.
An affordable and accurate conductivity probe for density measurements in stratified flows
NASA Astrophysics Data System (ADS)
Carminati, Marco; Luzzatto-Fegiz, Paolo
2015-11-01
In stratified flow experiments, conductivity (combined with temperature) is often used to measure density. The probes typically used can provide very fine spatial scales, but can be fragile, expensive to replace, and sensitive to environmental noise. A complementary instrument, comprising a low-cost conductivity probe, would prove valuable in a wide range of applications where resolving extremely small spatial scales is not needed. We propose using micro-USB cables as the actual conductivity sensors. By removing the metallic shield from a micro-B connector, 5 gold-plated microelectrodes are exposed and available for 4-wire measurements. These have a cell constant ~550m-1, an intrinsic thermal noise of at most 30pA/Hz1/2, as well as sub-millisecond time response, making them highly suitable for many stratified flow measurements. In addition, we present the design of a custom electronic board (Arduino-based and Matlab-controlled) for simultaneous acquisition from 4 sensors, with resolution (in conductivity, and resulting density) exceeding the performance of typical existing probes. We illustrate the use of our conductivity-measuring system through stratified flow experiments, and describe plans to release simple instructions to construct our complete system for around 200.
Multigrid Acceleration of Time-Accurate DNS of Compressible Turbulent Flow
NASA Technical Reports Server (NTRS)
Broeze, Jan; Geurts, Bernard; Kuerten, Hans; Streng, Martin
1996-01-01
An efficient scheme for the direct numerical simulation of 3D transitional and developed turbulent flow is presented. Explicit and implicit time integration schemes for the compressible Navier-Stokes equations are compared. The nonlinear system resulting from the implicit time discretization is solved with an iterative method and accelerated by the application of a multigrid technique. Since we use central spatial discretizations and no artificial dissipation is added to the equations, the smoothing method is less effective than in the more traditional use of multigrid in steady-state calculations. Therefore, a special prolongation method is needed in order to obtain an effective multigrid method. This simulation scheme was studied in detail for compressible flow over a flat plate. In the laminar regime and in the first stages of turbulent flow the implicit method provides a speed-up of a factor 2 relative to the explicit method on a relatively coarse grid. At increased resolution this speed-up is enhanced correspondingly.
Solution of 3-dimensional time-dependent viscous flows. Part 1: Investigation of candidate algoriths
NASA Technical Reports Server (NTRS)
Weinberg, B. C.; Mcdonald, H.
1979-01-01
There is considerable interest in developing a numerical scheme for solving the time dependent viscous compressible three dimensional flow to aid in the design of helicopter rotors. Numerical algorithms are examined to determine their overall suitability for the efficient and routine solution of an appropriate system of partial differential equations. It is concluded that a consistently split time linearized block implicit scheme using either quintic B spline collocation or the generalized operator compact implicit approach to generate a fourth order accurate algorithm is particularly well suited for use on the present problem. High cell Reynolds number behavior leads to favoring the generalized operator compact implicit approach over the quintic B spline collocation method.
An efficient solution for hazardous geophysical flows simulation using GPUs
NASA Astrophysics Data System (ADS)
Lacasta, A.; Juez, C.; Murillo, J.; García-Navarro, P.
2015-05-01
The movement of poorly sorted material over steep areas constitutes a hazardous environmental problem. Computational tools help in the understanding and predictions of such landslides. The main drawback is the high computational effort required for obtaining accurate numerical solutions due to the high number of cells involved in the calculus. In order to overcome this problem, this work proposes the use of GPUs for decreasing significantly the CPU simulation time. The numerical scheme implemented in GPU is based on a finite volume scheme and it was validated in previous work with exact solutions and experimental data. The computational cost time obtained with the Graphical Hardware technology, GPU, is compared against Single-Core (sequential) and Multi-Core (parallel) CPU implementations. The GPU implementation allows to reduce the computational cost time in two orders of magnitude.
A second-order accurate immersed boundary-lattice Boltzmann method for particle-laden flows
Zhou, Qiang; Fan, Liang-Shih
2014-07-01
A new immersed boundary-lattice Boltzmann method (IB-LBM) is presented for fully resolved simulations of incompressible viscous flows laden with rigid particles. The immersed boundary method (IBM) recently developed by Breugem (2012) [19] is adopted in the present method, development including the retraction technique, the multi-direct forcing method and the direct account of the inertia of the fluid contained within the particles. The present IB-LBM is, however, formulated with further improvement with the implementation of the high-order Runge–Kutta schemes in the coupled fluid–particle interaction. The major challenge to implement high-order Runge–Kutta schemes in the LBM is that the flow information such as density and velocity cannot be directly obtained at a fractional time step from the LBM since the LBM only provides the flow information at an integer time step. This challenge can be, however, overcome as given in the present IB-LBM by extrapolating the flow field around particles from the known flow field at the previous integer time step. The newly calculated fluid–particle interactions from the previous fractional time steps of the current integer time step are also accounted for in the extrapolation. The IB-LBM with high-order Runge–Kutta schemes developed in this study is validated by several benchmark applications. It is demonstrated, for the first time, that the IB-LBM has the capacity to resolve the translational and rotational motion of particles with the second-order accuracy. The optimal retraction distances for spheres and tubes that help the method achieve the second-order accuracy are found to be around 0.30 and −0.47 times of the lattice spacing, respectively. Simulations of the Stokes flow through a simple cubic lattice of rotational spheres indicate that the lift force produced by the Magnus effect can be very significant in view of the magnitude of the drag force when the practical rotating speed of the spheres is encountered
NASA Astrophysics Data System (ADS)
Bause, Markus
2008-02-01
In this work we study mixed finite element approximations of Richards' equation for simulating variably saturated subsurface flow and simultaneous reactive solute transport. Whereas higher order schemes have proved their ability to approximate reliably reactive solute transport (cf., e.g. [Bause M, Knabner P. Numerical simulation of contaminant biodegradation by higher order methods and adaptive time stepping. Comput Visual Sci 7;2004:61-78]), the Raviart- Thomas mixed finite element method ( RT0) with a first order accurate flux approximation is popular for computing the underlying water flow field (cf. [Bause M, Knabner P. Computation of variably saturated subsurface flow by adaptive mixed hybrid finite element methods. Adv Water Resour 27;2004:565-581, Farthing MW, Kees CE, Miller CT. Mixed finite element methods and higher order temporal approximations for variably saturated groundwater flow. Adv Water Resour 26;2003:373-394, Starke G. Least-squares mixed finite element solution of variably saturated subsurface flow problems. SIAM J Sci Comput 21;2000:1869-1885, Younes A, Mosé R, Ackerer P, Chavent G. A new formulation of the mixed finite element method for solving elliptic and parabolic PDE with triangular elements. J Comp Phys 149;1999:148-167, Woodward CS, Dawson CN. Analysis of expanded mixed finite element methods for a nonlinear parabolic equation modeling flow into variably saturated porous media. SIAM J Numer Anal 37;2000:701-724]). This combination might be non-optimal. Higher order techniques could increase the accuracy of the flow field calculation and thereby improve the prediction of the solute transport. Here, we analyse the application of the Brezzi- Douglas- Marini element ( BDM1) with a second order accurate flux approximation to elliptic, parabolic and degenerate problems whose solutions lack the regularity that is assumed in optimal order error analyses. For the flow field calculation a superiority of the BDM1 approach to the RT0 one is
NASA Astrophysics Data System (ADS)
Chae, Kyu-Hyun
2002-04-01
Fourier series solutions to the deflection and magnification by a family of three-dimensional cusped two-power-law ellipsoidal mass distributions are presented. The cusped two-power-law ellipsoidal mass distributions are characterized by inner and outer power-law radial indices and a break (or transition) radius. The model family includes mass models mimicking Jaffe, Hernquist, and η models and dark matter halo profiles from numerical simulations. The Fourier series solutions for the cusped two-power-law mass distributions are relatively simple and allow a very fast calculation, even for a chosen small fractional calculational error (e.g., 10-5). These results will be particularly useful for studying lensed systems that provide a number of accurate lensing constraints and for systematic analyses of large numbers of lenses. Subroutines employing these results for the two-power-law model and the results by Chae, Khersonsky, & Turnshek for the generalized single-power-law mass model are made publicly available.
The spatially nonuniform convergence of the numerical solution of flows
NASA Technical Reports Server (NTRS)
Panaras, Argyris G.
1987-01-01
The spatial distribution of the numerical disturbances that are generated during the numerical solution of a flow is examined. It is shown that the distribution of the disturbances is not uniform. In regions where the structure of a flow is simple, the magnitude of the generated disturbances is small and their decay is fast. However, in complex flow regions, as in separation and vortical areas, large magnitude disturbances appear and their decay may be very slow. The observed nonuniformity of the numerical disturbances makes possible the reduction of the calculation time by application of what may be called the partial-grid calculation technique, in which a major part of the calculation procedure is applied in selective subregions, where the velocity disturbances are large, and not within the whole grid. This technique is expected to prove beneficial in large-scale calculations such as the flow about complete aircraft configurations at high angle of attack. Also, it has been shown that if the Navier-Stokes equations are written in a generalized coordinate system, then in regions in which the grid is fine, such as near solid boundaries, the norms become infinitesimally small, because in these regions the Jacobian has very large values. Thus, the norms, unless they are unscaled by the Jacobians, reflect only the changes that happen at the outer boundaries of the computation domain, where the value of the Jacobian approaches unity, and not in the whole flow field.
NASA Astrophysics Data System (ADS)
Liu, Nansheng; Khomami, Bamin
2011-11-01
Despite tremendous progress in development of numerical techniques and constitutive theories for polymeric fluids in the past decade, Direct Numerical Simulation (DNS) of elastic turbulence has posed tremendous challenges to researchers engaged in developing first principles models and simulations that can accurately and robustly predict the dynamical behavior of polymeric flows. In this presentation, we report the first DNS of elastic turbulence in the Taylor-Couette (TC) flow. Specifically, our computations with prototypical constitutive equations for dilute polymeric solutions, such as the FENE-P model are capable of reproducing the essential features of the experimentally observed elastic turbulence in TC flow of this class of fluids, namely, randomly fluctuating fluid motion excited in a broad range of spatial and temporal scales, and a significant increase of the flow resistance. Moreover, the experimentally measured Power Spectral Density of radial velocity fluctuations, i.e., two contiguous regions of power-law decay, -1.1 at lower frequencies and -2.2 at high-frequencies is accurately computed. We would like to thank NSF through grant CBET-0755269 and NSFC through grant NO. 10972211 for supporting of this work.
Ghost Particle Velocimetry: Accurate 3D Flow Visualization Using Standard Lab Equipment
NASA Astrophysics Data System (ADS)
Buzzaccaro, Stefano; Secchi, Eleonora; Piazza, Roberto
2013-07-01
We describe and test a new approach to particle velocimetry, based on imaging and cross correlating the scattering speckle pattern generated on a near-field plane by flowing tracers with a size far below the diffraction limit, which allows reconstructing the velocity pattern in microfluidic channels without perturbing the flow. As a matter of fact, adding tracers is not even strictly required, provided that the sample displays sufficiently refractive-index fluctuations. For instance, phase separation in liquid mixtures in the presence of shear is suitable to be directly investigated by this “ghost particle velocimetry” technique, which just requires a microscope with standard lamp illumination equipped with a low-cost digital camera. As a further bonus, the peculiar spatial coherence properties of the illuminating source, which displays a finite longitudinal coherence length, allows for a 3D reconstruction of the profile with a resolution of few tenths of microns and makes the technique suitable to investigate turbid samples with negligible multiple scattering effects.
Accurate Angle Estimator for High-Frame-Rate 2-D Vector Flow Imaging.
Villagomez Hoyos, Carlos Armando; Stuart, Matthias Bo; Hansen, Kristoffer Lindskov; Nielsen, Michael Bachmann; Jensen, Jorgen Arendt
2016-06-01
This paper presents a novel approach for estimating 2-D flow angles using a high-frame-rate ultrasound method. The angle estimator features high accuracy and low standard deviation (SD) over the full 360° range. The method is validated on Field II simulations and phantom measurements using the experimental ultrasound scanner SARUS and a flow rig before being tested in vivo. An 8-MHz linear array transducer is used with defocused beam emissions. In the simulations of a spinning disk phantom, a 360° uniform behavior on the angle estimation is observed with a median angle bias of 1.01° and a median angle SD of 1.8°. Similar results are obtained on a straight vessel for both simulations and measurements, where the obtained angle biases are below 1.5° with SDs around 1°. Estimated velocity magnitudes are also kept under 10% bias and 5% relative SD in both simulations and measurements. An in vivo measurement is performed on a carotid bifurcation of a healthy individual. A 3-s acquisition during three heart cycles is captured. A consistent and repetitive vortex is observed in the carotid bulb during systoles. PMID:27093598
Step Bunching: Influence of Impurities and Solution Flow
NASA Technical Reports Server (NTRS)
Chernov, A. A.; Vekilov, P. G.; Coriell, S. R.; Murray, B. T.; McFadden, G. B.
1999-01-01
Step bunching results in striations even at relatively early stages of its development and in inclusions of mother liquor at the later stages. Therefore, eliminating step bunching is crucial for high crystal perfection. At least 5 major effects causing and influencing step bunching are known: (1) Basic morphological instability of stepped interfaces. It is caused by concentration gradient in the solution normal to the face and by the redistribution of solute tangentially to the interface which redistribution enhances occasional perturbations in step density due to various types of noise; (2) Aggravation of the above basic instability by solution flowing tangentially to the face in the same directions as the steps or stabilization of equidistant step train if these flows are antiparallel; (3) Enhanced bunching at supersaturation where step velocity v increases with relative supersaturation s much faster than linear. This v(s) dependence is believed to be associated with impurities. The impurities of which adsorption time is comparable with the time needed to deposit one lattice layer may also be responsible for bunching; (4) Very intensive solution flow stabilizes growing interface even at parallel solution and step flows; (5) Macrosteps were observed to nucleate at crystal corners and edges. Numerical simulation, assuming step-step interactions via surface diffusion also show that step bunching may be induced by random step nucleation at the facet edge and by discontinuity in the step density (a ridge) somewhere in the middle of a face. The corresponding bunching patterns produce the ones observed in experiment. The nature of step bunching generated at the corners and edges and by dislocation step sources, as well as the also relative importance and interrelations between mechanisms 1-5 is not clear, both from experimental and theoretical standpoints. Furthermore, several laws controlling the evolution of existing step bunches have been suggested, though
NASA Technical Reports Server (NTRS)
Usab, William J., Jr.; Jiang, Yi-Tsann
1991-01-01
The objective of the present research is to develop a general solution adaptive scheme for the accurate prediction of inviscid quasi-three-dimensional flow in advanced compressor and turbine designs. The adaptive solution scheme combines an explicit finite-volume time-marching scheme for unstructured triangular meshes and an advancing front triangular mesh scheme with a remeshing procedure for adapting the mesh as the solution evolves. The unstructured flow solver has been tested on a series of two-dimensional airfoil configurations including a three-element analytic test case presented here. Mesh adapted quasi-three-dimensional Euler solutions are presented for three spanwise stations of the NASA rotor 67 transonic fan. Computed solutions are compared with available experimental data.
Implementation of two-component advective flow solution in XSPEC
NASA Astrophysics Data System (ADS)
Debnath, Dipak; Chakrabarti, Sandip K.; Mondal, Santanu
2014-05-01
Spectral and temporal properties of black hole candidates can be explained reasonably well using Chakrabarti-Titarchuk solution of two-component advective flow (TCAF). This model requires two accretion rates, namely the Keplerian disc accretion rate and the halo accretion rate, the latter being composed of a sub-Keplerian, low-angular-momentum flow which may or may not develop a shock. In this solution, the relevant parameter is the relative importance of the halo (which creates the Compton cloud region) rate with respect to the Keplerian disc rate (soft photon source). Though this model has been used earlier to manually fit data of several black hole candidates quite satisfactorily, for the first time, we made it user friendly by implementing it into XSPEC software of Goddard Space Flight Center (GSFC)/NASA. This enables any user to extract physical parameters of the accretion flows, such as two accretion rates, the shock location, the shock strength, etc., for any black hole candidate. We provide some examples of fitting a few cases using this model. Most importantly, unlike any other model, we show that TCAF is capable of predicting timing properties from the spectral fits, since in TCAF, a shock is responsible for deciding spectral slopes as well as quasi-periodic oscillation frequencies. L86
NASA Astrophysics Data System (ADS)
Sakai, Yasumasa; Taki, Hirofumi; Kanai, Hiroshi
2016-07-01
In our previous study, the viscoelasticity of the radial artery wall was estimated to diagnose endothelial dysfunction using a high-frequency (22 MHz) ultrasound device. In the present study, we employed a commercial ultrasound device (7.5 MHz) and estimated the viscoelasticity using arterial pressure and diameter, both of which were measured at the same position. In a phantom experiment, the proposed method successfully estimated the elasticity and viscosity of the phantom with errors of 1.8 and 30.3%, respectively. In an in vivo measurement, the transient change in the viscoelasticity was measured for three healthy subjects during flow-mediated dilation (FMD). The proposed method revealed the softening of the arterial wall originating from the FMD reaction within 100 s after avascularization. These results indicate the high performance of the proposed method in evaluating vascular endothelial function just after avascularization, where the function is difficult to be estimated by a conventional FMD measurement.
NASA Technical Reports Server (NTRS)
Duque, Earl P. N.; Biswas, Rupak; Strawn, Roger C.
1995-01-01
This paper summarizes a method that solves both the three dimensional thin-layer Navier-Stokes equations and the Euler equations using overset structured and solution adaptive unstructured grids with applications to helicopter rotor flowfields. The overset structured grids use an implicit finite-difference method to solve the thin-layer Navier-Stokes/Euler equations while the unstructured grid uses an explicit finite-volume method to solve the Euler equations. Solutions on a helicopter rotor in hover show the ability to accurately convect the rotor wake. However, isotropic subdivision of the tetrahedral mesh rapidly increases the overall problem size.
A second-order accurate kinetic-theory-based method for inviscid compressible flows
NASA Technical Reports Server (NTRS)
Deshpande, Suresh M.
1986-01-01
An upwind method for the numerical solution of the Euler equations is presented. This method, called the kinetic numerical method (KNM), is based on the fact that the Euler equations are moments of the Boltzmann equation of the kinetic theory of gases when the distribution function is Maxwellian. The KNM consists of two phases, the convection phase and the collision phase. The method is unconditionally stable and explicit. It is highly vectorizable and can be easily made total variation diminishing for the distribution function by a suitable choice of the interpolation strategy. The method is applied to a one-dimensional shock-propagation problem and to a two-dimensional shock-reflection problem.
TRIM—3D: a three-dimensional model for accurate simulation of shallow water flow
Casulli, Vincenzo; Bertolazzi, Enrico; Cheng, Ralph T.
1993-01-01
A semi-implicit finite difference formulation for the numerical solution of three-dimensional tidal circulation is discussed. The governing equations are the three-dimensional Reynolds equations in which the pressure is assumed to be hydrostatic. A minimal degree of implicitness has been introduced in the finite difference formula so that the resulting algorithm permits the use of large time steps at a minimal computational cost. This formulation includes the simulation of flooding and drying of tidal flats, and is fully vectorizable for an efficient implementation on modern vector computers. The high computational efficiency of this method has made it possible to provide the fine details of circulation structure in complex regions that previous studies were unable to obtain. For proper interpretation of the model results suitable interactive graphics is also an essential tool.
Ma, Rui; Zheng, Chunmiao; Tonkin, Matt; Zachara, John M
2011-04-01
Correct interpretation of tracer test data is critical for understanding transport processes in the subsurface. This task can be greatly complicated by the presence of intraborehole flows in a highly dynamic flow environment. At a new tracer test site (Hanford IFRC) a dynamic flow field created by changes in the stage of the adjacent Columbia River, coupled with a heterogeneous hydraulic conductivity distribution, leads to considerable variations in vertical hydraulic gradients. These variations, in turn, create intraborehole flows in fully-screened (6.5m) observation wells with frequently alternating upward and downward movement. This phenomenon, in conjunction with a highly permeable aquifer formation and small horizontal hydraulic gradients, makes modeling analysis and model calibration a formidable challenge. Groundwater head data alone were insufficient to define the flow model boundary conditions, and the movement of the tracer was highly sensitive to the dynamics of the flow field. This study shows that model calibration can be significantly improved by explicitly considering (a) dynamic flow model boundary conditions and (b) intraborehole flow. The findings from this study underscore the difficulties in interpreting tracer tests and understanding solute transport under highly dynamic flow conditions. PMID:21216023
NASA Astrophysics Data System (ADS)
Xu, Li; Weng, Peifen
2014-02-01
An improved fifth-order weighted essentially non-oscillatory (WENO-Z) scheme combined with the moving overset grid technique has been developed to compute unsteady compressible viscous flows on the helicopter rotor in forward flight. In order to enforce periodic rotation and pitching of the rotor and relative motion between rotor blades, the moving overset grid technique is extended, where a special judgement standard is presented near the odd surface of the blade grid during search donor cells by using the Inverse Map method. The WENO-Z scheme is adopted for reconstructing left and right state values with the Roe Riemann solver updating the inviscid fluxes and compared with the monotone upwind scheme for scalar conservation laws (MUSCL) and the classical WENO scheme. Since the WENO schemes require a six point stencil to build the fifth-order flux, the method of three layers of fringes for hole boundaries and artificial external boundaries is proposed to carry out flow information exchange between chimera grids. The time advance on the unsteady solution is performed by the full implicit dual time stepping method with Newton type LU-SGS subiteration, where the solutions of pseudo steady computation are as the initial fields of the unsteady flow computation. Numerical results on non-variable pitch rotor and periodic variable pitch rotor in forward flight reveal that the approach can effectively capture vortex wake with low dissipation and reach periodic solutions very soon.
Workshop on electrodes for flowing solution batteries. Summary report
Nanis, L.
1981-02-01
The electrochemical technology of aqueous secondary cells with flowing electrolyte solutions was the subject of a workshop sponsored by EPRI with the cooperation of DOE. The workshop was held in Tampa, Florida, 5-7 November 1979, and was attended by a select group drawn from advanced battery developers, government agencies, universities, and research organizations. The workshop general objectives were to look at the significant parameters believed to govern the performance of the two basic types of electrodes now in use; namely, a porous flow-through electrode (PFTE), and an impervious flow-by electrode. Progress, problems, and prospects were informally discussed. Brief critical reviews were given by session chairmen as a means of introducing each of the key topics (Current Distribution in FTPE, Conversion Efficiency, Segmented FTPE Studies, General Discussion on FTPF Parameters, Surface Activation, Application of FTPE to Waste Recovery, Exxon Zinc-Bromine Flow-By System, FTPE In NASA Redox Energy Storage, and Application of FTPE In Lockheed Zinc/Ferricyanide Redox System). The interaction of this diverse group of engineers and scientists was said by all to be of great benefit in widening understanding of the problems and possible future approaches to new work. The main needs for future work that were identified in the final discussion session among the participants were: (1) engineering analysis, (2) porous structures, (3) materials characteristics, and (4) chemical characteristics. In generally comparing flow-through to flow-by electrodes, there were some surprising differences arising from experimental results that did not fit conventional thinking.
Lie group analysis and similarity solution for fractional Blasius flow
NASA Astrophysics Data System (ADS)
Pan, Mingyang; Zheng, Liancun; Liu, Fawang; Zhang, Xinxin
2016-08-01
This paper presents an investigation for boundary layer flow of viscoelastic fluids past a flat plate. Fractional-order Blasius equation with spatial fractional Riemann-Liouville derivative is derived firstly by using Lie group transformation. The solution is obtained numerically by the generalized shooting method, employing the shifted Grünwald formula and classical fourth order Runge-Kutta method as the iterative scheme. The effects of the order of fractional derivative and the generalized Reynolds number on the velocity profiles are analyzed and discussed. Numerical results show that the smaller the value of the fractional order derivative leads to the faster velocity of viscoelastic fluids near the plate but not to hold near the outer flow. As the Reynolds number increases, the fluid is moving faster in the whole boundary layer consistently.
Nonunique solutions to the transonic potential flow equation
NASA Technical Reports Server (NTRS)
Salas, M. D.; Gumbert, C. R.; Turkel, E.
1984-01-01
Steinhoff and Jameson (1981) have shown that within a certain range of angle of attack and freestream Mach number, numerical solutions of the full-potential equation for flow past an airfoil are not unique. This study was mainly concerned with showing that the anomaly is inherent to the partial-differential equation governing the flow and not a result of its discrete representation. Steinhoff and Jameson conjectured that the anomaly may have a physical basis. The present investigation has two objectives. Results are to be presented which indicate that the anomaly is due to a breakdown in the potential approximation, rather than a phenomenon associated with the inviscid flowfield. The second objective is to show that the lift coefficient, predicted by the potential equation, is a smooth but multivalued function of the angle of attack.
Numerical solution of periodic vortical flows about a thin airfoil
NASA Technical Reports Server (NTRS)
Scott, James R.; Atassi, Hafiz M.
1989-01-01
A numerical method is developed for computing periodic, three-dimensional, vortical flows around isolated airfoils. The unsteady velocity is split into a vortical component which is a known function of the upstream flow conditions and the Lagrangian coordinates of the mean flow, and an irrotational field whose potential satisfies a nonconstant-coefficient, inhomogeneous, convective wave equation. Solutions for thin airfoils at zero degrees incidence to the mean flow are presented in this paper. Using an elliptic coordinate transformation, the computational domain is transformed into a rectangle. The Sommerfeld radiation condition is applied to the unsteady pressure on the grid line corresponding to the far field boundary. The results are compared with a Possio solver, and it is shown that for maximum accuracy the grid should depend on both the Mach number and reduced frequency. Finally, in order to assess the range of validity of the classical thin airfoil approximation, results for airfoils with zero thickness are compared with results for airfoils with small thickness.
NASA Technical Reports Server (NTRS)
Chang, Chau-Lyan; Venkatachari, Balaji Shankar; Cheng, Gary
2013-01-01
With the wide availability of affordable multiple-core parallel supercomputers, next generation numerical simulations of flow physics are being focused on unsteady computations for problems involving multiple time scales and multiple physics. These simulations require higher solution accuracy than most algorithms and computational fluid dynamics codes currently available. This paper focuses on the developmental effort for high-fidelity multi-dimensional, unstructured-mesh flow solvers using the space-time conservation element, solution element (CESE) framework. Two approaches have been investigated in this research in order to provide high-accuracy, cross-cutting numerical simulations for a variety of flow regimes: 1) time-accurate local time stepping and 2) highorder CESE method. The first approach utilizes consistent numerical formulations in the space-time flux integration to preserve temporal conservation across the cells with different marching time steps. Such approach relieves the stringent time step constraint associated with the smallest time step in the computational domain while preserving temporal accuracy for all the cells. For flows involving multiple scales, both numerical accuracy and efficiency can be significantly enhanced. The second approach extends the current CESE solver to higher-order accuracy. Unlike other existing explicit high-order methods for unstructured meshes, the CESE framework maintains a CFL condition of one for arbitrarily high-order formulations while retaining the same compact stencil as its second-order counterpart. For large-scale unsteady computations, this feature substantially enhances numerical efficiency. Numerical formulations and validations using benchmark problems are discussed in this paper along with realistic examples.
NASA Astrophysics Data System (ADS)
Hrubý, Jan
2012-04-01
Mathematical modeling of the non-equilibrium condensing transonic steam flow in the complex 3D geometry of a steam turbine is a demanding problem both concerning the physical concepts and the required computational power. Available accurate formulations of steam properties IAPWS-95 and IAPWS-IF97 require much computation time. For this reason, the modelers often accept the unrealistic ideal-gas behavior. Here we present a computation scheme based on a piecewise, thermodynamically consistent representation of the IAPWS-95 formulation. Density and internal energy are chosen as independent variables to avoid variable transformations and iterations. On the contrary to the previous Tabular Taylor Series Expansion Method, the pressure and temperature are continuous functions of the independent variables, which is a desirable property for the solution of the differential equations of the mass, energy, and momentum conservation for both phases.
A detailed study of mean-flow solutions for stability analysis of transitional flows
NASA Technical Reports Server (NTRS)
Ramakrishnan, R.; Vatsa, V.; Otto, J.; Kumar, A.
1993-01-01
A finite-volume upwind-difference parabolized Navier-Stokes code is utilized to obtain laminar mean-flow solutions at Mach 3.5 on a half-angle cone of 5 deg at an angle-of-attack of 2 deg. A detailed study is conducted on this configuration; the main focus is the velocity profiles in the leeward and windward symmetry planes at various axial locations. Comparisons of the solution profiles are made with both a central-difference code that incorporates scalar and matrix dissipation models and another state-of-the-art upwind-difference finitevolume code. The results obtained emphasize the importance of using matrix dissipation models for schemes that require explicit artificial dissipation. These results also illustrate the accuracy and efficiency of the planeby-plane marching procedure for computing mean-flow solutions for predicting the onset of transition with linear instability.
Numerical error in groundwater flow and solute transport simulation
NASA Astrophysics Data System (ADS)
Woods, Juliette A.; Teubner, Michael D.; Simmons, Craig T.; Narayan, Kumar A.
2003-06-01
Models of groundwater flow and solute transport may be affected by numerical error, leading to quantitative and qualitative changes in behavior. In this paper we compare and combine three methods of assessing the extent of numerical error: grid refinement, mathematical analysis, and benchmark test problems. In particular, we assess the popular solute transport code SUTRA [Voss, 1984] as being a typical finite element code. Our numerical analysis suggests that SUTRA incorporates a numerical dispersion error and that its mass-lumped numerical scheme increases the numerical error. This is confirmed using a Gaussian test problem. A modified SUTRA code, in which the numerical dispersion is calculated and subtracted, produces better results. The much more challenging Elder problem [Elder, 1967; Voss and Souza, 1987] is then considered. Calculation of its numerical dispersion coefficients and numerical stability show that the Elder problem is prone to error. We confirm that Elder problem results are extremely sensitive to the simulation method used.
NASA Astrophysics Data System (ADS)
Mathias, Simon A.; Moutsopoulos, Konstantinos N.
2016-07-01
Understanding the hydraulics around injection and production wells in unconfined aquifers associated with rainwater and reclaimed water aquifer storage schemes is an issue of increasing importance. Much work has been done previously to understand the mathematics associated with Darcy's law in this context. However, groundwater flow velocities around injection and production wells are likely to be sufficiently large such as to induce significant non-Darcy effects. This article presents a mathematical analysis to look at Forchheimer's equation in the context of water injection and water production in unconfined aquifers. Three different approximate solutions are derived using quasi-steady-state assumptions and the method of matched asymptotic expansion. The resulting approximate solutions are shown to be accurate for a wide range of practical scenarios by comparison with a finite difference solution to the full problem of concern. The approximate solutions have led to an improved understanding of the flow dynamics. They can also be used as verification tools for future numerical models in this context.
Solution of the complete Curtiss-Bird model for polymeric liquids subjected to simple shear flow
NASA Astrophysics Data System (ADS)
Stephanou, Pavlos S.; Kröger, Martin
2016-03-01
The complete kinetic theory model for concentrated polymer solutions and melts proposed by Curtiss and Bird is solved for shear flow: (a) analytically by providing a solution for the single-link (or configurational) distribution function as a real basis spherical harmonics expansion and then calculating the materials functions in shear flow up to second order in the dimensionless shear rate and, (b) numerically via the execution of Brownian dynamics simulations. These two methods are actually complementary to each other as the former is accurate only for small dimensionless shear rates where the latter produces results with increasingly large uncertainties. The analytical expansions of the material functions with respect to the dimensionless shear rate reduce to those of the extensively studied, simplified Curtiss-Bird model when ɛ' = 0, and to the rigid rod when ɛ' = 1. It is known that the power-law behavior at high shear rates is very different for these two extremal cases. We employ Brownian dynamics simulation to not only recover the limiting cases but to find a gradual variation of the power-law behaviors at large dimensionless shear rates upon varying ɛ'. The fact that experimental data are usually located between these two extremes strongly advocates the significance of studying the solution of the Curtiss-Bird model. This is exemplified in this work by comparing the solution of this model with available rheological data for semiflexible biological systems that are clearly not captured by the original Doi-Edwards or simplified Curtiss-Bird models.
Solution of the complete Curtiss-Bird model for polymeric liquids subjected to simple shear flow.
Stephanou, Pavlos S; Kröger, Martin
2016-03-28
The complete kinetic theory model for concentrated polymer solutions and melts proposed by Curtiss and Bird is solved for shear flow: (a) analytically by providing a solution for the single-link (or configurational) distribution function as a real basis spherical harmonics expansion and then calculating the materials functions in shear flow up to second order in the dimensionless shear rate and, (b) numerically via the execution of Brownian dynamics simulations. These two methods are actually complementary to each other as the former is accurate only for small dimensionless shear rates where the latter produces results with increasingly large uncertainties. The analytical expansions of the material functions with respect to the dimensionless shear rate reduce to those of the extensively studied, simplified Curtiss-Bird model when ε' = 0, and to the rigid rod when ε' = 1. It is known that the power-law behavior at high shear rates is very different for these two extremal cases. We employ Brownian dynamics simulation to not only recover the limiting cases but to find a gradual variation of the power-law behaviors at large dimensionless shear rates upon varying ε'. The fact that experimental data are usually located between these two extremes strongly advocates the significance of studying the solution of the Curtiss-Bird model. This is exemplified in this work by comparing the solution of this model with available rheological data for semiflexible biological systems that are clearly not captured by the original Doi-Edwards or simplified Curtiss-Bird models. PMID:27036477
New discretization and solution techniques for incompressible viscous flow problems
NASA Technical Reports Server (NTRS)
Gunzburger, M. D.; Nicolaides, R. A.; Liu, C. H.
1983-01-01
Several topics arising in the finite element solution of the incompressible Navier-Stokes equations are considered. Specifically, the question of choosing finite element velocity/pressure spaces is addressed, particularly from the viewpoint of achieving stable discretizations leading to convergent pressure approximations. The role of artificial viscosity in viscous flow calculations is studied, emphasizing work by several researchers for the anisotropic case. The last section treats the problem of solving the nonlinear systems of equations which arise from the discretization. Time marching methods and classical iterative techniques, as well as some modifications are mentioned.
Numerical solution of a flow inside a labyrinth seal
NASA Astrophysics Data System (ADS)
Šimák, Jan; Straka, Petr; Pelant, Jaroslav
2012-04-01
The aim of this study is a behaviour of a flow inside a labyrinth seal on a rotating shaft. The labyrinth seal is a type of a non-contact seal where a leakage of a fluid is prevented by a rather complicated path, which the fluid has to overcome. In the presented case the sealed medium is the air and the seal is made by a system of 20 teeth on a rotating shaft situated against a smooth static surface. Centrifugal forces present due to the rotation of the shaft create vortices in each chamber and thus dissipate the axial velocity of the escaping air.The structure of the flow field inside the seal is studied through the use of numerical methods. Three-dimensional solution of the Navier-Stokes equations for turbulent flow is very time consuming. In order to reduce the computational time we can simplify our problem and solve it as an axisymmetric problem in a two-dimensional meridian plane. For this case we use a transformation of the Navier-Stokes equations and of the standard k-omega turbulence model into a cylindrical coordinate system. A finite volume method is used for the solution of the resulting problem. A one-side modification of the Riemann problem for boundary conditions is used at the inlet and at the outlet of the axisymmetric channel. The total pressure and total density (temperature) are to be used preferably at the inlet whereas the static pressure is used at the outlet for the compatibility. This idea yields physically relevant boundary conditions. The important characteristics such as a mass flow rate and a power loss, depending on a pressure ratio (1.1 - 4) and an angular velocity (1000 - 15000 rpm) are evaluated.
MAST solution of advection problems in irrotational flow fields
NASA Astrophysics Data System (ADS)
Aricò, Costanza; Tucciarelli, Tullio
2007-03-01
A new numerical-analytical Eulerian procedure is proposed for the solution of convection-dominated problems in the case of existing scalar potential of the flow field. The methodology is based on the conservation inside each computational elements of the 0th and 1st order effective spatial moments of the advected variable. This leads to a set of small ODE systems solved sequentially, one element after the other over all the computational domain, according to a MArching in Space and Time technique. The proposed procedure shows the following advantages: (1) it guarantees the local and global mass balance; (2) it is unconditionally stable with respect to the Courant number, (3) the solution in each cell needs information only from the upstream cells and does not require wider and wider stencils as in most of the recently proposed higher-order methods; (4) it provides a monotone solution. Several 1D and 2D numerical test have been performed and results have been compared with analytical solutions, as well as with results provided by other recent numerical methods.
Preferential flow and segregation of porewater solutes in Wetland sediment
Harvey, J.W.; Chambers, R.M.; Hoelscher, J.R.
1995-01-01
Sediment macropores (with effective diameters larger than 100 ??m) comprise 11% of the bulk sediment volume in a tidal freshwater wetland vegetated with Peltandra virginica. In order to determine effects of macroporous sediment structure on solute transport, we conducted a solute tracer experiment in the sediment. The effective transport volume (??eff, the volume of sediment through which solute was transported normalized to sediment bulk volume) was 0.15 cm3 cm-3, which is considerably smaller than the total pore space that is potentially available for transport (porosity of sediment is 0.63 cm3 cm-3). A mean transport time of 13 d was required to flush preferential flow paths in Peltandra hummocks; hydrologic turnover of the volumetrically dominant matrix pores (0.53 cm3 cm-3) was apparently much slower. Based on porewater sampler design and hydrological principles, we suggest that N2-purged tension solution samplers and diffusion equilibrators preferentially sample porewater from macropore and matrix domains, respectively. Dissolved ammonium and orthophosphate concentrations were three-fold higher in matrix pores compared to macropores, which is consistent with our finding that more rapid hydrological flushing occurred in macropores compared to matrix pores. Further evaluation of porewater sampler designs in macroporous sediment is needed to improve studies of hydrologic transport and biogeochemical cycling in wetlands. ?? 1995 Estuarine Research Federation.
Soil flushing with EDTA solutions: A model for channeled flow
Garcia-Delgado, R.A.; Rodriguez-Maroto, J.M.; Gomez-Lahoz, C.; Vereda-Alonso, C.; Garcia-Herruzo, F.
1998-04-01
A 1-D model for the flushing of metal contaminated soils with extracting aqueous solutions is presented. Previous experimental results of the flushing of carbonatic soil contaminated with lead with EDTA solutions showed the formation of channels of preferential flow as well as substantial rebounds in effluent lead concentration after periods of no pumping, indicating an important kinetic limitation for lead removal. This limitation is associated with the presence of a stagnant aqueous phase in addition to the mobile aqueous phase running through the channels. The model assumes an initial homogeneous distribution of lead in the soil, mainly present as small spheres of a solid carbonate which must dissolve. If the spheres are far from the channels, after solution the lead must diffuse through the stagnant aqueous phase until it reaches the channels and is washed out of the column. The model is able to simulate the rebound curves as well as the effluent concentration during the course of the operation. The importance of the way the channels arise is established by sensitivity studies performed for different mechanisms of the solution circulation and the formation of channels. More experimental results are needed to discriminate which of the alternatives studied is operative.
Bondi-Hoyle-Lyttleton accretion flow revisited: Analytic solution
NASA Astrophysics Data System (ADS)
Matsuda, Takuya; Isaka, Hiromu; Ohsugi, Yukimasa
2015-11-01
The time-steady equation for a 1D wind accretion flow, i.e. the Bondi-Hoyle-Lyttleton (BHL) equation, is investigated analytically. The BHL equation is well known to have infinitely many solutions. Traditionally, the accretion radius has been assumed to be 2textit {GM}/v_{infty }2, but its mathematical foundation has not been clarified because of the non-uniqueness of the solution. Here, we assume that the solution curves possess physically nice characteristics, i.e. velocity and line mass-density increase monotonically with radial distance. This condition restricts the accretion radius to the range left (0.71 - 1.0right ) × 2textit {GM}/v_{infty }2. Further assumptions, specifically, that the solution curves for velocity and line mass-density are convex upward, restrict the accretion radius to (0.84 - 0.94) × 2textit {GM}/v_{infty }2, and 0.90 × 2textit {GM}/v_{infty }2, respectively. Therefore, we conclude that the accretion radius is almost uniquely determined to be 0.90 × 2textit {GM}/v_{infty }2.
RELATIVISTIC GLOBAL SOLUTIONS OF NEUTRINO-DOMINATED ACCRETION FLOWS
Xue Li; Liu Tong; Gu Weimin; Lu Jufu
2013-08-15
Neutrino-dominated accretion flows (NDAFs) around rotating stellar-mass black holes are plausible candidates for the central engines of gamma-ray bursts (GRBs). We investigate one-dimensional global solutions of NDAFs, taking into account general relativity in the Kerr metric, neutrino physics, and nucleosynthesis more precisely than previous works. We calculate 16 solutions with different characterized accretion rates and black hole spins to exhibit the radial distributions of various physical properties in NDAFs. We confirm that the electron degeneracy has important effects in NDAFs and we find that the electron fraction is about 0.46 in the outer region for all 16 solutions. From the perspective of the mass fraction, free nucleons, {sup 4}He, and {sup 5}6Fe dominate in the inner, middle, and outer regions, respectively. The influence of neutrino trapping on the annihilation is of importance for the superhigh accretion ( M-dot =10 M{sub sun} s{sup -1}) and most of the 16 solutions have an adequate annihilation luminosity for GRBs.
Accurate calculation of Stokes drag for point-particle tracking in two-way coupled flows
NASA Astrophysics Data System (ADS)
Horwitz, J. A. K.; Mani, A.
2016-08-01
In this work, we propose and test a method for calculating Stokes drag applicable to particle-laden fluid flows where two-way momentum coupling is important. In the point-particle formulation, particle dynamics are coupled to fluid dynamics via a source term that appears in the respective momentum equations. When the particle Reynolds number is small and the particle diameter is smaller than the fluid scales, it is common to approximate the momentum coupling source term as the Stokes drag. The Stokes drag force depends on the difference between the undisturbed fluid velocity evaluated at the particle location, and the particle velocity. However, owing to two-way coupling, the fluid velocity is modified in the neighborhood of a particle, relative to its undisturbed value. This causes the computed Stokes drag force to be underestimated in two-way coupled point-particle simulations. We develop estimates for the drag force error as function of the particle size relative to the grid size. Because the disturbance field created by the particle contaminates the surrounding fluid, correctly calculating the drag force cannot be done solely by direct interpolation of the fluid velocity. Instead, we develop a correction method that calculates the undisturbed fluid velocity from the computed disturbed velocity field by adding an estimate of the velocity disturbance created by the particle. The correction scheme is tested for a particle settling in an otherwise quiescent fluid and is found to reduce the error in computed settling velocity by an order of magnitude compared with common interpolation schemes.
Caruso, Carlo; Burriesci, Matthew S.; Cella, Kristen; Pringle, John R.
2015-01-01
In studies of both the establishment and breakdown of cnidarian-dinoflagellate symbiosis, it is often necessary to determine the number of Symbiodinium cells relative to the quantity of host tissue. Ideally, the methods used should be rapid, precise, and accurate. In this study, we systematically evaluated methods for sample preparation and storage and the counting of algal cells using the hemocytometer, a custom image-analysis program for automated counting of the fluorescent algal cells, the Coulter Counter, or the Millipore Guava flow-cytometer. We found that although other methods may have value in particular applications, for most purposes, the Guava flow cytometer provided by far the best combination of precision, accuracy, and efficient use of investigator time (due to the instrument's automated sample handling), while also allowing counts of algal numbers over a wide range and in small volumes of tissue homogenate. We also found that either of two assays of total homogenate protein provided a precise and seemingly accurate basis for normalization of algal counts to the total amount of holobiont tissue. PMID:26291447
A numerical solution of 3D inviscid rotational flow in turbines and ducts
NASA Astrophysics Data System (ADS)
Oktay, Erdal; Akmandor, Sinan; Üçer, Ahmet
1998-04-01
The numerical solutions of inviscid rotational (Euler) flows were obtained using an explicit hexahedral unstructured cell vertex finite volume method. A second-order-accurate, one-step Lax-Wendroff scheme was used to solve the unsteady governing equations discretized in conservative form. The transonic circular bump, in which the location and the strength of the captured shock are well predicted, was used as the first test case. The nozzle guide vanes of the VKI low-speed turbine facility were used to validate the Euler code in highly 3D environment. Despite the high turning and the secondary flows which develop, close agreements have been obtained with experimental and numerical results associated with these test cases.
Numerical solution of transonic wing flows using an Euler/Navier-Stokes zonal approach
NASA Technical Reports Server (NTRS)
Holst, T. L.; Gundy, K. L.; Thomas, S. D.; Chaderjian, N. M.; Flores, J.
1985-01-01
Transonic flow fields about wing geometries are computed using an Euler/Navier-Stokes approach in which the flow field is divided into several zones. The grid zones immediately adjacent to the wing surface are suitably clustered and solved with the Navier-Stokes equations. Grid zones removed from the wing are less finely clustered and are solved with the Euler equations. Wind tunnel wall effects are easily and accurately modeled with the new grid-zoning algorithm because the wind tunnel grid is constructed as an exact subset of the corresponding free-air grid. Solutions are obtained that are in good agreement with experiment, including cases with significant wind tunnel wall effects and shock-induced separation on the upper wing surface.
Numerical Solutions of Supersonic and Hypersonic Laminar Compression Corner Flows
NASA Technical Reports Server (NTRS)
Hung, C. M.; MacCormack, R. W.
1976-01-01
An efficient time-splitting, second-order accurate, numerical scheme is used to solve the complete Navier-Stokes equations for supersonic and hypersonic laminar flow over a two-dimensional compression corner. A fine, exponentially stretched mesh spacing is used in the region near the wall for resolving the viscous layer. Good agreement is obtained between the present computed results and experimental measurement for a Mach number of 14.1 and a Reynolds number of 1.04 x 10(exp 5) with wedge angles of 15 deg, 18 deg, and 24 deg. The details of the pressure variation across the boundary layer are given, and a correlation between the leading edge shock and the peaks in surface pressure and heat transfer is observed.
Parabolized Navier-Stokes solutions of separation and trailing-edge flows
NASA Technical Reports Server (NTRS)
Brown, J. L.
1983-01-01
A robust, iterative solution procedure is presented for the parabolized Navier-Stokes or higher order boundary layer equations as applied to subsonic viscous-inviscid interaction flows. The robustness of the present procedure is due, in part, to an improved algorithmic formulation. The present formulation is based on a reinterpretation of stability requirements for this class of algorithms and requires only second order accurate backward or central differences for all streamwise derivatives. Upstream influence is provided for through the algorithmic formulation and iterative sweeps in x. The primary contribution to robustness, however, is the boundary condition treatment, which imposes global constraints to control the convergence path. Discussed are successful calculations of subsonic, strong viscous-inviscid interactions, including separation. These results are consistent with Navier-Stokes solutions and triple deck theory.
Francis, Patrick; von Lieres, Eric; Haynes, Charles A
2011-08-01
Conventional models of both packed-bed and stacked-membrane chromatography typically attribute elution band broadening to non-idealities within the column. However, when the column length to diameter ratio is greatly reduced, as in stacked-membrane chromatography, variations in solute residence times within the feed-distribution (inlet) and eluent-collection (outlet) manifolds can also contribute to band broadening. We report on a new zonal rate model (ZRM) for stacked-membrane chromatography that improves on existing hold-up volume models that rely on one plug-flow reactor and one stirred-tank reactor in series to describe dispersion of solute during transport into and out of the column. The ZRM radially partitions the membrane stack and the hold-up volumes within the inlet and outlet manifolds into zones to better capture non-uniform flow distribution effects associated with the large column diameter to height ratio. Breakthrough curves from a scaled-down anion-exchange membrane chromatography module using ovalbumin as a model protein were collected at flow rates ranging from 1.5 to 20 mL min(-1) under non-binding conditions and used to evaluate the ZRM as well as previous models. The ZRM was shown to be significantly more accurate in describing protein dispersion and breakthrough. The model was then used to decompose breakthrough data, where it was found that variations in solute residence time distributions within the inlet and outlet manifolds make the dominant contribution to solute dispersion over the recommended range of feed flow rates. The ZRM therefore identifies manifold design as a critical contributor to separation quality within stacked-membrane chromatography units. PMID:21703630
NASA Astrophysics Data System (ADS)
Saliba, H. T.
1995-06-01
The practical engineering problem of right angled triangular plates with combinations of clamped and simply supported boundary conditions is dealt with in this paper. A highly accurate, economical and practical solution is used for the transverse free vibration analysis of these plates. The solution is based on a modified superposition method. The accuracy of the solution is discussed. Numerical results are compared with previously published reliable data. The advantages of the solution used in the paper over previously published solutions are discussed. Eigenvalues, mode shapes and contour plots are provided for a large number of plates.
Invariant solutions organizing turbulence in pipe flow experiments
NASA Astrophysics Data System (ADS)
Altmeyer, Sebastian; Kühnen, Jakob; Schaner, Markus; Hof, Björn
2015-11-01
A large number of unstable invariant solutions, e.g. traveling waves (TWs) or (relative-) periodic orbits, has been discovered and numerically studied in recent years for pipe flow. The proposed role of such states as building blocks of turbulence is however less clear and so far only limited experimental evidence has been provided. In experiments we used a modulated pipe segment to impose a certain symmetry on the experimental velocity field and in the non-modulated downstream pipe traveling waves could be observed persisting for many wavelengths. Measured velocity fields (PIV) were used as initial conditions for a numerical Newton search and converged to the exact invariant traveling wave solutions. All the experimentally observed TW's correspond to lower branch states that are close to the laminar turbulent boundary (edge). Correspondingly in the experiments as the waves proceeded downstream flows would typically relaminarize but occasionally the TW's would grow to turbulence. The latter observation confirms the relevance of these invariant states for the transition process.
Precise and accurate measurement of U and Th isotopes via ICP-MS using a single solution
NASA Astrophysics Data System (ADS)
Mertz-Kraus, R.; Sharp, W. D.; Ludwig, K. R.
2012-04-01
, allowing the sample's 238U/235U ratio to be measured. In step 3, we monitor peak-tails at half-mass positions (229.5, 231.5, 234.5) and on mass 237 while aspirating sample solution. Tail measurement requires a distinct cup configuration to maintain 238U in the cups; however, no sample is consumed during automated cup reconfiguration. We monitor the accuracy of 234U/238U ratios using CRM 145, which gives a weighted mean atom ratio of (5.2846 ± 0.0029) - 10-5 (all errors 2σ), consistent with published and reference values. The reproducibility of 230Th/238U ratios is monitored using the Schwartzwalder Mine secular-equilibrium standard (SM). We detect no bias in 230Th/238U or 234U/238U ratios measured for SM at beam intensities ranging over a factor of four, consistent with accurate correction for IC yields. Aladdin's cave coral (AC-1) was analyzed to check our ICP-MS method (and the preceding purification by ion exchange) on a carbonate and yields a mean age of 125.43 ± 0.38 ka, in agreement with published values. We are currently applying the method to corals, speleothems, pedogenic coatings, and tufas.
Time-dependent transonic flow solutions for axial turbomachinery
NASA Technical Reports Server (NTRS)
Erdos, J.; Alzner, E.; Kalben, P.; Mcnally, W.; Slutsky, S.
1975-01-01
Three-dimensional unsteady transonic flow through an axial turbomachine stage is described in terms of a pair of two-dimensional formulations pertaining to orthogonal surfaces, namely, a blade-to-blade surface and a hub-to-casing surface. The resulting systems of nonlinear, inviscid, compressible equations of motion are solved by an explicit finite-difference technique. The blade-to-blade program includes the periodic interaction between rotor and stator blade rows. Treatment of the boundary conditions and of the blade slipstream motion by a characteristic type procedure is discussed in detail. Harmonic analysis of the acoustic far field produced by the blade row interaction, including an arbitrary initial transient, is outlined. Results from the blade-to-blade program are compared with experimental measurements of the rotating pressure field at the tip of a high-speed fan. The hub-to-casing program determines circumferentially averaged flow properties on a meridional plane. Blade row interactions are neglected in this formulation, but the force distributions over the entire blade surface for both the rotor and stator are obtained. Results from the hub-to-casing program are compared with a relaxation method solution for a subsonic rotor. Results are also presented for a quiet fan stage which includes transonic flow in both the rotor and stator and a normal shock in the stator.
NASA Astrophysics Data System (ADS)
Lee, Y. C.; Thompson, H. M.; Gaskell, P. H.
2009-12-01
, industrial and physical applications. However, despite recent modelling advances, the accurate numerical solution of the equations governing such problems is still at a relatively early stage. Indeed, recent studies employing a simplifying long-wave approximation have shown that highly efficient numerical methods are necessary to solve the resulting lubrication equations in order to achieve the level of grid resolution required to accurately capture the effects of micro- and nano-scale topographical features. Solution method: A portable parallel multigrid algorithm has been developed for the above purpose, for the particular case of flow over submerged topographical features. Within the multigrid framework adopted, a W-cycle is used to accelerate convergence in respect of the time dependent nature of the problem, with relaxation sweeps performed using a fixed number of pre- and post-Red-Black Gauss-Seidel Newton iterations. In addition, the algorithm incorporates automatic adaptive time-stepping to avoid the computational expense associated with repeated time-step failure. Running time: 1.31 minutes using 128 processors on BlueGene/P with a problem size of over 16.7 million mesh points.
The use of wavelet transformations in the solution of two-phase flow problems
Moridis, G.J.; Nikolaou, M.; You, Y.
1995-12-31
In this paper the authors present the use of wavelets to solve the non-linear Partial Differential Equation (PDE) of two-phase flow in one dimension. The wavelet transforms allow a drastically different approach in the discretization of space. In contrast to the traditional trigonometric basis functions, wavelets approximate a function not by cancellation but by placement of wavelets at appropriate locations. When an abrupt change, such as a shock wave or a spike, occurs in a function, only local coefficients in a wavelet approximation will be affected. The unique feature of wavelets is their Multi-Resolution Analysis (MRA) property, which allows seamless investigation at nay spatial resolution. The use of wavelets is tested in the solution of the one-dimensional Buckley-Leverett problem against analytical solutions and solutions obtained from standard numerical models. Two classes of wavelet bases (Daubechies and Chui-Wang) and two methods (Galerkin and collocation) are investigated. The authors determine that the Chui-Wang wavelets and a collection method provide the optimum wavelet solution for this type of problem. Increasing the resolution level improves the accuracy of the solution, but the order of the basis function seems to be far less important. The results indicate that wavelet transforms are an effective and accurate method which does not suffer from oscillations or numerical smearing in the presence of steep fronts.
The use of wavelet transforms in the solution of two-phase flow problems
Moridis, G.J.; Nikolaou, M.; You, Yong
1994-10-01
In this paper we present the use of wavelets to solve the nonlinear Partial Differential.Equation (PDE) of two-phase flow in one dimension. The wavelet transforms allow a drastically different approach in the discretization of space. In contrast to the traditional trigonometric basis functions, wavelets approximate a function not by cancellation but by placement of wavelets at appropriate locations. When an abrupt chance, such as a shock wave or a spike, occurs in a function, only local coefficients in a wavelet approximation will be affected. The unique feature of wavelets is their Multi-Resolution Analysis (MRA) property, which allows seamless investigational any spatial resolution. The use of wavelets is tested in the solution of the one-dimensional Buckley-Leverett problem against analytical solutions and solutions obtained from standard numerical models. Two classes of wavelet bases (Daubechies and Chui-Wang) and two methods (Galerkin and collocation) are investigated. We determine that the Chui-Wang, wavelets and a collocation method provide the optimum wavelet solution for this type of problem. Increasing the resolution level improves the accuracy of the solution, but the order of the basis function seems to be far less important. Our results indicate that wavelet transforms are an effective and accurate method which does not suffer from oscillations or numerical smearing in the presence of steep fronts.
NASA Technical Reports Server (NTRS)
Constantinescu, George S.; Lele, S. K.
2001-01-01
Numerical methods for solving the flow equations in cylindrical or spherical coordinates should be able to capture the behavior of the exact solution near the regions where the particular form of the governing equations is singular. In this work we focus on the treatment of these numerical singularities for finite-differences methods by reinterpreting the regularity conditions developed in the context of pseudo-spectral methods. A generally applicable numerical method for treating the singularities present at the polar axis, when nonaxisymmetric flows are solved in cylindrical, coordinates using highly accurate finite differences schemes (e.g., Pade schemes) on non-staggered grids, is presented. Governing equations for the flow at the polar axis are derived using series expansions near r=0. The only information needed to calculate the coefficients in these equations are the values of the flow variables and their radial derivatives at the previous iteration (or time) level. These derivatives, which are multi-valued at the polar axis, are calculated without dropping the accuracy of the numerical method using a mapping of the flow domain from (0,R)*(0,2pi) to (-R,R)*(0,pi), where R is the radius of the computational domain. This allows the radial derivatives to be evaluated using high-order differencing schemes (e.g., compact schemes) at points located on the polar axis. The proposed technique is illustrated by results from simulations of laminar-forced jets and turbulent compressible jets using large eddy simulation (LES) methods. In term of the general robustness of the numerical method and smoothness of the solution close to the polar axis, the present results compare very favorably to similar calculations in which the equations are solved in Cartesian coordinates at the polar axis, or in which the singularity is removed by employing a staggered mesh in the radial direction without a mesh point at r=0, following the method proposed recently by Mohseni and Colonius
NASA Astrophysics Data System (ADS)
Hiruta, Yoshiki; Toh, Sadayoshi
2015-12-01
Two-dimensional Kolmogorov flow in wide periodic boxes is numerically investigated. It is shown that the total flow rate in the direction perpendicular to the force controls the characteristics of the flow, especially the existence of spatially localized solitary solutions such as traveling waves, periodic solutions, and chaotic solutions, which can behave as elementary components of the flow. We propose a procedure to construct approximate solutions consisting of solitary solutions. It is confirmed by direct numerical simulations that these solutions are stable and represent interactions between elementary components such as collisions, coexistence, and collapse of chaos.
Better Strategies for Finite Element Solutions of Variable Viscosity Stokes Flow
NASA Astrophysics Data System (ADS)
Hasenclever, Jörg; Phipps Morgan, Jason; Shi, Chao
2010-05-01
Accurate numerical solution of variable viscosity Stokes Flow is one of the most important issues for better geodynamic understanding of mantle convection and mantle melting. While a good Stokes solver is usually an integral part of a good Navier-Stokes solver, typically Navier-Stokes equations are solved for flow of a fluid with uniform viscosity. The lumped-mass-matrix is an excellent and cheap preconditioner for uniform viscosity Stokes flow (cf. Maday and Patera, 1989), therefore for most applications to Navier-Stokes flow the ‘Stokes' part of the problem is viewed as well-resolved. Unfortunately, the inverse-viscosity-scaled lumped mass matrix does not work nearly as well to precondition Stokes flow in a fluid with strongly varying viscosity. This issue is already central to accurate numerical studies of convection in Earth's silicate-fluid mantle (May and Moresi, 2008; van Geenen et al., 2009; Burstedde et al., 2009) and may become central for researchers investigating Navier-Stokes problems with lateral variations in viscosity. Here we discuss several known computational hurdles to progress, and suggest strategies that offer promise in overcoming them. The choices for solving the discrete pressure equation arising from Stokes flow typically involve several tradeoffs between speed and storage requirements. In exact math, the discrete pressure matrix S is symmetric, so that it should be possible to use a symmetric preconditioned conjugate gradient (CG) Krylov algorithm instead of needing an asymmetric GMRES (cf. Saad, 2003) or GCR (Generalized Conjugate Residual, cf. Van der Vorst, 2003) that would require ~10-50 times more storage of past search directions. However, a CG-like method requires that the action of both S and any pressure preconditioner must be almost perfectly symmetric. This means that we must be very careful about the effects of roundoff in any iterative solver-based pressure preconditioner that may introduce numerically asymmetric operators
The development of solution algorithms for compressible flows
NASA Astrophysics Data System (ADS)
Slack, David Christopher
Three main topics were examined. The first is the development and comparison of time integration schemes on 2-D unstructured meshes. Both explicit and implicit solution grids are presented. Cell centered and cell vertex finite volume upwind schemes using Roe's approximate Riemann solver are developed. The second topic involves an interactive adaptive remeshing algorithm which uses a frontal grid generator and is compared to a single grid calculation. The final topic examined is the capabilities developed for a structured 3-D code called GASP. The capabilities include: generalized chemistry and thermodynamic modeling, space marching, memory management through the use of binary C I/O, and algebraic and two equation eddy viscosity turbulence modeling. Results are given for Mach 1.7 3-D analytic forebody, a Mach 1.38 axisymmetric nozzle with hydrogen-air combustion, a Mach 14.15 deg ramp, and Mach 0.3 viscous flow over a flat plate.
Real-time precision concentration measurement for flowing liquid solutions
NASA Astrophysics Data System (ADS)
Krishna, V.; Fan, C. H.; Longtin, J. P.
2000-10-01
The precise, real-time measurement of liquid concentration is important in fundamental research, chemical analysis, mixing processes, and manufacturing, e.g., in the food and semiconductor industries. This work presents a laser-based, noninvasive technique to measure concentration changes of flowing liquids in real time. The essential components in the system include a 5 mW laser diode coupled to a single-mode optical fiber, a triangular optical cell, and a high-resolution beam position sensor. The instrument provides a large range of concentration measurement, typically 0%-100% for binary liquid mixtures, while providing a resolution on the order of 0.05% concentration or better. The experimental configuration is small, reliable, and inexpensive. Results are presented for NaCl and MgCl2 aqueous solutions with concentrations ranging from 0% to 25%, with very good agreement found between measured and true concentrations.
NASA Astrophysics Data System (ADS)
Gerke, K.
2012-04-01
Most dye staining experiments in natural soils result in highly heterogeneous flow patterns which are usually explained with presence of preferential flow paths or different kinds of flow instabilities. It is quite logic that soil structure is one of the main factors affecting infiltrations regimes, however the degree of flow stochasticity is not studied enough. In this contribution a substantial amount of large scale (2-4 m lateral excavations) field experiment data is considered (including forested hillslopes and agricultural fields) with special attention to sprinkling of two different staining substances with different dyeing mechanisms (common dye is visible both in adsorbed and in solution states; fluorescent dye - only in solution). The latter method allows an estimation of the flow stability (stochasticity). Most staining field experiments are supported by undisturbed sample collections (laboratory measurements for hydraulic conductivity, water retention curves, X-ray microtomography scans, grain size distributions, etc.). Preliminary results strongly support the evidence of stability of flow under similar precipitation and moisture conditions. Infiltration also correlated with soil structure and microproperties. Numerical modeling using classical approach (single-porosity coupled Richard's and advection-dispersion equations, random hydraulic properties based on log-normal experimentally obtained distribution) fails to describe experimentally obtained staining patterns. Multi-porosity models may provide better tools to account for different soil heterogeneities, but their parameters can not be obtained experimentally. Small scale solutions using pore-network or lattice-Botzmann methods based on microtomography scans are accurate, but computationally expensive (volumes around tens of cm3). Based on field observations a simple cellular automata approach to model staining patterns is developed and tested on experimental data. Our results are much better then
Intercomparison of 3D pore-scale flow and solute transport simulation methods
Mehmani, Yashar; Schoenherr, Martin; Pasquali, Andrea; Perkins, William A.; Kim, Kyungjoo; Perego, Mauro; Parks, Michael L.; Balhoff, Matthew T.; Richmond, Marshall C.; Geier, Martin; et al
2015-09-28
Multiple numerical approaches have been developed to simulate porous media fluid flow and solute transport at the pore scale. These include 1) methods that explicitly model the three-dimensional geometry of pore spaces and 2) methods that conceptualize the pore space as a topologically consistent set of stylized pore bodies and pore throats. In previous work we validated a model of the first type, using computational fluid dynamics (CFD) codes employing a standard finite volume method (FVM), against magnetic resonance velocimetry (MRV) measurements of pore-scale velocities. Here we expand that validation to include additional models of the first type based onmore » the lattice Boltzmann method (LBM) and smoothed particle hydrodynamics (SPH), as well as a model of the second type, a pore-network model (PNM). The PNM approach used in the current study was recently improved and demonstrated to accurately simulate solute transport in a two-dimensional experiment. While the PNM approach is computationally much less demanding than direct numerical simulation methods, the effect of conceptualizing complex three-dimensional pore geometries on solute transport in the manner of PNMs has not been fully determined. We apply all four approaches (FVM-based CFD, LBM, SPH and PNM) to simulate pore-scale velocity distributions and (for capable codes) nonreactive solute transport, and intercompare the model results. Comparisons are drawn both in terms of macroscopic variables (e.g., permeability, solute breakthrough curves) and microscopic variables (e.g., local velocities and concentrations). Generally good agreement was achieved among the various approaches, but some differences were observed depending on the model context. The intercomparison work was challenging because of variable capabilities of the codes, and inspired some code enhancements to allow consistent comparison of flow and transport simulations across the full suite of methods. This paper provides support for
Intercomparison of 3D pore-scale flow and solute transport simulation methods
Mehmani, Yashar; Schoenherr, Martin; Pasquali, Andrea; Perkins, William A.; Kim, Kyungjoo; Perego, Mauro; Parks, Michael L.; Balhoff, Matthew T.; Richmond, Marshall C.; Geier, Martin; Krafczyk, Manfred; Luo, Li -Shi; Tartakovsky, Alexandre M.; Yang, Xiaofan; Scheibe, Timothy D.; Trask, Nathaniel
2015-09-28
Multiple numerical approaches have been developed to simulate porous media fluid flow and solute transport at the pore scale. These include 1) methods that explicitly model the three-dimensional geometry of pore spaces and 2) methods that conceptualize the pore space as a topologically consistent set of stylized pore bodies and pore throats. In previous work we validated a model of the first type, using computational fluid dynamics (CFD) codes employing a standard finite volume method (FVM), against magnetic resonance velocimetry (MRV) measurements of pore-scale velocities. Here we expand that validation to include additional models of the first type based on the lattice Boltzmann method (LBM) and smoothed particle hydrodynamics (SPH), as well as a model of the second type, a pore-network model (PNM). The PNM approach used in the current study was recently improved and demonstrated to accurately simulate solute transport in a two-dimensional experiment. While the PNM approach is computationally much less demanding than direct numerical simulation methods, the effect of conceptualizing complex three-dimensional pore geometries on solute transport in the manner of PNMs has not been fully determined. We apply all four approaches (FVM-based CFD, LBM, SPH and PNM) to simulate pore-scale velocity distributions and (for capable codes) nonreactive solute transport, and intercompare the model results. Comparisons are drawn both in terms of macroscopic variables (e.g., permeability, solute breakthrough curves) and microscopic variables (e.g., local velocities and concentrations). Generally good agreement was achieved among the various approaches, but some differences were observed depending on the model context. The intercomparison work was challenging because of variable capabilities of the codes, and inspired some code enhancements to allow consistent comparison of flow and transport simulations across the full suite of methods. This paper provides support for confidence
Analytical solutions to non-Fickian subsurface dispersion in uniform groundwater flow
Zou, S.; Xia, J.; Koussis, A.D.
1996-01-01
Analytical solutions are obtained by the Fourier transform technique for the one-, two-, and three-dimensional transport of a conservative solute injected instantaneously in a uniform groundwater flow. These solutions account for dispersive non-linearity caused by the heterogeneity of the hydraulic properties of aquifer systems and can be used as building blocks to construct solutions by convolution (principle of superposition) for source conditions other than slug injection. The dispersivity is assumed to vary parabolically with time and is thus constant for the entire system at any given time. Two approaches for estimating time-dependent dispersion parameters are developed for two-dimensional plumes. They both require minimal field tracer test data and, therefore, represent useful tools for assessing real-world aquifer contamination sites. The first approach requires mapped plume-area measurements at two specific times after the tracer injection. The second approach requires concentration-versus-time data from two sampling wells through which the plume passes. Detailed examples and comparisons with other procedures show that the methods presented herein are sufficiently accurate and easier to use than other available methods.
NASA Astrophysics Data System (ADS)
Chen, Bingyan; Zhu, Changping; Chen, Longwei; Fei, Juntao; Gao, Ying; Wen, Wen; Shan, Minglei; Ren, Zhaoxing
2014-12-01
The organic compounds of p-nitrophenol (PNP) solution was treated by the active species generated in a stirred reactor by an atmospheric pressure plasma jet (APPJ). The emission intensities of hydroxyl (OH), oxygen (O), nitric oxide (NO), hydrogen (H) and molecular (N2) were measured by optical emission spectroscopy (OES). The relations between the flow rates of the PNP solution and degradation, the degradation effects and initial pH value of the solution were also investigated. Experimental results show that there exist intense emissions of O (777.1 nm), N2 (337.1 nm), OH (306-310 nm) and NO band (200-290 nm) in the region of plasma. Given the treatment time and gas flow rate, the degradation increased as a function of discharge energy and solution flow rate, respectively. The solution flow rate for the most efficient degradation ranged from 1.414 m/s to 1.702 m/s, and contributed very little when it exceeded 2.199 m/s. This indicates the existence of diffusion-controlled reactions at a low solution flow rate and activation-controlled reactions at a high solution flow rate. Moreover, increasing or decreasing the initial pH value of neutral PNP solution (pH=5.95) could improve the degradation efficiency. Treated by APPJ, the PNP solutions with different initial pH values of 5.95, 7.47 and 2.78 turned more acidic in the end, while the neutral solution had the lowest degradation efficiency. This work clearly demonstrates the close coupling of active species, photolysis of ultraviolet, the organic solution flow rate and the initial pH value, and thus is helpful in the study of the mechanism and application of plasma in wastewater treatment.
NASA Astrophysics Data System (ADS)
Awojoyogbe, O. B.
2004-08-01
Various biological and physiological properties of living tissue can be studied by means of nuclear magnetic resonance techniques. Unfortunately, the basic physics of extracting the relevant information from the solution of Bloch nuclear magnetic resource (NMR) equations to accurately monitor the clinical state of biological systems is still not yet fully understood. Presently, there are no simple closed solutions known to the Bloch equations for a general RF excitation. Therefore the translational mechanical analysis of the Bloch NMR equations presented in this study, which can be taken as definitions of new functions to be studied in detail may reveal very important information from which various NMR flow parameters can be derived. Fortunately, many of the most important but hidden applications of blood flow parameters can be revealed without too much difficulty if appropriate mathematical techniques are used to solve the equations. In this study we are concerned with a mathematical study of the laws of NMR physics from the point of view of translational mechanical theory. The important contribution of this study is that solutions to the Bloch NMR flow equations do always exist and can be found as accurately as desired. We shall restrict our attention to cases where the radio frequency field can be treated by simple analytical methods. First we shall derive a time dependant second-order non-homogeneous linear differential equation from the Bloch NMR equation in term of the equilibrium magnetization M0, RF B1( t) field, T1 and T2 relaxation times. Then, we would develop a general method of solving the differential equation for the cases when RF B1( t)=0, and when RF B1( t)≠0. This allows us to obtain the intrinsic or natural behavior of the NMR system as well as the response of the system under investigation to a specific influence of external force to the system. Specifically, we consider the case where the RF B1 varies harmonically with time. Here the complete
NASA Astrophysics Data System (ADS)
Zhang, Na; Yao, Jun; Huang, Zhaoqin; Wang, Yueying
2013-06-01
Numerical simulation in naturally fractured media is challenging because of the coexistence of porous media and fractures on multiple scales that need to be coupled. We present a new approach to reservoir simulation that gives accurate resolution of both large-scale and fine-scale flow patterns. Multiscale methods are suitable for this type of modeling, because it enables capturing the large scale behavior of the solution without solving all the small features. Dual-porosity models in view of their strength and simplicity can be mainly used for sugar-cube representation of fractured media. In such a representation, the transfer function between the fracture and the matrix block can be readily calculated for water-wet media. For a mixed-wet system, the evaluation of the transfer function becomes complicated due to the effect of gravity. In this work, we use a multiscale finite element method (MsFEM) for two-phase flow in fractured media using the discrete-fracture model. By combining MsFEM with the discrete-fracture model, we aim towards a numerical scheme that facilitates fractured reservoir simulation without upscaling. MsFEM uses a standard Darcy model to approximate the pressure and saturation on a coarse grid, whereas fine scale effects are captured through basis functions constructed by solving local flow problems using the discrete-fracture model. The accuracy and the robustness of MsFEM are shown through several examples. In the first example, we consider several small fractures in a matrix and then compare the results solved by the finite element method. Then, we use the MsFEM in more complex models. The results indicate that the MsFEM is a promising path toward direct simulation of highly resolution geomodels.
High-order solution-adaptive central essentially non-oscillatory (CENO) method for viscous flows
NASA Astrophysics Data System (ADS)
Ivan, Lucian; Groth, Clinton P. T.
2014-01-01
A high-order, central, essentially non-oscillatory (CENO), finite-volume scheme in combination with a block-based adaptive mesh refinement (AMR) algorithm is proposed for solution of the Navier-Stokes equations on body-fitted multi-block mesh. In contrast to other ENO schemes which require reconstruction on multiple stencils, the proposed CENO method uses a hybrid reconstruction approach based on a fixed central stencil. This feature is crucial to avoiding the complexities associated with multiple stencils of ENO schemes, providing high-order accuracy at relatively lower computational cost as well as being very well suited for extension to unstructured meshes. The spatial discretization of the inviscid (hyperbolic) fluxes combines an unlimited high-order k-exact least-squares reconstruction technique following from the optimal central stencil with a monotonicity-preserving, limited, linear, reconstruction algorithm. This hybrid reconstruction procedure retains the unlimited high-order k-exact reconstruction for cells in which the solution is fully resolved and reverts to the limited lower-order counterpart for cells with under-resolved/discontinuous solution content. Switching in the hybrid procedure is determined by a smoothness indicator. The high-order viscous (elliptic) fluxes are computed to the same order of accuracy as the hyperbolic fluxes based on a k-order accurate cell interface gradient derived from the unlimited, cell-centred, reconstruction. A somewhat novel h-refinement criterion based on the solution smoothness indicator is used to direct the steady and unsteady mesh adaptation. The proposed numerical procedure is thoroughly analyzed for advection-diffusion problems characterized by the full range of Péclet numbers, and its predictive capabilities are also demonstrated for several inviscid and laminar flows. The ability of the scheme to accurately represent solutions with smooth extrema and yet robustly handle under-resolved and/or non
Early turbulence in von Karman swirling flow of polymer solutions
NASA Astrophysics Data System (ADS)
Burnishev, Yuri; Steinberg, Victor
2015-01-01
We present quantitative experimental results on the transition to early turbulence in von Karman swirling flow of water- and water-sugar-based polymer solutions compared to the transition to turbulence in their Newtonian solvents by measurements of solely global quantities as torque Γ(t) and pressure p(t) with large statistics as a function of Re. For the first time the transition values of Re_c\\textit{turb} to fully developed turbulence and turbulent drag reduction regime Re_c\\textit{TDR} are obtained as functions of elasticity El by using the solvents with different viscosities and polymer concentrations ϕ. Two scaling regions for fundamental turbulent characteristics are identified and they correspond to the turbulent and TDR regimes. Both Re_c\\textit{turb} and Re_c\\textit{TDR} are found via the dependence of the friction coefficient Cf and Cp, defined through scaled average torque \\barΓ and rms pressure fluctuations p\\textit{rms} , respectively, on Re for different El and ϕ and via the limits of the two scaling regions.
NASA Astrophysics Data System (ADS)
Nassar, Mohamed K.; Ginn, Timothy R.
2014-08-01
We investigate the effect of computational error on the inversion of a density-dependent flow and transport model, using SEAWAT and UCODE-2005 in an inverse identification of hydraulic conductivity and dispersivity using head and concentration data from a 2-D laboratory experiment. We investigated inversions using three different solution schemes including variation of number of particles and time step length, in terms of the three aspects: the shape and smoothness of the objective function surface, the consequent impacts to the optimization, and the resulting Pareto analyses. This study demonstrates that the inversion is very sensitive to the choice of the forward model solution scheme. In particular, standard finite difference methods provide the smoothest objective function surface; however, this is obtained at the cost of numerical artifacts that can lead to erroneous warping of the objective function surface. Total variation diminishing (TVD) schemes limit these impacts at the cost of more computation time, while the hybrid method of characteristics (HMOC) approach with increased particle numbers and/or reduced time step gives both smoothed and accurate objective function surface. Use of the most accurate methods (TVD and HMOC) did lead to successful inversion of the two parameters; however, with distinct results for Pareto analyses. These results illuminate the sensitivity of the inversion to a number of aspects of the forward solution of the density-driven flow problem and reveal that parameter values may result that are erroneous but that counteract numerical errors in the solution.
Navier-Stokes solutions for rotating 3-D duct flows
NASA Astrophysics Data System (ADS)
Srivastava, B. N.
1988-07-01
This paper deals with the computation of three-dimensional viscous turbulent flow in a rotating rectangular duct of low aspect ratio using thin-layer Navier-Stokes equations. Scalar form of an approximate factorization implicit scheme along with a modified q-omega turbulence model has been utilized for mean flow predictions. The predicted mean flow behavior has been favorably compared with the experimental data for mean axial velocity, channel pressure and cross-flow velocities at a flow Mach number of 0.05 and a rotational speed of 300 rpm.
NASA Technical Reports Server (NTRS)
Kylling, Arve; Stamnes, Knut
1992-01-01
The present solutions to the linear transport equation pertain to monoenergetic particles' interaction with a multiple scattering/absorbing layered medium with a general anisotropic internal source term. Attention is given to a novel exponential-linear approximation to the internal source, as a function of scattering depth, which furnishes an at-once efficient and accurate solution to the linear transport equation through its reduction of the spatial mesh size. The great superiority of the proposed method is demonstrated by the numerical results obtained in the illustrative cases of (1) an embedded thermal source and (2) a rapidly varying beam pseudosource.
Flow dynamics and solute transport in unsaturated rock fractures
Su, G. W.
1999-10-01
Rock fractures play an important role in flow and contaminant transport in fractured aquifers, production of oil from petroleum reservoirs, and steam generation from geothermal reservoirs. In this dissertation, phenomenological aspects of flow in unsaturated fractures were studied in visualization experiments conducted on a transparent replica of a natural, rough-walled rock fracture for inlet conditions of constant pressure and flow rate over a range of angles of inclination. The experiments demonstrated that infiltrating liquid proceeds through unsaturated rock fractures along non-uniform, localized preferential flow paths. Even in the presence of constant boundary conditions, intermittent flow was a persistent flow feature observed, where portions of the flow channel underwent cycles of snapping and reforming. Two modes of intermittent flow were observed, the pulsating blob mode and the rivulet snapping mode. A conceptual model for the rivulet snapping mode was proposed and examined using idealized, variable-aperture fractures. The frequency of intermittent flow events was measured in several experiments and related to the capillary and Bond numbers to characterize this flow behavior.
Compressible seal flow analysis using the finite element method with Galerkin solution technique
NASA Technical Reports Server (NTRS)
Zuk, J.
1974-01-01
A finite element method with a Galerkin solution (FEMGS) technique is formulated for the solution of nonlinear problems in high-pressure compressible seal flow analyses. An example of a three-dimensional axisymmetric flow having nonlinearities, due to compressibility, area expansion, and convective inertia, is used for illustrating the application of the technique.
Numerical solutions of atmospheric flow over semielliptical simulated hills
NASA Technical Reports Server (NTRS)
Shieh, C. F.; Frost, W.
1981-01-01
Atmospheric motion over obstacles on plane surfaces to compute simulated wind fields over terrain features was studied. Semielliptical, two dimensional geometry and numerical simulation of flow over rectangular geometries is also discussed. The partial differential equations for the vorticity, stream function, turbulence kinetic energy, and turbulence length scale were solved by a finite difference technique. The mechanism of flow separation induced by a semiellipse is the same as flow over a gradually sloping surface for which the flow separation is caused by the interaction between the viscous force, the pressure force, and the turbulence level. For flow over bluff bodies, a downstream recirculation bubble is created which increases the aspect ratio and/or the turbulence level results in flow reattachment close behind the obstacle.
Koopmans, G F; Hiemstra, T; Regelink, I C; Molleman, B; Comans, R N J
2015-05-01
Manufactured metallic silver nanoparticles (AgNP) are intensively utilized in consumer products and this will inevitably lead to their release to soils. To assess the environmental risks of AgNP in soils, quantification of both their concentration and size in soil solution is essential. We developed a methodology consisting of asymmetric flow field-flow fractionation (AF4) in combination with on-line detection by UV-vis spectroscopy and off-line HR-ICP-MS measurements to quantify the concentration and size of AgNP, coated with either citrate or polyvinylpyrrolidone (PVP), in water extracts of three different soils. The type of mobile phase was a critical factor in the fractionation of AgNP by AF4. In synthetic systems, fractionation of a series of virgin citrate- and PVP-coated AgNP (10-90 nm) with reasonably high recoveries could only be achieved with ultrahigh purity water as a mobile phase. For the soil water extracts, 0.01% (w:v) sodium dodecyl sulfate (SDS) at pH 8 was the key to a successful fractionation of the AgNP. With SDS, the primary size of AgNP in all soil water extracts could be determined by AF4, except for PVP-coated AgNP when clay colloids were present. The PVP-coated AgNP interacted with colloidal clay minerals, leading to an overestimation of their primary size. Similar interactions between PVP-coated AgNP and clay colloids can take place in the environment and facilitate their transport in soils, aquifers, and surface waters. In conclusion, AF4 in combination with UV-vis spectroscopy and HR-ICP-MS measurements is a powerful tool to characterize AgNP in soil solution if the appropriate mobile phase is used. PMID:25798868
Wexler, Eliezer J.
1989-01-01
Analytical solutions to the advective-dispersive solute transport equation are useful in predicting the fate of solutes in groundwater. Analytical solutions compiled from available literature or derived by the author are presented in this report for a variety of boundary condition types and solute-source configuration in one-, two-, and three-dimensional systems with uniform groundwater flow. A set of user-oriented computer programs was created to evaluate these solutions and to display the results in tabular and computer-graphics format. These programs incorporate many features that enhance their accuracy, ease of use, and versatility. Documentation for the programs describes their operation and required input data, and presents the results of sample problems. Derivations of select solutions, source codes for the computer programs, and samples of program input and output also are described. (USGS)
Wexler, Eliezer J.
1992-01-01
Analytical solutions to the advective-dispersive solute-transport equation are useful in predicting the fate of solutes in ground water. Analytical solutions compiled from available literature or derived by the author are presented for a variety of boundary condition types and solute-source configurations in one-, two-, and three-dimensional systems having uniform ground-water flow. A set of user-oriented computer programs was created to evaluate these solutions and to display the results in tabular and computer-graphics format. These programs incorporate many features that enhance their accuracy, ease of use, and versatility. Documentation for the programs describes their operation and required input data, and presents the results of sample problems. Derivations of selected solutions, source codes for the computer programs, and samples of program input and output also are included.
NASA Astrophysics Data System (ADS)
Rehbinder, G.
2010-03-01
The generalized radial flow model describes mathematically nonsteady flow of arbitrary dimensionality from a source in a porous medium. Closed solutions of the corresponding equation have hitherto been considered as impractical except for one simple special case. Two closed solutions of the generalized radial flow equation, corresponding to given head in or given discharge from the source have been derived. The noninteger dimensionality is the only parameter in the problem. The solutions become not valid if the time tends to infinity, such as for 1-D and 2-D flows. The influence of a possible noninteger dimensionality has attracted interest in connection with the flow of groundwater in fractured rock, particularly around a repository for nuclear waste or in connection with grouting. In contrast to numerical solutions, the closed solutions offer simple means for evaluation of field tests.
NASA Technical Reports Server (NTRS)
Ballhaus, W. F.; Jameson, A.; Albert, J.
1977-01-01
Implicit approximate-factorization algorithms (AF) are developed for the solution of steady-state transonic flow problems. The performance of the AF solution method is evaluated relative to that of the standard solution method for transonic flow problems, successive line over-relaxation (SLOR). Both methods are applied to the solution of the nonlinear, two-dimensional transonic small-disturbance equation. Results indicate that the AF method requires substantially less computer time than SLOR to solve the nonlinear finite-difference matrix equation for a transonic flow field. This increase in computational efficiency is achieved with no appreciable increase in computer storage or coding complexity.
NASA Technical Reports Server (NTRS)
Thompson, D. S.
1980-01-01
The full Navier-Stokes equations for incompressible turbulent flow must be solved to accurately represent all flow phenomena which occur in a high Reynolds number incompressible flow. A two layer algebraic eddy viscosity turbulence model is used to represent the Reynolds stress in the primitive variable formulation. The development of the boundary-fitted coordinate systems makes the numerical solution of these equations feasible for arbitrarily shaped bodies. The nondimensional time averaged Navier-Stokes equations, including the turbulence mode, are represented by finite difference approximations in the transformed plane. The resulting coupled system of nonlinear algebraic equations is solved using a point successive over relaxation iteration. The test case considered was a NACA 64A010 airfoil section at an angle of attack of two degrees and a Reynolds number of 2,000,000.
Water flow and solute transport in floating fen root mats
NASA Astrophysics Data System (ADS)
Stofberg, Sija F.; EATM van der Zee, Sjoerd
2015-04-01
be very similar and likely functionally related. Our experimental field data were used for modelling water flow and solute transport in floating fens, using HYDRUS 2D. Fluctuations of surface water and root mat, as well as geometry and unsaturated zone parameters can have a major influence on groundwater fluctuations and the exchange between rain and surface water and the water in the root mats. In combination with the duration of salt pulses in surface water, and sensitivity of fen plants to salinity (Stofberg et al. 2014, submitted), risks for rare plants can be anticipated.
Miyagawa, Yoichi; Morisada, Shintaro; Ohto, Keisuke; Hidetaka, Kawakita
2016-08-01
Separation of colloidal particles in non-Newtonian fluid is important in food engineering. Using hydrodynamic chromatography, colloidal particles and starch granules originating from corn were individually injected into dextran solutions (Mw 2,000,000g/mol) flowing through a coiled tube for efficient size separation. Rheological properties of dextran solutions ranging from 50 to 250g/L were determined, revealing pseudoplastic fluid behavior. Velocity profiles for dextran solution flow in coiled tubes were obtained from rheological power law parameters. Suspensions of colloidal particles of diameters 1.0 and 20μm were individually injected into the dextran flows, demonstrating that dextran solutions at high concentration separated colloidal particles. Starch granules were separated by size using a dextran solution flow (250g/L). Thus, we expect to obtain efficient separation of colloidal particles in foods using highly concentrated dextran solutions. PMID:27112856
NASA Astrophysics Data System (ADS)
Bhushan, R.; Ng, T. L.
2014-12-01
Accurate stream flow forecasts are critical for reservoir operations for water supply planning. As the world urban population increases, the demand for water in cities is also increasing, making accurate forecasts even more important. However, accurate forecasting of stream flows is difficult owing to short- and long-term weather variations. We propose to reduce this need for accurate stream flow forecasts by augmenting reservoir operations with seawater desalination and wastewater recycling. We develop a robust operating policy for the joint operation of the three sources. With the joint model, we tap into the unlimited reserve of seawater through desalination, and make use of local supplies of wastewater through recycling. However, both seawater desalination and recycling are energy intensive and relatively expensive. Reservoir water on the other hand, is generally cheaper but is limited and variable in its availability, increasing the risk of water shortage during extreme climate events. We operate the joint system by optimizing it using a genetic algorithm to maximize water supply reliability and resilience while minimizing vulnerability subject to a budget constraint and for a given stream flow forecast. To compute the total cost of the system, we take into account the pumping cost of transporting reservoir water to its final destination, and the capital and operating costs of desalinating seawater and recycling wastewater. We produce results for different hydro climatic regions based on artificial stream flows we generate using a simple hydrological model and an autoregressive time series model. The artificial flows are generated from precipitation and temperature data from the Canadian Regional Climate model for present and future scenarios. We observe that the joint operation is able to effectively minimize the negative effects of stream flow forecast uncertainty on system performance at an overall cost that is not significantly greater than the cost of a
Numerical Solution of Inviscid Compressible Steady Flows around the RAE 2822 Airfoil
NASA Astrophysics Data System (ADS)
Kryštůfek, P.; Kozel, K.
2015-05-01
The article presents results of a numerical solution of subsonic, transonic and supersonic flows described by the system of Euler equations in 2D compressible flows around the RAE 2822 airfoil. Authors used FVM multistage Runge-Kutta method to numerically solve the flows around the RAE 2822 airfoil. The results are compared with the solution using the software Ansys Fluent 15.0.7.
Viscous-shock-layer solutions for turbulent flow of radiating gas mixtures in chemical equilibrium
NASA Technical Reports Server (NTRS)
Anderson, E. C.; Moss, J. N.
1975-01-01
The viscous-shock-layer equations for hypersonic laminar and turbulent flows of radiating or nonradiating gas mixtures in chemical equilibrium are presented for two-dimensional and axially-symmetric flow fields. Solutions were obtained using an implicit finite-difference scheme and results are presented for hypersonic flow over spherically-blunted cone configurations at freestream conditions representative of entry into the atmosphere of Venus. These data are compared with solutions obtained using other methods of analysis.
Viscous shock layer solutions for turbulent flow of radiating gas mixtures in chemical equilibrium
NASA Technical Reports Server (NTRS)
Anderson, E. C.; Moss, J. N.
1975-01-01
The viscous shock layer equations for hypersonic laminar and turbulent flows of radiating or nonradiating gas mixtures in chemical equilibrium are presented for two-dimensional and axially symmetric flow fields. Solutions are obtained using an implicit finite difference scheme and results are presented for hypersonic flow over spherically blunted cone configurations at free stream conditions representative of entry into the atmosphere of Venus. These data are compared with solutions obtained using other methods of analysis.
Adaptive multigrid domain decomposition solutions for viscous interacting flows
NASA Technical Reports Server (NTRS)
Rubin, Stanley G.; Srinivasan, Kumar
1992-01-01
Several viscous incompressible flows with strong pressure interaction and/or axial flow reversal are considered with an adaptive multigrid domain decomposition procedure. Specific examples include the triple deck structure surrounding the trailing edge of a flat plate, the flow recirculation in a trough geometry, and the flow in a rearward facing step channel. For the latter case, there are multiple recirculation zones, of different character, for laminar and turbulent flow conditions. A pressure-based form of flux-vector splitting is applied to the Navier-Stokes equations, which are represented by an implicit lowest-order reduced Navier-Stokes (RNS) system and a purely diffusive, higher-order, deferred-corrector. A trapezoidal or box-like form of discretization insures that all mass conservation properties are satisfied at interfacial and outflow boundaries, even for this primitive-variable, non-staggered grid computation.
Navier-Stokes solution for steady two-dimensional transonic cascade flows
Kwon, O.K.
1987-01-01
A robust, time-marching Navier-Stokes solution procedure based on the explicit hopscotch method is presented for solution of steady, two-dimensional, transonic turbine cascade flows. The method is applied to the strong conservation form of the unsteady Navier-Stokes equations written in arbitrary curvilinear coordinates. Cascade flow solutions are obtained on an orthogonal, body-conforming ''O'' grid with the standard k-epsilon turbulence model. Computed results are presented and compared with experimental data.
Numerical Solution of Compressible Steady Flows around the RAE 2822 Airfoil
NASA Astrophysics Data System (ADS)
Kryštůfek, P.; Kozel, K.
2014-03-01
The article presents results of a numerical solution of subsonic, transonic and supersonic flows described by the system of Navier-Stokes equations in 2D laminar compressible flows around the RAE 2822 airfoil. Authors used FVM multistage Runge-Kutta method to numerically solve the flows around the RAE 2822 airfoil.
Evaluation of the flow properties of xanthan gum solution
Duda, J.L.; Klaus, E.E.; Leung, W.C.
1981-02-01
In this study, the solution properties of two forms of xanthan gum, a powder and a broth, which are commercially available were evaluated. As previous studies have shown, the solutions prepared from the broth do exhibit better injectivity properties. However, this investigation also shows that other properties of these solutions are not equivalent. In its natural state, xanthane gum exists as a multistranded helix. This ordered confirmation can be destroyed and in a denatured state, the xanthan gum exhibits a more random configuration and consequently higher viscosity. One of the major conclusions of this study is that the xanthan powder is partially denatured when compared to the xanthan molecules which exist in the broth. This denaturing may occur during the drying process in which the xanthan solids are removed from the broth. Solutions prepared from the broth in the absence of the added salt show a transition in the viscosity-temperature relationship at approximately 40 to 50/sup 0/C. This is consistent with the behavior of native xanthan gum solutions. At approximately 50/sup 0/C, the molecules in solution go into a more random state and consequently, an abrupt rise in the viscosity is observed. However, solutions prepared from the polymer powder do not show any evidence of such a transition. The solutions prepared from the broth can be thermally denatured, and this denaturing results in viscosities which are equivalent to the viscosities realized with the powdered polymer. Before denaturing, the broth solution showed a lower viscosity. Further, intrinsic viscosity measurements indicate that the hydrodynamic volume of the polymer solutions prepared from the borth are smaller than the hydrodynamic volumes of solutions prepared from the powder.
Analytical solution for two-phase flow in a wellbore using the drift-flux model
Pan, L.; Webb, S.W.; Oldenburg, C.M.
2011-11-01
This paper presents analytical solutions for steady-state, compressible two-phase flow through a wellbore under isothermal conditions using the drift flux conceptual model. Although only applicable to highly idealized systems, the analytical solutions are useful for verifying numerical simulation capabilities that can handle much more complicated systems, and can be used in their own right for gaining insight about two-phase flow processes in wells. The analytical solutions are obtained by solving the mixture momentum equation of steady-state, two-phase flow with an assumption that the two phases are immiscible. These analytical solutions describe the steady-state behavior of two-phase flow in the wellbore, including profiles of phase saturation, phase velocities, and pressure gradients, as affected by the total mass flow rate, phase mass fraction, and drift velocity (i.e., the slip between two phases). Close matching between the analytical solutions and numerical solutions for a hypothetical CO{sub 2} leakage problem as well as to field data from a CO{sub 2} production well indicates that the analytical solution is capable of capturing the major features of steady-state two-phase flow through an open wellbore, and that the related assumptions and simplifications are justified for many actual systems. In addition, we demonstrate the utility of the analytical solution to evaluate how the bottomhole pressure in a well in which CO{sub 2} is leaking upward responds to the mass flow rate of CO{sub 2}-water mixture.
High-order exact solutions for pseudo-plane ideal flows
NASA Astrophysics Data System (ADS)
Sun, Che
2016-08-01
A steady pseudo-plane ideal flow (PIF) model is derived from the 3D Euler equations under Boussinesq approximation. The model is solved analytically to yield high-degree polynomial exact solutions. Unlike quadratic flows, the cubic and quartic solutions display reduced geometry in the form of straightline jet, circular vortex, and multipolar strain field. The high-order circular-vortex solutions are vertically aligned and even the non-aligned multipolar strain-field solutions display vertical concentricity. Such geometry reduction is explained by an analytical theorem stating that only straightline jet and circular vortex have functional solutions to the PIF model.
Numerical solutions for unsteady subsonic vortical flows around loaded cascades
NASA Technical Reports Server (NTRS)
Fang, J.; Atassi, H. M.
1992-01-01
A frequency domain linearized unsteady aerodynamic analysis is presented for three-dimensional unsteady vortical flows around a cascade of loaded airfoils. The analysis fully accounts for the distortion of the impinging vortical disturbances by the mean flow. The entire unsteady flow field is calculated in response to upstream three-dimensional harmonic disturbances. Numerical results are presented for two standard cascade configurations representing turbine and compressor bladings for a reduced frequency range from 0.1 to 5. Results show that the upstream gust conditions and blade sweep strongly affect the unsteady blade response.
On the emergence of diel solute signals in flowing waters
NASA Astrophysics Data System (ADS)
Hensley, Robert T.; Cohen, Matthew J.
2016-02-01
Biota imprint their stoichiometry on relative rates of elemental cycling in the environment. Despite this coupling, producer-driven diel solute variation in rivers and streams is more apparent for some solutes (e.g., dissolved oxygen—DO) than others (e.g., nitrate—NO3-). We hypothesized that these differences arise from atmospheric equilibration, with signals emerging and evolving differently for gaseous and nongaseous solutes. Measurements of DO and NO3 in a spring-fed river, where constant inputs isolate in-stream processing, support this hypothesis, as do results from reactive transport modeling of river solute dynamics. Atmospheric equilibration dramatically shortens the benthic footprint over which signals integrate, facilitating emergence of diel DO signals in response to in-stream metabolism. In contrast, upstream influences persist much further downstream for nongaseous solutes, confounding and potentially obscuring the diel signals from in-stream assimilatory processing. Isolating diel NO3 signals from in-stream processing requires a two-station approach wherein metabolic impacts on solute variation are measured by difference between upstream and downstream sensors. Notably, two-station inference improves markedly when hydraulic controls on signal propagation such as dispersion and storage are explicitly considered. We conclude that the absence of diel signals at a single station for nongaseous solutes such as NO3- cannot be interpreted as lack of autotroph demand or element coupling. As advances in sensors enable the acquisition of an increasingly rich array of solute signals, controlling for differences in the emergence and downstream evolution of gaseous versus nongaseous solutes will dramatically improve inferences regarding the timing and magnitude of coupled elemental processing.
Multiple solutions in a rotating annulus flow model
NASA Technical Reports Server (NTRS)
Lu, Huei-Iin; Miller, Timothy L.; Butler, Karen A.
1993-01-01
A series of numerical experiments is conducted for rotating annulus flow using Miller et al.'s (1992) Geophysical Flow Simulation (GFS) model; a mixture of 25-percent upwind-differencing and 75-percent center-differencing is employed to approximate the temperature advective terms. Attention is given to the wavenumber selection time and wavenumber regimes, the sensitivity in the wavenumber transition regions, and hysteresis and irregular wavenumber selections.
NASA Technical Reports Server (NTRS)
Parikh, Paresh; Pirzadeh, Shahyar; Loehner, Rainald
1990-01-01
A set of computer programs for 3-D unstructured grid generation, fluid flow calculations, and flow field visualization was developed. The grid generation program, called VGRID3D, generates grids over complex configurations using the advancing front method. In this method, the point and element generation is accomplished simultaneously, VPLOT3D is an interactive, menudriven pre- and post-processor graphics program for interpolation and display of unstructured grid data. The flow solver, VFLOW3D, is an Euler equation solver based on an explicit, two-step, Taylor-Galerkin algorithm which uses the Flux Corrected Transport (FCT) concept for a wriggle-free solution. Using these programs, increasingly complex 3-D configurations of interest to aerospace community were gridded including a complete Space Transportation System comprised of the space-shuttle orbitor, the solid-rocket boosters, and the external tank. Flow solutions were obtained on various configurations in subsonic, transonic, and supersonic flow regimes.
Inverse solutions for laminar boundary-layer flows with separation and reattachment
NASA Technical Reports Server (NTRS)
Carter, J. E.
1975-01-01
Numerical solutions of the laminar, incompressible boundary layer equations are presented for flows involving separation and reattachment. Regular solutions are obtained with an inverse approach in which either the displacement thickness or the skin friction is specified; the pressure is deduced from the solution. A vorticity-stream-function formulation of the boundary layer equations is used to eliminate the unknown pressure. Solutions of the resulting finite difference equations, in which the flow direction is taken into account, are obtained by several global iteration schemes which are stable and have unconditional diagonal dominance. Results are compared with Klineberg and Steger's separated boundary layer calculations, and with Briley's solution of Navier-Stokes equations for a separated region. In addition, an approximate technique is presented in which the streamwise convection of vorticity is set equal to zero in the reversed flow region; such a technique results in a quick forward marching procedure for separated flows.
Numerical solution of inviscid and viscous laminar and turbulent flow around the airfoil
NASA Astrophysics Data System (ADS)
Slouka, Martin; Kozel, Karel
2016-03-01
This work deals with the 2D numerical solution of inviscid compressible flow and viscous compressible laminar and turbulent flow around the profile. In a case of turbulent flow algebraic Baldwin-Lomax model is used and compared with Wilcox k-omega model. Calculations are done for NACA 0012 and RAE 2822 airfoil profile for the different angles of upstream flow. Numerical results are compared and discussed with experimental data.
Solution of nonlinear flow equations for complex aerodynamic shapes
NASA Technical Reports Server (NTRS)
Djomehri, M. Jahed
1992-01-01
Solution-adaptive CFD codes based on unstructured methods for 3-D complex geometries in subsonic to supersonic regimes were investigated, and the computed solution data were analyzed in conjunction with experimental data obtained from wind tunnel measurements in order to assess and validate the predictability of the code. Specifically, the FELISA code was assessed and improved in cooperation with NASA Langley and Imperial College, Swansea, U.K.
Compressible seal flow analysis using the finite element method with Galerkin solution technique
NASA Technical Reports Server (NTRS)
Zuk, J.
1974-01-01
High pressure gas sealing involves not only balancing the viscous force with the pressure gradient force but also accounting for fluid inertia--especially for choked flow. The conventional finite element method which uses a Rayleigh-Ritz solution technique is not convenient for nonlinear problems. For these problems, a finite element method with a Galerkin solution technique (FEMGST) was formulated. One example, a three-dimensional axisymmetric flow formulation has nonlinearities due to compressibility, area expansion, and convective inertia. Solutions agree with classical results in the limiting cases. The development of the choked flow velocity profile is shown.
Rheological properties and the mechanism of a viscous flow of aqueous pectin solutions
NASA Astrophysics Data System (ADS)
Netesova, G. A.; Kotov, V. V.; Bodyakina, I. M.; Lukin, A. L.
2012-09-01
The rheological properties and mechanisms of a viscous flow of diluted apple pectin solutions are investigated. It is found that the rise in solution viscosity upon an increase in concentration and a drop in temperature is, along with the corresponding degree to which the interaction between pectin molecules and solvent is reduced, associated with the processes of structuring. The entropy of a viscous flow of pectin solutions is found to be positive: it grows with a rise in concentration is virtually temperature independent. It is established that the entropy factor makes the main contribution to the free energy value of a viscous flow.
Thin airfoil theory based on approximate solution of the transonic flow equation
NASA Technical Reports Server (NTRS)
Spreiter, John R; Alksne, Alberta Y
1957-01-01
A method is presented for the approximate solution of the nonlinear equations transonic flow theory. Solutions are found for two-dimensional flows at a Mach number of 1 and for purely subsonic and purely supersonic flows. Results are obtained in closed analytic form for a large and significant class of nonlifting airfoils. At a Mach number of 1 general expressions are given for the pressure distribution on an airfoil of specified geometry and for the shape of an airfoil having a prescribed pressure distribution. Extensive comparisons are made with available data, particularly for a Mach number of 1, and with existing solutions.
Thin airfoil theory based on approximate solution of the transonic flow equation
NASA Technical Reports Server (NTRS)
Spreiter, John R; Alksne, Alberta Y
1958-01-01
A method is presented for the approximate solution of the nonlinear equations of transonic flow theory. Solutions are found for two-dimensional flows at a Mach number of 1 and for purely subsonic and purely supersonic flows. Results are obtained in closed analytic form for a large and significant class of nonlifting airfoils. At a Mach number of 1 general expressions are given for the pressure distribution on an airfoil of specified geometry and for the shape of an airfoil having a prescribed pressure distribution. Extensive comparisons are made with available data, particularly for a Mach number of 1, and with existing solutions.
NASA Technical Reports Server (NTRS)
Yu, Sheng-Tao
2001-01-01
This document reports the conclusion and findings of our research activities for this grant. The goal of the project is the development and application of the method of Space-Time Conservation Element and Solution Element, or the CE/SE method, to simulate chemically reacting flows. The product of this project will be a high-fidelity, time-accurate flow solver analyzing unsteady flow fields advanced propulsion concepts, including the low-emission turbojet engine combustion and flow fields of the Pulse Detonation Engines (PDE). Based on the documents and computer software of the CE/SE method that we have received from the CE/SE working group at NASA Lewis, we have focused our research effort on addressing outstanding technical issues related to the extension of the CE/SE method for unsteady, chemically reactive flows. In particular, we have made progresses in the following three aspects: (1) Derivation of the governing equations for reacting flows; (2) Numerical treatments of stiff source terms; and (3) Detailed simulations of ZND detonation waves.
Boundary Integral Solutions to Three-Dimensional Unconfined Darcy's Flow
NASA Astrophysics Data System (ADS)
Lennon, Gerard P.; Liu, Philip L.-F.; Liggett, James A.
1980-08-01
The boundary integral equation method (BIEM) is used to solve three-dimensional potential flow problems in porous media. The problems considered here are time dependent and have a nonlinear boundary condition on the free surface. The entire boundary, including the moving free surface, discretized into linear finite elements for the purpose of evaluating the boundary integrals. The technique allows transient, three-dimensional problems to be solved with reasonable computational costs. Numerical examples include recharge through rectangular and circular areas and seepage flow from a surface pond. The examples are used to illustrate the method and show the nonlinear effects.
Analytical solution for subsurface gas flow to a well induced by surface pressure fluctuations.
Rossabi, Joseph; Falta, Ronald W
2002-01-01
A simple analytical model is presented for predicting subsurface gas flow to a vadose-zone well in response to atmospheric pressure fluctuations (barometric pumping). The effective radial permeability (kr) in the vicinity of the well is determined during model calibration using less than two weeks worth of data. By combining the flow solution with a solution for the vertical gas pressure, only atmospheric pressure data are required to predict the induced flow through a well. The ability to quantitatively predict naturally induced flow in vadose-zone wells by simple and inexpensive measurements is invaluable for systems using barometric pumping for remediation. PMID:11798048
Analytical Solution for Subsurface Gas Flow to a Well Induced by Surface Pressure Fluctuations
Rossabi, J.
2001-06-20
A simple analytical model is presented for predicting subsurface gas flow to a vadose zone well in response to atmospheric pressure fluctuations (barometric pumping). The effective radial permeability (kr) in the vicinity of the well is determined during model calibration using less than two weeks of data. By combining the flow solution with a solution for the vertical gas pressure, only atmospheric pressure data are required to predict the induced flow through a well. The ability to quantitatively predict naturally induced flow in vadose zone wells by simple and inexpensive measurements is invaluable for systems using barometric pumping for remediation.
A flow simulation study of protein solution under magnetic forces
NASA Astrophysics Data System (ADS)
Okada, Hidehiko; Hirota, Noriyuki; Matsumoto, Shinji; Wada, Hitoshi
2013-02-01
We have developed a superconducting magnet system generating magnetic forces able to compensate gravity and suppress convection of diamagnetic protein solution from which protein crystals precipitate. A simulation model has been proposed to elucidate the motion of protein solutions and search for the optimal conditions of the crystal formation process. This model incorporates general, non-uniform magnetic forces as external forces, while the previous models involve only simple, uniform magnetic forces. The simulation results indicate that the vertical component can suppress the convection of protein solution, while the horizontal component induces minimal convection. We, therefore, need to take into account the both components when considering the formation of protein crystals under magnetic forces.
NASA Astrophysics Data System (ADS)
Artrith, Nongnuch; Kolpak, Alexie
2014-03-01
The shape, size, and composition of catalyst nanoparticles can have a significant influence on their catalytic activity. Understanding such structure-reactivity relationships is crucial for the optimization of industrial catalysts and the design of novel catalysts with enhanced properties. In this work, we investigate the equilibrium shape and surface structure/composition of Au/Cu nanoparticles in solution, which have recently been shown to be stable and efficient catalysts for CO2 reduction. Using a combination of density functional theory calculations and large-scale Monte-Carlo and molecular dynamics simulations with reactive atomistic potentials, we determine how the nanoparticle shape, surface structure, and surface stoichiometry (i.e., fraction of Au at the surface relative to overall composition), evolve as a function of varying catalytic conditions. We discuss the effects of these changes on the surface electronic structure and binding energies of CO2, H2, and CH3OH. Our results emphasize the important relationships between catalytic environment (e.g., solvent effects), catalyst structure, and catalytic activity. We thank the Schlumberger Foundation Faculty for the Future for financial support. Computing time at XSEDE and NERSC clusters are gratefully acknowledged.
NASA Astrophysics Data System (ADS)
Alcoba, D. R.; Valdemoro, C.; Tel, L. M.; Pérez-Romero, E.
The equation obtained by mapping the matrix representation of the Schrödinger equation with the 2nd-order correlation transition matrix elements into the 2-body space is the so called correlation contracted Schrödinger equation (CCSE) (Alcoba, Phys Rev A 2002, 65, 032519). As shown by Alcoba (Phys Rev A 2002, 65, 032519) the solution of the CCSE coincides with that of the Schrödinger equation. Here the attention is focused in the vanishing hypervirial of the correlation operator (GHV), which can be identified with the anti-Hermitian part of the CCSE. A comparative analysis of the GHV and the anti-Hermitian part of the contracted Schrödinger equation (ACSE) indicates that the former is a stronger stationarity condition than the latter. By applying a Heisenberg-like unitary transformation to the G-particle-hole operator (Valdemoro et al., Phys Rev A 2000, 61, 032507), a good approximation of the expectation value of this operator as well as of the GHV is obtained. The method is illustrated for the case of the Beryllium isoelectronic series as well as for the Li2 and BeH2 molecules. The correlation energies obtained are within 98.80-100.09% of the full-configuration interaction ones. The convergence of these calculations was faster when using the GHV than with the ACSE.
On steady solutions to vacuumless Newtonian models of compressible flow
NASA Astrophysics Data System (ADS)
Łasica, Michał
2014-11-01
We prove the existence of weak solutions to the steady compressible Navier-Stokes system in the barotropic case for a class of pressure laws that are singular at vacuum. We consider the problem in a bounded domain in R2 with slip boundary conditions. Due to the appropriate construction of approximate solutions used in the proof, the obtained density is bounded away from 0 (and infinity). Owing to a classical result, this implies that the density and gradient of velocity are at least Hölder continuous, which does not generally hold for the classical isentropic model of a perfect gas in the presence of vacuum.
On Potential Flow Solutions from the Division Algebras
NASA Astrophysics Data System (ADS)
Dijkhuis, G. C.
2009-01-01
We write planar potential flow equations in real matrix form symmetrized by the Cauchy-Riemann conditions. From complex functions in matrix form we obtain parametric plots of a line vortex, of a vortex doublet and of vortex circulation confined by a wedge. For 3D potential flows we write quaternion functions in real matrix form regularized by six local and six global conditions for smooth closure. We identify the leading partial derivative in the Jacobian matrix as eigenvalue of its sub-matrix. Matrix symmetries ensure a nonzero expression for the Jacobian determinant. With quaternion inversion in matrix form we map planar vortex flow conformally on spherical surfaces as belts, lattices and Von Karman vortex streets. Likewise exponential quaternion functions map uniform 3D flow on concentric equipotential spheres orthogonal to stream surfaces with full-twist Möbius band topology. We connect the division algebras by a group structure resolving 8D octavian space into three quaternion sub- spaces, each resolving into three complex sub-planes.
Calcium phosphate crystallization on titania in a flowing Kokubo solution.
Hayakawa, Satoshi; Tsuru, Kanji; Uetsuki, Keita; Akasaka, Keisuke; Shirosaki, Yuki; Osaka, Akiyoshi
2015-08-01
Dry titania layers on air-oxidized titanium substrates have been found to be active enough to cause apatite to be deposited in Kokubo's simulated body fluid (SBF) in narrow confined spaces, such as those in narrow grooves and thin gaps. Such in vitro apatite deposition is the basis of the GRAPE(®) technique. The aim of the present study is to determine why GRAPE conditions favor apatite deposition when laminar SBF flow (at 0.01-0.3 ml/min) passes through a shallow channel (0.5 mm) between a pair of titanium substrates each with a dry layer of titania. Assessing the factors that control the heterogeneous nucleation process led to the proposal of the working hypothesis that there are nucleation pre-embryos, ion assemblies that can be stabilized to form embryos, on the titania layer but that they are removed by the SBF flow. Specimens were subjected to different combinations of processes. One combination was that titania layers were exposed to still or flowing SBF, and the other was that half of a specimen, the inlet or outlet side, was exposed to still or flowing SBF with the other half being covered. The surface morphologies of the specimens were then compared in detail. The conclusion was that exposure to still SBF for 2 days before exposure to flowing SBF was required for apatite to be deposited. Some complicated apatite deposition modes were observed, e.g., apatite was deposited even on areas unexposed to still SBF. All of the results were successfully interpreted using the working hypothesis. The conclusion was that the GRAPE(®) technique depends on the confined space holding pre-embryo and embryo assemblies. PMID:26264385
NASA Astrophysics Data System (ADS)
Trujillo Bueno, J.; Fabiani Bendicho, P.
1995-12-01
Iterative schemes based on Gauss-Seidel (G-S) and optimal successive over-relaxation (SOR) iteration are shown to provide a dramatic increase in the speed with which non-LTE radiation transfer (RT) problems can be solved. The convergence rates of these new RT methods are identical to those of upper triangular nonlocal approximate operator splitting techniques, but the computing time per iteration and the memory requirements are similar to those of a local operator splitting method. In addition to these properties, both methods are particularly suitable for multidimensional geometry, since they neither require the actual construction of nonlocal approximate operators nor the application of any matrix inversion procedure. Compared with the currently used Jacobi technique, which is based on the optimal local approximate operator (see Olson, Auer, & Buchler 1986), the G-S method presented here is faster by a factor 2. It gives excellent smoothing of the high-frequency error components, which makes it the iterative scheme of choice for multigrid radiative transfer. This G-S method can also be suitably combined with standard acceleration techniques to achieve even higher performance. Although the convergence rate of the optimal SOR scheme developed here for solving non-LTE RT problems is much higher than G-S, the computing time per iteration is also minimal, i.e., virtually identical to that of a local operator splitting method. While the conventional optimal local operator scheme provides the converged solution after a total CPU time (measured in arbitrary units) approximately equal to the number n of points per decade of optical depth, the time needed by this new method based on the optimal SOR iterations is only √n/2√2. This method is competitive with those that result from combining the above-mentioned Jacobi and G-S schemes with the best acceleration techniques. Contrary to what happens with the local operator splitting strategy currently in use, these novel
Techniques for correcting approximate finite difference solutions. [applied to transonic flow
NASA Technical Reports Server (NTRS)
Nixon, D.
1979-01-01
A method of correcting finite-difference solutions for the effect of truncation error or the use of an approximate basic equation is presented. Applications to transonic flow problems are described and examples given.
A GENERAL MASS-CONSERVATIVE NUMERICAL SOLUTION FOR THE UNSATURATED FLOW EQUATION
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...
A block-corrected subdomain solution procedure for recirculating flow calculations
NASA Technical Reports Server (NTRS)
Braaten, M. E.; Patankar, S. V.
1989-01-01
This paper describes a robust and efficient subdomain solution procedure for two-dimensional recirculating flows. The solution domain is divided into a number of overlapping subdomains, and a direct fully coupled solution is obtained for each subdomain using a sparse matrix form of LU decomposition. An effective parabolic block correction procedure, which calculates global corrections to the tentative solution by a marching technique similar to that used for boundary layer flows, is used to accelerate the convergence of the basic procedure. The use of effective block correction is found to be essential for the success of the subdomain approach on strongly recirculating flows. In a number of laminar two-dimensional flows, the new block-corrected method performed extremely well, rivaling the best direct methods in execution time, while requiring substantially less computer storage. The new method proved to be from two to ten times faster than conventional iterative methods, while requiring only a moderate increase in storage.
ERIC Educational Resources Information Center
Sanger, Michael J.; Greenbowe, Thomas J.
1997-01-01
Examines students' misconceptions and proposed mechanisms related to current flow in electrolyte solutions and the salt bridge. Confirms reported misconceptions and identifies several new ones. Discusses probable sources of misconceptions and some methods for preventing them. Contains 27 references. (JRH)
NASA Astrophysics Data System (ADS)
Ngo-Cong, D.; Mohammed, F. J.; Strunin, D. V.; Skvortsov, A. T.; Mai-Duy, N.; Tran-Cong, T.
2015-06-01
The contaminant transport process governed by the advection-diffusion equation plays an important role in modelling industrial and environmental flows. In this article, our aim is to accurately reduce the 2-D advection-diffusion equation governing the dispersion of a contaminant in a turbulent open channel flow to its 1-D approximation. The 1-D model helps to quickly estimate the horizontal size of contaminant clouds based on the values of the model coefficients. We derive these coefficients analytically and investigate numerically the model convergence. The derivation is based on the centre manifold theory to obtain successively more accurate approximations in a consistent manner. Two types of the average velocity profile are considered: the classical logarithmic profile and the power profile. We further develop the one-dimensional integrated radial basis function network method as a numerical approach to obtain the numerical solutions to both the original 2-D equation and the approximate 1-D equations. We compare the solutions of the original models with their centre-manifold approximations at very large Reynolds numbers. The numerical results obtained from the approximate 1-D models are in good agreement with those of the original 2-D model for both the logarithmic and power velocity profiles.
NASA Astrophysics Data System (ADS)
Laine-Kaulio, H.; Karvonen, T.; Koivusalo, H.; Lauren, A.; Saastamoinen, S.
2009-04-01
horizon, and based on the groundwater model from 6E-5 m/s in the subsoil to 3E-4 m/s in the eluvial horizon. The dual nature of the soil structure complicated the simulation of the chloride plume in the study slope. The closest correspondence between the observed and simulated flow velocity and concentration of the chloride plume was reached by i) using the conductivity values from the inverse groundwater model, and by ii) restricting the transport of water and solute to an active fraction of the total pore space in the model. The modelled flow velocity did not increase to the observed level with increasing conductivities, because in the highly conductive soil the irrigation intensity was no longer able to saturate the soil. As for the strength of the plume, the modelled chloride concentrations remained too low when the solution was allowed to spread to the entire pore space. The study suggests that a more accurate simulation of the fast preferential flow and chloride transport requires parallel and coupled simulation of water and solutes in the two domains of slow and fast flow.
Prolonged river water pollution due to variable-density flow and solute transport in the riverbed
NASA Astrophysics Data System (ADS)
Jin, Guangqiu; Tang, Hongwu; Li, Ling; Barry, D. A.
2015-04-01
A laboratory experiment and numerical modeling were used to examine effects of density gradients on hyporheic flow and solute transport under the condition of a solute pulse input to a river with regular bed forms. Relatively low-density gradients due to an initial salt pulse concentration of 1.55 kg m-3 applied in the experiment were found to modulate significantly the pore-water flow and solute transport in the riverbed. Such density gradients increased downward flow and solute transport in the riverbed by factors up to 1.6. This resulted in a 12.2% increase in the total salt transfer from the water column to the riverbed over the salt pulse period. As the solute pulse passed, the effect of the density gradients reversed, slowing down the release of the solute back to the river water by a factor of 3.7. Numerical modeling indicated that these density effects intensified as salt concentrations in the water column increased. Simulations further showed that the density gradients might even lead to unstable flow and result in solute fingers in the bed of large bed forms. The slow release of solute from the bed back to the river led to a long tail of solute concentration in the river water. These findings have implications for assessment of impact of pollution events on river systems, in particular, long-term effects on both the river water and riverbed due to the hyporheic exchange.
NASA Astrophysics Data System (ADS)
Ryu, Jaiyoung; Hu, Xiao; Shadden, Shawn C.
2014-11-01
The cerebral circulation is unique in its ability to maintain blood flow to the brain under widely varying physiologic conditions. Incorporating this autoregulatory response is critical to cerebral blood flow modeling, as well as investigations into pathological conditions. We discuss a one-dimensional nonlinear model of blood flow in the cerebral arteries that includes coupling of autoregulatory lumped parameter networks. The model is tested to reproduce a common clinical test to assess autoregulatory function - the carotid artery compression test. The change in the flow velocity at the middle cerebral artery (MCA) during carotid compression and release demonstrated strong agreement with published measurements. The model is then used to investigate vasospasm of the MCA, a common clinical concern following subarachnoid hemorrhage. Vasospasm was modeled by prescribing vessel area reduction in the middle portion of the MCA. Our model showed similar increases in velocity for moderate vasospasms, however, for serious vasospasm (~ 90% area reduction), the blood flow velocity demonstrated decrease due to blood flow rerouting. This demonstrates a potentially important phenomenon, which otherwise would lead to false-negative decisions on clinical vasospasm if not properly anticipated.
Microbial Growth, Water Flow, and Solute Transport in Unsaturated Porous Media
NASA Astrophysics Data System (ADS)
Yarwood, R. R.; Rockhold, M. L.; Niemet, M. R.; Bottomley, P. J.; Selker, J. S.
2004-05-01
We present an investigation that studied interactions between microbial growth, water flow, and solute transport in variably saturated porous media. The experimental system provided for continuous, noninvasive observation of microbial activity, while simultaneously monitoring water content and solute flow paths in a two-dimensional porous matrix. The spatial and temporal development of microbial colonization by a Pseudomonas fluorescens bacterium was monitored by induction of a bioluminescent phenotype. A model was developed that allowed quantification of population density from bioluminescence measurements. Liquid saturation was quantified from the transmission of light through the system, and solute flow paths were determined with a dye tracer. Dramatic changes in microbial colonization were observed, including upward migration against flow. This migration was particularly interesting because it cannot be explained by passive transport. Bacterial growth and accumulation significantly impacted the hydrologic properties of the media, including apparent desaturation within the colonized region, diversion of flow around the colonized region, and lowering of the capillary fringe height.
Solution of non-isoenergetic supersonic flows by method of characteristics, volume 3
NASA Technical Reports Server (NTRS)
Prozan, R. J.
1972-01-01
The calculation of supersonic flow fields by the method of characteristics. The theoretical approach to the solution of these flow fields and a computer program to implement the numerical solution of the flow equations are discussed. This versatile program has a flexible set of boundary conditions enabling the calculation of nozzles, plumes and many other complex flow fields. A complete derivation of the equations of motion for reacting gas systems is presented. An important consequence of this derivation is that, for the reaction assumptions which were made, the thermochemistry was shown to be uncoupled from the flow solution and as such could be solved separately. The methods of characteristics equations are shown to be formally the same for ideal, frozen, and equilibrium reacting gas mixtures.
NASA Astrophysics Data System (ADS)
Reitman, L.; Wolfshtein, M.; Adler, D.
1982-11-01
A finite difference method is developed for solving the non-viscous formulation of a three-dimensional compressible flow problem for turbomachinery impellers. The numerical results and the time efficiency of this method are compared to that provided by a finite element method for this problem. The finite difference method utilizes a numerical, curvilinear, and non-orthogonal coordinate transformation and the ADI scheme. The finite difference method is utilized to solve a test problem of a centrifugal compressor impeller. It is shown that the finite difference method produces results in good agreement with the experimentally determined flow fields and is as accurate as the finite element technique. However, the finite difference method only requires about half the time in order to obtain the solution for this problem as that required by the finite element method.
Solution of Reactive Compressible Flows Using an Adaptive Wavelet Method
NASA Astrophysics Data System (ADS)
Zikoski, Zachary; Paolucci, Samuel; Powers, Joseph
2008-11-01
This work presents numerical simulations of reactive compressible flow, including detailed multicomponent transport, using an adaptive wavelet algorithm. The algorithm allows for dynamic grid adaptation which enhances our ability to fully resolve all physically relevant scales. The thermodynamic properties, equation of state, and multicomponent transport properties are provided by CHEMKIN and TRANSPORT libraries. Results for viscous detonation in a H2:O2:Ar mixture, and other problems in multiple dimensions, are included.
An analytic solution for barotropic flow along a variable slope topography
NASA Astrophysics Data System (ADS)
Kuehl, Joseph J.
2014-11-01
An analytic solution is derived for the generic oceanographic situation of a barotropic current flowing along sloping topography. It is shown that the shallow water equations can be reduced to a heat-like equation in which βeffect is balanced by Ekman dissipation. For constant topography, the system is found to admit a well-known similarity solution and this solution is generalized to the case of variable topography. Several properties of the solution are explored, and an example is given for flow along the northern Gulf of Mexico slope, between the De Soto Canyon and the Mississippi Canyon. This "Topographic β-plume" solution may serve as a model for further research concerning the influence exerted by geophysical boundary layers on the interior flow via their structure and stability.
A semi-analytical solution for slug tests in an unconfined aquifer considering unsaturated flow
NASA Astrophysics Data System (ADS)
Sun, Hongbing
2016-01-01
A semi-analytical solution considering the vertical unsaturated flow is developed for groundwater flow in response to a slug test in an unconfined aquifer in Laplace space. The new solution incorporates the effects of partial penetrating, anisotropy, vertical unsaturated flow, and a moving water table boundary. Compared to the Kansas Geological Survey (KGS) model, the new solution can significantly improve the fittings of the modeled to the measured hydraulic heads at the late stage of slug tests in an unconfined aquifer, particularly when the slug well has a partially submerged screen and moisture drainage above the water table is significant. The radial hydraulic conductivities estimated with the new solution are comparable to those from the KGS, Bouwer and Rice, and Hvorslev methods. In addition, the new solution also can be used to examine the vertical conductivity, specific storage, specific yield, and the moisture retention parameters in an unconfined aquifer based on slug test data.
NASA Technical Reports Server (NTRS)
Mcfarland, E. R.
1981-01-01
A solution method was developed for calculating compressible inviscid flow through a linear cascade of arbitrary blade shapes. The method uses advanced surface singularity formulations which were adapted from those in current external flow analyses. The resulting solution technique provides a fast flexible calculation for flows through turbomachinery blade rows. The solution method and some examples of the method's capabilities are presented.
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.
An analytical solution for transient flow of Bingham viscoplastic materials in rock fractures
Amadei, B.; Savage, W.Z.
2001-01-01
We present below an analytical solution to model the one-dimensional transient flow of a Bingham viscoplastic material in a fracture with parallel walls (smooth or rough) that is subjected to an applied pressure gradient. The solution models the acceleration and the deceleration of the material as the pressure gradient changes with time. Two cases are considered: A pressure gradient applied over a finite time interval and an applied pressure gradient that is constant over time. The solution is expressed in dimensionless form and can therefore be used for a wide range of Bingham viscoplastic materials. The solution is also capable of capturing the transition that takes place in a fracture between viscoplastic flow and rigid plug flow. Also, it shows the development of a rigid central layer in fractures, the extent of which depends on the fluid properties (viscosity and yield stress), the magnitude of the pressure gradient, and the fracture aperture and surface roughness. Finally, it is shown that when a pressure gradient is applied and kept constant, the solution for the fracture flow rate converges over time to a steady-state solution that can be defined as a modified cubic law. In this case, the fracture transmissivity is found to be a non-linear function of the head gradient. This solution provides a tool for a better understanding of the flow of Bingham materials in rock fractures, interfaces, and cracks. ?? 2001 Elsevier Science Ltd. All rights reserved.
NASA Astrophysics Data System (ADS)
Baldner, Charles; Bogart, Richard S.
2016-05-01
The use of helioseismology to study the properties of the Sun has yielded very high precision measurements of solar flows throughout much of the interior. It has been apparent for many years, however, that the accuracy of many of these measurements is suspect due to significant systematic effects in helioseismic techniques. The most well-known effect in flow measurements is sometimes referred to as the `center-to-limb' effect, in which flow measurements depend strongly on the distance of the measurement from the center of the observed solar disk. Attempts have already been made to explain the origin of this error (e.g. Balder & Schou 2012) and to correct it (e.g. Zhao et al. 2011). Significant work remains, however.In this work, we report on continued efforts to precisely characterize the effect of position on the observed disk on flow measurements in the HMI ring diagram pipeline, and from other HMI data. Our efforts are focused on 1) quantifying the non-radial systematic effect in flow measurements; 2) understanding the effect of the underlying model used in the mode parameter estimations; and 3) characterizing the difference between helioseismic measurements made with different observed quantities.
Analytical solution of laminar-laminar stratified two-phase flows with curved interfaces
Brauner, N.; Rovinsky, J.; Maron, D.M.
1995-09-01
The present study represents a complete analytical solution for laminar two-phase flows with curved interfaces. The solution of the Navier-Stokes equations for the two-phases in bipolar coordinates provides the `flow monograms` describe the relation between the interface curvature and the insitu flow geometry when given the phases flow rates and viscosity ratios. Energy considerations are employed to construct the `interface monograms`, whereby the characteristic interfacial curvature is determined in terms of the phases insitu holdup, pipe diameter, surface tension, fluids/wall adhesion and gravitation. The two monograms are then combined to construct the system `operational monogram`. The `operational monogram` enables the determination of the interface configuration, the local flow characteristics, such as velocity profiles, wall and interfacial shear stresses distribution as well as the integral characteristics of the two-phase flow: phases insitu holdup and pressure drop.
Exact solution of cilia induced flow of a Jeffrey fluid in an inclined tube.
Maqbool, K; Shaheen, S; Mann, A B
2016-01-01
The present study investigated the cilia induced flow of MHD Jeffrey fluid through an inclined tube. This study is carried out under the assumptions of long wavelength and low Reynolds number approximations. Exact solutions for the velocity profile, pressure rise, pressure gradient, volume flow rate and stream function are obtained. Effects of pertinent physical parameters on the computational results are presented graphically. PMID:27610298
Technology Transfer Automated Retrieval System (TEKTRAN)
[1] Laboratory and numerical studies were conducted to investigate the transport and fate of Escherichia coli D21g and coliphage f174 in saturated soils with preferential flow under different solution ionic strength (IS'='1, 5, 20, and 100 mM) conditions. Preferential flow systems were created by em...
An analytical solution for Dean flow in curved ducts with rectangular cross section
NASA Astrophysics Data System (ADS)
Norouzi, M.; Biglari, N.
2013-05-01
In this paper, a full analytical solution for incompressible flow inside the curved ducts with rectangular cross-section is presented for the first time. The perturbation method is applied to solve the governing equations and curvature ratio is considered as the perturbation parameter. The previous perturbation solutions are usually restricted to the flow in curved circular or annular pipes related to the overly complex form of solutions or singularity situation for flow in curved ducts with non-circular shapes of cross section. This issue specifies the importance of analytical studies in the field of Dean flow inside the non-circular ducts. In this study, the main flow velocity, stream function of lateral velocities (secondary flows), and flow resistance ratio in rectangular curved ducts are obtained analytically. The effect of duct curvature and aspect ratio on flow field is investigated as well. Moreover, it is important to mention that the current analytical solution is able to simulate the Taylor-Görtler and Dean vortices (vortices in stable and unstable situations) in curved channels.
Numerical solution of boundary layer MHD flow with viscous dissipation.
Mishra, S R; Jena, S
2014-01-01
The present paper deals with a steady two-dimensional laminar flow of a viscous incompressible electrically conducting fluid over a shrinking sheet in the presence of uniform transverse magnetic field with viscous dissipation. Using suitable similarity transformations the governing partial differential equations are transformed into ordinary differential equations and then solved numerically by fourth-order Runge-Kutta method with shooting technique. Results for velocity and temperature profiles for different values of the governing parameters have been discussed in detail with graphical representation. The numerical evaluation of skin friction and Nusselt number are also given in this paper. PMID:24672367
Numerical solution of compressible viscous flows at high Reynolds numbers
NASA Technical Reports Server (NTRS)
Maccormack, R. W.
1981-01-01
A new numerical method which was used to reduce the computation time required in fluid dynamics to solve the Navier-Stokes equations at flight Reynolds numbers is described. The method is the implicit analogue of the explicit finite different method. It uses this as its first stage, while the second stage removes the restrictive stability condition by recasting the difference equations in an implicit form. The resulting matrix equations to be solved are either upper or lower block bidiagonal equations. The new method makes it possible and practical to calculate many important three dimensional, high Reynolds number flow fields on computers.
Similarity solutions of jet flows using a multiple-scale turbulence model
NASA Technical Reports Server (NTRS)
Chen, C. P.; Guo, K. L.
1989-01-01
An accurate finite difference scheme is used to study the performance of a newly developed multiple-scale turbulence model in the similarity region of plane/radial/round jet flows. Under the assumption that molecular viscosity can be neglected, the governing equations contain a hidden eigenvalue which corresponds to the sharp boundary of the flowfield. It is found that this eigenvalue is the locus of the free boundary separating the turbulent shear flow and the irrotational ambient fluid.
Analytical Solution to the MHD Flow of Micropolar Fluid Over a Linear Stretching Sheet
NASA Astrophysics Data System (ADS)
Siddheshwar, P. G.; Mahabaleshwar, U. S.
2015-05-01
The flow due to a linear stretching sheet in a fluid with suspended particles, modeled as a micropolar fluid, is considered. All reported works on the problem use numerical methods of solution or a regular perturbation technique. An analytical solution is presented in the paper for the coupled non-linear differential equations with inhomogeneous boundary conditions.
On Exact Solutions for Oscillatory Flows in a Generalized Burgers Fluid with Slip Condition
NASA Astrophysics Data System (ADS)
Hayat, Tasawar; Najam, Saher; Sajid, Muhammad; Ayub, Muhammad; Mesloub, Said
2010-05-01
An analysis is performed for the slip effects on the exact solutions of flows in a generalized Burgers fluid. The flow modelling is based upon the magnetohydrodynamic (MHD) nature of the fluid and modified Darcy law in a porous space. Two illustrative examples of oscillatory flows are considered. The results obtained are compared with several limiting cases. It has been shown here that the derived results hold for all values of frequencies including the resonant frequency.
The effect of viscosity on steady transonic flow with a nodal solution topology
NASA Technical Reports Server (NTRS)
Owocki, Stanley P.; Zank, Gary P.
1991-01-01
The effect of viscosity on a steady, transonic flow for which the inviscid limit has a nodal solution topology near the critical point is investigated. For the accelerating case, viscous solutions tend to repel each other, so that a very delicate choice of initial conditions is required to prevent them from diverging. Only the two critical solutions extend to arbitrarily large distances into both the subsonic and supersonic flows. For the decelerating case, the solutions tend to attract, and so an entire two-parameter family of solutions now extends over large distances. The general effect of viscosity on the solution degeneracy of a nodal topology is thus to reduce or limit it for the accelerating case and to enhance it for the decelerating case. The astrophysical implications of these findings are addressed.
Travelling-wave solutions bifurcating from relative periodic orbits in plane Poiseuille flow
NASA Astrophysics Data System (ADS)
Rawat, Subhandu; Cossu, Carlo; Rincon, François
2016-06-01
Travelling-wave solutions are shown to bifurcate from relative periodic orbits in plane Poiseuille flow at Re = 2000 in a saddle-node infinite-period bifurcation. These solutions consist in self-sustaining sinuous quasi-streamwise streaks and quasi-streamwise vortices located in the bulk of the flow. The lower branch travelling-wave solutions evolve into spanwise localized states when the spanwise size Lz of the domain in which they are computed is increased. On the contrary, the upper branch of travelling-wave solutions develops multiple streaks when Lz is increased. Upper-branch travelling-wave solutions can be continued into coherent solutions to the filtered equations used in large-eddy simulations where they represent turbulent coherent large-scale motions.
Manufactured solutions for steady-flow Reynolds-averaged Navier-Stokes solvers
NASA Astrophysics Data System (ADS)
Eça, L.; Hoekstra, M.; Vaz, G.
2012-06-01
This paper presents manufactured solutions (MS's) for code verification of incompressible flow solvers based on the Reynolds-averaged Navier-Stokes (RANS) equations. The proposed solutions mimic statistically steady, two-dimensional or three-dimensional near-wall turbulent flows in a simple domain (rectangle or rectangular box) at a given Reynolds number. The proposed analytical functions cover the mean flow quantities and the dependent variables of several eddy-viscosity turbulence models. Namely, the undamped eddy-viscosity of the Spalart and Allmaras and Menter one-equations models, from the one (SKL) and two-equation (KSKL) models proposed by Menter, the turbulence kinetic energy and the turbulence frequency included in two-equation k - ω models. A basic flow field resembling a turbulent flat plate flow is constructed with the turbulence quantities defined from 'automatic wall functions' that are supposed to reproduce more or less the normal behaviour of these variables. Alternative flow fields are constructed superposing a perturbation flow field that creates a 'recirculation zone'. However, the near-wall solution of the basic flow is kept to avoid zero friction at the wall. Three-dimensional MS's are obtained from the blending of the basic two-dimensional MS's in the transverse direction. All flow fields satisfy mass conservation, i.e. mean velocity fields are divergence-free. The source functions required for the balancing of momentum and turbulence quantities transport equations and all the dependent variables and their derivatives are available in Fortran 90 modules.
Solution of the Falkner-Skan wedge flow by a revised optimal homotopy asymptotic method.
Madaki, A G; Abdulhameed, M; Ali, M; Roslan, R
2016-01-01
In this paper, a revised optimal homotopy asymptotic method (OHAM) is applied to derive an explicit analytical solution of the Falkner-Skan wedge flow problem. The comparisons between the present study with the numerical solutions using (fourth order Runge-Kutta) scheme and with analytical solution using HPM-Padé of order [4/4] and order [13/13] show that the revised form of OHAM is an extremely effective analytical technique. PMID:27186477
Streamwise-Localized Solutions at the Onset of Turbulence in Pipe Flow
NASA Astrophysics Data System (ADS)
Avila, M.; Mellibovsky, F.; Roland, N.; Hof, B.
2013-05-01
Although the equations governing fluid flow are well known, there are no analytical expressions that describe the complexity of turbulent motion. A recent proposition is that in analogy to low dimensional chaotic systems, turbulence is organized around unstable solutions of the governing equations which provide the building blocks of the disordered dynamics. We report the discovery of periodic solutions which just like intermittent turbulence are spatially localized and show that turbulent transients arise from one such solution branch.
Influence of microgels in polysaccharide solutions on their flow behavior through porous media
Chauveteau, G.; Kohler, N.
1984-06-01
Microgels existing in xanthan solutions, which are partly responsible for the poor injectability of such solutions, are retained around the injection wells. Therefore, most of the oil is swept by microgel-free solutions. This paper shows that even a few microgels can strongly modify flow behavior in porous media. Consequently, their careful elimination is required in laboratory tests for proper design of a polymer flood.
Long-term degradation of dilute polyacrylamide solutions in turbulent pipe flow
Choi, U.S.; Kasza, K.E.
1989-05-01
The long-term degradation behavior of 200 wppM polyacrylamide solution was studied experimentally in a closed recirculatory flow loop at temperatures of 7.2, 25 and 87.8/degree/C. The degradation behavior was found to be strongly dependent on temperature. The results indicate that, with flow shear similar to that encountered in practical DHC pipe flow, polyacrylamide solutions are highly effective and have a reasonable lifetime at chilled water temperature of 7.2/degree/C. 9 refs., 4 figs.
A pressure based method for the solution of viscous incompressible turbomachinery flows
NASA Technical Reports Server (NTRS)
Hobson, Garth Victor; Lakshminarayana, B.
1991-01-01
A new technique was developed for the solution of the incompressible Navier-Stokes equations. The numerical technique, derived from a pressure substitution method (PSM), overcomes many of the deficiencies of the pressure correction method. This technique allows for the direct solution of the actual pressure in the form of a Poisson equation which is derived from the pressure weighted substitution of the full momentum equations into the continuity equation. Two dimensional internal flows are computed with this method. The prediction of cascade performance is presented. The extention of the pressure correction method for the solution of three dimensional flows is also presented.
Evaluation of alkanolamine solutions for carbon dioxide removal in cross-flow rotating packed beds.
Lin, Chia-Chang; Lin, Yu-Hong; Tan, Chung-Sung
2010-03-15
The removal of CO(2) from a 10 vol% CO(2) gas by chemical absorption with 30 wt% alkanolamine solutions containing monoethanolamine (MEA), piperazine (PZ), and 2-amino-2-methyl-1-propanol (AMP) in the cross-flow rotating packed bed (RPB) was investigated. The CO(2) removal efficiency increased with rotor speed, liquid flow rate and inlet liquid temperature. However, the CO(2) removal efficiency decreased with gas flow rate. Also, the CO(2) removal efficiency was independent of inlet gas temperature. The 30 wt% alkanolamine solutions containing PZ with MEA were the appropriate absorbents compared with the single alkanolamine (MEA, AMP) and the mixed alkanolamine solutions containing AMP with MEA. A higher portion of PZ in alkanolamine solutions was more favorable to CO(2) removal. Owing to less contact time in the cross-flow RPB, alkanolamines having high reaction rates with CO(2) are suggested to be used. For the mixed alkanolamine solution containing 12 wt% PZ and 18 wt% MEA, the highest gas flow rate allowed to achieve the CO(2) removal efficiency more than 90% at a liquid flow rate of 0.54 L/min was of 29 L/min. The corresponding height of a transfer unit (HTU) was found to be less than 5.0 cm, lower than that in the conventional packed bed. PMID:19910115
An electric impedance based microelectromechanical system flow sensor for ionic solutions
Ayliffe, H Edward; Rabbitt, RD
2008-01-01
Microfluidic devices with channel cross sections measuring 4 × 10 μm2 instrumented with gold microelectrodes were used to sense flow rates of ionic solutions on the basis of electric impedance (EI) measured perpendicular to the flow. Negative pressures were applied to access ports of the microdevices to generate flow of saline solutions (physiologic concentrations 0.9%) through the micro-EI recording zone with flow rates between 2.4 and 4.8 μl min−1. The EI spectra (100 Hz–20 MHz) recorded under flow conditions were compared with the no-flow condition. Changes in the magnitude of EI (at 350 Hz) for flow rates as low as 2.4 μl min−1 were statistically significant compared with the no-flow condition. The observed dependence of EI on flow rate is attributed to the relative difference between the rate of migration of charge-balancing electrolyte ions to the electrode surface and the rate of removal of the same ions by forced convection. An electrochemical convection–diffusion model was used to study the observed dependence on flow. Simulations support the conceptual model that passing DC current from the gold electrodes into the ionic solution results in an increase in ionic concentration near the electrode surface (due to the inward migration of counter-balancing ions). When the fluid flow rates increase, these counter-balancing ions are replaced by the bulk solution, thereby lowering the average ionic concentration within the recording zone. This local concentration drop results in an increase in the real part of the impedance. PMID:19672321
Navier-Stokes solutions for two-dimensional subsonic base flow
NASA Technical Reports Server (NTRS)
Rudy, D. H.
1984-01-01
Methods for determining the effects of mass injection from the trailing edge of a bluff body at low speeds and in transonic flow were numerically studied along with an unmodified blunt-based body to gain insight into the effects of vortex shedding on the base drag. The methodology used to obtain finite-difference solutions to the Navier-Stokes equations for subsonic compressible two-dimensional near-wake flows is presented. The effectiveness of an introduced outflow boundary condition which minimizes reflections back into the computational domain was demonstrated with the solution of a model vortex problem. Calculations of the near-wake flow past a circular cylinder were in excellent agreement with experimental data. Laminar-flow solutions for a blunt-based model with and without a base cavity and with mass injection into the wake agreed qualitatively with experimental observations. The drag reduction capability provided by such base modifications was demonstrated.
Approximate analytic solutions to 3D unconfined groundwater flow within regional 2D models
NASA Astrophysics Data System (ADS)
Luther, K.; Haitjema, H. M.
2000-04-01
We present methods for finding approximate analytic solutions to three-dimensional (3D) unconfined steady state groundwater flow near partially penetrating and horizontal wells, and for combining those solutions with regional two-dimensional (2D) models. The 3D solutions use distributed singularities (analytic elements) to enforce boundary conditions on the phreatic surface and seepage faces at vertical wells, and to maintain fixed-head boundary conditions, obtained from the 2D model, at the perimeter of the 3D model. The approximate 3D solutions are analytic (continuous and differentiable) everywhere, including on the phreatic surface itself. While continuity of flow is satisfied exactly in the infinite 3D flow domain, water balance errors can occur across the phreatic surface.
Zhi-Gang Feng
2012-05-31
The simulation of particulate flows for industrial applications often requires the use of two-fluid models, where the solid particles are considered as a separate continuous phase. One of the underlining uncertainties in the use of the two-fluid models in multiphase computations comes from the boundary condition of the solid phase. Typically, the gas or liquid fluid boundary condition at a solid wall is the so called no-slip condition, which has been widely accepted to be valid for single-phase fluid dynamics provided that the Knudsen number is low. However, the boundary condition for the solid phase is not well understood. The no-slip condition at a solid boundary is not a valid assumption for the solid phase. Instead, several researchers advocate a slip condition as a more appropriate boundary condition. However, the question on the selection of an exact slip length or a slip velocity coefficient is still unanswered. Experimental or numerical simulation data are needed in order to determinate the slip boundary condition that is applicable to a two-fluid model. The goal of this project is to improve the performance and accuracy of the boundary conditions used in two-fluid models such as the MFIX code, which is frequently used in multiphase flow simulations. The specific objectives of the project are to use first principles embedded in a validated Direct Numerical Simulation particulate flow numerical program, which uses the Immersed Boundary method (DNS-IB) and the Direct Forcing scheme in order to establish, modify and validate needed energy and momentum boundary conditions for the MFIX code. To achieve these objectives, we have developed a highly efficient DNS code and conducted numerical simulations to investigate the particle-wall and particle-particle interactions in particulate flows. Most of our research findings have been reported in major conferences and archived journals, which are listed in Section 7 of this report. In this report, we will present a
Elasto-inertial particle focusing under the viscoelastic flow of DNA solution in a square channel.
Kim, Bookun; Kim, Ju Min
2016-03-01
Particle focusing is an essential step in a wide range of applications such as cell counting and sorting. Recently, viscoelastic particle focusing, which exploits the spatially non-uniform viscoelastic properties of a polymer solution under Poiseuille flow, has attracted much attention because the particles are focused along the channel centerline without any external force. Lateral particle migration in polymer solutions in square channels has been studied due to its practical importance in lab-on-a-chip applications. However, there are still many questions about how the rheological properties of the medium alter the equilibrium particle positions and about the flow rate ranges for particle focusing. In this study, we investigated lateral particle migration in a viscoelastic flow of DNA solution in a square microchannel. The elastic property is relevant due to the long relaxation time of a DNA molecule, even when the DNA concentration is extremely low. Further, the shear viscosity of the solution is essentially constant irrespective of shear rate. Our current results demonstrate that the particles migrate toward the channel centerline and the four corners of a square channel in the dilute DNA solution when the inertia is negligible (elasticity-dominant flow). As the flow rate increases, the multiple equilibrium particle positions are reduced to a single file along the channel centerline, due to the elasto-inertial particle focusing mechanism. The current results support that elasto-inertial particle focusing mechanism is a universal phenomenon in a viscoelastic fluid with constant shear viscosity (Boger fluid). Also, the effective flow rate ranges for three-dimensional particle focusing in the DNA solution were significantly higher and wider than those for the previous synthetic polymer solution case, which facilitates high throughput analysis of particulate systems. In addition, we demonstrated that the DNA solution can be applied to focus a wide range of
D4Z - a new renumbering for iterative solution of ground-water flow and solute- transport equations
Kipp, K.L.; Russell, T.F.; Otto, J.S.
1992-01-01
D4 zig-zag (D4Z) is a new renumbering scheme for producing a reduced matrix to be solved by an incomplete LU preconditioned, restarted conjugate-gradient iterative solver. By renumbering alternate diagonals in a zig-zag fashion, a very low sensitivity of convergence rate to renumbering direction is obtained. For two demonstration problems involving groundwater flow and solute transport, iteration counts are related to condition numbers and spectra of the reduced matrices.
NASA Astrophysics Data System (ADS)
Wu, Lei; Liu, Haihu; Zhang, Yonghao; Reese, Jason M.
2015-08-01
The Boltzmann equation with an arbitrary intermolecular potential is solved by the fast spectral method. As examples, noble gases described by the Lennard-Jones potential are considered. The accuracy of the method is assessed by comparing both transport coefficients with variational solutions and mass/heat flow rates in Poiseuille/thermal transpiration flows with results from the discrete velocity method. The fast spectral method is then applied to Fourier and Couette flows between two parallel plates, and the influence of the intermolecular potential on various flow properties is investigated. It is found that for gas flows with the same rarefaction parameter, differences in the heat flux in Fourier flow and the shear stress in Couette flow are small. However, differences in other quantities such as density, temperature, and velocity can be very large.
NASA Astrophysics Data System (ADS)
Farsiani, Yasaman; Elbing, Brian
2015-11-01
Adding trace amounts of long chain polymers into a liquid flow is known to reduce skin friction drag by up to 80%. While polymer drag reduction (PDR) has been successfully implemented in internal flows, diffusion and degradation have limited its external flow applications. A weakness in many previous PDR studies is that there was no characterization of the polymer being injected into the turbulent boundary layer, which can be accomplished by testing a sample in a pressure-drop tube. An implicit assumption in polymer characterization is that the flow is fully developed at the differential pressure measurement. While available data in the literature shows that the entry length to achieve fully developed flow increases with polymeric solutions, it is unclear how long is required to achieve fully developed flow for non-Newtonian turbulent flows. In the present study, the pressure-drop is measured across a 1.05 meter length section of a 1.04 cm inner diameter pipe. Differential pressure is measured with a pressure transducer for different entry lengths, flow and polymer solution properties. This presentation will present preliminary data on the required entrance length as well as characterization of polymer solution an estimate of the mean molecular weight.
NASA Astrophysics Data System (ADS)
Wang, L.; Cardenas, M.; Slottke, D. T.; Ketcham, R. A.; Sharp, J. M.
2013-12-01
Fundamental understanding of flow and transport processes through single rough-walled fractures remains a challenge to gain insight for interpreting hydrological phenomena at continuum scale. The Generalized Local Cubic Law (GLCL) developed here is based on (1) modifying the aperture field by orienting it with the flow direction accounting for tortuosity, and (2) correcting for roughness changes associated with flow expansion/contraction and inertial effects. We compared its performance in estimating flow rate to results of direct numerical simulations with the Navier-Stokes equations (NSE) and physical flow experiments for real and synthetic three-dimensional rough-walled fractures. We also evaluated the performance of the Local Cubic Law (LCL). The LCL consistently overestimates flow rate with relative error δ ranging from 20% to 100% with arithmetic mean of |δ| (<|δ|>) equal to 45.4% depending on the degree of tortuosity and roughness. However, the GLCL performs well and improves the performance of the LCL, where δ in flow rate range from -3.1% to 11.4% with <|δ|>=4.7%. Furthermore, we generated breakthrough curves (BTCs) through direct numerical simulations based on the advection-diffusion equation with flow field resulting from solving the NSE (which are considered to the true or experimental BTCs). We revisited the applicability of random walk particle tracking (RWPT) to simulate solute transport dynamics through real fractures, where flow fields resulted from the GLCL and LCL, respectively. We found persistent early arrival and heavy tailing in the BTCs from both direct numerical simulations and RWPT, which are the salient characteristics of non-Fickian behavior. The LCL consistently overestimates mean flow velocity; whereas the GLCL improves estimating flow field, and markedly improves fits to the BTCs relative to those fitted with LCL solutions. Therefore, PWPT with flow field resulting from the GLCL is robust in predicting solute transport through
Code and Solution Verification of 3D Numerical Modeling of Flow in the Gust Erosion Chamber
NASA Astrophysics Data System (ADS)
Yuen, A.; Bombardelli, F. A.
2014-12-01
Erosion microcosms are devices commonly used to investigate the erosion and transport characteristics of sediments at the bed of rivers, lakes, or estuaries. In order to understand the results these devices provide, the bed shear stress and flow field need to be accurately described. In this research, the UMCES Gust Erosion Microcosm System (U-GEMS) is numerically modeled using Finite Volume Method. The primary aims are to simulate the bed shear stress distribution at the surface of the sediment core/bottom of the microcosm, and to validate the U-GEMS produces uniform bed shear stress at the bottom of the microcosm. The mathematical model equations are solved by on a Cartesian non-uniform grid. Multiple numerical runs were developed with different input conditions and configurations. Prior to developing the U-GEMS model, the General Moving Objects (GMO) model and different momentum algorithms in the code were verified. Code verification of these solvers was done via simulating the flow inside the top wall driven square cavity on different mesh sizes to obtain order of convergence. The GMO model was used to simulate the top wall in the top wall driven square cavity as well as the rotating disk in the U-GEMS. Components simulated with the GMO model were rigid bodies that could have any type of motion. In addition cross-verification was conducted as results were compared with numerical results by Ghia et al. (1982), and good agreement was found. Next, CFD results were validated by simulating the flow within the conventional microcosm system without suction and injection. Good agreement was found when the experimental results by Khalili et al. (2008) were compared. After the ability of the CFD solver was proved through the above code verification steps. The model was utilized to simulate the U-GEMS. The solution was verified via classic mesh convergence study on four consecutive mesh sizes, in addition to that Grid Convergence Index (GCI) was calculated and based on
NASA Technical Reports Server (NTRS)
Vekilov, P. G.; Rosenberger, F.
1998-01-01
We have experimentally studied the effects of solution flow on the growth kinetics of the protein lysozyme. To this end, we have expanded our interferometry setup by a novel crystallization cell and solution recirculation system. This combination permits monitoring of interface morphology and kinetics with a depth resolution of 200 A at bulk flow rates of up to 2000 micron/s. Particular attention was paid to the prevention of protein denaturation that is often associated with the pumping of protein solutions. We found that at bulk flow rates it less than 250 microns/s the average growth rate and step velocity, R(sub avg) and upsilon(sub avg) increase with increasing it. This can be quantitatively understood in terms of the enhanced, convective solute supply to the interface. With high-purity solutions, it u greater than 250 microns/s lead to growth deceleration, and, at low supersaturations sigma, to growth cessation. When solutions containing approx. 1% of other protein impurities were used, growth deceleration occurred at any u greater than 0 and cessation in the low sigma experiments was reached at about half the it causing cessation with pure solution. The flow-induced changes in R(sub avg) and upsilon(sub avg) including growth cessation, were reversible and reproducible, independent of the direction of the u-changes and solution purity. Hence, we attribute the deceleration to the convection-enhanced supply of impurities to the interface, which at higher flow rates overpowers the effects of enhanced interfacial solute concentration. Most importantly, we found that convective transport leads to a significant reduction in kinetics fluctuations, in agreement with our earlier expectations for the lysozyme system. This supports our hypothesis that these long-term fluctuations represent an intrinsic response feature of the coupled bulk transport-interfacial kinetics system in the mixed growth control regime.
NASA Astrophysics Data System (ADS)
Ben Slimene, Erij; Lassabatere, Laurent; Winiarski, Thierry; Gourdon, Remy
2016-04-01
The understanding of the fate of pollutants in the vadose zone is a prerequisite to manage soil and groundwater quality. Water infiltrates into the soil and carries a large amount of pollutants (heavy metals, organic compounds, etc.). The quality of groundwater depends on the capability of soils to remove pollutants while water infiltrates. The capability of soils to remove pollutants depends not only on their geochemical properties and affinity with pollutants but also on the quality of the contact between the reactive particles of the soil and pollutants. In such a context, preferential flows are the worst scenario since they prevent pollutants from reaching large parts of the soil including reactive zones that could serve for pollutant removal. The negative effects of preferential flow have already been pointed out by several studies. In this paper, we investigate numerically the effect of the establishment of preferential flow in a numerical section (13.5m long and 2.5m deep) that mimics a strongly heterogeneous deposit. The modelled deposit is made of several lithofacies with contrasting hydraulic properties. The numerical study proves that this strong contrast in hydraulic properties triggers the establishment of preferential flow (capillary barriers and funneled flow). Preferential flow develops mainly for low initial water contents and low fluxes imposed at the soil surface. The impact of these flows on solute transfer is also investigated as a function of solute reactivity and affinity to soil sorption sites. Modeled results clearly show that solute transport is greatly impacted by flow heterogeneity. Funneled flows have the same impacts as water fractionation into mobile and immobile transfer with a fast transport of solutes by preferential flow and solute diffusion to zones where the flow is slower. Such a pattern greatly impacts retention and reduces the access of pollutants into large parts of the soil. Retention is thus greatly reduced at the section
NASA Astrophysics Data System (ADS)
Liu, Wei; Wen, Jizhou; Chao, Jiangyue; Yin, Weiyou; Shen, Chen; Lai, Dayi; Lin, Chao-Hsin; Liu, Junjie; Sun, Hejiang; Chen, Qingyan
2012-09-01
Flow fields in commercial airliner cabins are crucial for creating a thermally comfortable and healthy cabin environment. Flow fields depend on the thermo-fluid boundary conditions at the diffusers, in addition to the cabin geometry and furnishing. To study the flow fields in cabins, this paper describes a procedure to obtain the cabin geometry, boundary conditions at the diffusers, and flow fields. This investigation used a laser tracking system and reverse engineering to generate a digital model of an MD-82 aircraft cabin. Even though the measuring error by the system was very small, approximations and assumptions were needed to reduce the workload and data size. The geometric model can also be easily used to calculate the space volume. A combination of hot-sphere anemometers (HSA) and ultrasonic anemometers (UA) were applied to obtain the velocity magnitude, velocity direction, and turbulence intensity at the diffusers. The measured results indicate that the flow boundary conditions in a real cabin were rather complex and the velocity magnitude, velocity direction, and turbulence intensity varied significantly from one slot opening to another. UAs were also applied to measure the three-dimensional air velocity at 20 Hz, which could also be used to determine the turbulence intensity. Due to the instability of the flow, it should at least be measured for 4 min to obtain accurate averaged velocity and turbulence information. It was found that the flow fields were of low speed and high turbulence intensity. This study provides high quality data for validating Computational Fluid Dynamics (CFD) models, including cabin geometry, boundary conditions of diffusers, and high-resolution flow field in the first-class cabin of a functional MD-82 commercial airliner.
Existence of Global Solutions for Unsteady Isentropic Gas Flow in a Laval Nozzle
NASA Astrophysics Data System (ADS)
Tsuge, Naoki
2012-07-01
In this paper, we study the motion of isentropic gas in the Laval nozzle. The Laval nozzle is the most important type of nozzle utilized in some turbines. In particular, we consider unsteady flows, including transonic gas flows, and prove the existence of global solutions for the Cauchy problem. In spite of its importance, this problem has received little attention until now. The most difficult point is to obtain bounded estimates for approximate solutions. To overcome this, we introduce a modified Godunov scheme. The corresponding approximate solutions consist of piecewise steady-state solutions of an auxiliary equation and yield a sharper bounded estimate. As a result, we find an invariant region for our solutions. Finally, in order to prove their convergence, we use the compensated compactness framework.
Similarity Solutions of the Compressible Flow Equations for a General Equation of State
NASA Astrophysics Data System (ADS)
Boyd, Zachary; Ramsey, Scott; Baty, Roy
2015-11-01
The Euler compressible flow equations admit discontinuous (e.g. shock) solutions regardless of the equation of state (EOS) used to close them. In addition, certain classes of initial conditions and EOS admit special flows known as similarity solutions, including some containing shocks. These are useful (1) as test problems for hydrocodes, (2) as intermediate asymptotic estimates for non-symmetric problems, and (3) in forecasting experimental results. To date, the vast majority of work pertaining to similarity solutions of the Euler equations has been accomplished in the context of the ideal gas EOS; the case where the material is arbitrary is less well-understood. In this work, we classify using Lie-group analysis those materials which admit similarity solutions. We also indicate how such solutions may be found for a variety of materials of interest, including those characterized by particular forms of the Gruneisen EOS. Graduate Student Department of Mathematics, UCLA.
Grid generation and flow solution method for Euler equations on unstructured grids
NASA Technical Reports Server (NTRS)
Anderson, W. Kyle
1992-01-01
A grid generation and flow solution algorithm for the Euler equations on unstructured grids is presented. The grid generation scheme, which uses Delaunay triangulation, generates the field points for the mesh based on cell aspect ratios and allows clustering of grid points near solid surfaces. The flow solution method is an implicit algorithm in which the linear set of equations arising at each time step is solved using a Gauss-Seidel procedure that is completely vectorizable. Also, a study is conducted to examine the number of subiterations required for good convergence of the overall algorithm. Grid generation results are shown in two dimensions for an NACA 0012 airfoil as well as a two element configuration. Flow solution results are shown for a two dimensional flow over the NACA 0012 airfoil and for a two element configuration in which the solution was obtained through an adaptation procedure and compared with an exact solution. Preliminary three dimensional results also are shown in which the subsonic flow over a business jet is computed.
A grid generation and flow solution method for the Euler equations on unstructured grids
NASA Technical Reports Server (NTRS)
Anderson, W. Kyle
1994-01-01
A grid generation and flow solution algorithm for the Euler equations on unstructured grids is presented. The grid generation scheme utilizes Delaunay triangulation and self-generates the field points for the mesh based on cell aspect ratios and allows for clustering near solid surfaces. The flow solution method is an implicit algorithm in which the linear set of equations arising at each time step is solved using a Gauss Seidel procedure which is completely vectorizable. In addition, a study is conducted to examine the number of subiterations required for good convergence of the overall algorithm. Grid generation results are shown in two dimensions for a National Advisory Committee for Aeronautics (NACA) 0012 airfoil as well as a two-element configuration. Flow solution results are shown for two-dimensional flow over the NACA 0012 airfoil and for a two-element configuration in which the solution has been obtained through an adaptation procedure and compared to an exact solution. Preliminary three-dimensional results are also shown in which subsonic flow over a business jet is computed.
A grid generation and flow solution method for the Euler equations on unstructured grids
Anderson, W.K. )
1994-01-01
A grid generation and flow solution algorithm for the Euler equations on unstructured grids is presented. The grid generation scheme utilizes Delaunay triangulation and self-generates the field points for the mesh based on cell aspect ratios and allows for clustering near solid surfaces. The flow solution method is an implicit algorithm in which the linear set or equations arising at each time step is solved using a Gauss Seidel procedure which is completely vectorizable. In addition, a study is conducted to examine the number of subiterations required for good convergence of the overall algorithm. Grid generation results are shown in two dimensions for a NACA 0012 airfoil as well as two-element configuration. Flow solution results are shown for two-dimensional flow over the NACA 0012 airfoil and for a two-element configuration in which the solution has been obtained through an adaptation procedure and compared to an exact solution. Preliminary three-dimensional results are also shown in which subsonic flow over a business jet is computed. 31 refs. 30 figs.
Numerical solution of potential flow about arbitrary 2-dimensional multiple bodies
NASA Technical Reports Server (NTRS)
Thompson, J. F.; Thames, F. C.
1982-01-01
A procedure for the finite-difference numerical solution of the lifting potential flow about any number of arbitrarily shaped bodies is given. The solution is based on a technique of automatic numerical generation of a curvilinear coordinate system having coordinate lines coincident with the contours of all bodies in the field, regardless of their shapes and number. The effects of all numerical parameters involved are analyzed and appropriate values are recommended. Comparisons with analytic solutions for single Karman-Trefftz airfoils and a circular cylinder pair show excellent agreement. The technique of application of the boundary-fitted coordinate systems to the numerical solution of partial differential equations is illustrated.
Sheng, F.; Wang, K.; Zhang, R.; Liu, H.H.
2009-03-15
Preferential flow and solute transport are common processes in the unsaturated soil, in which distributions of soil water content and solute concentrations are often characterized as fractal patterns. An active region model (ARM) was recently proposed to describe the preferential flow and transport patterns. In this study, ARM governing equations were derived to model the preferential soil water flow and solute transport processes. To evaluate the ARM equations, dye infiltration experiments were conducted, in which distributions of soil water content and Cl{sup -} concentration were measured. Predicted results using the ARM and the mobile-immobile region model (MIM) were compared with the measured distributions of soil water content and Cl{sup -} concentration. Although both the ARM and the MIM are two-region models, they are fundamental different in terms of treatments of the flow region. The models were evaluated based on the modeling efficiency (ME). The MIM provided relatively poor prediction results of the preferential flow and transport with negative ME values or positive ME values less than 0.4. On the contrary, predicted distributions of soil water content and Cl- concentration using the ARM agreed reasonably well with the experimental data with ME values higher than 0.8. The results indicated that the ARM successfully captured the macroscopic behavior of preferential flow and solute transport in the unsaturated soil.
Diffusional solute flux during osmotic water flow across the human red cell membrane.
Brahm, J; Galey, W R
1987-05-01
The effect of solvent drag on the unidirectional efflux of labeled water, urea, and chloride from human red cells was studied by means of the continuous flow tube method under conditions of osmotic equilibrium and net volume flow. Solvent (water) flow out of cells was created by mixing cells equilibrated in 100 mM salt solution with a 200-mM or 250-mM salt solution, while flow of water into cells was obtained by equilibrating the cells in the higher concentration and mixing them with the 100-mM solution. Control experiments constitute measurements of efflux of [14C]ethanol in normal cells and 3H2O in cells treated with p-chloromercuribenzosulfonate under the conditions described above. In both instances, the solute is known to penetrate the membrane through nonporous pathways. As anticipated, the tracer flux of neither urea nor chloride showed any dependence on net solvent flow, regardless of the direction. If one assumes the recently reported reflection coefficient for urea of 0.7, the urea tracer flux should change by at least 24% under volume flow conditions. Since such changes would be easily detected with our method, we conclude that the pathways for water, for urea, and for chloride are functionally separated. PMID:3037007
Weathering of plagioclase across variable flow and solute transport regimes
NASA Astrophysics Data System (ADS)
Pacheco, Fernando A. L.; Van der Weijden, Cornelis H.
2012-02-01
SummaryThe study area is situated in a fault zone with fractured granites and metasediments. In a conceptual model, infiltrating water first passes the bedrock cover of soil and saprolite and then partly enters the fractures. Weathering reactions of minerals occur in small pores and fissures in the bedrock cover zone to continue in the larger fractures. Pumping tests were carried out in a number of boreholes to measure the drawdown as a function of pumping time. From the results, values of transmissivity ( T) could be derived. In combination with the storage coefficient ( S) for similar fault zones, the hydraulic diffusivity ( D = T/ S) could be computed. Water samples, collected from the boreholes, represent fluid packets with a history of weathering reactions in the bedrock cover and in the larger fractures. The major element composition of these samples was used by means of the SiB mass balance algorithm ( Pacheco and Van der Weijden, 1996) to calculate the moles L -1 of dissolved plagioclase (oligoclase with An ≈ 0.20) and the moles L -1 of secondary phases (gibbsite, halloysite, smectite) precipitated along the flow paths of the samples. These results were then used to calculate the net dissolved silica concentrations ( [HSiO40]) related to dissolution of plagioclase followed by precipitation of each of the secondary phases. An interpretation of a plot of each of these [HSiO40] 's versusD is that at D < 0.7 m 2 s -1, dissolution of plagioclase is followed by precipitation of halloysite in the large fractures of the fault zone (open system), whereas at D ⩾ 0.7 m 2 s -1 precipitation of both halloysite and smectite occurs in the rock matrix with small fissures and pores (semi-open system). Before being pumped, the percolating fluids travelled 0.01-13.7 years. During these periods, plagioclase weathered at rates ( W Pl) of 10 -(12.9±1.1) moles m -2 s -1, which are approximately 2.2 orders of magnitude higher than solid-state weathering rates reported in
NASA Astrophysics Data System (ADS)
Lemoine, X.; Sriram, S.; Kergen, R.
2011-05-01
ArcelorMittal continuously develops new steel grades (AHSS) with high performance for the automotive industry to improve the weight reduction and the passive safety. The wide market introduction of AHSS raises a new challenge for manufacturers in terms of material models in the prediction of forming—especially formability and springback. The relatively low uniform elongation, the high UTS and the low forming limit curve of these AHSS may cause difficulties in forming simulations. One of these difficulties is the consequence of the relatively low uniform elongation on the parameters identification of isotropic hardening model. Different experimental tests allow to reach large plastic strain levels (hydraulic bulge test, stack compression test, shear test…). After a description on how to determine the flow curve in these experimental tests, a comparison of the different flow curves is made for different steel grades. The ArcelorMittal identification protocol for hardening models is only based on stress-strain curves determined in uniaxial tension. Experimental tests where large plastic strain levels are reached are used to validate our identification protocol and to recommend some hardening models. Finally, the influence of isotropic hardening models and yield loci in forming prediction for AHSS steels will be presented.
A 3D-CFD code for accurate prediction of fluid flows and fluid forces in seals
NASA Astrophysics Data System (ADS)
Athavale, M. M.; Przekwas, A. J.; Hendricks, R. C.
1994-01-01
Current and future turbomachinery requires advanced seal configurations to control leakage, inhibit mixing of incompatible fluids and to control the rotodynamic response. In recognition of a deficiency in the existing predictive methodology for seals, a seven year effort was established in 1990 by NASA's Office of Aeronautics Exploration and Technology, under the Earth-to-Orbit Propulsion program, to develop validated Computational Fluid Dynamics (CFD) concepts, codes and analyses for seals. The effort will provide NASA and the U.S. Aerospace Industry with advanced CFD scientific codes and industrial codes for analyzing and designing turbomachinery seals. An advanced 3D CFD cylindrical seal code has been developed, incorporating state-of-the-art computational methodology for flow analysis in straight, tapered and stepped seals. Relevant computational features of the code include: stationary/rotating coordinates, cylindrical and general Body Fitted Coordinates (BFC) systems, high order differencing schemes, colocated variable arrangement, advanced turbulence models, incompressible/compressible flows, and moving grids. This paper presents the current status of code development, code demonstration for predicting rotordynamic coefficients, numerical parametric study of entrance loss coefficients for generic annular seals, and plans for code extensions to labyrinth, damping, and other seal configurations.
Evaluation of a higher order differencing method for the solution of the fluid flow equations
Tzanos, C.P.
1991-01-01
For the numerical solution of the transport equations that describe the convection and diffusion of various physical quantities (e.g., momentum, heat, material concentrations), first-order upwind schemes are widely used. These schemes are simple and give physically plausible solutions. However, due to false diffusion, at high Peclet or Reynolds numbers, their accuracy on practical meshes is poor. On the other hand, at these numbers, central difference schemes and Galerkin finite-element methods require a fine mesh to eliminate spurious spatial oscillations. A higher order differencing method was recently presented by Tzanos that even with a coarse mesh produces oscillation-free solutions and of superior accuracy than those of the upwind scheme. This method has been successfully tested for the solution of the heat transfer equations with a known flow field, and for the solution of the incompressible fluid flow equations in the vorticity-stream function formulation. In this work this method was evaluated for the solution of the incompressible fluid flow equations in their primitive-variables (velocities, pressure) formulation. The flow in a square cavity was used as a test problem. 6 refs., 1 tab.
Comparing analytical and numerical solution of nonlinear two and three-dimensional hydrostatic flows
NASA Astrophysics Data System (ADS)
Casulli, Vincenzo; Zanolli, Paola
2007-02-01
New test cases for frictionless, three-dimensional hydrostatic flows have been derived from some known analytical solutions of the two-dimensional shallow water equations. The flow domain is a paraboloid of revolution and the flow is determined by the initial conditions, the nonlinear advective terms, the Coriolis acceleration and by the hydrostatic pressure. Wetting and drying is also included.Some specific properties of the exact solutions are discussed under different hypothesis and relative importance of the forcing terms. These solutions are proposed for testing the stability, the accuracy and the efficiency of numerical models to be used for simulating environmental hydrostatic flows.The computed solutions obtained with a semi-implicit finite difference - finite volume algorithm on unstructured grid are compared with the corresponding analytical solutions in both two and three space dimension. Excellent agreement are obtained for the velocity and for the resulting water surface elevation. Comparison of the computed inundation area also shows a good agreement with the analytical solution with degrading accuracy observed when the inundation area becomes relatively large and for long simulation time.
NASA Astrophysics Data System (ADS)
Wen, Chaofan; Poole, Robert; Dennis, David
2014-11-01
Previous studies of shear-thinning fluids in pipe flow discovered that, although the time-averaged velocity profile was axisymmetric when the flow was laminar or fully turbulent, contrary to expectations it was asymmetric in the laminar-turbulent transition regime. The general consensus of these previous experiments was that the location of the peak velocity remained at a fixed point in space. We present new experimental data which demonstrates that this is in fact not the case. The experiment was performed using an aqueous solution of Xanthan Gum (0.15 wt%), a shear-thinning polymer solution. Stereoscopic particle image velocimetry (SPIV) was used to measure the 3C velocity vectors over the entire circular cross-section of the pipe, 220 pipe diameters downstream of the inlet. The exhibition of significant departures from axisymmetry in transitional flows of shear-thinning fluids was observed and in addition it was discovered that the asymmetric flow pattern is not stationary, although the peak velocity does preferentially arise at certain azimuthal locations. The ensemble average of all the SPIV data results in the recovery of the velocity profile measured using laser Doppler velocimetry in previous studies: still asymmetric but to a lesser extent than the instantaneous flow.
A tale of two solutes: Dual-domain flow and the role of the mass transfer coefficient
NASA Astrophysics Data System (ADS)
Callaghan, M. V.; Bishop, J. M.; Cey, E. E.; Bentley, L. R.
2011-12-01
' histories were different because of the difference in their distribution at the beginning of the experiment. Dual-permeability water flow and solute transport has been modeled using the HYDRUS software package. The numerical model was calibrated to both the observed salt and tracer concentrations, and, consequently, the distinct behavior of the two solutes. The numerical modeling results indicate that salt and tracer transport are sensitive to the mass transfer coefficient between matrix and macropore domains and, consequently, proper selection of the coefficient value is key to the accurate prediction of transport in dual permeability media.
NASA Astrophysics Data System (ADS)
Furuichi, Mikito; May, Dave A.
2015-07-01
We present implicit time integration schemes suitable for modeling free surface Stokes flow dynamics with marker in cell (MIC) based spatial discretization. Our target is for example thermal convection surrounded by deformable surface boundaries to simulate the long term planetary formation process. The numerical system becomes stiff when the dynamical balancing time scale for the increasing/decreasing load by surface deformation is very short compared with the time scale associated with thermal convection. Any explicit time integration scheme will require very small time steps; otherwise, serious numerical oscillation (spurious solutions) will occur. The implicit time integration scheme possesses a wider stability region than the explicit method; therefore, it is suitable for stiff problems. To investigate an efficient solution method for the stiff Stokes flow system, we apply first (backward Euler (BE)) and second order (trapezoidal method (TR) and trapezoidal rule-backward difference formula (TR-BDF2)) accurate implicit methods for the MIC solution scheme. The introduction of implicit time integration schemes results in nonlinear systems of equations. We utilize a Jacobian free Newton Krylov (JFNK) based Newton framework to solve the resulting nonlinear equations. In this work we also investigate two efficient implicit solution strategies to reduce the computational cost when solving stiff nonlinear systems. The two methods differ in how the advective term in the material transport evolution equation is treated. We refer to the method that employs Lagrangian update as "fully implicit" (Imp), whilst the method that employs Eulerian update is referred to as "semi-implicit" (SImp). Using a finite difference (FD) method, we have performed a series of numerical experiments which clarify the accuracy of solutions and trade-off between the computational cost associated with the nonlinear solver and time step size. In comparison with the general explicit Euler method
Faragò, Giuseppe; Caldiera, Valentina; Tempra, Giovanni; Ciceri, Elisa
2016-02-01
In recent years there has been a progressive increase in interventional neuroradiology procedures, partially due to improvements in devices, but also to the simultaneous development of technologies and radiological images. Cone beam CT (Dyna-CT; Siemens) is a method recently used to obtain pseudo CT images from digital subtraction angiography (DSA) with a flat panel detector. Using dedicated software, it is then possible to merge Dyna-CT images with images from a different source. We report here the usefulness of advanced DSA techniques (Syngo-Dyna CT, three-dimensional DSA iPilot) for the treatment of an intracranial aneurysm with a flow diverter device. Merging MR and Dyna-CT images at the end of the procedure proved to be a simple and rapid additional method of verifying the success of the intervention. PMID:25589548
Perturbation solutions for transonic flow on the blade-to-blade surface of compressor blade rows
NASA Technical Reports Server (NTRS)
Stahara, S. S.; Chaussee, D. S.; Spreiter, J. R.
1978-01-01
A preliminary investigation was conducted to establish the theoretical basis of perturbation techniques with the objective of minimizing computational requirements associated with parametric studies of transonic flows in turbomachines. The theoretical analysis involved the development of perturbation methods for determining first order changes in the flow solution due to variations of one or more geometrical or flow parameters. The formulation is primarily directed toward transonic flows on the blade to blade surface of a single blade row compressor. Two different perturbation approaches were identified and studied. Applications and results of these methods for various perturbations are presented for selected two dimensional transonic cascade flows to illustrate the advantages and disadvantages of each technique. Additionally, it was found that, for flows with shock waves, proper account of shock displacement was crucial.
An analytical solution for transient radial flow through unsaturated fractured porous media
Wu, Yu-Shu; Pan, Lehua
2004-02-13
This paper presents analytical solutions for one-dimensional radial transient flow through horizontal, unsaturated fractured rock formation. In these solutions, unsaturated flow through fractured media is described by a linearized Richards' equation, while fracture-matrix interaction is handled using the dual-continuum concept. Although linearizing Richards' equation requires a specially correlated relationship between relative permeability and capillary pressure functions for both fractures and matrix, these specially formed relative permeability and capillary pressure functions are still physically meaningful. These analytical solutions can thus be used to describe the transient behavior of unsaturated flow in fractured media under the described model conditions. They can also be useful in verifying numerical simulation results, which, as demonstrated in this paper, are otherwise difficult to validate.
Aiding flows non-unique similarity solutions of mixed-convection boundary-layer equations
NASA Astrophysics Data System (ADS)
Ridha, A.; Curie, Marie
1996-05-01
The similarity equations for mixed-convection boundary-layer flow past a wedge having one of its surfaces parallel to the horizontal are derived for the latter surface. Both cases of prescribed wall temperature and heat flux are considered. It is shown that non-unique solutions exist for aiding (α > 0) as well as opposing flows (α < 0); α being the buoyancy parameter. In some situations there are four simultaneous solutions. Dual solutions for two previously studied mixed-convection boundary-layer flows are shown to exist for α > 0 in addition to those already reported in the literature for α < 0. Namely, these correspond to vertical flat plate and vertical cylinder problems.
Rockhold, M L
1993-02-01
A field-scale, unsaturated flow and solute transport experiment at the Las Cruces trench site in New Mexico was simulated as part of a blind'' modeling exercise to demonstrate the ability or inability of uncalibrated models to predict unsaturated flow and solute transport in spatially variable porous media. Simulations were conducted using a recently developed multiphase flow and transport simulator. Uniform and heterogeneous soil models were tested, and data from a previous experiment at the site were used with an inverse procedure to estimate water retention parameters. A spatial moment analysis was used to provide a quantitative basis for comparing the mean observed and simulated flow and transport behavior. The results of this study suggest that defensible predictions of waste migration and fate at low-level waste sites will ultimately require site-specific data for model calibration.
Emergence of spatio-temporal dynamics from exact coherent solutions in pipe flow
NASA Astrophysics Data System (ADS)
Ritter, Paul; Mellibovsky, Fernando; Avila, Marc
2016-08-01
Turbulent-laminar patterns are ubiquitous near transition in wall-bounded shear flows. Despite recent progress in describing their dynamics in analogy to non-equilibrium phase transitions, there is no theory explaining their emergence. Dynamical-system approaches suggest that invariant solutions to the Navier–Stokes equations, such as traveling waves and relative periodic orbits in pipe flow, act as building blocks of the disordered dynamics. While recent studies have shown how transient chaos arises from such solutions, the ensuing dynamics lacks the strong fluctuations in size, shape and speed of the turbulent spots observed in experiments. We here show that chaotic spots with distinct dynamical and kinematic properties merge in phase space and give rise to the enhanced spatio-temporal patterns observed in pipe flow. This paves the way for a dynamical-system foundation to the phenomenology of turbulent-laminar patterns in wall-bounded extended shear flows.
Slow rarefied gas flow past a cylinder: Analytical solution in comparison to the sphere
NASA Astrophysics Data System (ADS)
Westerkamp, Armin; Torrilhon, Manuel
2012-11-01
In the variety of approaches to tackle the challenges of rarefied gas flows, the regularized 13-moment equations (R13) have become a very promising contender. The equations are based on moment approximations in kinetic gas theory which can be interpreted as a non-linear discretization of the Boltzmann equation in the velocity space. In order to get a deeper insight into rarefaction effects, an analytic solution for the flow around a sphere has been constructed in [M. Torrilhon, Phys. Fluids. 22, 072001:1-16 (2010)]. In the present work, an analytic solution for the flow past a cylinder is derived, which is another very important text book problem. Again, the investigation is restricted to slow flows (Ma ≪ 1), which means a linearized system of the original R13 equations is analyzed. The results for the sphere and the cylinder are then compared and typical rarefaction effects are pointed out.
PIV measurements of flow in drying polymer solutions during solvent casting
NASA Astrophysics Data System (ADS)
Mansoor, Iman; Stoeber, Boris
2011-05-01
An experimental method based on confocal microscopy and particle image velocimetry (PIV) is used to characterize the flow in a polymer solution during solvent casting. The flow inside a 200-μm-thick film of a poly(vinyl alcohol) (PVA) solution is visualized near a vertical wall of a mold using confocal microscopy of seed particles during solvent evaporation at 25, 35, and 45°C, and the corresponding velocity vector fields are determined from projections of the confocal images. Flow toward the vertical wall is observed inside the film as well as a slower Marangoni-type counter flow at the film surface during the initial phase of solvent evaporation, resulting from a polymer concentration gradient along the film due to a local variation in evaporation rate. Total volume of the polymer solution in the observation volume as well as solvent evaporation rate are determined as a function of time, both revealing close correlation to average horizontal velocity data from PIV. The PIV measurements show significant differences in the flow velocity fields at different temperatures. The PIV measurements correlate with the solvent evaporation rates as well as the final polymer thicknesses on the vertical wall of the mold. Surface tension and viscosity measurements are taken for different concentrations of PVA solution.
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.
Amundsen, Erik K; Henriksson, Carola E; Holthe, Mette R; Urdal, Petter
2012-01-01
We compared the performance of the basophil count of 3 hematology instruments with a flow cytometric method (FCM) in which CD123 and CD193 were used as basophil markers. By analyzing 112 patient samples, we found the ADVIA 120 (Siemens Healthcare Diagnostics, Deerfield, IL) and CELL-DYN Sapphire (Abbott Diagnostics, Santa Clara, CA) to underestimate the number of basophils by approximately 50% and the Sysmex XE-2100 (Sysmex, Kobe, Japan) and ADVIA to overestimate the basophil count in some samples with pathologic leukocytes. All 3 instruments had large (25%-50%) analytic within-run coefficients of variation. Compared with the FCM, we found a relatively good correlation for the CELL-DYN basophil count (r = 0.81), an intermediate correlation for the Sysmex (r = 0.64), and a poor correlation for the ADVIA (r = 0.24). When excluding the 52 samples flagged for the presence of pathologic leukocytes, these correlations were found to be 0.84, 0.90, and 0.57, respectively. The basophil count of the 3 instruments is, at least presently, of unsatisfactory quality. PMID:22180481
Soliton solutions and their stability for the flow of relativistic fluids through channels
NASA Technical Reports Server (NTRS)
Lerche, I.; Wiita, P. J.
1980-01-01
The flow of a perfect relativistic fluid through channels of various cross-sections is considered with reference to models of radio galaxies. Soliton-like solutions are found and their topologies are discussed. The calculations show that these solutions are unstable. It is suggested that under realistic astrophysical conditions the growth rate of the instabilities is so slow that soliton-type blobs may persist for a significant time.
NASA Technical Reports Server (NTRS)
Voorhies, Coerte V.; Nishihama, Masahiro
1993-01-01
The effects of laterally homogeneous mantle electrical conductivity were included in steady, frozen-flux core surface flow estimation along with refinements in method and weighting. The refined method allows simultaneous solution for both the initial radial geomagnetic field component at the core-mantle boundary (CMB) and the sub-adjacent fluid motion; it also features Gauss' method for solving the non-linear inverse problem associated with steady motional induction. The tradeoff between spatial complexity of the derived flows and misfit to the weighted Definitive Geomagnetic Reference Field models (DGRF's) is studied for various mantle conductivity profiles. For simple flow and a fixed initial geomagnetic condition, a fairly high deep-mantle conductivity performs better than either insulating or weakly conducting profiles; however, a thin, very high conductivity layer at the base of the mantle performs almost as well. Simultaneous solution for both initial geomagnetic field and flow reduces the misfit per degree of freedom even more than does changing the mantle conductivity profile. Moreover, when both core field and flow are estimated, the performance of the solutions and the derived flows become insensitive to the conductivity profile.
NASA Technical Reports Server (NTRS)
Voorhies, Goerte V.; Nishihama, Masahiro
1994-01-01
The effects of laterally homogeneous mantle electrical conductivity have been included in steady, frozen-flux core surface flow estimation along with refinements in method and weighting. The refined method allows simultaneous solution for both the initial radial geomagnetic field component at the core-mantle boundary and the subadjacent fluid motion; it also features Gauss' method for solving the nonlinear inverse problem associated with steady motional induction. The trade-off between spatial complexity of the derived flows and misfit to the weighted Definitive Geomagnetic Reference Field models is studied for various mantle conductivity profiles. For simple flow and a fixed initial geomagnetic condition a fairly high deep-mantle conductivity performs better than either insulating or weakly conducting profiles; however, a thin, very high conductivity layer at the base of the mantle performs almost as well. Simultaneous solution for both initial geomagnetic field and fluid flow reduces the misfit per degree of freedom even more than does changing the mantle conductivity profile. Moreover, when both core field and flow are estimated, the performance of the solutions and the derived flows become insensitive to the conductivity profile.
NASA Astrophysics Data System (ADS)
Voorhies, Goerte V.; Nishihama, Masahiro
1994-04-01
The effects of laterally homogeneous mantle electrical conductivity have been included in steady, frozen-flux core surface flow estimation along with refinements in method and weighting. The refined method allows simultaneous solution for both the initial radial geomagnetic field component at the core-mantle boundary and the subadjacent fluid motion; it also features Gauss' method for solving the nonlinear inverse problem associated with steady motional induction. The trade-off between spatial complexity of the derived flows and misfit to the weighted Definitive Geomagnetic Reference Field models is studied for various mantle conductivity profiles. For simple flow and a fixed initial geomagnetic condition a fairly high deep-mantle conductivity performs better than either insulating or weakly conducting profiles; however, a thin, very high conductivity layer at the base of the mantle performs almost as well. Simultaneous solution for both initial geomagnetic field and fluid flow reduces the misfit per degree of freedom even more than does changing the mantle conductivity profile. Moreover, when both core field and flow are estimated, the performance of the solutions and the derived flows become insensitive to the conductivity profile.
Flow Solution for Advanced Separate Flow Nozzles Response A: Structured Grid Navier-Stokes Approach
NASA Technical Reports Server (NTRS)
Kenzakowski, D. C.; Shipman, J.; Dash, S. M.; Saiyed, Naseem (Technical Monitor)
2001-01-01
NASA Glenn Research Center funded a computational study to investigate the effect of chevrons and tabs on the exhaust plume from separate flow nozzles. Numerical studies were conducted at typical takeoff power with 0.28 M flight speed. Report provides numerical data and insights into the mechanisms responsible for increased mixing.
{N} =2 supersymmetric Janus solutions and flows: from gauged supergravity to M theory
NASA Astrophysics Data System (ADS)
Pilch, Krzysztof; Tyukov, Alexander; Warner, Nicholas P.
2016-05-01
We investigate a family of SU(3)×U(1)×U(1)-invariant holographic flows and Janus solutions obtained from gauged {N} = 8 supergravity in four dimensions. We give complete details of how to use the uplift formulae to obtain the corresponding solutions in M theory. While the flow solutions appear to be singular from the four-dimensional perspective, we find that the eleven-dimensional solutions are much better behaved and give rise to interesting new classes of compactification geometries that are smooth, up to orbifolds, in the infra-red limit. Our solutions involve new phases in which M2 branes polarize partially or even completely into M5 branes. We derive the eleven-dimensional supersymmetries and show that the eleven-dimensional equations of motion and BPS equations are indeed satisfied as a consequence of their four-dimensional counterparts. Apart from elucidating a whole new class of eleven-dimensional Janus and flow solutions, our work provides extensive and highly non-trivial tests of the recently-derived uplift formulae.
NASA Technical Reports Server (NTRS)
Weinberg, B. C.; Mcdonald, H.
1982-01-01
A numerical scheme is developed for solving the time dependent, three dimensional compressible viscous flow equations to be used as an aid in the design of helicopter rotors. In order to further investigate the numerical procedure, the computer code developed to solve an approximate form of the three dimensional unsteady Navier-Stokes equations employing a linearized block implicit technique in conjunction with a QR operator scheme is tested. Results of calculations are presented for several two dimensional boundary layer flows including steady turbulent and unsteady laminar cases. A comparison of fourth order and second order solutions indicate that increased accuracy can be obtained without any significant increases in cost (run time). The results of the computations also indicate that the computer code can be applied to more complex flows such as those encountered on rotating airfoils. The geometry of a symmetric NACA four digit airfoil is considered and the appropriate geometrical properties are computed.
Calculation procedures for potential and viscous flow solutions for engine inlets
NASA Technical Reports Server (NTRS)
Albers, J. A.; Stockman, N. O.
1973-01-01
The method and basic elements of computer solutions for both potential flow and viscous flow calculations for engine inlets are described. The procedure is applicable to subsonic conventional (CTOL), short-haul (STOL), and vertical takeoff (VTOL) aircraft engine nacelles operating in a compressible viscous flow. The calculated results compare well with measured surface pressure distributions for a number of model inlets. The paper discusses the uses of the program in both the design and analysis of engine inlets, with several examples given for VTOL lift fans, acoustic splitters, and for STOL engine nacelles. Several test support applications are also given.
Solutions of turbulent backward-facing step flow with heat transfer using the finite volume method
Horstman, R.H.; Cochran, R.J.; Emergy, A.F.
1995-12-31
The heated turbulent flow over a backward-facing step is numerically solved using the commercial computational fluid dynamics program FLUENT. The methods used here consist of the default power-law upwinding scheme, default multigrid equation solution method and a standard k-{var_epsilon} turbulence model with wall functions. A total of four separate cases are reported. The four cases consist of combinations of partially and fully developed flow at the inlet with uniform or developed temperature profiles. Three mesh refinements are reported for each flow.
Solutions of turbulent backward-facing step flow with heat transfer using the finite volume method
NASA Astrophysics Data System (ADS)
Horstman, R. H.; Cochran, R. J.; Emergy, A. F.
1995-03-01
The heated turbulent flow over a backward-facing step is numerically solved using the commercial computational fluid dynamics program FLUENT. The methods used here consist of the default power-law upwinding scheme, default multigrid equation solution method and a standard k-epsilon turbulence model with wall functions. A total of four separate cases are reported. The four cases consist of combinations of partially and fully developed flow at the inlet with uniform or developed temperature profiles. Three mesh refinements are reported for each flow.
NASA Technical Reports Server (NTRS)
Reed, D. A.; Patrick, M. L.
1985-01-01
The applicability of static data flow architectures to the iterative solution of sparse linear systems of equations is investigated. An analytic performance model of a static data flow computation is developed. This model includes both spatial parallelism, concurrent execution in multiple PE's, and pipelining, the streaming of data from array memories through the PE's. The performance model is used to analyze a row partitioned iterative algorithm for solving sparse linear systems of algebraic equations. Based on this analysis, design parameters for the static data flow architecture as a function of matrix sparsity and dimension are proposed.
Practical aspects of spatially high accurate methods
NASA Technical Reports Server (NTRS)
Godfrey, Andrew G.; Mitchell, Curtis R.; Walters, Robert W.
1992-01-01
The computational qualities of high order spatially accurate methods for the finite volume solution of the Euler equations are presented. Two dimensional essentially non-oscillatory (ENO), k-exact, and 'dimension by dimension' ENO reconstruction operators are discussed and compared in terms of reconstruction and solution accuracy, computational cost and oscillatory behavior in supersonic flows with shocks. Inherent steady state convergence difficulties are demonstrated for adaptive stencil algorithms. An exact solution to the heat equation is used to determine reconstruction error, and the computational intensity is reflected in operation counts. Standard MUSCL differencing is included for comparison. Numerical experiments presented include the Ringleb flow for numerical accuracy and a shock reflection problem. A vortex-shock interaction demonstrates the ability of the ENO scheme to excel in simulating unsteady high-frequency flow physics.
NASA Technical Reports Server (NTRS)
Liu, C. H.; Wong, T. C.; Kandil, O. A.
1988-01-01
The two-dimensional flow over a blunt leading-edge plate is simulated on the basis of an Euler/Navier-Stokes zonal scheme. The scheme uses an implicit upwind finite-volume scheme, which is based on the van Leer flux-vector splitting. It is shown that the Euler/Navier-Stokes zonal scheme with downstream boundary-layer compatibility conditions is accurate and efficient.
Analytical and Numerical Solutions of a Generalized Hyperbolic Non-Newtonian Fluid Flow
NASA Astrophysics Data System (ADS)
Pakdemirli, Mehmet; Sarı, Pınar; Solmaz, Bekir
2010-03-01
The generalized hyperbolic non-Newtonian fluid model first proposed by Al-Zahrani [J. Petroleum Sci. Eng. 17, 211 (1997)] is considered. This model was successfully applied to some drilling fluids with a better performance in relating shear stress and velocity gradient compared to power-law and the Hershel-Bulkley model. Special flow geometries namely pipe flow, parallel plate flow, and flow between two rotating cylinders are treated. For the first two cases, analytical solutions of velocity profiles and discharges in the form of integrals are presented. These quantities are calculated by numerically evaluating the integrals. For the flow between two rotating cylinders, the differential equation is solved by the Runge-Kutta method combined with shooting. For all problems, the power-law approximation of the model is compared with the generalized hyperbolic model, too.
Testing and benchmarking of a three-dimensional groundwater flow and solute transport model
Sims, P.N.; Andersen, P.F.; Faust, C.R.; Stephenson, D.E.
1988-12-31
A three-dimensional finite-difference model was developed to simulate groundwater flow and solute transport. The model is intended for application to a variety of groundwater resource and solute migration evaluations, including several complex sites at the Savannah River Plant (SRP). Because the model, FTWORK, is relatively new, there is a need to provide confidence in the model results. Methodologies that test models include comparisons with analytical solutions, comparisons with empirical data, and checking that conservation properties hold. Another level of testing is the comparison of one code against another. This paper describes the testing and benchmarking procedure used to verify the validate FTWORK.
Influence of spatial and temporal flow variability on solute transport in catchments
NASA Astrophysics Data System (ADS)
Selroos, Jan-Olof; Destouni, Georgia
2015-04-01
The present study quantifies the separate and combined effects of spatial and temporal variability of waterborne solute transport through catchments. The questions addressed are whether, when and why different types of variability may dominate catchment-scale transport. We utilize a versatile numerical solute transport code with a particle-based Monte Carlo time domain random walk method to simulate waterborne transport through a generic catchment. The methodology is exemplified by performing simulations using data on spatiotemporal flow and transport variability from direct stream discharge observations and independently calculated advective solute travel time distributions for catchments within the water management district Northern Baltic Proper (NBP) in Mid-Eastern Sweden. A main conclusion of the study is that projections of catchment mass loading based on spatial variability alone are robust estimates of long-term average solute transport development. This is especially true when annually aggregated mass load rather than finer temporal resolution of mass flux is considered. Temporal variability yields short-term fluctuations around the long-term average solute breakthrough development, and earlier or later arrival than the latter, depending on the timing and duration of solute input relative to the temporal flow variability. The exact temporal characteristics of future solute breakthroughs are thus fundamentally uncertain but their statistical expectation may be well quantified by only spatial variability account.
NASA Astrophysics Data System (ADS)
Tucciarelli, T.
2012-12-01
A new methodology for the solution of irrotational 2D flow problems in domains with strongly unstructured meshes is presented. A fractional time step procedure is applied to the original governing equations, solving consecutively a convective prediction system and a diffusive corrective system. The non linear components of the problem are concentrated in the prediction step, while the correction step leads to the solution of a linear system, of the order of the number of computational cells. A MArching in Space and Time (MAST) approach is applied for the solution of the convective prediction step. The major advantages of the model, as well as its ability to maintain the solution monotonicity even in strongly irregular meshes, are briefly described. The algorithm is applied to the solution of diffusive shallow water equations in a simple domain.
Field monitoring of water flow and solute transport under different manure amendments.
Technology Transfer Automated Retrieval System (TEKTRAN)
Organic matter (OM) affects water flow and solute transport in the vadose zone. The main objective of this work was to study the effects of different OM types (dairy and chicken manure), rates (O, 168, 336, and 672 kg/ha total equivalent Nitrogen), and levels (one and two time applications) on water...
Solute dispersion under electric and pressure driven flows; pore scale processes
NASA Astrophysics Data System (ADS)
Li, Shuai; Raoof, Amir; Schotting, Ruud
2014-09-01
Solute dispersion is one of the major mixing mechanisms in transport through porous media, originating from velocity variations at different scales, starting from the pore scale. Different driving forces, such as pressure driven flow (PDF) and electro-osmotic flow (EOF), establish different velocity profiles within individual pores, resulting in different spreading of solutes at this scale. While the velocity profile in PDF is parabolic due to the wall friction effects, the velocity in EOF is typically plug flow, due to the wall charge effects. In this study, we applied a pore network modeling formulation to simulate the velocity field driven by pressure and electric potential to calculate and compare the corresponding average solute dispersivity values. The influence of different driving forces on the hydrodynamic dispersion of a tracer solute is investigated. Applying the pore network modeling, we could capture the velocity variations among different pores, which is the main contribution for the dispersion coefficient. The correlation between pore velocities against pore sizes is found to be different for EOF and PDF, causing different solute dispersion coefficients. The results can provide insight into modeling of electrokinetic remediation for contaminant cleanup in low permeable soils.
Genesis of Streamwise-Localized Solutions from Globally Periodic Traveling Waves in Pipe Flow
NASA Astrophysics Data System (ADS)
Chantry, M.; Willis, A. P.; Kerswell, R. R.
2014-04-01
The aim in the dynamical systems approach to transitional turbulence is to construct a scaffold in phase space for the dynamics using simple invariant sets (exact solutions) and their stable and unstable manifolds. In large (realistic) domains where turbulence can coexist with laminar flow, this requires identifying exact localized solutions. In wall-bounded shear flows, the first of these has recently been found in pipe flow, but questions remain as to how they are connected to the many known streamwise-periodic solutions. Here we demonstrate that the origin of the first localized solution is in a modulational symmetry-breaking Hopf bifurcation from a known global traveling wave that has twofold rotational symmetry about the pipe axis. Similar behavior is found for a global wave of threefold rotational symmetry, this time leading to two localized relative periodic orbits. The clear implication is that many global solutions should be expected to lead to more realistic localized counterparts through such bifurcations, which provides a constructive route for their generation.
Weir, Alexander J; Sayer, Robin; Cheng-Xiang Wang; Parks, Stuart
2015-08-01
Medical phantoms are frequently required to verify image and signal processing systems, and are often used to support algorithm development for a wide range of imaging and blood flow assessments. A phantom with accurate scattering properties is a crucial requirement when assessing the effects of multi-path propagation channels during the development of complex signal processing techniques for Transcranial Doppler (TCD) ultrasound. The simulation of physiological blood flow in a phantom with tissue and blood equivalence can be achieved using a variety of techniques. In this paper, poly (vinyl alcohol) cryogel (PVA-C) tissue mimicking material (TMM) is evaluated in conjunction with a number of potential scattering agents. The acoustic properties of the TMMs are assessed and an acoustic velocity of 1524ms(-1), an attenuation coefficient of (0:49) × 10(-4)fdBm(1)Hz(-1), a characteristic impedance of (1.72) × 10(6)Kgm(-2)s(-1) and a backscatter coefficient of (1.12) × 10(-28)f(4)m(-1)Hz(-4)sr(-1) were achieved using 4 freeze-thaw cycles and an aluminium oxide (Al(2)O(3)) scattering agent. This TMM was used to make an anatomically realistic wall-less flow phantom for studying the effects of multipath propagation in TCD ultrasound. PMID:26736851
NASA Astrophysics Data System (ADS)
Majer, G.; Zick, K.
2015-04-01
A pulsed field gradient spin-echo nuclear magnetic resonance (NMR) sequence with solvent suppression (PGSE-WATERGATE) was applied to accurately measure the diffusion coefficients of Rhodamine 6G (Rh6G) in low-concentration aqueous solutions. Three samples with Rh6G concentrations of CRh6G = 1, 4.5, and 25 μM were investigated. The precise determination of the diffusion coefficients in this low-concentration range was made possible by using a cryogenically cooled NMR probe and by the effective solvent suppression of the PGSE-WATERGATE sequence. The present results bridge the gap between diffusion data measured by fluorescence correlation spectroscopy in the single molecule limit and diffusivities obtained by pulsed field gradient NMR (PFG-NMR) without solvent suppression at higher concentrations. To further extend the concentration range, the diffusion coefficient of Rh6G was also measured on a sample with CRh6G = 410 μM by PFG-NMR. The overall concentration dependence of the Rh6G diffusion at 25 °C is discussed in terms of dimerization of the Rh6G molecules. The concentration-dependent monomer/dimer proportion is deduced from the diffusion data.
Majer, G.; Zick, K.
2015-04-28
A pulsed field gradient spin-echo nuclear magnetic resonance (NMR) sequence with solvent suppression (PGSE-WATERGATE) was applied to accurately measure the diffusion coefficients of Rhodamine 6G (Rh6G) in low-concentration aqueous solutions. Three samples with Rh6G concentrations of C{sub Rh6G} = 1, 4.5, and 25 μM were investigated. The precise determination of the diffusion coefficients in this low-concentration range was made possible by using a cryogenically cooled NMR probe and by the effective solvent suppression of the PGSE-WATERGATE sequence. The present results bridge the gap between diffusion data measured by fluorescence correlation spectroscopy in the single molecule limit and diffusivities obtained by pulsed field gradient NMR (PFG-NMR) without solvent suppression at higher concentrations. To further extend the concentration range, the diffusion coefficient of Rh6G was also measured on a sample with C{sub Rh6G} = 410 μM by PFG-NMR. The overall concentration dependence of the Rh6G diffusion at 25 °C is discussed in terms of dimerization of the Rh6G molecules. The concentration-dependent monomer/dimer proportion is deduced from the diffusion data.
Flow-enhanced solution printing of all-polymer solar cells
Diao, Ying; Zhou, Yan; Kurosawa, Tadanori; Shaw, Leo; Wang, Cheng; Park, Steve; Guo, Yikun; Reinspach, Julia A.; Gu, Kevin; Gu, Xiaodan; Tee, Benjamin C. K.; Pang, Changhyun; Yan, Hongping; Zhao, Dahui; Toney, Michael F.; Mannsfeld, Stefan C. B.; Bao, Zhenan
2015-08-12
Morphology control of solution coated solar cell materials presents a key challenge limiting their device performance and commercial viability. Here we present a new concept for controlling phase separation during solution printing using an all-polymer bulk heterojunction solar cell as a model system. The key aspect of our method lies in the design of fluid flow using a microstructured printing blade, on the basis of the hypothesis of flow-induced polymer crystallization. Our flow design resulted in a similar to 90% increase in the donor thin film crystallinity and reduced microphase separated donor and acceptor domain sizes. The improved morphology enhanced all metrics of solar cell device performance across various printing conditions, specifically leading to higher short-circuit current, fill factor, open circuit voltage and significantly reduced device-to-device variation. However, we expect our design concept to have broad applications beyond all-polymer solar cells because of its simplicity and versatility.
Flow-enhanced solution printing of all-polymer solar cells
Diao, Ying; Zhou, Yan; Kurosawa, Tadanori; Shaw, Leo; Wang, Cheng; Park, Steve; Guo, Yikun; Reinspach, Julia A.; Gu, Kevin; Gu, Xiaodan; Tee, Benjamin C. K.; Pang, Changhyun; Yan, Hongping; Zhao, Dahui; Toney, Michael F.; Mannsfeld, Stefan C. B.; Bao, Zhenan
2015-01-01
Morphology control of solution coated solar cell materials presents a key challenge limiting their device performance and commercial viability. Here we present a new concept for controlling phase separation during solution printing using an all-polymer bulk heterojunction solar cell as a model system. The key aspect of our method lies in the design of fluid flow using a microstructured printing blade, on the basis of the hypothesis of flow-induced polymer crystallization. Our flow design resulted in a ∼90% increase in the donor thin film crystallinity and reduced microphase separated donor and acceptor domain sizes. The improved morphology enhanced all metrics of solar cell device performance across various printing conditions, specifically leading to higher short-circuit current, fill factor, open circuit voltage and significantly reduced device-to-device variation. We expect our design concept to have broad applications beyond all-polymer solar cells because of its simplicity and versatility. PMID:26264528
An exact solution for Stokes flow in an infinite channel with permeable walls
NASA Astrophysics Data System (ADS)
Herschlag, Gregory; Liu, Jian-Guo; Layton, Anita
2014-11-01
We derive an exact solution for Stokes flow in an infinite channel with permeable walls. We assume that at the channel walls, the normal component of the fluid velocity is described by Darcy's law and the tangential component of the fluid velocity is described by the no slip condition. The pressure exterior to the channel is assumed to be constant. We verify that in the limit of small permeability, Poiseuille flow is recovered to leading order, and demonstrate that our exact result agrees with previous approximate results in this limit. By comparing our solution to existing assumptions on inlet profiles in the literature, we find that although the error is small, Poiseuille and Berman flow do not provide correct inlet conditions. DK089066, DMS1263995, DMS0943760, DMS1107444.
Flow-enhanced solution printing of all-polymer solar cells
NASA Astrophysics Data System (ADS)
Diao, Ying; Zhou, Yan; Kurosawa, Tadanori; Shaw, Leo; Wang, Cheng; Park, Steve; Guo, Yikun; Reinspach, Julia A.; Gu, Kevin; Gu, Xiaodan; Tee, Benjamin C. K.; Pang, Changhyun; Yan, Hongping; Zhao, Dahui; Toney, Michael F.; Mannsfeld, Stefan C. B.; Bao, Zhenan
2015-08-01
Morphology control of solution coated solar cell materials presents a key challenge limiting their device performance and commercial viability. Here we present a new concept for controlling phase separation during solution printing using an all-polymer bulk heterojunction solar cell as a model system. The key aspect of our method lies in the design of fluid flow using a microstructured printing blade, on the basis of the hypothesis of flow-induced polymer crystallization. Our flow design resulted in a ~90% increase in the donor thin film crystallinity and reduced microphase separated donor and acceptor domain sizes. The improved morphology enhanced all metrics of solar cell device performance across various printing conditions, specifically leading to higher short-circuit current, fill factor, open circuit voltage and significantly reduced device-to-device variation. We expect our design concept to have broad applications beyond all-polymer solar cells because of its simplicity and versatility.
An Exact Dual Adjoint Solution Method for Turbulent Flows on Unstructured Grids
NASA Technical Reports Server (NTRS)
Nielsen, Eric J.; Lu, James; Park, Michael A.; Darmofal, David L.
2003-01-01
An algorithm for solving the discrete adjoint system based on an unstructured-grid discretization of the Navier-Stokes equations is presented. The method is constructed such that an adjoint solution exactly dual to a direct differentiation approach is recovered at each time step, yielding a convergence rate which is asymptotically equivalent to that of the primal system. The new approach is implemented within a three-dimensional unstructured-grid framework and results are presented for inviscid, laminar, and turbulent flows. Improvements to the baseline solution algorithm, such as line-implicit relaxation and a tight coupling of the turbulence model, are also presented. By storing nearest-neighbor terms in the residual computation, the dual scheme is computationally efficient, while requiring twice the memory of the flow solution. The scheme is expected to have a broad impact on computational problems related to design optimization as well as error estimation and grid adaptation efforts.
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.
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.
1989-01-01
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.
NASA Technical Reports Server (NTRS)
Wong, T.-C.; Liu, C. H.; Geer, J.
1985-01-01
Approximate solutions for potential flow past an axisymmetric slender body and past a thin airfoil are calculated using a uniform perturbation method and then compared with either the exact analytical solution or the solution obtained using a purely numerical method. The perturbation method is based upon a representation of the disturbance flow as the superposition of singularities distributed entirely within the body, while the numerical (panel) method is based upon a distribution of singularities on the surface of the body. It is found that the perturbation method provides very good results for small values of the slenderness ratio and for small angles of attack. Moreover, for comparable accuracy, the perturbation method is simpler to implement, requires less computer memory, and generally uses less computation time than the panel method. In particular, the uniform perturbation method yields good resolution near the regions of the leading and trailing edges where other methods fail or require special attention.
CFEST Coupled Flow, Energy & Solute Transport Version CFEST005 Theory Guide
Freedman, Vicky L.; Chen, Yousu; Gupta, Sumant K.
2005-11-01
This document presents the mathematical theory implemented in the CFEST (Coupled Flow, Energy, and Solute Transport) simulator. The simulator is a three-dimensional finite element model that can be used for evaluating flow and solute mass transport. Although the theory for thermal transport is presented in this guide, it has not yet been fully implemented in the simulator. The flow module is capable of simulating both confined and unconfined aquifer systems, as well as constant and variable density fluid flows. For unconfined aquifers, the model uses a moving boundary for the water table, deforming the numerical mesh so that the uppermost nodes are always at the water table. For solute transport, changes in concentration of a single dissolved chemical constituent are computed for advective and hydrodynamic transport, linear sorption represented by a retardation factor, and radioactive decay. Once fully implemented, transport of thermal energy in the groundwater and solid matrix of the aquifer can also be used to model aquifer thermal regimes. Mesh construction employs “collapsible”, hexahedral finite elements in a three-dimensional coordinate system. CFEST uses the Galerkin finite element method to convert the partial differential equations to algebraic form. To solve the coupled equations for momentum, solute and heat transport, either Picard or Newton-Raphson iterative schemes are used to treat nonlinearities. An upstream weighted residual finite-element method is used to solve the advective-dispersive transport and energy transfer equations, which circumvents problems of numerical oscillation problems. Matrix solutions of the flow and transport problems are performed using efficient iterative solvers available in ITPACK and PETSc, solvers that are available in the public domain. These solvers are based on the preconditioned conjugate gradient and ORTHOMIN methods for symmetric and a nonsymmetric matrices, respectively.
NASA Astrophysics Data System (ADS)
Bonilla, Jose; Kalwa, Fritz; Händel, Falk; Binder, Martin; Stefan, Catalin
2016-04-01
The Dupuit-Thiem equation is normally used to assess flow towards a pumping well in unconfined aquifers under steady-state conditions. For the formulation of the equation it is assumed that flow is laminar, radial and horizontal towards the well. It is well known that these assumptions are not met in the vicinity of the well; some authors restrict the application of the equation only to a radius larger than 1.5-fold the aquifer thickness. In this study, the equation accuracy to predict the pressure head is evaluated as a simple and quick analytical method to describe the flow pattern for different injection rates in the LSAW. A laboratory scale aquifer-well system (LSAW) was implemented to study the aquifer recharge through wells. The LSAW consists of a 1.0 m-diameter tank with a height of 1.1 meters, filled with sand and a screened well in the center with a diameter of 0.025 m. A regulated outflow system establishes a controlled water level at the tank wall to simulate various aquifer thicknesses. The pressure head at the bottom of the tank along one axis can be measured to assess the flow profile every 0.1 m between the well and the tank wall. In order to evaluate the accuracy of the Dupuit-Thiem equation, a combination of different injection rates and aquifer thicknesses were simulated in the LSAW. Contrary to what was expected (significant differences between the measured and calculated pressure heads in the well), the absolute difference between the calculated and measured pressure head is less than 10%. Beside this, the highest differences are not observed in the well itself, but in the near proximity of it, at a radius of 0.1 m. The results further show that the difference between the calculated and measured pressure heads tends to decrease with higher flow rates. Despite its limitations (assumption of laminar and horizontal flow throughout the whole aquifer), the Dupuit-Thiem equation is considered to accurately represent the flow system in the LSAW.
Flow Boiling Heat Transfer to Lithium Bromide Aqueous Solution in Subcooled Region
NASA Astrophysics Data System (ADS)
Furukawa, Masahiro; Kaji, Masao; Nishizumi, Takeharu; Ozaki, Shinji; Sekoguchi, Kotohiko
To improve the thermal performance of high temperature generator of absorption chiller/heater, heat transfer characteristics of flow boiling of lithium bromide aqueous solution in the subcooled region were experimentally investigated. Experiments were made for water and lithium bromide aqueous solution flowing in a rectangular channel (5 mm × 20 mm cross section) with one side wall heated. Boiling onset quality of lithium bromide aqueous solution is greater than that of water. The heat transfer coefficient of lithium bromide aqueous solution is about a half of that of water under the same experimental conditions of inlet velocity and heat flux. The experimental data of heat transfer coefficient for water are compared with the empirical correlation of Thom et al.11) and a fairly good agreement is obtained. The predictive calculations by the method of Sekoguchi et al.12) are compared with the data for water and lithium bromide aqueous solution. Agreement between them is good for water, while the results for lithium bromide aqueous solution are not satisfactory.
NASA Astrophysics Data System (ADS)
Kallendorf, Christina; Fath, Anja; Oberlack, Martin; Wang, Yongqi
2015-08-01
In the research literature there exist very rare analytical solutions of the surfactant transport equation on an interface. In the present article, we derive sets of exact solutions to interfacial convection-diffusion equations which describe the interfacial transport of insoluble surfactants in a two-phase flow. The investigated model is based on a Stokes flow setting where a spherical shaped inner phase is dispersed in an outer phase. Under the assumption of the small capillary number, the deformation of the spherical phase interface is not taken into account. Neglecting the dependence of the surface tension on the interfacial surfactant concentration, hence neglecting the Marangoni effect, general exact solutions to the surfactant conservation law on the spherical surface with both convective and diffusive terms are provided by means of Heun's confluent function. For the steady case, it is shown that these solutions collapse to a simple exponential form. Furthermore, for the purely diffusive problem, exact solutions are constructed using Legendre polynomials. Such analytical solutions are very valuable as benchmark problems in numerical investigations.
Combined LAURA-UPS solution procedure for chemically-reacting flows. M.S. Thesis
NASA Technical Reports Server (NTRS)
Wood, William A.
1994-01-01
A new procedure seeks to combine the thin-layer Navier-Stokes solver LAURA with the parabolized Navier-Stokes solver UPS for the aerothermodynamic solution of chemically-reacting air flowfields. The interface protocol is presented and the method is applied to two slender, blunted shapes. Both axisymmetric and three dimensional solutions are included with surface pressure and heat transfer comparisons between the present method and previously published results. The case of Mach 25 flow over an axisymmetric six degree sphere-cone with a noncatalytic wall is considered to 100 nose radii. A stability bound on the marching step size was observed with this case and is attributed to chemistry effects resulting from the noncatalytic wall boundary condition. A second case with Mach 28 flow over a sphere-cone-cylinder-flare configuration is computed at both two and five degree angles of attack with a fully-catalytic wall. Surface pressures are seen to be within five percent with the present method compared to the baseline LAURA solution and heat transfers are within 10 percent. The effect of grid resolution is investigated and the nonequilibrium results are compared with a perfect gas solution, showing that while the surface pressure is relatively unchanged by the inclusion of reacting chemistry the nonequilibrium heating is 25 percent higher. The procedure demonstrates significant, order of magnitude reductions in solution time and required memory for the three dimensional case over an all thin-layer Navier-Stokes solution.
NASA Astrophysics Data System (ADS)
Chen, Po-Chia; Chuang, Mo-Hsiung; Tan, Yih-Chi
2014-05-01
In recent years the urban and industrial developments near the coastal area are rapid and therefore the associated population grows dramatically. More and more water demand for human activities, agriculture irrigation, and aquaculture relies on heavy pumping in coastal area. The decline of groundwater table may result in the problems of seawater intrusion and/or land subsidence. Since the 1950s, numerous studies focused on the effect of tidal fluctuation on the groundwater flow in the coastal area. Many studies concentrated on the developments of one-dimensional (1D) and two-dimensional (2D) analytical solutions describing the tide-induced head fluctuations. For example, Jacob (1950) derived an analytical solution of 1D groundwater flow in a confined aquifer with a boundary condition subject to sinusoidal oscillation. Jiao and Tang (1999) derived a 1D analytical solution of a leaky confined aquifer by considered a constant groundwater head in the overlying unconfined aquifer. Jeng et al. (2002) studied the tidal propagation in a coupled unconfined and confined costal aquifer system. Sun (1997) presented a 2D solution for groundwater response to tidal loading in an estuary. Tang and Jiao (2001) derived a 2D analytical solution in a leaky confined aquifer system near open tidal water. This study aims at developing a general analytical solution describing the head fluctuations in a 2D estuarine aquifer system consisted of an unconfined aquifer, a confined aquifer, and an aquitard between them. Both the confined and unconfined aquifers are considered to be anisotropic. The predicted head fluctuations from this solution will compare with the simulation results from the MODFLOW program. In addition, the solutions mentioned above will be shown to be special cases of the present solution. Some hypothetical cases regarding the head fluctuation in costal aquifers will be made to investigate the dynamic effects of water table fluctuation, hydrogeological conditions, and
NASA Technical Reports Server (NTRS)
Wang, Jai-Ching
1992-01-01
Semiconductor crystals such as Hg(1-x)Cd(x)Te grown by unidirectional solidification Bridgmann method have shown compositional segregations in both the axial and radial directions. Due to the wide separation between the liquidus and the solidus of its pseudobinary phase diagram, there is a diffusion layer of higher HgTe content built up in the melt near the melt-solid interface which gives a solute concentration gradient in the axial direction. Because of the higher thermal conductivity in the melt than that in the crystal there is a thermal leakage through the fused silica crucible wall near the melt-solid interface. This gives a thermal gradient in the radial direction. Hart (1971), Thorpe, Hutt and Soulsby (1969) have shown that under such condition a fluid will become convectively unstable as a result of different diffusivities of temperature and solute. It is quite important to understand the effects of this thermosolute convection on the compositional segregation in the unidirectionally solidified crystals. To reach this goal, we start with a simplified problem. We study the nature of fluid flows of a stratified solution in a cylindrical container with a radial temperature gradient. The cylindrical container wall is considered to be maintained at a higher temperature than that at the center of the solution and the solution in the lower gravitational direction has higher solute concentration which decrease linearly to a lower concentration and then remain constant to the top of the solution. The sample solution is taken to be salt water.
Comparison of finite difference and finite element solutions to the variably saturated flow equation
NASA Astrophysics Data System (ADS)
Simpson, M. J.; Clement, T. P.
2003-01-01
Numerical solutions to the equation governing variably saturated flow are usually obtained using either the finite difference (FD) method or the finite element (FE) method. A detailed comparison of these methods shows that the main difference between them is in how the numerical schemes spatially average the variation of material properties. Further differences are also observed in the way that flux boundaries are represented in FE and FD methods. A modified finite element (MFE) algorithm is used to explore the significance of these differences. The MFE algorithm enables a direct comparison with a typical FD solution scheme, and explicitly demonstrates the differences between FE and FD methods. The MFE algorithm provides an improved approximation to the partial differential equation over the usual FD approach while being computationally simpler to implement than the standard FE solution. One of the main limitations of the MFE algorithm is that the algorithm was developed by imposing several restrictions upon the more general FE solution; however, the MFE is shown to be preferable over the usual FE and FD solutions for some of the test problems considered in this study. The comparison results show that the FE (or MFE) solution can avoid the erroneous results encountered in the FD solution for coarsely discretized problems. The improvement in the FE solution is attributed to the broader hydraulic conductivity averaging and differences in the representation of flux type boundaries.
Slender-Body Theory Based On Approximate Solution of the Transonic Flow Equation
NASA Technical Reports Server (NTRS)
Spreiter, John R.; Alksne, Alberta Y.
1959-01-01
Approximate solution of the nonlinear equations of the small disturbance theory of transonic flow are found for the pressure distribution on pointed slender bodies of revolution for flows with free-stream, Mach number 1, and for flows that are either purely subsonic or purely supersonic. These results are obtained by application of a method based on local linearization that was introduced recently in the analysis of similar problems in two-dimensional flows. The theory is developed for bodies of arbitrary shape, and specific results are given for cone-cylinders and for parabolic-arc bodies at zero angle of attack. All results are compared either with existing theoretical results or with experimental data.
Second-order small-disturbance solutions for hypersonic flow over power-law bodies
NASA Technical Reports Server (NTRS)
Townsend, J. C.
1975-01-01
Similarity solutions were found which give the adiabatic flow of an ideal gas about two-dimensional and axisymmetric power-law bodies at infinite Mach number to second order in the body slenderness parameter. The flow variables were expressed as a sum of zero-order and perturbation similarity functions for which the axial variations in the flow equations separated out. The resulting similarity equations were integrated numerically. The solutions, which are universal functions, are presented in graphic and tabular form. To avoid a singularity in the calculations, the results are limited to body power-law exponents greater than about 0.85 for the two-dimensional case and 0.75 for the axisymmetric case. Because of the entropy layer induced by the nose bluntness (for power-law bodies other than cones and wedges), only the pressure function is valid at the body surface. The similarity results give excellent agreement with the exact solutions for inviscid flow over wedges and cones having half-angles up to about 20 deg. They give good agreement with experimental shock-wave shapes and surface-pressure distributions for 3/4-power axisymmetric bodies, considering that Mach number and boundary-layer displacement effects are not included in the theory.
He, L.; Denton, J.D. . Whittle Lab.)
1994-07-01
A three-dimensional nonlinear time-marching method of solving the thin-layer Navier-Stokes equations in a simplified form has been developed for blade flutter calculations. The discretization of the equations is made using the cell-vertex finite volume scheme in space and the four-stage Runge-Kutta scheme in time. Calculations are carried out in a single-blade-passage domain and the phase-shifted periodic condition is implemented by using the shape correction method. The three-dimensional unsteady Euler solution is obtained at conditions of zero viscosity, and is validated against a well-established three-dimensional semi-analytical method. For viscous solutions, the time-step limitation on the explicit temporal discretization scheme is effectively relaxed by using a time-consistent two-grid time-marching technique. A transonic rotor blade passage flow (with tip-leakage) is calculated using the present three-dimensional unsteady viscous solution method. Calculated steady flow results agree well with the corresponding experiment and with other calculations. Calculated unsteady loadings due to oscillations of the rotor blades reveal some notable three-dimensional viscous flow features. The feasibility of solving the simplified thin-layer Navier-Stokes solver for oscillating blade flows at practical conditions is demonstrated.
Application of a solution adaptive grid scheme, SAGE, to complex three-dimensional flows
NASA Technical Reports Server (NTRS)
Davies, Carol B.; Venkatapathy, Ethiraj
1991-01-01
A new three-dimensional (3D) adaptive grid code based on the algebraic, solution-adaptive scheme of Nakahashi and Deiwert is developed and applied to a variety of problems. The new computer code, SAGE, is an extension of the same-named two-dimensional (2D) solution-adaptive program that has already proven to be a powerful tool in computational fluid dynamics applications. The new code has been applied to a range of complex three-dimensional, supersonic and hypersonic flows. Examples discussed are a tandem-slot fuel injector, the hypersonic forebody of the Aeroassist Flight Experiment (AFE), the 3D base flow behind the AFE, the supersonic flow around a 3D swept ramp and a generic, hypersonic, 3D nozzle-plume flow. The associated adapted grids and the solution enhancements resulting from the grid adaption are presented for these cases. Three-dimensional adaption is more complex than its 2D counterpart, and the complexities unique to the 3D problems are discussed.
Implicit unified gas-kinetic scheme for steady state solutions in all flow regimes
NASA Astrophysics Data System (ADS)
Zhu, Yajun; Zhong, Chengwen; Xu, Kun
2016-06-01
This paper presents an implicit unified gas-kinetic scheme (UGKS) for non-equilibrium steady state flow computation. The UGKS is a direct modeling method for flow simulation in all regimes with the updates of both macroscopic flow variables and microscopic gas distribution function. By solving the macroscopic equations implicitly, a predicted equilibrium state can be obtained first through iterations. With the newly predicted equilibrium state, the evolution equation of the gas distribution function and the corresponding collision term can be discretized in a fully implicit way for fast convergence through iterations as well. The lower-upper symmetric Gauss-Seidel (LU-SGS) factorization method is implemented to solve both macroscopic and microscopic equations, which improves the efficiency of the scheme. Since the UGKS is a direct modeling method and its physical solution depends on the mesh resolution and the local time step, a physical time step needs to be fixed before using an implicit iterative technique with a pseudo-time marching step. Therefore, the physical time step in the current implicit scheme is determined by the same way as that in the explicit UGKS for capturing the physical solution in all flow regimes, but the convergence to a steady state speeds up through the adoption of a numerical time step with large CFL number. Many numerical test cases in different flow regimes from low speed to hypersonic ones, such as the Couette flow, cavity flow, and the flow passing over a cylinder, are computed to validate the current implicit method. The overall efficiency of the implicit UGKS can be improved by one or two orders of magnitude in comparison with the explicit one.
Analytical Solution to the Riemann Problem of Three-Phase Flow in Porous Media
Juanes, Ruben; Patzek, Tadeusz W.
2002-09-26
In this paper we study one-dimensional three-phase flow through porous media of immiscible, incompressible fluids. The model uses the common multiphase flow extension of Darcy's equation, and does not include gravity and capillarity effects. Under these conditions, the mathematical problem reduces to a 2 x 2 system of conservation laws whose essential features are: (1) the system is strictly hyperbolic; (2) both characteristic fields are nongenuinely nonlinear, with single, connected inflection loci. These properties, which are natural extensions of the two-phase flow model, ensure that the solution is physically sensible. We present the complete analytical solution to the Riemann problem (constant initial and injected states) in detail, and describe the characteristic waves that may arise, concluding that only nine combinations of rarefactions, shocks and rarefaction-shocks are possible. We demonstrate that assuming the saturation paths of the solution are straightlines may result in inaccurate predictions for some realistic systems. Efficient algorithms for computing the exact solution are also given, making the analytical developments presented here readily applicable to interpretation of lab displacement experiments, and implementation of streamline simulators.
Multigrid solution of incompressible turbulent flows by using two-equation turbulence models
Zheng, X.; Liu, C.; Sung, C.H.
1996-12-31
Most of practical flows are turbulent. From the interest of engineering applications, simulation of realistic flows is usually done through solution of Reynolds-averaged Navier-Stokes equations and turbulence model equations. It has been widely accepted that turbulence modeling plays a very important role in numerical simulation of practical flow problem, particularly when the accuracy is of great concern. Among the most used turbulence models today, two-equation models appear to be favored for the reason that they are more general than algebraic models and affordable with current available computer resources. However, investigators using two-equation models seem to have been more concerned with the solution of N-S equations. Less attention is paid to the solution method for the turbulence model equations. In most cases, the turbulence model equations are loosely coupled with N-S equations, multigrid acceleration is only applied to the solution of N-S equations due to perhaps the fact the turbulence model equations are source-term dominant and very stiff in sublayer region.
NASA Astrophysics Data System (ADS)
Chang, Ching-Min; Yeh, Hund-Der
2016-09-01
This work describes an investigation of the spatial statistical structure of specific discharge field and solute transport process of a nonreactive solute at the field scale through a heterogeneous deformable porous medium. The flow field is driven by a vertical gradient in the excess pore water pressure induced by a step increase in load applied on the upper part of a finite-thickness aquifer. The non-stationary spectral representation is adopted to characterize the spatial covariance of the specific discharge field necessary for the development of the solute particle trajectory statistics using the Lagrangian formalism. We show that the statistics of the specific discharge and particle trajectory derived herein are non-stationary and functions of the coefficient of soil compressibility, μ. The effect of μ on the relative variation of specific discharge and the solute particle trajectory statistics are analyzed upon evaluating our expressions.
Long-time behavior of solution for the compressible nematic liquid crystal flows in R3
NASA Astrophysics Data System (ADS)
Gao, Jincheng; Tao, Qiang; Yao, Zheng-an
2016-08-01
In this paper, we investigate the global existence and long-time behavior of classical solution for the compressible nematic liquid crystal flows in three-dimensional whole space. First of all, the global existence of classical solution is established under the condition that the initial data are close to the constant equilibrium state in HN (R3) (N ≥ 3)-framework. Then, one establishes algebraic time decay for the classical solution by weighted energy method. Finally, the algebraic decay rate of classical solution in Lp (R3)-norm with 2 ≤ p ≤ ∞ and optimal decay rate of their spatial derivative in L2 (R3)-norm are obtained if the initial perturbation belong to L1 (R3) additionally.
NASA Astrophysics Data System (ADS)
Nassar, M.; Ginn, T.
2012-12-01
The purpose of this study is to investigate the effect of the computational error on the solution of the inverse problem connecting with density-dependent flow problem. This effect will be addressed by evaluating the uniqueness of the inverse via monitoring objective function surface behavior in two dimensions parameter space, hydraulic conductivity and longitudinal dispersivity. In addition, the Pareto surface will be generated to evaluate the trade-offs between two calibration objectives based on head and concentration measurement errors. This is conducted by changing the aspects of forward model solution scheme, Eulerian and Lagrangian methods with associated variables. The data used for this study is based on the lab study of Nassar et al (2008). The seepage tank is essentially 2D (in an x-z vertical plane) with relatively homogenous coarse sand media with assigned flux in the upstream and constant head or assigned flux boundary condition at the downstream. The forward model solution is conducted with SEAWAT and it is utilized jointly with the inverse code UCODE-2005. This study demonstrates that the choice of the different numerical scheme with associated aspects of the forward problem is a vital step in the solution of the inverse problem in indirect manner. The method of characteristics gives good results by increasing the initial particles numbers and/ or reducing the time step. The advantage of using more particles concept over decreasing the time step is in smoothing the objective function surface that enable the gradient based search technique works in efficient way. Also, the selected points on the Pareto surface is collapsed to two points on the objective function space. Most likely they are not collapsed to a single point in objective function space with one best parameter set because the problem is advection dominating problem.
NASA Astrophysics Data System (ADS)
Li, Y.; Ma, X.; Su, N.
2013-12-01
The movement of water and solute into and through the vadose zone is, in essence, an issue of immiscible displacement in pore-space network of a soil. Therefore, multiphase flow and transport in porous media, referring to three medium: air, water, and the solute, pose one of the largest unresolved challenges for porous medium fluid seepage. However, this phenomenon has always been largely neglected. It is expected that a reliable analysis model of the multi-phase flow in soil can truly reflect the process of natural movement about the infiltration, which is impossible to be observed directly. In such cases, geophysical applications of the nuclear magnetic resonance (NMR) provides the opportunity to measure the water movements into soils directly over a large scale from tiny pore to regional scale, accordingly enable it available both on the laboratory and on the field. In addition, the NMR provides useful information about the pore space properties. In this study, we proposed both laboratory and field experiments to measure the multi-phase flow parameters, together with optimize the model in computer programming based on the fractional partial differential equations (fPDE). In addition, we establish, for the first time, an infiltration model including solute flowing with water, which has huge influence on agriculture and soil environment pollution. Afterwards, with data collected from experiments, we simulate the model and analyze the spatial variability of parameters. Simulations are also conducted according to the model to evaluate the effects of airflow on water infiltration and other effects such as solute and absorption. It has significant meaning to oxygen irrigation aiming to higher crop yield, and shed more light into the dam slope stability. In summary, our framework is a first-time model added in solute to have a mathematic analysis with the fPDE and more instructive to agriculture activities.
Buoyancy-driven flow in a peat moss layer as a mechanism for solute transport
Rappoldt, Cornelis; Pieters, Gert-Jan J. M.; Adema, Erwin B.; Baaijens, Gerrit J.; Grootjans, Ab P.; van Duijn, Cornelis J.
2003-01-01
Transport of nutrients, CO2, methane, and oxygen plays an important ecological role at the surface of wetland ecosystems. A possibly important transport mechanism in a water-saturated peat moss layer (usually Sphagnum cuspidatum) is nocturnal buoyancy flow, the downward flow of relatively cold surface water, and the upward flow of warm water induced by nocturnal cooling. Mathematical stability analysis showed that buoyancy flow occurs in a cooling porous layer if the system's Rayleigh number (Ra) exceeds 25. For a temperature difference of 10 K between day and night, a typical Ra value for a peat moss layer is 80, which leads to quickly developing buoyancy cells. Numerical simulation demonstrated that fluid flow leads to a considerable mixing of water. Temperature measurements in a cylindrical peat sample of 50-cm height and 35-cm diameter were in agreement with the theoretical results. The nocturnal flow and the associated mixing of the water represent a mechanism for solute transport in water-saturated parts of peat land and in other types of terrestrializing vegetation. This mechanism may be particularly important in continental wetlands, where Ra values in summer are often much larger than the threshold for fluid flow. PMID:14657381
Parkhurst, David L.; Kipp, Kenneth L.; Charlton, Scott R.
2010-01-01
The computer program PHAST (PHREEQC And HST3D) simulates multicomponent, reactive solute transport in three-dimensional saturated groundwater flow systems. PHAST is a versatile groundwater flow and solute-transport simulator with capabilities to model a wide range of equilibrium and kinetic geochemical reactions. The flow and transport calculations are based on a modified version of HST3D that is restricted to constant fluid density and constant temperature. The geochemical reactions are simulated with the geochemical model PHREEQC, which is embedded in PHAST. Major enhancements in PHAST Version 2 allow spatial data to be defined in a combination of map and grid coordinate systems, independent of a specific model grid (without node-by-node input). At run time, aquifer properties are interpolated from the spatial data to the model grid; regridding requires only redefinition of the grid without modification of the spatial data. PHAST is applicable to the study of natural and contaminated groundwater systems at a variety of scales ranging from laboratory experiments to local and regional field scales. PHAST can be used in studies of migration of nutrients, inorganic and organic contaminants, and radionuclides; in projects such as aquifer storage and recovery or engineered remediation; and in investigations of the natural rock/water interactions in aquifers. PHAST is not appropriate for unsaturated-zone flow, multiphase flow, or density-dependent flow. A variety of boundary conditions are available in PHAST to simulate flow and transport, including specified-head, flux (specified-flux), and leaky (head-dependent) conditions, as well as the special cases of rivers, drains, and wells. Chemical reactions in PHAST include (1) homogeneous equilibria using an ion-association or Pitzer specific interaction thermodynamic model; (2) heterogeneous equilibria between the aqueous solution and minerals, ion exchange sites, surface complexation sites, solid solutions, and gases; and
Segregation behavior of magnetic ions in continuous flowing solution under gradient magnetic field
NASA Astrophysics Data System (ADS)
Bing, Ji; Ping, Wu; Han, Ren; Shiping, Zhang; Abdul, Rehman; Li, Wang
2016-07-01
The research of magnetic separation starts from magnetic solid particles to nanoparticles, and in the research progress, particles become smaller gradually with the development of application of magnetic separation technology. Nevertheless, little experimental study of magnetic separation of molecules and ions under continuous flowing conditions has been reported. In this work, we designed a magnetic device and a “layered” flow channel to study the magnetic separation at the ionic level in continuous flowing solution. A segregation model was built to discuss the segregation behavior as well as the factors that may affect the separation. The magnetic force was proved to be the driving force which plays an indispensable role leading to the segregation and separation. The flow velocity has an effect on the segregation behavior of magnetic ions, which determines the separation result. On the other hand, the optimum flow velocity which makes maximum separation is related to the initial concentration of solution. Project supported by the National Natural Science Foundation of China (Grant No. 51276016).
A boundary-layer solution for flow at the soil-root interface.
Severino, Gerardo; Tartakovsky, Daniel M
2015-06-01
Transpiration, a process by which plants extract water from soil and transmit it to the atmosphere, is a vital (yet least quantified) component of the hydrological cycle. We propose a root-scale model of water uptake, which is based on first principles, i.e. employs the generally accepted Richards equation to describe water flow in partially saturated porous media (both in a root and the ambient soil) and makes no assumptions about the kinematic structure of flow in a root-soil continuum. Using the Gardner (exponential) constitutive relation to represent the relative hydraulic conductivities in the Richards equations and treating the root as a cylinder, we use a matched asymptotic expansion technique to derive approximate solutions for transpiration rate and the size of a plant capture zone. These solutions are valid for roots whose size is larger than the macroscopic capillary length of a host soil. For given hydraulic properties, the perturbation parameter used in our analysis relates a root's size to the macroscopic capillary length of the ambient soil. This parameter determines the width of a boundary layer surrounding the soil-root interface, within which flow is strictly horizontal (perpendicular to the root). Our analysis provides a theoretical justification for the standard root-scale cylindrical flow model of plant transpiration that imposes a number of kinematic constraints on water flow in a root-soil continuum. PMID:25008964
Dynamics of polymer solutions and polymer/vesicle mixtures during microchannel flow
NASA Astrophysics Data System (ADS)
Graham, Michael; Anekal, Samartha; Hernandez-Ortiz, Juan
2008-11-01
Addition of small amounts of long-chain polymers to blood has been found to have dramatic effects on its flow in the microcirculation. To address the mechanisms underlying these phenomena, we use a real-space P^3M method for Stokes flow including Brownian fluctuations to study the dynamics of polymer solutions and polymer/vesicle mixtures in microscale flows. Both a simple slit geometry and a grooved cavity flow are studied and polymer concentrations from ultradilute up to near the overlap concentration are considered. As concentration increases, the hydrodynamic migration effects observed in dilute solution unidirectional flows become less prominent, virtually vanishing as the overlap concentration is approached. In a grooved channel geometry, the groove is almost completely depleted of polymer chains at high Weissenberg number in the dilute limit, but at finite concentration this depletion effect is dramatically reduced. In suspensions of vesicles, the presence of polymer molecules has a substantial effect on the dynamics of pair collisions and on migration of the vesicles from microchannel walls.
Frolov, Andrey I
2015-05-12
Accurate calculation of solvation free energies (SFEs) is a fundamental problem of theoretical chemistry. In this work we perform a careful validation of the theory of solutions in energy representation (ER method) developed by Matubayasi et al. [J. Chem. Phys. 2000, 113, 6070-6081] for SFE calculations in supercritical solvents. This method can be seen as a bridge between the molecular simulations and the classical (not quantum) density functional theory (DFT) formulated in energy representation. We performed extensive calculations of SFEs of organic molecules of different chemical natures in pure supercritical CO2 (sc-CO2) and in sc-CO2 with addition of 6 mol % of ethanol, acetone, and n-hexane as cosolvents. We show that the ER method reproduces SFE data calculated by a method free of theoretical approximations (the Bennett's acceptance ratio) with the mean absolute error of only 0.05 kcal/mol. However, the ER method requires by an order less computational resources. Also, we show that the quality of ER calculations should be carefully monitored since the lack of sampling can result into a considerable bias in predictions. The present calculations reproduce the trends in the cosolvent-induced solubility enhancement factors observed in experimental data. Thus, we think that molecular simulations coupled with the ER method can be used for quick calculations of the effect of variation of temperature, pressure, and cosolvent concentration on SFE and hence solubility of bioactive compounds in supercritical fluids. This should dramatically reduce the burden of experimental work on optimizing solvency of supercritical solvents. PMID:26574423
Yuan, Qiao-ying; Zhang, Ling; Xiao, Dan; Zhao, Kun; Lin, Chun; Si, Liang-yi
2014-01-01
Because of the limitations of existing methods and techniques for directly obtaining real-time blood data, no accurate microflow in vivo real-time analysis method exists. To establish a novel technical platform for real-time in vivo detection and to analyze average blood pressure and other blood flow parameters, a small, accurate, flexible, and nontoxic Fabry-Perot fiber sensor was designed. The carotid sheath was implanted through intubation of the rabbit carotid artery (n = 8), and the blood pressure and other detection data were determined directly through the veins. The fiber detection results were compared with test results obtained using color Doppler ultrasound and a physiological pressure sensor recorder. Pairwise comparisons among the blood pressure results obtained using the three methods indicated that real-time blood pressure information obtained through the fiber sensor technique exhibited better correlation than the data obtained with the other techniques. The highest correlation (correlation coefficient of 0.86) was obtained between the fiber sensor and pressure sensor. The blood pressure values were positively related to the total cholesterol level, low-density lipoprotein level, number of red blood cells, and hemoglobin level, with correlation coefficients of 0.033, 0.129, 0.358, and 0.373, respectively. The blood pressure values had no obvious relationship with the number of white blood cells and high-density lipoprotein and had a negative relationship with triglyceride levels, with a correlation coefficient of –0.031. The average ambulatory blood pressure measured by the fiber sensor exhibited a negative correlation with the quantity of blood platelets (correlation coefficient of −0.839, P<0.05). The novel fiber sensor can thus obtain in vivo blood pressure data accurately, stably, and in real time; the sensor can also determine the content and status of the blood flow to some extent. Therefore, the fiber sensor can obtain partially real
Numerical solution of a three-dimensional cubic cavity flow by using the Boltzmann equation
NASA Technical Reports Server (NTRS)
Hwang, Danny P.
1992-01-01
A three-dimensional cubic cavity flow has been analyzed for diatomic gases by using the Boltzmann equation with the Bhatnagar-Gross-Krook (B-G-K) model. The method of discrete ordinate was applied, and the diffuse reflection boundary condition was assumed. The results, which show a consistent trend toward the Navier-Stokes solution as the Knudson number is reduced, give us confidence to apply the method to a three-dimensional geometry for practical predictions of rarefied-flow characteristics. The CPU time and the main memory required for a three-dimensional geometry using this method seem reasonable.
Over-reflection of slow magnetosonic waves by homogeneous shear flow: Analytical solution
Dimitrov, Z. D.; Maneva, Y. G.; Hristov, T. S.; Mishonov, T. M.
2011-08-15
We have analyzed the amplification of slow magnetosonic (or pseudo-Alfvenic) waves (SMW) in incompressible shear flow. As found here, the amplification depends on the component of the wave-vector perpendicular to the direction of the shear flow. Earlier numerical results are consistent with the general analytic solution for the linearized magnetohydrodynamic equations, derived here for the model case of pure homogeneous shear (without Coriolis force). An asymptotically exact analytical formula for the amplification coefficient is derived for the case when the amplification is sufficiently large.
NASA Astrophysics Data System (ADS)
Wang, Li-yong; Li, Le; Zhang, Zhi-hua
2016-07-01
Hot compression tests of Ti-6Al-4V alloy in a wide temperature range of 1023-1323 K and strain rate range of 0.01-10 s-1 were conducted by a servo-hydraulic and computer-controlled Gleeble-3500 machine. In order to accurately and effectively characterize the highly nonlinear flow behaviors, support vector regression (SVR) which is a machine learning method was combined with genetic algorithm (GA) for characterizing the flow behaviors, namely, the GA-SVR. The prominent character of GA-SVR is that it with identical training parameters will keep training accuracy and prediction accuracy at a stable level in different attempts for a certain dataset. The learning abilities, generalization abilities, and modeling efficiencies of the mathematical regression model, ANN, and GA-SVR for Ti-6Al-4V alloy were detailedly compared. Comparison results show that the learning ability of the GA-SVR is stronger than the mathematical regression model. The generalization abilities and modeling efficiencies of these models were shown as follows in ascending order: the mathematical regression model < ANN < GA-SVR. The stress-strain data outside experimental conditions were predicted by the well-trained GA-SVR, which improved simulation accuracy of the load-stroke curve and can further improve the related research fields where stress-strain data play important roles, such as speculating work hardening and dynamic recovery, characterizing dynamic recrystallization evolution, and improving processing maps.
NASA Astrophysics Data System (ADS)
Ono, Naoki; Yoshida, Takahiro; Kaneko, Takahiro; Nishiguchi, Shotaro; Shoji, Masahiro
The temperature dependency of surface tension of aqueous solutions of some alcohol such as butanol behaves in a nonlinear manner. Namely, the value of surface tension tends to increase, when the solution is heated beyond a temperature. This type of solution is named “nonlinear thermocapillary solution” here. The direction of thermocapillary force in liquid film of the solution on a heated surface acts in the same direction to that of the solutocapillary force. This characteristic will be more marked in small scale systems such as mini⁄micro channels. In this study the liquid behavior of the solution in flow boiling experiments with mini⁄micro tubes was investigated. Butanol aqueous solutions were adopted as test fluids. Pure water and ethanol aqueous solution were also used for comparison. The aim of the study is to observe the liquid motion and to investigate temperature fluctuation in mini⁄micro channels with inner diameter of 1 mm and 0.42 mm. The surface temperature of the tube was measured by using fine K-type thermocouples at the surface of the tubes and the liquid motion was observed by CCD camera system.
Vijayakumar, M.; Li, Liyu; Graff, Gordon L.; Liu, Jun; Zhang, Huamin; Yang, Zhenguo; Hu, Jian Z.
2011-04-01
The V5+ electrolyte solution from vanadium redox flow batteries was studied by variable temperature 17O and 51V Nuclear Magnetic Resonance (NMR) spectroscopy and DFT based computational modeling. It was found that the V5+ species exist as hydrated penta co-ordinated vanadate ion, i.e. [VO2(H2O)3]1+. This hydrated structure is not stable at elevated temperature and change into neutral H3VO4 molecule via a deprotonation process. H3VO4 species is also knowingly unstable, leading to the observed V2O5 precipitation in V5+ electrolyte solutions.
NASA Technical Reports Server (NTRS)
Farrell, C.; Adamczyk, J.
1981-01-01
The three-dimensional flow in a turbomachinery blade row was approximated by correcting for streamtube convergence and radius change in the throughflow direction. The method is a fully conservative solution of the full potential equation incorporating the finite volume technique on body fitted periodic mesh, with an artificial density imposed in the transonic region to insure stability and the capture of shock waves. Comparison of results for several supercritical blades shows good agreement with their hodograph solutions. Other calculations for these profiles as well as standard NACA blade sections indicate that this is a useful scheme analyzing both the design and off-design performance of turbomachinery blading.
Numerical Solutions for Supersonic Flow of an Ideal Gas Around Blunt Two-Dimensional Bodies
NASA Technical Reports Server (NTRS)
Fuller, Franklyn B.
1961-01-01
The method described is an inverse one; the shock shape is chosen and the solution proceeds downstream to a body. Bodies blunter than circular cylinders are readily accessible, and any adiabatic index can be chosen. The lower limit to the free-stream Mach number available in any case is determined by the extent of the subsonic field, which in turn depends upon the body shape. Some discussion of the stability of the numerical processes is given. A set of solutions for flows about circular cylinders at several Mach numbers and several values of the adiabatic index is included.
Kousera, C A; Nijjer, S; Torii, R; Petraco, R; Sen, S; Foin, N; Hughes, A D; Francis, D P P; Xu, X Y; Davies, J E
2014-06-01
Computational fluid dynamics (CFD) is increasingly being developed for the diagnostics of arterial diseases. Imaging methods such as computed tomography (CT) and angiography are commonly used. However, these have limited spatial resolution and are subject to movement artifact. This study developed a new approach to generate CFD models by combining high-fidelity, patient-specific coronary anatomy models derived from optical coherence tomography (OCT) imaging with patient-specific pressure and velocity phasic data. Additionally, we used a new technique which does not require the catheter to be used to determine the centerline of the vessel. The CFD data were then compared with invasively measured pressure and velocity. Angiography imaging data of 21 vessels collected from 19 patients were fused with OCT visualizations of the same vessels using an algorithm that produces reconstructions inheriting the in-plane (10 μm) and longitudinal (0.2 mm) resolution of OCT. Proximal pressure and distal velocity waveforms ensemble averaged from invasively measured data were used as inlet and outlet boundary conditions, respectively, in CFD simulations. The resulting distal pressure waveform was compared against the measured waveform to test the model. The results followed the shape of the measured waveforms closely (cross-correlation coefficient = 0.898 ± 0.005, ), indicating realistic modeling of flow resistance, the mean of differences between measured and simulated results was -3. 5 mmHg, standard deviation of differences (SDD) = 8.2 mmHg over the cycle and -9.8 mmHg, SDD = 16.4 mmHg at peak flow. Models incorporating phasic velocity in patient-specific models of coronary anatomy derived from high-resolution OCT images show a good correlation with the measured pressure waveforms in all cases, indicating that the model results may be an accurate representation of the measured flow conditions. PMID:24845301
Flow Boiling Heat Transfer to Lithium Bromide Aqueous Solution in Subcooled Region
NASA Astrophysics Data System (ADS)
Kaji, Masao; Furukawa, Masahiro; Nishizumi, Takeharu; Ozaki, Shinji; Sekoguchi, Kotohiko
A theoretical prediction model of the boiling heat transfer coefficient in the subcooled region for water and lithium bromide aqueous solution flowing in a rectangular channel is proposed. In the present heat transfer model, a heat flux is assumed to consist of both the forced convective and the boiling effect components. The forced convective component is evaluated from the empirical correlation of convective heat transfer coefficient for single-phase flow considering the effect of increase of liquid velocity due to net vapor generation. Empirical correlations for determining the heat flux due to the boiling effect and the quality at the onset point of net vapor generation are obtained from the data presented in the first report1). Agreement between the present theoretical prediction and the experimental data is satisfactorily good both for water and lithium bromide aqueous solution.
Steady and Unsteady Numerical Solution of Generalized Newtonian Fluids Flow by Runge-Kutta method
NASA Astrophysics Data System (ADS)
Keslerová, R.; Kozel, K.; Prokop, V.
2010-09-01
In this paper the laminar viscous incompressible flow for generalized Newtonian (Newtonian and non-Newtonian) fluids is considered. The governing system of equations is the system of Navier-Stokes equations and the continuity equation. The steady and unsteady numerical solution for this system is computed by finite volume method combined with an artificial compressibility method. For time discretization the explicit multistage Runge-Kutta numerical scheme is considered. Steady state solution is achieved for t→∞ using steady boundary conditions and followed by steady residual behavior. The dual time-stepping method is considered for unsteady computation. The high artificial compressibility coefficient is used in the artificial compressibility method applied in the dual time τ. The steady and unsteady numerical results of Newtonian and non-Newtonian (shear thickening and shear thinning) fluids flow in the branching channel are presented.
NASA Astrophysics Data System (ADS)
Česenek, Jan
2016-03-01
In this article we deal with numerical simulation of the non-stationary compressible turbulent flow. Compressible turbulent flow is described by the Reynolds-Averaged Navier-Stokes (RANS) equations. This RANS system is equipped with two-equation k-omega turbulence model. These two systems of equations are solved separately. Discretization of the RANS system is carried out by the space-time discontinuous Galerkin method which is based on piecewise polynomial discontinuous approximation of the sought solution in space and in time. Discretization of the two-equation k-omega turbulence model is carried out by the implicit finite volume method, which is based on piecewise constant approximation of the sought solution. We present some numerical experiments to demonstrate the applicability of the method using own-developed code.
Degradation of homogeneous polymer solutions in high shear turbulent pipe flow
NASA Astrophysics Data System (ADS)
Elbing, B. R.; Winkel, E. S.; Solomon, M. J.; Ceccio, S. L.
2009-12-01
This study quantifies degradation of polyethylene oxide (PEO) and polyacrylamide (PAM) polymer solutions in large diameter (2.72 cm) turbulent pipe flow at Reynolds numbers to 3 × 105 and shear rates greater than 105 1/s. The present results support a universal scaling law for polymer chain scission reported by Vanapalli et al. (2006) that predicts the maximum chain drag force to be proportional to Re 3/2, validating this scaling law at higher Reynolds numbers than prior studies. Use of this scaling gives estimated backbone bond strengths from PEO and PAM of 3.2 and 3.8 nN, respectively. Additionally, with the use of synthetic seawater as a solvent the onset of drag reduction occurred at higher shear rates relative to the pure water solvent solutions, but had little influence on the extent of degradation at higher shear rates. These results are significant for large diameter pipe flow applications that use polymers to reduce drag.
Investigation of ALEGRA shock hydrocode algorithms using an exact free surface jet flow solution.
Hanks, Bradley Wright.; Robinson, Allen Conrad
2014-01-01
Computational testing of the arbitrary Lagrangian-Eulerian shock physics code, ALEGRA, is presented using an exact solution that is very similar to a shaped charge jet flow. The solution is a steady, isentropic, subsonic free surface flow with significant compression and release and is provided as a steady state initial condition. There should be no shocks and no entropy production throughout the problem. The purpose of this test problem is to present a detailed and challenging computation in order to provide evidence for algorithmic strengths and weaknesses in ALEGRA which should be examined further. The results of this work are intended to be used to guide future algorithmic improvements in the spirit of test-driven development processes.
Solute transport processes in flow-event-driven stream-aquifer interaction
NASA Astrophysics Data System (ADS)
Xie, Yueqing; Cook, Peter G.; Simmons, Craig T.
2016-07-01
The interaction between streams and groundwater controls key features of the stream hydrograph and chemograph. Since surface runoff is usually less saline than groundwater, flow events are usually accompanied by declines in stream salinity. In this paper, we use numerical modelling to show that, at any particular monitoring location: (i) the increase in stream stage associated with a flow event will precede the decrease in solute concentration (arrival time lag for solutes); and (ii) the decrease in stream stage following the flow peak will usually precede the subsequent return (increase) in solute concentration (return time lag). Both arrival time lag and return time lag increase with increasing wave duration. However, arrival time lag decreases with increasing wave amplitude, whereas return time lag increases. Furthermore, while arrival time lag is most sensitive to parameters that control river velocity (channel roughness and stream slope), return time lag is most sensitive to groundwater parameters (aquifer hydraulic conductivity, recharge rate, and dispersitivity). Additionally, the absolute magnitude of the decrease in river concentration is sensitive to both river and groundwater parameters. Our simulations also show that in-stream mixing is dominated by wave propagation and bank storage processes, and in-stream dispersion has a relatively minor effect on solute concentrations. This has important implications for spreading of contaminants released to streams. Our work also demonstrates that a high contribution of pre-event water (or groundwater) within the flow hydrograph can be caused by the combination of in-stream and bank storage exchange processes, and does not require transport of pre-event water through the catchment.
Analytical solution to the equations for parallel-flow four-channel heat exchangers
Malinowski, L.
2000-04-01
Assuming that the thermophysical parameters of the fluids are independent on temperature, the stationary temperature field in a parallel-flow multi-channel heat exchanger can be described by a set of linear differential equations of the first order with constant coefficients. A compact analytical solution to this set is presented for the case of four-channel exchangers and simple eigenvalues of the coefficient matrix of the set.
Global solution to a hyperbolic problem arising in the modeling of blood flow in circulatory systems
NASA Astrophysics Data System (ADS)
Ruan, Weihua; Clark, M. E.; Zhao, Meide; Curcio, Anthony
2007-07-01
This paper considers a system of first-order, hyperbolic, partial differential equations in the domain of a one-dimensional network. The system models the blood flow in human circulatory systems as an initial-boundary-value problem with boundary conditions of either algebraic or differential type. The differential equations are nonhomogeneous with frictional damping terms and the state variables are coupled at internal junctions. The existence and uniqueness of the local classical solution have been established in our earlier work [W. Ruan, M.E. Clark, M. Zhao, A. Curcio, A hyperbolic system of equations of blood flow in an arterial network, J. Appl. Math. 64 (2) (2003) 637-667; W. Ruan, M.E. Clark, M. Zhao, A. Curcio, Blood flow in a network, Nonlinear Anal. Real World Appl. 5 (2004) 463-485; W. Ruan, M.E. Clark, M. Zhao, A. Curcio, A quasilinear hyperbolic system that models blood flow in a network, in: Charles V. Benton (Ed.), Focus on Mathematical Physics Research, Nova Science Publishers, Inc., New York, 2004, pp. 203-230]. This paper continues the analysis and gives sufficient conditions for the global existence of the classical solution. We prove that the solution exists globally if the boundary data satisfy the dissipative condition (2.3) or (3.2), and the norms of the initial and forcing functions in a certain Sobolev space are sufficiently small. This is only the first step toward establishing the global existence of the solution to physiologically realistic models, because, in general, the chosen dissipative conditions (2.3) and (3.2) do not appear to hold for the originally proposed boundary conditions (1.3)-(1.12).
An analytic solution for periodic thermally-driven flows over an infinite slope
NASA Astrophysics Data System (ADS)
Zardi, Dino; Serafin, Stefano
2013-04-01
The flow generated along an infinite slope in an unperturbed stably stratified atmosphere at rest by a time periodic surface temperature forcing is examined. Following Defant (1949), a set of equations is derived which extends Prandtl's (1942) theory to allow for nonstationary conditions. Uniform boundary conditions are conducive to an along-slope parallel flow, governed by a periodically reversing local imbalance between along-slope advection and slope-normal fluxes of momentum and heat. Solutions include both a transient part and a subsequent periodic regime. The former can only be expressed in an integral form, whereas the latter is a combination of exponential and sine or cosine functions of time and height normal to the slope. Key parameters are the quantity Nα = N sinα (where α is the slope angle, and N is the Brunt-Väisälä frequency of the unperturbed atmosphere) and the angular frequency of the driving surface temperature cycle, ?. Three different flow regimes may occur, namely subcritical (Nα < ?), critical (Nα = ?) and supercritical (Nα > ?). The properties of the solutions in each regime are examined and discussed. The relationship between the present solutions and the earlier time-dependent slope flow model by Defant (1949) is also discussed. References Defant, F., 1949: Zur Theorie der Hangwinde, nebst Bemerkungen zur Theorie der Berg- und Talwinde. [A theory of slope winds, along with remarks on the theory of mountain winds and valley winds]. Arch. Meteor. Geophys. Bioclimatol., Ser. A, 1, 421-450 (Theoretical and Applied Climatology). [English translation: Whiteman, C.D., and E. Dreiseitl, 1984: Alpine meteorology: Translations of classic contributions by A. Wagner, E. Ekhart and F. Defant. PNL-5141 / ASCOT-84-3. Pacific Northwest Laboratory, Richland, Washington, 121 pp]. Prandtl, L., 1942: Strömungslehre [Flow Studies]. Vieweg und Sohn, Braunschweig, 382 pp.
Effects of alongshore morphology on groundwater flow and solute transport in a nearshore aquifer
NASA Astrophysics Data System (ADS)
Zhang, Ying; Li, Ling; Erler, Dirk V.; Santos, Isaac; Lockington, David
2016-02-01
Variations of beach morphology in both the cross-shore and alongshore directions, associated with tidal creeks, are common at natural coasts, as observed at a field site on the east coast of Rarotonga, Cook Islands. Field investigations and three-dimensional (3-D) numerical simulations were conducted to study the nearshore groundwater flow and solute transport in such a system. The results show that the beach morphology, combined with tides, induced a significant alongshore flow and modified local pore water circulation and salt transport in the intertidal zone substantially. The bathymetry and hydraulic head of the creek enabled further and more rapid landward intrusion of seawater along the creek than in the aquifer, which created alongshore hydraulic gradient and solute concentration gradient to drive pore water flow and salt transport in the alongshore direction within the aquifer. The effects of the creek led to the formation of a saltwater plume in groundwater at an intermediate depth between fresher water zones on a cross-shore transect. The 3-D pore water flow in the nearshore zone was also complicated by the landward hydraulic head condition, resulting in freshwater drainage across the inland section of the creek while seawater infiltrating the seaward section. These results provided new insights into the complexity, intensity, and time scales of mixing among fresh groundwater, recirculating seawater and creek water in three dimensions. The 3-D characteristics of nearshore pore water flow and solute transport have important implications for studies of submarine groundwater discharge and associated chemical input to the coastal sea, and for evaluation of the beach habitat conditions.
Flow and Reactive Transport of Miscible and Immiscible Solutions in Fractured & Porous Media
NASA Astrophysics Data System (ADS)
Ryerson, F. J.; Ezzedine, S. M.; Antoun, T.
2012-12-01
Miscible and immiscible flows are important phenomena encountered in many industrial and engineering applications such as hydrothermal systems, oil and gas reservoirs, salt/water intrusion, geological carbon sequestration etc… Under the influence of gravity, the flow of fluids with sufficiently large density ratios may become unstable leading to instabilities, mixing and in some instances reactions at the interfacial contact between fluids. Flow is governed by a combination of momentum and mass conservation equations that describe the flow of the fluid phase and a convection-diffusion equation describing the change of concentration in the fluid phase. When hydrodynamic instabilities develop it may be difficult to use standard grid-based methods to model miscible/immiscible flow because the domains occupied by fluids evolve constantly with time. In the current study, adaptive mesh refinement finite elements method has been used to solve for flow and transport equations. Furthermore, a particle tracking scheme has also been implemented to track the kinematics of swarm of particles injected into the porous fractured media to quantify surface area, sweeping zones, and their impact on porosity changes. Spatial and temporal moments of the fingering instabilities and the development of reaction zones and the impact of kinetic reaction at the fluid/solution interfaces have also been analyzed. This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
Wall slip, shear banding, and instability in the flow of a triblock copolymer micellar solution
NASA Astrophysics Data System (ADS)
Manneville, Sébastien; Colin, Annie; Waton, Gilles; Schosseler, François
2007-06-01
The shear flow of a triblock copolymer micellar solution (PEO-PPO-PEO Pluronic P84 in brine) is investigated using simultaneous rheological and velocity profile measurements in the concentric cylinder geometry. We focus on two different temperatures below and above the transition temperature Tc which was previously associated with the apparition of a stress plateau in the flow curve. (i) At T=37.0°C
NASA Astrophysics Data System (ADS)
Yoshida, Hiroaki; Mizuno, Hideyuki; Kinjo, Tomoyuki; Washizu, Hitoshi; Barrat, Jean-Louis
2014-06-01
Electrokinetic flows of an aqueous NaCl solution in nanochannels with negatively charged surfaces are studied using molecular dynamics simulations. The four transport coefficients that characterize the response to weak electric and pressure fields, namely, the coefficients for the electrical current in response to the electric field (Mjj) and the pressure field (Mjm), and those for the mass flow in response to the same fields (Mmj and Mmm), are obtained in the linear regime using a Green-Kubo approach. Nonequilibrium simulations with explicit external fields are also carried out, and the current and mass flows are directly obtained. The two methods exhibit good agreement even for large external field strengths, and Onsager's reciprocal relation (Mjm = Mmj) is numerically confirmed in both approaches. The influence of the surface charge density on the flow is also considered. The values of the transport coefficients are found to be smaller for larger surface charge density, because the counter-ions strongly bound near the channel surface interfere with the charge and mass flows. A reversal of the streaming current and of the reciprocal electro-osmotic flow, with a change of sign of Mmj due to the excess co-ions, takes places for very high surface charge density.
Yoshida, Hiroaki; Mizuno, Hideyuki; Kinjo, Tomoyuki; Washizu, Hitoshi; Barrat, Jean-Louis
2014-06-01
Electrokinetic flows of an aqueous NaCl solution in nanochannels with negatively charged surfaces are studied using molecular dynamics simulations. The four transport coefficients that characterize the response to weak electric and pressure fields, namely, the coefficients for the electrical current in response to the electric field (M(jj)) and the pressure field (M(jm)), and those for the mass flow in response to the same fields (M(mj) and M(mm)), are obtained in the linear regime using a Green-Kubo approach. Nonequilibrium simulations with explicit external fields are also carried out, and the current and mass flows are directly obtained. The two methods exhibit good agreement even for large external field strengths, and Onsager's reciprocal relation (M(jm) = M(mj)) is numerically confirmed in both approaches. The influence of the surface charge density on the flow is also considered. The values of the transport coefficients are found to be smaller for larger surface charge density, because the counter-ions strongly bound near the channel surface interfere with the charge and mass flows. A reversal of the streaming current and of the reciprocal electro-osmotic flow, with a change of sign of M(mj) due to the excess co-ions, takes places for very high surface charge density. PMID:24908029
Lie Algebraic Analysis of Thin Film Marangoni Flows: Multiplicity of Self-Similar Solutions
NASA Astrophysics Data System (ADS)
Nicolaou, Zachary; Troian, Sandra
The rapid advance of an insoluble surfactant monolayer on a thin liquid film of higher surface tension is controlled by distinct flow regimes characterized by the relative strength of viscous, Marangoni and capillary forces. Such flows play a critical role in human pulmonary and ocular systems. During the past quarter century, researchers have focused exclusively on self-similar solutions to the governing pair of nonlinear PDEs for the film thickness, H (r /ta) , and surface concentration, Γ (r /ta) /tb , in the limit where the Marangoni or capillary terms vanish, where r denotes the spatial variable, t is time, and a and b are fractional exponents. Using Lie algebraic techniques, we demonstrate for the first time the existence of several embedded symmetries in this system of equations which yield multiple self-similar solutions describing more complex scaling behavior, even when all three forces are incorporated. A special and previously unrecognized subset of these solutions reveals the dynamical behavior of film thinning and surfactant distribution near the origin, which ultimately meters the downstream flow. Finite element simulations confirm the suite of scaling exponents obtained analytically.
Approximation of traveling wave solutions in wall-bounded flows using resolvent modes
NASA Astrophysics Data System (ADS)
McKeon, Beverley; Graham, Michael; Moarref, Rashad; Park, Jae Sung; Sharma, Ati; Willis, Ashley
2014-11-01
Significant recent attention has been devoted to computing and understanding exact traveling wave solutions of the Navier-Stokes equations. These solutions can be interpreted as the state-space skeleton of turbulence and are attractive benchmarks for studying low-order models of wall turbulence. Here, we project such solutions onto the velocity response (or resolvent) modes supplied by the gain-based resolvent analysis outlined by McKeon & Sharma (JFM, 2010). We demonstrate that in both pipe (Pringle et al., Phil. Trans. R. Soc. A, 2009) and channel (Waleffe, JFM, 2001) flows, the solutions can be well-described by a small number of resolvent modes. Analysis of the nonlinear forcing modes sustaining these solutions reveals the importance of small amplitude forcing, consistent with the large amplifications admitted by the resolvent operator. We investigate the use of resolvent modes as computationally cheap ``seeds'' for the identification of further traveling wave solutions. The support of AFOSR under Grants FA9550-09-1-0701, FA9550-12-1-0469, FA9550-11-1-0094 and FA9550-14-1-0042 (program managers Rengasamy Ponnappan, Doug Smith and Gregg Abate) is gratefully acknowledged.
Multidimensional self-similar analytical solutions of two-phase flow in porous media
NASA Astrophysics Data System (ADS)
Fučík, Radek; Illangasekare, Tissa H.; Beneš, Michal
2016-04-01
In general, analytical solutions serve a useful purpose to obtain better insights and to verify numerical codes. For flow of two incompressible and immiscible phases in homogeneous porous media without gravity, one such method that neglects capillary pressure in the solution was first developed by Buckley and Leverett (1942). Subsequently, McWhorter and Sunada (1990) derived an exact solution for the one and two dimensional cases that factored in capillary effects. This solution used a similarity transform that allowed to reduce the governing equations into a single ordinary differential equation (ODE) that can be further integrated into an equivalent integral equation. We present a revision to McWhorter and Sunada solution by extending the self-similar solution into a general multidimensional space. Inspired by the derivation proposed by McWhorter and Sunada (1990), we integrate the resulting ODE in the third and higher dimensions into a new integral equation that can be subsequently solved iteratively by means of numerical integration. We developed implementations of the iterative schemes for one- and higher dimensional cases that can be accessed online on the authors' website.
Generalization of one-dimensional solute transport. A stochastic-convective flow conceptualization
Simmons, C.S.
1986-04-01
A stochastic-convective representation of one-dimensional solute transport is derived. It is shown to conceptually encompass solutions of the conventional convection-dispersion equation. This stochastic approach, however, does not rely on the assumption that dispersive flux satisfies Fick's diffusion law. Observable values of solute concentration and flux, which together satisfy a conservation equation, are expressed as expectations over a flow velocity ensemble, representing the inherent random processess that govern dispersion. Solute concentration is determined by a Lagrangian pdf for random spatial displacements, while flux is determined by an equivalent Eulerian pdf for random travel times. A condition for such equivalence is derived for steady nonuniform flow, and it is proven that both Lagrangian and Eulerian pdfs are required to account for specified initial and boundary conditions on a global scale. Furthermore, simplified modeling of transport is justified by proving that an ensemble of effectively constant velocities always exists that constitutes an equivalent representation. An example of how a two-dimensional transport problems can be reduced to a single-dimensional stochastic viewpoint is also presented to further clarify concepts.
Generalization of one-dimensional solute transport: A stochastic-convective flow conceptualization
NASA Astrophysics Data System (ADS)
Simmons, C. S.
1986-04-01
A stochastic-convective representation of one-dimensional solute transport is derived. It is shown to conceptually encompass solutions of the conventional convection-dispersion equation. This stochastic approach, however, does not rely on the assumption that dispersive flux satisfies Fick's diffusion law. Observable values of solute concentration and flux, which together satisfy a conservation equation, are expressed as expectations over a flow velocity ensemble, representing the inherent random processess that govern dispersion. Solute concentration is determined by a Lagrangian pdf for random spatial displacements, while flux is determined by an equivalent Eulerian pdf for random travel times. A condition for such equivalence is derived for steady nonuniform flow, and it is proven that both Lagrangian and Eulerian pdfs are required to account for specified initial and boundary conditions on a global scale. Furthermore, simplified modeling of transport is justified by proving that an ensemble of effectively constant velocities always exists that constitutes an equivalent representation. An example of how a two-dimensional transport problem can be reduced to a single-dimensional stochastic viewpoint is also presented to further clarify concepts.
Helical Groundwater Flow in Braided-River Sediments and its Effects on Solute Mixing
NASA Astrophysics Data System (ADS)
Arie Cirpka, Olaf; Bennett, Jeremy Paul; Haslauer, Claus; Ye, Yu; Rolle, Massimo; Chiogna, Gabriele
2016-04-01
Spatially variable orientation of anisotropy can cause helical flow in porous media. In previous studies (Chiogna et al., 2015; Cirpka et al., 2015; see also Figure 1), we analyzed hydraulic conductivity fields with blockwise constant anisotropic correlation structure showing that macroscopically helical flow evolves, and leads to enhanced solute dilution in steady-state advective-dispersive transport. While these studies demonstrated the potential importance of helical flow in heterogeneous porous media, the likelihood of its occurrence remained unclear. In particular, natural sediments do not exhibit extended stripes of materials with diagonally oriented internal anisotropy. In the present study, we generated realistic looking sedimentary structures mimicking scour fills that may be created in braided-river sediments. The individual geobodies are filled with anisotropic porous material. Cross-sections show typical cross-bedding. In particular we analyzed how the variability in bulk hydraulic conductivity between the geobodies and the differences in the orientation of anisotropy affect flow and transverse solute mixing. While the variance of log-hydraulic conductivity controls longitudinal spreading, the variability in the orientation of anisotropy is decisive for folding and mixing perpendicular to the mean flow direction. The importance of non-stationary anisotropy for transverse mixing poses a challenge for the hydraulic characterization of sediments when predicting lengths of mixing-controlled quasi steady-state plumes. References [1] O.A. Cirpka, G. Chiogna, M. Rolle, A. Bellin: Transverse mixing in three-dimensional non-stationary anisotropic heterogeneous porous media. Water Resour. Res. 51(1): 241-260 (2015). [2] G. Chiogna, O.A. Cirpka, M. Rolle, A. Bellin: Helical flow in three-dimensional non-stationary anisotropic heterogeneous porous media. Water Resour. Res. 51(1): 261-280 (2015).
Impact of microbial growth on water flow and solute transport in unsaturated porous media
Yarwood, R. R.; Rockhold, M. L.; Niemet, M. R.; Selker, John S.; Bottomley, Peter J.
2006-10-05
A novel analytical method was developed that permitted real-time, noninvasive measurements of microbial growth and associated changes in hydrodynamic properties in porous media under unsaturated flowing conditions. Salicylate-induced, lux gene-based bioluminescence was used to quantify the temporal and spatial development of colonization over a seven day time course. Water contents were determined daily by measuring light transmission through the system. Hydraulic flow paths were determined daily by pulsing a bromophenol blue dye solution through the colonized region of the sand. Bacterial growth and accumulation had a significant impact on the hydraulic properties of the porous media. Microbial colonization caused localized drying within the colonized zone, with decreases in saturation approaching 50% of antecedent values, and a 25% lowering of the capillary fringe height. Flow was retarded within the colonized zone and diverted around it. The apparent solute velocity through the colonized region was reduced from 0.41 cm min 1 (R2 = 0.99) to 0.25 cm min 1 (R2 = 0.99) by the sixth day of the experiment, associated with maximum population densities that would occupy about 7% of the available pore space within the colonized region. Changes in the extent of colonization occurred over the course of the experiment, including upward migration against flow. The distribution of cells was not determined by water flow alone, but rather by a dynamic interaction between water flow and microbial growth. This experimental system provides rich data sets for the testing of conceptualizations expressed through numerical modeling.
Canonical solutions for unsteady flow fields. M.S. Thesis - George Washington Univ.
NASA Technical Reports Server (NTRS)
Liu, G. C.
1984-01-01
The initial value problem of one-dimensional gas-dynamics involving discontinuous, nonuniform initial data is discussed. Canonical solutions which are valid in a small x, t region aroung a discontinuity, and which include the first order effects of nonuniformities in the data, are derived explicitly. The theory is derived by considering a group of elementary piston problems. Solutions with a shock or with a centered expansion wave are worked out individually in order to relate initial flow properties and their gradients to the speed and acceleration of the discontinuity waves. They are then combined to represent the solution of a general initial value problem by regarding the piston path as a contact line. In addition, problems with chemical reaction are discussed in terms of elementary piston problems which involve strong detonation waves, Chapman-Jouguet detonation waves, and deflagration waves.
Analytical solutions for two-dimensional groundwater flow with subsurface drainage tiles
NASA Astrophysics Data System (ADS)
Liang, Xiuyu; Zhang, You-Kuan; Schilling, Keith E.
2015-02-01
The tile drainage problem in an unconfined aquifer was investigated. A mathematical model was established that describes two-dimensional groundwater flow in an unconfined aquifer near a river with a linearized Boussinesq equation, time-dependent sources and a sloped tile. Analytical solutions for groundwater level and discharge were derived and used to compare hydrologic conditions in a system with and without tile (natural drainage). We found that the spatial and temporal variations of groundwater level and discharge were significantly altered by the presence of drainage tile. In an aquifer with tile drainage, the groundwater level was lower and total groundwater discharge to the river increased compared to an aquifer with no tile. Application of the solutions to a synthetic case demonstrates that the analytical solutions derived can be used to quantify effect of tiles on nitrate loads in the baseflow of a river and assess the effectiveness of various conservation practices.
NASA Technical Reports Server (NTRS)
Chen, Y. K.; Henline, W. D.
1993-01-01
The general boundary conditions including mass and energy balances of chemically equilibrated or nonequilibrated gas adjacent to ablating surfaces have been derived. A computer procedure based on these conditions was developed and interfaced with the Navier-Stokes solver for predictions of the flow field, surface temperature, and surface ablation rates over re-entry space vehicles with ablating Thermal Protection Systems (TPS). The Navier-Stokes solver with general surface thermochemistry boundary conditions can predict more realistic solutions and provide useful information for the design of TPS. A test case with a proposed hypersonic test vehicle configuration and associated free stream conditions was developed. Solutions with various surface boundary conditions were obtained, and the effect of nonequilibrium gas as well as surface chemistry on surface heating and ablation rate were examined. The solutions of the GASP code with complete ablating surface conditions were compared with those of the ASC code. The direction of future work is also discussed.
Xu, Wentao; Cheng, Nan; Huang, Kunlun; Lin, Yuehe; Wang, Chenguang; Xu, Yuancong; Zhu, Longjiao; Du, Dan; Luo, Yunbo
2016-06-15
Many types of diagnostic technologies have been reported for DNA methylation, but they require a standard curve for quantification or only show moderate accuracy. Moreover, most technologies have difficulty providing information on the level of methylation at specific contiguous multi-sites, not to mention easy-to-use detection to eliminate labor-intensive procedures. We have addressed these limitations and report here a cascade strategy that combines proportion competitive quantitative PCR (PCQ-PCR) and lateral flow nucleic acid biosensor (LFNAB), resulting in accurate and easy-to-use assessment. The P16 gene with specific multi-methylated sites, a well-studied tumor suppressor gene, was used as the target DNA sequence model. First, PCQ-PCR provided amplification products with an accurate proportion of multi-methylated sites following the principle of proportionality, and double-labeled duplex DNA was synthesized. Then, a LFNAB strategy was further employed for amplified signal detection via immune affinity recognition, and the exact level of site-specific methylation could be determined by the relative intensity of the test line and internal reference line. This combination resulted in all recoveries being greater than 94%, which are pretty satisfactory recoveries in DNA methylation assessment. Moreover, the developed cascades show significantly high usability as a simple, sensitive, and low-cost tool. Therefore, as a universal platform for sensing systems for the detection of contiguous multi-sites of DNA methylation without external standards and expensive instrumentation, this PCQ-PCR-LFNAB cascade method shows great promise for the point-of-care diagnosis of cancer risk and therapeutics. PMID:26914373
Johnston, M; Jung, Y
2014-06-01
Purpose: Arterial spin labeling (ASL) is an MRI perfusion imaging method from which quantitative cerebral blood flow (CBF) maps can be calculated. Acquisition with variable post-labeling delays (PLD) and variable TRs allows for arterial transit time (ATT) mapping and leads to more accurate CBF quantification with a scan time saving of 48%. In addition, T1 and M0 maps can be obtained without a separate scan. In order to accurately estimate ATT and T1 of brain tissue from the ASL data, variable labeling durations were invented, entitled variable-bolus ASL. Methods: All images were collected on a healthy subject with a 3T Siemens Skyra scanner. Variable-bolus Psuedo-continuous ASL (PCASL) images were collected with 7 TI times ranging 100-4300ms in increments of 700ms with TR ranging 1000-5200ms. All boluses were 1600ms when the TI allowed, otherwise the bolus duration was 100ms shorter than the TI. All TI times were interleaved to reduce sensitivity to motion. Voxel-wise T1 and M0 maps were estimated using a linear least squares fitting routine from the average singal from each TI time. Then pairwise subtraction of each label/control pair and averaging for each TI time was performed. CBF and ATT maps were created using the standard model by Buxton et al. with a nonlinear fitting routine using the T1 tissue map. Results: CBF maps insensitive to ATT were produced along with ATT maps. Both maps show patterns and averages consistent with literature. The T1 map also shows typical T1 contrast. Conclusion: It has been demonstrated that variablebolus ASL produces CBF maps free from the errors due to ATT and tissue T1 variations and provides M0, T1, and ATT maps which have potential utility. This is accomplished with a single scan in a feasible scan time (under 6 minutes) with low sensivity to motion.
NASA Technical Reports Server (NTRS)
Hamilton, H. Harris, II; Millman, Daniel R.; Greendyke, Robert B.
1992-01-01
A computer code was developed that uses an implicit finite-difference technique to solve nonsimilar, axisymmetric boundary layer equations for both laminar and turbulent flow. The code can treat ideal gases, air in chemical equilibrium, and carbon tetrafluoride (CF4), which is a useful gas for hypersonic blunt-body simulations. This is the only known boundary layer code that can treat CF4. Comparisons with experimental data have demonstrated that accurate solutions are obtained. The method should prove useful as an analysis tool for comparing calculations with wind tunnel experiments and for making calculations about flight vehicles where equilibrium air chemistry assumptions are valid.
Parkhurst, David L.; Kipp, Kenneth L.; Engesgaard, Peter; Charlton, Scott R.
2004-01-01
The computer program PHAST simulates multi-component, reactive solute transport in three-dimensional saturated ground-water flow systems. PHAST is a versatile ground-water flow and solute-transport simulator with capabilities to model a wide range of equilibrium and kinetic geochemical reactions. The flow and transport calculations are based on a modified version of HST3D that is restricted to constant fluid density and constant temperature. The geochemical reactions are simulated with the geochemical model PHREEQC, which is embedded in PHAST. PHAST is applicable to the study of natural and contaminated ground-water systems at a variety of scales ranging from laboratory experiments to local and regional field scales. PHAST can be used in studies of migration of nutrients, inorganic and organic contaminants, and radionuclides; in projects such as aquifer storage and recovery or engineered remediation; and in investigations of the natural rock-water interactions in aquifers. PHAST is not appropriate for unsaturated-zone flow, multiphase flow, density-dependent flow, or waters with high ionic strengths. A variety of boundary conditions are available in PHAST to simulate flow and transport, including specified-head, flux, and leaky conditions, as well as the special cases of rivers and wells. Chemical reactions in PHAST include (1) homogeneous equilibria using an ion-association thermodynamic model; (2) heterogeneous equilibria between the aqueous solution and minerals, gases, surface complexation sites, ion exchange sites, and solid solutions; and (3) kinetic reactions with rates that are a function of solution composition. The aqueous model (elements, chemical reactions, and equilibrium constants), minerals, gases, exchangers, surfaces, and rate expressions may be defined or modified by the user. A number of options are available to save results of simulations to output files. The data may be saved in three formats: a format suitable for viewing with a text editor; a
A dual-permeability approach to preferential water flow and solute transport in shrinking soils
NASA Astrophysics Data System (ADS)
Coppola, Antonio; dragonetti, giovanna; Comegna, Alessandro; Gerke, Horst H.; Basile, Angelo
2016-04-01
The pore systems in most natural soils is dynamically changing due to alternating swelling and shrinkage processes, which induces changes in pore volume and pore size distribution including deformations in pore geometry. This is a serious difficulty for modeling flow and transport in dual permeability approaches, as it will also require that the geometrical deformation of both the soil matrix and the fracture porous systems be taken into account, as well as the dynamics of soil hydraulic properties in response to the domain deformations. This study follows up a previous work by the same authors extending the classical rigid (RGD) approach formerly proposed by Gerke and van Genuchten, to account for shrinking effects (SHR) in modeling water flow and solute transport in dual-permeability porous media. In this study we considered three SHR scenarios, assuming that aggregate shrinkage may change either: (i) the hydraulic properties of the two pore domains, (ii) their relative fractions, and (iii) both, hydraulic properties and fractions of the two domains. The objective was to compare simulation results obtained under the RGD and the SHR assumptions to illustrate the impact of matrix volume changes on water storage, water fluxes and solute concentrations during: 1) An infiltration process bringing an initially dry soil to saturation, 2) A drainage process starting from an initially saturated soil. For an infiltration process, the simulated wetting front and the solute concentration propagation velocity, as well as the water fluxes, water and solute exchange rates, for the three SHR scenarios significantly deviated from the RGD. By contrast, relatively similar water content profiles evolved under all scenarios during drying. Overall, compared to the RGD approach, the effect of changing the hydraulic properties and the weight of the two domains according to the shrinkage behavior of the soil aggregates induced a much more rapid response in terms of water fluxes and
NASA Astrophysics Data System (ADS)
Frampton, Andrew; Destouni, Georgia
2016-04-01
In cold regions, flow in the unsaturated zone is highly dynamic with seasonal variability and changes in temperature, moisture, and heat and water fluxes, all of which affect ground freeze-thaw processes and influence transport of inert and reactive waterborne substances. In arctic permafrost environments, near-surface groundwater flow is further restricted to a relatively shallow and seasonally variable active layer, confined by perennially frozen ground below. The active layer is typically partially saturated with ice, liquid water and air, and is strongly dependent on seasonal temperature fluctuations, thermal forcing and infiltration patterns. Here there is a need for improved understanding of the mechanisms controlling subsurface solute transport in the partially saturated active layer zone. Studying solute transport in cold regions is relevant to improve the understanding of how natural and anthropogenic pollution may change as activities in arctic and sub-arctic regions increase. It is also particularly relevant for understanding how dissolved carbon is transported in coupled surface and subsurface hydrological systems under climate change, in order to better understand the permafrost-hydrological-carbon climate feedback. In this contribution subsurface solute transport under surface warming and degrading permafrost conditions is studied using a physically based model of coupled cryotic and hydrogeological flow processes combined with a particle tracking method. Changes in subsurface water flows and solute transport travel times are analysed for different modelled geological configurations during a 100-year warming period. Results show that for all simulated cases, the minimum and mean travel times increase non-linearly with warming irrespective of geological configuration and heterogeneity structure. The travel time changes are shown to depend on combined warming effects of increase in pathway length due to deepening of the active layer, reduced transport
Colloid release and clogging in porous media: Effects of solution ionic strength and flow velocity.
Torkzaban, Saeed; Bradford, Scott A; Vanderzalm, Joanne L; Patterson, Bradley M; Harris, Brett; Prommer, Henning
2015-10-01
The release and retention of in-situ colloids in aquifers play an important role in the sustainable operation of managed aquifer recharge (MAR) schemes. The processes of colloid release, retention, and associated permeability changes in consolidated aquifer sediments were studied by displacing native groundwater with reverse osmosis-treated (RO) water at various flow velocities. Significant amounts of colloid release occurred when: (i) the native groundwater was displaced by RO-water with a low ionic strength (IS), and (ii) the flow velocity was increased in a stepwise manner. The amount of colloid release and associated permeability reduction upon RO-water injection depended on the initial clay content of the core. The concentration of released colloids was relatively low and the permeability reduction was negligible for the core sample with a low clay content of about 1.3%. In contrast, core samples with about 6 and 7.5% clay content exhibited: (i) close to two orders of magnitude increase in effluent colloid concentration and (ii) more than 65% permeability reduction. Incremental improvement in the core permeability was achieved when the flow velocity increased, whereas a short flow interruption provided a considerable increase in the core permeability. This dependence of colloid release and permeability changes on flow velocity and colloid concentration was consistent with colloid retention and release at pore constrictions due to the mechanism of hydrodynamic bridging. A mathematical model was formulated to describe the processes of colloid release, transport, retention at pore constrictions, and subsequent permeability changes. Our experimental and modeling results indicated that only a small fraction of the in-situ colloids was released for any given change in the IS or flow velocity. Comparison of the fitted and experimentally measured effluent colloid concentrations and associated changes in the core permeability showed good agreement, indicating that the
NASA Astrophysics Data System (ADS)
Sebben, Megan L.; Werner, Adrian D.
2016-08-01
Preferential flow features (PFFs, e.g. fractures and faults) are common features in rocks that otherwise have significant matrix permeability. Despite this, few studies have explored the influence of a PFF on the distribution of solute plumes in permeable rock formations, and the current understanding of PFF effects on solute plumes is based almost entirely on low-permeability rock matrices. This research uses numerical modelling to examine solute plumes that pass through a PFF in permeable rock, to explore the PFF's influence on plume migration. The study adopts intentionally simplified arrangements involving steady-state solute plumes in idealised, moderate-to-high-permeability rock aquifers containing a single PFF. A range of matrix-PFF permeability ratios (4.9 × 10-6-2.5 × 10-2), typical of fractured sedimentary aquifers, is considered. The results indicate that for conditions representative of high-to-moderate-permeability sedimentary rock matrices containing a medium-sized fracture, the effect of the PFF on solute plume displacement and spreading can be considerable. For example, plumes are between 1.3 and 19 times wider than in associated porous media only scenarios, and medium-sized PFFs in moderately permeable matrices can reduce the maximum solute concentration by up to 104 times. Plume displacement and spreading is lower in aquifers of higher matrix-PFF permeability ratios, and where solute plumes are more dispersed at the point of intersection with the PFF. Asymmetry in the plume caused by the passage through the PFF is more pronounced for more dispersive plumes. The current study demonstrates that PFFs most likely govern solute plume characteristics in typical permeable matrices, given that a single PFF of aperture representing a medium-sized fracture (i.e. 5.0 × 10-4m) produces the equivalent spreading effects of 0.22-7.88 m of plume movement through the permeable matrix.
Semi-analytical solution of groundwater flow in a leaky aquifer system subject to bending effect
NASA Astrophysics Data System (ADS)
Yu, Chia-Chi; Yang, Shaw-Yang; Yeh, Hund-Der
2013-04-01
SummaryThe bending of aquitard like a plate due to aquifer pumping and compression is often encountered in many practical problems of subsurface flow. This reaction will have large influence on the release of the volume of water from the aquifer, which is essential for the planning and management of groundwater resources in aquifers. However, the groundwater flow induced by pumping in a leaky aquifer system is often assumed that the total stress of aquifer maintains constant all the time and the mechanical behavior of the aquitard formation is negligible. Therefore, this paper devotes to the investigation of the effect of aquitard bending on the drawdown distribution in a leaky aquifer system, which is obviously of interest in groundwater hydrology. Based on the work of Wang et al. (2004) this study develops a mathematical model for investigating the impacts of aquitard bending and leakage rate on the drawdown of the confined aquifer due to a constant-rate pumping in the leaky aquifer system. This model contains three equations; two flow equations delineate the transient drawdown distributions in the aquitard and the confined aquifer, while the other describes the vertical displacement in response to the aquitard bending. For the case of no aquitard bending, this new solution can reduce to the Hantush Laplace-domain solution (Hantush, 1960). On the other hand, this solution without the leakage effect can reduce to the time domain solution of Wang et al. (2004). The results show that the aquifer drawdown is influenced by the bending effect at early time and by the leakage effect at late time. The results of sensitivity analysis indicate that the aquifer compaction is sensitive only at early time, causing less amount of water released from the pumped aquifer than that predicted by the traditional groundwater theory. The dimensionless drawdown is rather sensitive to aquitard's hydraulic conductivity at late time. Additionally, both the hydraulic conductivity and
On the propagation of diel signals in river networks using analytic solutions of flow equations
NASA Astrophysics Data System (ADS)
Fonley, Morgan; Mantilla, Ricardo; Small, Scott J.; Curtu, Rodica
2016-07-01
Several authors have reported diel oscillations in streamflow records and have hypothesized that these oscillations are linked to evapotranspiration cycles in the watershed. The timing of oscillations in rivers, however, lags behind those of temperature and evapotranspiration in hillslopes. Two hypotheses have been put forth to explain the magnitude and timing of diel streamflow oscillations during low-flow conditions. The first suggests that delays between the peaks and troughs of streamflow and daily evapotranspiration are due to processes occurring in the soil as water moves toward the channels in the river network. The second posits that they are due to the propagation of the signal through the channels as water makes its way to the outlet of the basin. In this paper, we design and implement a theoretical model to test these hypotheses. We impose a baseflow signal entering the river network and use a linear transport equation to represent flow along the network. We develop analytic streamflow solutions for the case of uniform velocities in space over all river links. We then use our analytic solution to simulate streamflows along a self-similar river network for different flow velocities. Our results show that the amplitude and time delay of the streamflow solution are heavily influenced by transport in the river network. Moreover, our equations show that the geomorphology and topology of the river network play important roles in determining how amplitude and signal delay are reflected in streamflow signals. Finally, we have tested our theoretical formulation in the Dry Creek Experimental Watershed, where oscillations are clearly observed in streamflow records. We find that our solution produces streamflow values and fluctuations that are similar to those observed in the summer of 2011.
On the Solution of the Three-Dimensional Flowfield About a Flow-Through Nacelle. Ph.D. Thesis
NASA Technical Reports Server (NTRS)
Compton, William Bernard
1985-01-01
The solution of the three dimensional flow field for a flow through nacelle was studied. Both inviscid and viscous inviscid interacting solutions were examined. Inviscid solutions were obtained with two different computational procedures for solving the three dimensional Euler equations. The first procedure employs an alternating direction implicit numerical algorithm, and required the development of a complete computational model for the nacelle problem. The second computational technique employs a fourth order Runge-Kutta numerical algorithm which was modified to fit the nacelle problem. Viscous effects on the flow field were evaluated with a viscous inviscid interacting computational model. This model was constructed by coupling the explicit Euler solution procedure with a flag entrainment boundary layer solution procedure in a global iteration scheme. The computational techniques were used to compute the flow field for a long duct turbofan engine nacelle at free stream Mach numbers of 0.80 and 0.94 and angles of attack of 0 and 4 deg.
A closed-form solution for steady-state coupled phloem/xylem flow using the Lambert-W function.
Hall, A J; Minchin, P E H
2013-12-01
A closed-form solution for steady-state coupled phloem/xylem flow is presented. This incorporates the basic Münch flow model of phloem transport, the cohesion model of xylem flow, and local variation in the xylem water potential and lateral water flow along the transport pathway. Use of the Lambert-W function allows this solution to be obtained under much more general and realistic conditions than has previously been possible. Variation in phloem resistance (i.e. viscosity) with solute concentration, and deviations from the Van't Hoff expression for osmotic potential are included. It is shown that the model predictions match those of the equilibrium solution of a numerical time-dependent model based upon the same mechanistic assumptions. The effect of xylem flow upon phloem flow can readily be calculated, which has not been possible in any previous analytical model. It is also shown how this new analytical solution can handle multiple sources and sinks within a complex architecture, and can describe competition between sinks. The model provides new insights into Münch flow by explicitly including interactions with xylem flow and water potential in the closed-form solution, and is expected to be useful as a component part of larger numerical models of entire plants. PMID:23617886
NASA Astrophysics Data System (ADS)
Shiau, Jenq-Tzong; Wu, Fu-Chun
2007-06-01
The temporal variations of natural flows are essential elements for preserving the ecological health of a river which are addressed in this paper by the environmental flow schemes that incorporate the intra-annual and interannual variability of the natural flow regime. We present an optimization framework to find the Pareto-optimal solutions for various flow schemes. The proposed framework integrates (1) the range of variability approach for evaluating the hydrologic alterations; (2) the standardized precipitation index approach for establishing the variation criteria for the wet, normal, and dry years; (3) a weir operation model for simulating the system of flows; and (4) a multiobjective optimization genetic algorithm for search of the Pareto-optimal solutions. The proposed framework is applied to the Kaoping diversion weir in Taiwan. The results reveal that the time-varying schemes incorporating the intra-annual variability in the environmental flow prescriptions promote the ecosystem and human needs fitness. Incorporation of the interannual flow variability using different criteria established for three types of water year further promotes both fitnesses. The merit of incorporating the interannual variability may be superimposed on that of incorporating only the intra-annual flow variability. The Pareto-optimal solutions searched with a limited range of flows replicate satisfactorily those obtained with a full search range. The limited-range Pareto front may be used as a surrogate of the full-range one if feasible prescriptions are to be found among the regular flows.
Extensional flow of hyaluronic acid solutions in an optimized microfluidic cross-slot devicea
Haward, S. J.; Jaishankar, A.; Oliveira, M. S. N.; Alves, M. A.; McKinley, G. H.
2013-01-01
We utilize a recently developed microfluidic device, the Optimized Shape Cross-slot Extensional Rheometer (OSCER), to study the elongational flow behavior and rheological properties of hyaluronic acid (HA) solutions representative of the synovial fluid (SF) found in the knee joint. The OSCER geometry is a stagnation point device that imposes a planar extensional flow with a homogenous extension rate over a significant length of the inlet and outlet channel axes. Due to the compressive nature of the flow generated along the inlet channels, and the planar elongational flow along the outlet channels, the flow field in the OSCER device can also be considered as representative of the flow field that arises between compressing articular cartilage layers of the knee joints during running or jumping movements. Full-field birefringence microscopy measurements demonstrate a high degree of localized macromolecular orientation along streamlines passing close to the stagnation point of the OSCER device, while micro-particle image velocimetry is used to quantify the flow kinematics. The stress-optical rule is used to assess the local extensional viscosity in the elongating fluid elements as a function of the measured deformation rate. The large limiting values of the dimensionless Trouton ratio, Tr ∼ O(50), demonstrate that these fluids are highly extensional-thickening, providing a clear mechanism for the load-dampening properties of SF. The results also indicate the potential for utilizing the OSCER in screening of physiological SF samples, which will lead to improved understanding of, and therapies for, disease progression in arthritis sufferers. PMID:24738010
Use of secondary equilibria for the separation of small solutes by field-flow fractionation
Berthod, A.; Armstrong, D.W.; Myers, M.N.; Giddings, J.C.
1988-10-01
The dynamic range and selectivity of field-flow fractionation (FFF) can be increased by using secondary chemical equilibria (SCE). SCE are established by adding a macromolecular additive or aggregate, which strongly interacts with the field, to the carrier solution. In this study an oil-in-water (O/W) microemulsion was used as the carrier solution in a sedimentation FFF apparatus. The microemulsion droplets (referred to as the support) interact with the field and are retained relative to the bulk water. Small solutes that partition or bind to the microemulsion droplets are also retained relative to solutes that do not interact with the support. In this way it is possible to separate somewhat polar compounds, such as ascorbic acid and sodium benzoate, which prefer bulk water, from apolar solutes, such as toluene, which prefers the support. In addition, the study of retention times in this system allows one to calculate the average microemulsion droplet radius. It appears that SCE-FFF could be a useful way to obtain important information on the physicochemical properties of a variety of colloidal supports.
Some new exact analytical solutions for helical flows of second grade fluids
NASA Astrophysics Data System (ADS)
Jamil, M.; Zafar, A. A.; Rauf, A.; Khan, N. A.
2012-01-01
The helical flow of a second grade fluid, between two infinite coaxial circular cylinders, is studied using Laplace and finite Hankel transforms. The motion of the fluid is due to the inner cylinder that, at time t = 0 + begins to rotate around its axis, and to slide along the same axis due to hyperbolic sine or cosine shear stresses. The components of the velocity field and the resulting shear stresses are presented in series form in terms of Bessel functions J0(•), Y0(•), J1(•), Y1(•), J2(•) and Y2(•). The solutions that have been obtained satisfy all imposed initial and boundary conditions and are presented as a sum of large-time and transient solutions. Furthermore, the solutions for Newtonian fluids performing the same motion are also obtained as special cases of general solutions. Finally, the solutions that have been obtained are compared and the influence of pertinent parameters on the fluid motion is discussed. A comparison between second grade and Newtonian fluids is analyzed by graphical illustrations.
Analytical solutions of tidal groundwater flow in coastal two-aquifer system
NASA Astrophysics Data System (ADS)
Li, Hailong; Jiao, Jiu Jimmy
This paper presents a complete analytical solution to describe tidal groundwater level fluctuations in a coastal subsurface system. The system consists of two aquifers and a leaky layer between them. Previous solutions of Jacob [Flow of groundwater, in: H. Rouse (Ed.), Engineering Hydraulics, Wiley, New York, 1950, pp. 321-386], Jiao and Tang [Water Resour. Res. 35 (3) (1999) 747], Li and Jiao [Adv. Water Resour. 24 (5) (2001a) 565], Li et al. [Water Resour. Res. 37 (2001) 1095] and Jeng et al. [Adv. Water Resour. (in press)] are special cases of the new solution. The present solution differs from previous work in that both the effects of the leaky layer's elastic storage and the tidal wave interference between the two aquifers are considered. If the upper and lower aquifers have the same storativities and transimissivities, the system can be simplified into an equivalent double-layered, aquifer-aquitard system bounded by impermeable layers from up and down. It is found that the leaky layer's elastic storage behaves as a buffer to the tidal wave interference between the two aquifers. The buffer capacity increases with the leaky layer's thickness, specific storage, and decreases with the leaky layer's vertical permeability. Great buffer capacity can result in negligible tidal wave interference between the upper and lower aquifers so that the Li and Jiao (loc. cit.) solution applies.
Semi-analytical solutions for flow to a well in an unconfined-fractured aquifer system
NASA Astrophysics Data System (ADS)
Sedghi, Mohammad M.; Samani, Nozar
2015-09-01
Semi-analytical solutions of flow to a well in an unconfined single porosity aquifer underlain by a fractured double porosity aquifer, both of infinite radial extent, are obtained. The upper aquifer is pumped at a constant rate from a pumping well of infinitesimal radius. The solutions are obtained via Laplace and Hankel transforms and are then numerically inverted to time domain solutions using the de Hoog et al. algorithm and Gaussian quadrature. The results are presented in the form of dimensionless type curves. The solution takes into account the effects of pumping well partial penetration, water table with instantaneous drainage, leakage with storage in the lower aquifer into the upper aquifer, and storativity and hydraulic conductivity of both fractures and matrix blocks. Both spheres and slab-shaped matrix blocks are considered. The effects of the underlying fractured aquifer hydraulic parameters on the dimensionless drawdown produced by the pumping well in the overlying unconfined aquifer are examined. The presented solution can be used to estimate hydraulic parameters of the unconfined and the underlying fractured aquifer by type curve matching techniques or with automated optimization algorithms. Errors arising from ignoring the underlying fractured aquifer in the drawdown distribution in the unconfined aquifer are also investigated.
Schvidler, M.; Karasaki, K.
2011-06-15
In previous papers (Shvidler and Karasaki, 1999, 2001, 2005, and 2008) we presented and analyzed an approach for finding the general forms of exactly averaged equations of flow and transport in porous media. We studied systems of basic equations for steady flow with sources in unbounded domains with stochastically homogeneous conductivity fields. A brief analysis of exactly averaged equations of nonsteady flow and nonreactive solute transport was also presented. At the core of this approach is the existence of appropriate random Green's functions. For example, we showed that in the case of a 3-dimensional unbounded domain the existence of appropriate random Green's functions is sufficient for finding the exact nonlocal averaged equations for flow velocity using the operator with a unique kernel-vector. Examination of random fields with global symmetry (isotropy, transversal isotropy and orthotropy) makes it possible to describe significantly different types of averaged equations with nonlocal unique operators. It is evident that the existence of random Green's functions for physical linear processes is equivalent to assuming the existence of some linear random operators for appropriate stochastic equations. If we restricted ourselves to this assumption only, as we have done in this paper, we can study the processes in any dimensional bounded or unbounded fields and in addition, cases in which the random fields of conductivity and porosity are stochastically nonhomogeneous, nonglobally symmetrical, etc.. It is clear that examining more general cases involves significant difficulty and constricts the analysis of structural types for the processes being studied. Nevertheless, we show that we obtain the essential information regarding averaged equations for steady and transient flow, as well as for solute transport.
NASA Astrophysics Data System (ADS)
Guevara, Carlos; Graf, Thomas
2013-04-01
Subsurface water systems are endangered due to salt water intrusion in coastal aquifers, leachate infiltration from waste disposal sites and salt transport in agricultural sites. This leads to the situation where more dense fluid overlies a less dense fluid creating a density gradient. Under certain conditions this density gradient produces instabilities in form dense plume fingers that move downwards. This free convection increases solute transport over large distances and shorter times. In cases where a significantly larger density gradient exists, the effect of free convection on transport is non-negligible. The assumption of a constant density distribution in space and time is no longer valid. Therefore variable-density flow must be considered. The flow equation and the transport equation govern the numerical modeling of variable-density flow and solute transport. Computer simulation programs mathematically describe variable-density flow using the Oberbeck-Boussinesq Approximation (OBA). Three levels of simplifications can de considered, which are denoted by OB1, OB2 and OB3. OB1 is the usually applied simplification where variable density is taken into account in the hydraulic potential. In OB2 variable density is considered in the flow equation and in OB3 variable density is additionally considered in the transport equation. Using the results from a laboratory-scale experiment of variable-density flow and solute transport (Simmons et al., Transp. Porous Medium, 2002) it is investigated which level of mathematical accuracy is required to represent the physical experiment the most accurate. Differences between the physical and mathematical model are evaluated using qualitative indicators (e.g. mass fluxes, Nusselt number). Results show that OB1 is required for small density gradients and OB3 is required for large density gradients.
Flow-enhanced solution printing of all-polymer solar cells
Diao, Ying; Zhou, Yan; Kurosawa, Tadanori; Shaw, Leo; Wang, Cheng; Park, Steve; Guo, Yikun; Reinspach, Julia A.; Gu, Kevin; Gu, Xiaodan; et al
2015-08-12
Morphology control of solution coated solar cell materials presents a key challenge limiting their device performance and commercial viability. Here we present a new concept for controlling phase separation during solution printing using an all-polymer bulk heterojunction solar cell as a model system. The key aspect of our method lies in the design of fluid flow using a microstructured printing blade, on the basis of the hypothesis of flow-induced polymer crystallization. Our flow design resulted in a similar to 90% increase in the donor thin film crystallinity and reduced microphase separated donor and acceptor domain sizes. The improved morphology enhancedmore » all metrics of solar cell device performance across various printing conditions, specifically leading to higher short-circuit current, fill factor, open circuit voltage and significantly reduced device-to-device variation. However, we expect our design concept to have broad applications beyond all-polymer solar cells because of its simplicity and versatility.« less
Gupta, Diksha; Singh, Bani
2014-01-01
The objective of this investigation is to analyze the effect of unsteadiness on the mixed convection boundary layer flow of micropolar fluid over a permeable shrinking sheet in the presence of viscous dissipation. At the sheet a variable distribution of suction is assumed. The unsteadiness in the flow and temperature fields is caused by the time dependence of the shrinking velocity and surface temperature. With the aid of similarity transformations, the governing partial differential equations are transformed into a set of nonlinear ordinary differential equations, which are solved numerically, using variational finite element method. The influence of important physical parameters, namely, suction parameter, unsteadiness parameter, buoyancy parameter and Eckert number on the velocity, microrotation, and temperature functions is investigated and analyzed with the help of their graphical representations. Additionally skin friction and the rate of heat transfer have also been computed. Under special conditions, an exact solution for the flow velocity is compared with the numerical results obtained by finite element method. An excellent agreement is observed for the two sets of solutions. Furthermore, to verify the convergence of numerical results, calculations are conducted with increasing number of elements. PMID:24672310
Gupta, Diksha; Kumar, Lokendra; Singh, Bani
2014-01-01
The objective of this investigation is to analyze the effect of unsteadiness on the mixed convection boundary layer flow of micropolar fluid over a permeable shrinking sheet in the presence of viscous dissipation. At the sheet a variable distribution of suction is assumed. The unsteadiness in the flow and temperature fields is caused by the time dependence of the shrinking velocity and surface temperature. With the aid of similarity transformations, the governing partial differential equations are transformed into a set of nonlinear ordinary differential equations, which are solved numerically, using variational finite element method. The influence of important physical parameters, namely, suction parameter, unsteadiness parameter, buoyancy parameter and Eckert number on the velocity, microrotation, and temperature functions is investigated and analyzed with the help of their graphical representations. Additionally skin friction and the rate of heat transfer have also been computed. Under special conditions, an exact solution for the flow velocity is compared with the numerical results obtained by finite element method. An excellent agreement is observed for the two sets of solutions. Furthermore, to verify the convergence of numerical results, calculations are conducted with increasing number of elements. PMID:24672310
Local velocity measurements in heterogeneous and time-dependent flows of a micellar solution.
Decruppe, J P; Greffier, O; Manneville, S; Lerouge, S
2006-06-01
We present and discuss the results of pointwise velocity measurements performed on a viscoelastic micellar solution made of cetyltrimethylammonium bromide and sodium salicylate in water, respectively, at the concentrations of 50 and 100 mmol. The sample is contained in a Couette device and subjected to flow in the strain controlled mode. This particular solution shows shear banding and, in a narrow range of shear rates at the right end of the stress plateau, apparent shear thickening occurs. Time-dependent recordings of the shear stress in this range reveal that the flow has become unstable and that large sustained oscillations of the shear stress and of the first normal stresses difference emerge and grow in the flow. Local pointwise velocity measurements clearly reveal a velocity profile typical of shear banding when the imposed shear rate belongs to the plateau, but also important wall slip in the entire range of velocity gradients investigated. In the oscillations regime, the velocity is recorded as a function of time at a fixed point close to the rotor of the Couette device. The time-dependent velocity profile reveals random fluctuations but, from time to time, sharp decreases much larger than the standard deviation are observed. An attempt is made to correlate these strong variations with the stress oscillations and a correlation coefficient r is computed. However, the small value found for the coefficient r does not allow us to draw a final conclusion as concerns the correlation between stress oscillations and velocity fast decreases. PMID:16906838
Some exact solutions to the Lighthill-Whitham-Richards-Payne traffic flow equations
NASA Astrophysics Data System (ADS)
Rowlands, G.; Infeld, E.; Skorupski, A. A.
2013-09-01
We find a class of exact solutions to the Lighthill-Whitham-Richards-Payne (LWRP) traffic flow equations. Using two consecutive Lagrangian transformations, a linearization is achieved. Next, depending on the initial density, we either apply (again two) Lambert functions and obtain exact formulae for the dependence of the car density and velocity on x, t, or else, failing that, the same result in a parametric representation. The calculation always involves two possible factorizations of a consistency condition. Both must be considered. In physical terms, the lineup usually separates into two offshoots at different velocities. Each velocity soon becomes uniform. This outcome in many ways resembles the two soliton solution to the Korteweg-de Vries equation. We check general conservation requirements. Although traffic flow research has developed tremendously since LWRP, this calculation, being exact, may open the door to solving similar problems, such as gas dynamics or water flow in rivers. With this possibility in mind, we outline the procedure in some detail at the end.
Exact analytical solutions for steady three-dimensional inviscid vortical flows
NASA Astrophysics Data System (ADS)
Bhattacharya, S.
Vortical flows with an axial (z-axis) swirl and a toroidal circulation (in the (rho,z)-plane) can be observed in a wide range of fluid mechanical phenomena such as flow around rotary machines or natural vortices like tornadoes and hurricanes. In this paper, we obtain exact analytical solutions for a general class of steady systems with such three-dimensional circulating structures. Assuming incompressible ideal fluid, a general single-variable equation, known as the Squire-Long equation, can be constructed which can uniquely describe the velocity fields with steady axial and toroidal circulations. In this paper, we consider the case where this type of flow can be analysed by solving a linear homogeneous partial differential equation. The derived equation resembles the governing equation of the hydrogen problem. As a result, we obtain a quantization relation which is similar to the expression for the quantized energy states in a hydrogen atom.For circulating flows, this formalism provides a complete set of orthogonal basis functions which are regular and localized. Hence, each of the basis solutions can be used as a simplified model for a realistic phenomenon. Moreover, an arbitrary circulating field can be expanded in terms of these orthogonal functions. Such an expansion can be potentially useful in the study of more general vortices. As illustrations, we present a few examples where we solve the linear homogeneous equation to analyse fluid mechanical systems which can be models for circulating flow in confined geometry. First, we consider three-dimensional vortices confined between two parallel planar walls. Our examples include flows between two infinite planar walls, inside and outside a vertical cylinder bounded at the ends by horizontal plates, and in an axially confined annular region. Then we describe the special way in which the basis functions should be superposed so that a complicated steady velocity-field with three-dimensional vortical structures can
Water Flow and Solute Transport Processes in Deep Sandy Vadose Zone
NASA Astrophysics Data System (ADS)
Rimon, Y.; Dahan, O.
2010-12-01
Water percolation and solute transport through an unsaturated sandy formation were investigated using a vadose-zone monitoring system (VMS) that enables in-situ, real-time, monitoring of the percolating water. The VMS includes flexible time-domain reflectometry (FTDR) probes which allow continuous monitoring of the temporal variations of the vadose zone water contents, and vadose-zone sampling ports (VSPs) which are designed to allow frequent sampling of the sediment pore-water as well as measurements of the pore-water pressure. Several years of continuous operation of the VMS provided insight into the dynamics of rainfall-induced infiltration events in a 22-m thick sandy formation. Measurements of the temporal variations in vadose-zone water contents as well as continuous monitoring of the vadose-zone pore water, allowed detailed tracking of the wetting fronts' propagation velocities and determination of flow patterns governing solute transport. It has been shown that the chemical composition of mobile flowing water along the vadose zone is not in equilibrium with the total soluble solute potential of the sediment. This phenomenon is usually attributed to preferential flow. However, wetting-front propagation patterns, as monitored continuously over four rainy seasons through the entire vadose zone, as well as a tracer experiment, showed relatively uniform wetting-front propagation with no direct evidence for significant preferential flow. These results were confirmed HYDRUS simulation. The contradictory observations on matrix and preferential flow as governing mechanisms led to conceptualization of the percolation process as pore-scale dual domain flow. Measurements of vadose zone water pressure through a separate set of VSPs, revealed the critical relationship between temporal variations in vadose zone water contents and water pressure, as well as the dynamic connectivity of the vadose zone gas phase to the atmosphere. As expected, variation in the sediments
Solution-Adaptive Cartesian Cell Approach for Viscous and Inviscid Flows
NASA Technical Reports Server (NTRS)
Coirier, William J.; Powell, Kenneth G.
1996-01-01
A Cartesian cell-based approach for adaptively refined solutions of the Euler and Navier-Stokes equations in two dimensions is presented. Grids about geometrically complicated bodies are generated automatically, by the recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, polygonal cut cells are created using modified polygon-clipping algorithms. The grid is stored in a binary tree data structure that provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite volume formulation. The convective terms are upwinded: A linear reconstruction of the primitive variables is performed, providing input states to an approximate Riemann solver for computing the fluxes between neighboring cells. The results of a study comparing the accuracy and positivity of two classes of cell-centered, viscous gradient reconstruction procedures is briefly summarized. Adaptively refined solutions of the Navier-Stokes equations are shown using the more robust of these gradient reconstruction procedures, where the results computed by the Cartesian approach are compared to theory, experiment, and other accepted computational results for a series of low and moderate Reynolds number flows.
A finite difference solution for the propagation of sound in near sonic flows
NASA Technical Reports Server (NTRS)
Hariharan, S. I.; Lester, H. C.
1983-01-01
An explicit time/space finite difference procedure is used to model the propagation of sound in a quasi one-dimensional duct containing high Mach number subsonic flow. Nonlinear acoustic equations are derived by perturbing the time-dependent Euler equations about a steady, compressible mean flow. The governing difference relations are based on a fourth-order, two-step (predictor-corrector) MacCormack scheme. The solution algorithm functions by switching on a time harmonic source and allowing the difference equations to iterate to a steady state. The principal effect of the non-linearities was to shift acoustical energy to higher harmonics. With increased source strengths, wave steepening was observed. This phenomenon suggests that the acoustical response may approach a shock behavior at at higher sound pressure level as the throat Mach number aproaches unity. On a peak level basis, good agreement between the nonlinear finite difference and linear finite element solutions was observed, even through a peak sound pressure level of about 150 dB occurred in the throat region. Nonlinear steady state waveform solutions are shown to be in excellent agreement with a nonlinear asymptotic theory.
NASA Technical Reports Server (NTRS)
Pozzi, Lorenzo
1952-01-01
The author previously discovered two interesting particular solutions to the equations of motion describing unsteady flow in a gas confined solely to a one-dimensional duct. These solutions are now extended to cover the more noteworthy cases of central symmetry in two and three dimensional.
NASA Technical Reports Server (NTRS)
Gupta, R. N.; Moss, J. N.; Simmonds, A. L.
1982-01-01
Two flow-field codes employing the time- and space-marching numerical techniques were evaluated. Both methods were used to analyze the flow field around a massively blown Jupiter entry probe under perfect-gas conditions. In order to obtain a direct point-by-point comparison, the computations were made by using identical grids and turbulence models. For the same degree of accuracy, the space-marching scheme takes much less time as compared to the time-marching method and would appear to provide accurate results for the problems with nonequilibrium chemistry, free from the effect of local differences in time on the final solution which is inherent in time-marching methods. With the time-marching method, however, the solutions are obtainable for the realistic entry probe shapes with massive or uniform surface blowing rates; whereas, with the space-marching technique, it is difficult to obtain converged solutions for such flow conditions. The choice of the numerical method is, therefore, problem dependent. Both methods give equally good results for the cases where results are compared with experimental data.
Interface evolution of a particle in a supersaturated solution affected by a far-field uniform flow
NASA Astrophysics Data System (ADS)
Chen, Ming-Wen; Wang, Zi-Dong
2013-09-01
The effect of far-field uniform flow on the morphological evolution of a spherical particle in a supersaturated solution affected by a far-field uniform flow is studied by using the matched asymptotic expansion method. The analytical solution for the interface shape, concentration field, and interface velocity of the particle growth shows that the convection induced by the far-field uniform flow facilitates the growth of the spherical particle, the upstream flow imposed on the particle enhances the growth velocity of the interface when the flow comes in, the downstream flow lowers the growth velocity of the surface when the flow goes out, and the interface morphology evolves into a peach-like shape.
CFEST Coupled Flow, Energy & Solute Transport Version CFEST005 User’s Guide
Freedman, Vicky L.; Chen, Yousu; Gilca, Alex; Cole, Charles R.; Gupta, Sumant K.
2006-07-20
The CFEST (Coupled Flow, Energy, and Solute Transport) simulator described in this User’s Guide is a three-dimensional finite-element model used to evaluate groundwater flow and solute mass transport. Confined and unconfined aquifer systems, as well as constant and variable density fluid flows can be represented with CFEST. For unconfined aquifers, the model uses a moving boundary for the water table, deforming the numerical mesh so that the uppermost nodes are always at the water table. For solute transport, changes in concentra¬tion of a single dissolved chemical constituent are computed for advective and hydrodynamic transport, linear sorption represented by a retardation factor, and radioactive decay. Although several thermal parameters described in this User’s Guide are required inputs, thermal transport has not yet been fully implemented in the simulator. Once fully implemented, transport of thermal energy in the groundwater and solid matrix of the aquifer can also be used to model aquifer thermal regimes. The CFEST simulator is written in the FORTRAN 77 language, following American National Standards Institute (ANSI) standards. Execution of the CFEST simulator is controlled through three required text input files. These input file use a structured format of associated groups of input data. Example input data lines are presented for each file type, as well as a description of the structured FORTRAN data format. Detailed descriptions of all input requirements, output options, and program structure and execution are provided in this User’s Guide. Required inputs for auxillary CFEST utilities that aide in post-processing data are also described. Global variables are defined for those with access to the source code. Although CFEST is a proprietary code (CFEST, Inc., Irvine, CA), the Pacific Northwest National Laboratory retains permission to maintain its own source, and to distribute executables to Hanford subcontractors.
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.
Modeling in nuclear waste isolation: Approximate solutions for flow in unsaturated porous media
Martinez, M.J.; McTigue, D.F.
1996-12-31
Mathematical modeling plays a key role in the design and licensing of repositories for radioactive waste. Because safe isolation of nuclear waste involves extremely long time scales, and there exists very little engineering experience upon which to draw, modeling takes on a particularly crucial role. An example of a model problem motivated by hydrological issues in high-level waste isolation is presented. A repository concept involving storage in rock above the water table requires models for the flow of groundwater in unsaturated, porous media. Such flow is governed by an extremely nonlinear diffusion equation, and poses some difficult numerical challenges. A special form of the hydraulic conductivity function however, results in a linear field equation for steady-state problems, for which a boundary integral method yields very fast solutions.
Numerical solution of flow problems using body-fitted coordinate systems
NASA Technical Reports Server (NTRS)
Thompson, J. F.
1980-01-01
The paper deals with numerically generated boundary-fitted coordinate systems. This procedure eliminates the shape of the boundaries as a complicating factor and allows the flow about arbitrary boundaries to be treated essentially as easily as that about simple boundaries. The technique of boundary-fitted coordinate systems is based on a method of automatic numerical generation of a general curvilinear coordinate system having a coordinate line coincident with each boundary of a general multiconnected region involving any number of arbitrarily shaped boundaries. Once the curvilinear coordinate system is generated, any partial differential system of interest may be solved on the coordinate system by transforming the equations and solving the resulting system in finite-difference approximation on the rectangular transformed plane. Attention is given to the types of boundary-fitted coordinate systems, coordinate system control, operation of the coordinate codes, solution of partial differential equations, application to free-surface flow, and other applications of interest.
NASA Technical Reports Server (NTRS)
Karageorghis, Andreas; Phillips, Timothy N.
1990-01-01
The numerical simulation of steady planar two-dimensional, laminar flow of an incompressible fluid through an abruptly contracting channel using spectral domain decomposition methods is described. The key features of the method are the decomposition of the flow region into a number of rectangular subregions and spectral approximations which are pointwise C(1) continuous across subregion interfaces. Spectral approximations to the solution are obtained for Reynolds numbers in the range 0 to 500. The size of the salient corner vortex decreases as the Reynolds number increases from 0 to around 45. As the Reynolds number is increased further the vortex grows slowly. A vortex is detected downstream of the contraction at a Reynolds number of around 175 that continues to grow as the Reynolds number is increased further.
Relaxation solutions for inviscid axisymmetric transonic flow over blunt or pointed bodies.
NASA Technical Reports Server (NTRS)
South, J. C., Jr.; Jameson, A.
1973-01-01
A finite-difference relaxation method is presented for numerical solution of the full potential equation and exact boundary conditions for general axisymmetric bodies is inviscid, steady transonic flow. Body-normal coordinates are used in the nose region and sheared cylindrical coordinates are used on the afterbody to accommodate corners such as boattails and flares. An improved difference scheme is used which does not require that the flow be nearly alined with a coordinate direction in supersonic regions, and which treats either subsonic or supersonic free streams. Numerical results are illustrated for some simple classical shapes such as spheres and ellipsoids, and for more practical shapes like tangent-ogives with boattails. Special attention is given to bodies which have been studied for area-rule applications. Agreement with available experimental results is good in cases where viscous effects and wind-tunnel wall interference are not important.
Parallel solution of high-order numerical schemes for solving incompressible flows
NASA Technical Reports Server (NTRS)
Milner, Edward J.; Lin, Avi; Liou, May-Fun; Blech, Richard A.
1993-01-01
A new parallel numerical scheme for solving incompressible steady-state flows is presented. The algorithm uses a finite-difference approach to solving the Navier-Stokes equations. The algorithms are scalable and expandable. They may be used with only two processors or with as many processors as are available. The code is general and expandable. Any size grid may be used. Four processors of the NASA LeRC Hypercluster were used to solve for steady-state flow in a driven square cavity. The Hypercluster was configured in a distributed-memory, hypercube-like architecture. By using a 50-by-50 finite-difference solution grid, an efficiency of 74 percent (a speedup of 2.96) was obtained.
Mustafa, Meraj; Farooq, Muhammad A.; Hayat, Tasawar; Alsaedi, Ahmed
2013-01-01
This investigation is concerned with the stagnation-point flow of nanofluid past an exponentially stretching sheet. The presence of Brownian motion and thermophoretic effects yields a coupled nonlinear boundary-value problem (BVP). Similarity transformations are invoked to reduce the partial differential equations into ordinary ones. Local similarity solutions are obtained by homotopy analysis method (HAM), which enables us to investigate the effects of parameters at a fixed location above the sheet. The numerical solutions are also derived using the built-in solver bvp4c of the software MATLAB. The results indicate that temperature and the thermal boundary layer thickness appreciably increase when the Brownian motion and thermophoresis effects are strengthened. Moreover the nanoparticles volume fraction is found to increase when the thermophoretic effect intensifies. PMID:23671576
Transonic Navier-Stokes solutions of three-dimensional afterbody flows
NASA Technical Reports Server (NTRS)
Compton, William B., III; Thomas, James L.; Abeyounis, William K.; Mason, Mary L.
1989-01-01
The performance of a three-dimensional Navier-Stokes solution technique in predicting the transonic flow past a nonaxisymmetric nozzle was investigated. The investigation was conducted at free-stream Mach numbers ranging from 0.60 to 0.94 and an angle of attack of 0 degrees. The numerical solution procedure employs the three-dimensional, unsteady, Reynolds-averaged Navier-Stokes equations written in strong conservation form, a thin layer assumption, and the Baldwin-Lomax turbulence model. The equations are solved by using the finite-volume principle in conjunction with an approximately factored upwind-biased numerical algorithm. In the numerical procedure, the jet exhaust is represented by a solid sting. Wind-tunnel data with the jet exhaust simulated by high pressure air were also obtained to compare with the numerical calculations.
NASA Technical Reports Server (NTRS)
Hanson, R. K.; Presley, L. L.; Williams, E. V.
1972-01-01
The method of characteristics for a chemically reacting gas is used in the construction of the time-dependent, one-dimensional flow field resulting from the normal reflection of an incident shock wave at the end wall of a shock tube. Nonequilibrium chemical reactions are allowed behind both the incident and reflected shock waves. All the solutions are evaluated for oxygen, but the results are generally representative of any inviscid, nonconducting, and nonradiating diatomic gas. The solutions clearly show that: (1) both the incident- and reflected-shock chemical relaxation times are important in governing the time to attain steady state thermodynamic properties; and (2) adjacent to the end wall, an excess-entropy layer develops wherein the steady state values of all the thermodynamic variables except pressure differ significantly from their corresponding Rankine-Hugoniot equilibrium values.