Computations of turbulent lean premixed combustion using conditional moment closure
NASA Astrophysics Data System (ADS)
Amzin, Shokri; Swaminathan, Nedunchezhian
2013-12-01
Conditional Moment Closure (CMC) is a suitable method for predicting scalars such as carbon monoxide with slow chemical time scales in turbulent combustion. Although this method has been successfully applied to non-premixed combustion, its application to lean premixed combustion is rare. In this study the CMC method is used to compute piloted lean premixed combustion in a distributed combustion regime. The conditional scalar dissipation rate of the conditioning scalar, the progress variable, is closed using an algebraic model and turbulence is modelled using the standard k-ɛ model. The conditional mean reaction rate is closed using a first order CMC closure with the GRI-3.0 chemical mechanism to represent the chemical kinetics of methane oxidation. The PDF of the progress variable is obtained using a presumed shape with the Beta function. The computed results are compared with the experimental measurements and earlier computations using the transported PDF approach. The results show reasonable agreement with the experimental measurements and are consistent with the transported PDF computations. When the compounded effects of shear-turbulence and flame are strong, second order closures may be required for the CMC.
Turbulence models and their applications. Volume 2 Second-moment closure: Methodology and practice
NASA Astrophysics Data System (ADS)
Launder, B. E.; Reynolds, W. C.; Rodi, W.
The level of turbulence modeling which is known as second-moment closure is discussed, taking into account the basis of second-moment closure, the closure of the second-moment equations, dissipation and spectral transfer rates in turbulence, low-Reynolds-number turbulence near walls, and buoyant effects on turbulent transport. The physical and analytical foundations, concepts, and new directions in turbulence modeling and simulation are examined. Attention is given to fundamentals of fluid motion, turbulence equations, structure and scaling in free shear flows, the structure and scaling of wall-bound turbulent flows, the statistical properties of homogeneous turbulence, rapid distortion theory, a provisional model for homogeneous turbulence, transport modeling, and the numerical simulations of turbulence. A description of examples of turbulence model applications is provided. Two-dimensional boundary-layer-type flows are considered along with two-dimensional separated flows, the numerical treatment of the convection terms, and three-dimensional flows.
Comparison of PDF and Moment Closure Methods in the Modeling of Turbulent Reacting Flows
NASA Technical Reports Server (NTRS)
Norris, Andrew T.; Hsu, Andrew T.
1994-01-01
In modeling turbulent reactive flows, Probability Density Function (PDF) methods have an advantage over the more traditional moment closure schemes in that the PDF formulation treats the chemical reaction source terms exactly, while moment closure methods are required to model the mean reaction rate. The common model used is the laminar chemistry approximation, where the effects of turbulence on the reaction are assumed negligible. For flows with low turbulence levels and fast chemistry, the difference between the two methods can be expected to be small. However for flows with finite rate chemistry and high turbulence levels, significant errors can be expected in the moment closure method. In this paper, the ability of the PDF method and the moment closure scheme to accurately model a turbulent reacting flow is tested. To accomplish this, both schemes were used to model a CO/H2/N2- air piloted diffusion flame near extinction. Identical thermochemistry, turbulence models, initial conditions and boundary conditions are employed to ensure a consistent comparison can be made. The results of the two methods are compared to experimental data as well as to each other. The comparison reveals that the PDF method provides good agreement with the experimental data, while the moment closure scheme incorrectly shows a broad, laminar-like flame structure.
Second moment closure modeling for rotating stably stratified turbulent shear flow
NASA Astrophysics Data System (ADS)
Ji, Minsuk
The general linear second moment closure (SMC) turbulence model is considered for flows subjected to buoyancy and rotation. Model response to external forces are analyzed with the aid of structural equilibrium analysis. A closed form equilibrium solution for the anisotropy tensor bij, dispersion tensor Kij, dimensionless scalar variance q2 /k(S/Stheta )2, and the ratio of mean to turbulent time scale epsilon/ Sk is obtained. The variable of particular interest to bifurcation analysis, epsilon/Sk is shown as a function of the parameters characterizing the body forces: O/S (the ratio of the rotation rate to the mean shear rate) for rotation and Rig (the gradient Richardson number) for buoyancy; it determines the bifurcation surface in the epsilon/Sk-O/S-Rig space. It is shown, with the use of the closed form solution, that the conventional general linear models do not have a real and stable equilibrium solution when rotational and buoyant forces of certain magnitudes are simultaneously imposed on the flow. When this occurs, time integration of the turbulence model results in a diverging solution. A new model is proposed that removes this unphysical behavior. It ensures the existence of stable, real solutions for all combinations of rotation and buoyancy. Further improvements to the model are made through bifurcation analysis. Model constants are adjusted such that the model's bifurcation characteristics are in agreement with the physically observed onset of turbulence stabilization due to stable stratification. Experimental data and numerical simulation results for stably stratified homogeneous shear flow suggest the critical gradient Richardson number of Ricrg = 0.25, and the new model is able to predict it correctly. In connection with the bifurcation analysis of SMC models, rapid distortion theory (RDT) of turbulence is applied to rotating, stably stratified shear flow to provide the stability characteristics of such flows. It is shown that the RDT predictions are
Prediction of turbulent flow through a transition duct using a second-moment closure
NASA Astrophysics Data System (ADS)
Sotiropoulos, F.; Patel, V. C.
1994-11-01
The near-wall, full Reynolds-stress closure of Launder and Shima is employed to calculate the three-dimensional turbulent flow through a circular-to-rectangular transition duct. The solutions are compared with the recent experimental data of Davis and Gessner. The comparisons reveal that the computed streamwise velocity and vorticity fields are in remarkable agreement with the measurements. Downstream of the transition region, however, the computed Reynolds stresses appear to decay at a much faster rate than observed in the measurements. These results point to the need for further refinement of Reynolds-stress models to correctly predict the relaxation of rapidly strained turbulence towards equilibrium.
NASA Technical Reports Server (NTRS)
Amano, R. S.; Goel, P.
1986-01-01
Four parts of the Reynolds-stress closure modeling are reported: (1) improvement of the k and epsilon equaitons; (2) development of the third-moment transport equation; (3) formulation of the diffusion coefficient of the momentum equation by using the algebraic-stress model of turbulence; and (4) the application of the Reynolds-stress model to a heat exchanger problem. It was demonstrated that the third-moment transport model improved the prediction of the triple-velocity products in the recirculating and reattaching flow regions in comparison with the existing algebraic models for the triple-velocity products. Optimum values for empirical coefficients are obtained for the prediction of the backward-facing step flows. A functional expression is derived for the coefficient of the momentum diffusion by employing the algebraic-stress model. The second-moment closure is applied to a heat transfer problem. The computations for the flow in a corrugated-wall channel show that the second-moment closure improves the prediction of the heat transfer rates by 30% over the k - epsilon model.
NASA Technical Reports Server (NTRS)
Amano, R. S.; Goel, P.
1986-01-01
A numerical study of computations in backward-facing steps with flow separation and reattachment, using the Reynolds stress closure is presented. The highlight of this study is the improvement of the Reynold-stress model (RSM) by modifying the diffusive transport of the Reynolds stresses through the formulation, solution and subsequent incorporation of the transport equations of the third moments, bar-u(i)u(j)u(k), into the turbulence model. The diffusive transport of the Reynolds stresses, represented by the gradients of the third moments, attains greater significance in recirculating flows. The third moments evaluated by the development and solution of the complete transport equations are superior to those obtained by existing algebraic correlations. A low-Reynolds number model for the transport equations of the third moments is developed and considerable improvement in the near-wall profiles of the third moments is observed. The values of the empirical constants utilized in the development of the model are recommended. The Reynolds-stress closure is consolidated by incorporating the equations of k and e, containing the modified diffusion coefficients, and the transport equations of the third moments into the Reynolds stress equations. Computational results obtained by the original k-e model, the original RSM and the consolidated and modified RSM are compared with experimental data. Overall improvement in the predictions is seen by consolidation of the RMS and a marked improvement in the profiles of bar-u(i)u(j)u(k) is obtained around the reattachment region.
NASA Astrophysics Data System (ADS)
Vie, Aymeric; Masi, Enrica; Simonin, Olivier; Massot, Marc; EM2C/Ecole Centrale Paris Team; IMFT Team
2012-11-01
To simulate particulate flows, a convenient formalism for HPC is to use Eulerian moment methods, which describe the evolution of velocity moments instead of tracking directly the number density function (NDF) of the droplets. By using a conditional PDF approach, the Mesoscopic Eulerian Formalism (MEF) of Février et al. 2005 offers a solution for the direct numerical simulation of turbulent particulate flows, even at relatively high Stokes number. Here, we propose to compare to existing approaches used to solved for this formalism: the Algebraic-Closure-Based Moment method (Kaufmann et al. 2008, Masi et al. 2011), and the Kinetic-Based Moment Method (Yuan et al. 2010, Chalons et al. 2010, Vié et al. 2012). Therefore, the goal of the current work is to evaluate both strategies in turbulent test cases. For the ACBMM, viscosity-type and non-linear closures are envisaged, whereas for the KBMM, isotropic and anisotropic closures are investigated. A main aspect of the current methodology for the comparison is that the same numerical methods are used for both approaches. Results show that the new non-linear closure and the Anisotropic Gaussian closures are both accurate in shear flows, whereas viscosity-type and isotropic closures lead to wrong results.
Conditional Moment Closure of Mixing and Reaction in Turbulent Nonpremixed Combustion
NASA Technical Reports Server (NTRS)
Smith, Nigel S. A.
1996-01-01
Nonpremixed combustion is the process whereby fuel and oxidizer species, which are each nonflammable in isolation, concurrently mix to burn a flammable mixture, and chemically react in the flammable mixture. In cases of practical industrial interest, the bulk of nonpremixed combustion occurs in a turbulent mixing regime where enhanced mass transfer rates flow the maximum power density to be achieved in any given thermochemical device.
Milford, A.; Devaud, C.B.
2010-08-15
The present paper examines the case of autoignition of high pressure methane jets in a shock tube over a range of pre-heated air temperatures in engine-relevant conditions. The two objectives of the present paper are: (i) to examine the effect of the inhomogeneous mixing model on the autoignition predictions relative to the results obtained using homogeneous mixing models and (ii) to see if the magnitude of the change can explain the discrepancy between the predictions of ignition delay previously obtained with homogeneous mixing models and the experimental data. The governing equation of the scalar dissipation rate is solved for transient conditions and two different formulations of the same model are tested and compared: one using the linear model for the conditional velocity and one including the gradient diffusion model. The predicted ignition kernel location and time delay over a range of pre-combustion air temperatures are compared with results obtained using two homogeneous turbulent mixing models and available experimental data. The profiles of conditional velocity and the conditional scalar dissipation rate are examined. Issues related to the conditional velocity model are discussed. It is found that the differences in the predictions are due to the mixing model only. The inhomogeneous model using the gradient conditional velocity model produces much larger ignition delays compared to the other models, whereas the inhomogeneous form including the linear model does not produce any significant differences. The effect of the turbulent inhomogeneous model is larger at high air temperatures and decreases with decreasing air temperatures. In comparison with the measured ignition delays, the inhomogeneous-Gradient model brings a small improvement at high air temperatures over the results from the turbulent homogeneous models. At low air temperatures, other parameters need to be investigated in order to bring the predicted ignition delays and locations within the
A Quadratic Closure for Compressible Turbulence
Futterman, J A
2008-09-16
We have investigated a one-point closure model for compressible turbulence based on third- and higher order cumulant discard for systems undergoing rapid deformation, such as might occur downstream of a shock or other discontinuity. In so doing, we find the lowest order contributions of turbulence to the mean flow, which lead to criteria for Adaptive Mesh Refinement. Rapid distortion theory (RDT) as originally applied by Herring closes the turbulence hierarchy of moment equations by discarding third order and higher cumulants. This is similar to the fourth-order cumulant discard hypothesis of Millionshchikov, except that the Millionshchikov hypothesis was taken to apply to incompressible homogeneous isotropic turbulence generally, whereas RDT is applied only to fluids undergoing a distortion that is 'rapid' in the sense that the interaction of the mean flow with the turbulence overwhelms the interaction of the turbulence with itself. It is also similar to Gaussian closure, in which both second and fourth-order cumulants are retained. Motivated by RDT, we develop a quadratic one-point closure for rapidly distorting compressible turbulence, without regard to homogeneity or isotropy, and make contact with two equation turbulence models, especially the K-{var_epsilon} and K-L models, and with linear instability growth. In the end, we arrive at criteria for Adaptive Mesh Refinement in Finite Volume simulations.
NASA Technical Reports Server (NTRS)
Demuren, A. O.
1990-01-01
A multigrid method is presented for calculating turbulent jets in crossflow. Fairly rapid convergence is obtained with the k-epsilon turbulence model, but computations with a full Reynolds stress turbulence model (RSM) are not yet very efficient. Grid dependency tests show that there are slight differences between results obtained on the two finest grid levels. Computations using the RSM are significantly different from those with k-epsilon model and compare better to experimental data. Some work is still required to improve the efficiency of the computations with the RSM.
Turbulence closure modeling near rigid boundaries
NASA Technical Reports Server (NTRS)
Durbin, Paul A.
1991-01-01
The near-wall region plays an essential role in turbulent boundary layers: it is a region of high shear; the peak rate of production and peak intensity of turbulence occurs there; and the peak rate of dissipation occurs right at the wall. Nevertheless, this region has received less attention from modelers than have more nearly homogeneous flows. One reason for this is that when the boundary layer is near equilibrium, experimental data can be used to prescribe the flow in the wall layer. Another reason is that most turbulence models are developed under assumptions of near homogeneity. This is a poor approximation in the wall region. A single-point moment closure model for the strongly non-homogeneous A turbulent flow near a rigid boundary is developed.
Second Moment Closure Near the Two-component Limit
NASA Technical Reports Server (NTRS)
Rubinstein, Robert; Girimaji, Sharath S.
2006-01-01
The purpose of this paper is to explore some wider implications of the two-component limit for both single point turbulence models and spectral closure theories. Although the two-component limit arises most naturally in inhomogeneous problems like wall-bounded turbulence, the analysis will be restricted to homogeneous turbulence. But since homogeneous turbulence is the crucial case for realizability, the conclusions will nevertheless be applicable to modeling. Th essential point of our argument is that whereas the evolution of the stochastic velocity field is Markovian because it is governed by the Navier-Stokes equations, the exact stress evolution equation is not Markovian because it is unclosed. This property of moment evolution has been stressed by Kraichnan (1959). We will show that modeling stress evolution at the two-component limit with a closure that is Markovian in the stresses alone leads to basic inconsistencies in single-point modeling and, perhaps surprisingly, in spectral modes as well.
Quasi-explicit algebraic turbulence closures for compressible reacting flows
NASA Astrophysics Data System (ADS)
Adumitroaie, Virgil
A consistent and complete set of quasi-explicit algebraic closures for turbulent reacting flows is proposed as approximate solutions to the full second order moment equations. Quasi-explicit algebraic scalar flux models that are valid for three-dimensional turbulent flows are derived from a hierarchy of second-order moment closures. The mathematical procedure is based on the Cayley-Hamilton theorem and is an extension of the scheme developed by Taulbee (1992). Several closures for the pressure-scalar gradient correlations are considered and explicit algebraic relations are provided for the velocity-scalar correlations in both non-reacting and reacting flows. In the latter, the role of the Damkohler number is exhibited in isothermal turbulent flows with nonpremixed reactants. The relationship between these closures and traditional models based on the linear gradient diffusion approximation is theoretically established. The results of model predictions are assessed via comparison with available laboratory data in turbulent jet flows. The development of the quasi-explicit algebraic models for Reynolds stresses, temperature fluxes and reacting scalar fluxes is extended to high-speed turbulent reacting flows under a density weighted average formalism. New closures are proposed for the pressure-strain and the pressure-scalar gradient correlations. These accommodate compressibility corrections subject to the magnitude of the turbulent Mach number, the density gradient, the pressure gradient and the mean dilatation effects. Non-reacting and reacting flows with heat release are considered. In the latter, a second-order irreversible chemical reactions in turbulent flows with initially segregated reactants is considered. The models are tested in simple compressible free-shear flows. Comparisons are made between the full second order moment computations and the algebraic closure predictions. For a mixing layer, experimental data are used to validate the predicted results.
Higher order turbulence closure models
NASA Technical Reports Server (NTRS)
Amano, Ryoichi S.; Chai, John C.; Chen, Jau-Der
1988-01-01
Theoretical models are developed and numerical studies conducted on various types of flows including both elliptic and parabolic. The purpose of this study is to find better higher order closure models for the computations of complex flows. This report summarizes three new achievements: (1) completion of the Reynolds-stress closure by developing a new pressure-strain correlation; (2) development of a parabolic code to compute jets and wakes; and, (3) application to a flow through a 180 deg turnaround duct by adopting a boundary fitted coordinate system. In the above mentioned models near-wall models are developed for pressure-strain correlation and third-moment, and incorporated into the transport equations. This addition improved the results considerably and is recommended for future computations. A new parabolic code to solve shear flows without coordinate tranformations is developed and incorporated in this study. This code uses the structure of the finite volume method to solve the governing equations implicitly. The code was validated with the experimental results available in the literature.
Sreedhara, S.; Huh, Kang Y.
2005-10-01
First- and second-order conditional moment closure (CMC) models are applied to a turbulent CH{sub 4}/H{sub 2} flame anchored on a bluffbody. Significant extinction is involved as the jet velocity increases for the three test flames: HM1, HM2, and HM3 (in a turbulent nonpremixed flame (TNF) database). The flow and mixing field are calculated with the k-| model with a modified constant, C{sub |1}. Elliptic CMC formulation is employed to calculate reacting scalar fields with chemical kinetic mechanisms, GRI Mech 2.11 and 3.0. Second-order corrections are limited to three rate-limiting steps to avoid solving a huge number of variance and covariance equations. Even though first-order CMC captures temperature and major species within agreeable limits, the predictions of OH and NO are considerably improved with second-order CMC in both mixture fraction and real space. Results show that the equilibrium assumption performs better than the cold mixture as the conditional inflow boundary condition. There is no noticeable conditional cross-stream dependence downstream, while care needs to be taken in interpretation of the upstream results near the nozzle.
Turbulence processes and simple closure schemes
NASA Technical Reports Server (NTRS)
Deissler, R. G.
1977-01-01
The problem of closure in turbulence in the case of two-point correlations resides in the existence of two unknowns E and W, the energy spectrum function and the transfer function, respectively, in the spectrum equation. In the case of weak turbulence, W is negligible. In case of higher correlations, closure can be effective by neglecting the inertia term in the highest order term used. Specifying a certain number of spectra at an initial time is also a way of getting around the closure problem. A simple case of turbulent shear flow is then considered, where two-point correlation equations are used and the velocity is broken into mean and fluctuating components. This yields a differential equation for the energy spectrum, the three terms of which are the energy spectrum, production term and dissipation term. They are plotted for a particular time. Similar analyses and comparisons with experiment are made for pipe and boundary layer flows.
Moment Closures on Two-Dimensional Cartesian Grids
Garrett, Charles K.
2015-07-31
Some moment methods for kinetic equations are complicated and take time to develop. Over the course of a couple years, this software was developed to test different closures on standard test problems in the literature. With this software, researchers in the field of moment closures will be able to rapidly test new methods.
Formulation and closure of compressible turbulence equations in the light of kinetic theory
NASA Technical Reports Server (NTRS)
Tsuge, S.; Sagara, K.
1976-01-01
Fluid-dynamic moment equations, based on a kinetic hierarchy system, are derived governing the interaction between turbulent and thermal fluctuations. The kinetic theory is shown to reduce the inherent complexity of the conventional formalism of compressible turbulence theory and to minimize arbitrariness in formulating the closure condition.
Yamada, Tetsuji; Bunker, S.; Niccum, E.
1987-01-01
Yamade and Bunker (1986) demonstrated that a three-dimensional hydrodynamic model, HOTMAC (Higher Order Turbulence Model for Atmospheric Circulations) reproduced nocturnal drainage flows, morning transition and convective upvalley and upslope flows observed during the 1982 ASCOT (Atmospheric Studies in COmplex Terrain) field campaign in Brush Creek, Colorado. We also showed that a Monte Carlo statistical diffusion model, RAPTAD (RAndom Particle Transport And Diffusion) driven by the outputs (mean and turbulence variables) from HOTMAC simulated well the structure of an SF6 tracer plume and obtained a vertical profile of concentration similar to the one observed. A ''Kernel'' density estimator is used in this study where each particle represents a center of a puff. In this study, the concentration was recomputed by applying the Gaussian kernel estimator. A total of only 900 particles were released. The vertical profile of the modeled SF6 concentration averaged over one hour between 6 and 7 a.m. at a site near the mouth of Brush Creek was compared with observation. The modeled and observed concentrations agreed well although the modeled values were slightly smaller than the observations for the first 250 m above the ground.
Approximate maximum-entropy moment closures for gas dynamics
NASA Astrophysics Data System (ADS)
McDonald, James G.
2016-11-01
Accurate prediction of flows that exist between the traditional continuum regime and the free-molecular regime have proven difficult to obtain. Current methods are either inaccurate in this regime or prohibitively expensive for practical problems. Moment closures have long held the promise of providing new, affordable, accurate methods in this regime. The maximum-entropy hierarchy of closures seems to offer particularly attractive physical and mathematical properties. Unfortunately, several difficulties render the practical implementation of maximum-entropy closures very difficult. This work examines the use of simple approximations to these maximum-entropy closures and shows that physical accuracy that is vastly improved over continuum methods can be obtained without a significant increase in computational cost. Initially the technique is demonstrated for a simple one-dimensional gas. It is then extended to the full three-dimensional setting. The resulting moment equations are used for the numerical solution of shock-wave profiles with promising results.
Multivariate moment closure techniques for stochastic kinetic models.
Lakatos, Eszter; Ale, Angelique; Kirk, Paul D W; Stumpf, Michael P H
2015-09-07
Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs.
Multivariate moment closure techniques for stochastic kinetic models
Lakatos, Eszter Ale, Angelique; Kirk, Paul D. W.; Stumpf, Michael P. H.
2015-09-07
Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs.
Multivariate moment closure techniques for stochastic kinetic models
NASA Astrophysics Data System (ADS)
Lakatos, Eszter; Ale, Angelique; Kirk, Paul D. W.; Stumpf, Michael P. H.
2015-09-01
Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs.
Sreedhara, S.; Huh, Kang Y.
2005-12-01
The performance of second-order conditional moment closure (CMC) depends on models to evaluate conditional variances and covariances of temperature and species mass fractions. In this paper the closure schemes based on the steady laminar flamelet model (SLFM) are validated against direct numerical simulation (DNS) involving extinction and ignition. Scaling is performed to reproduce proper absolute magnitudes, irrespective of the origin of mismatch between local flamelet structures and scalar dissipation rates. DNS based on the pseudospectral method is carried out to study hydrogen-air combustion with a detailed kinetic mechanism, in homogeneous, isotropic, and decaying turbulent media. Lewis numbers are set equal to unity to avoid complication of differential diffusion. The SLFM-based closures for correlations among fluctuations of reaction rate, scalar dissipation rate, and species mass fractions show good comparison with DNS. The variance parameter in lognormal PDF and the constants in the dissipation term have been estimated from DNS results. Comparison is made for the resulting conditional profiles from DNS, first-order CMC, and second-order CMC with correction to the most critical reaction step according to sensitivity analysis. Overall good agreement ensures validity of the SLFM-based closures for modeling conditional variances and covariances in second-order CMC.
Modeling hypersonic boundary-layer flows with second-moment closure
NASA Technical Reports Server (NTRS)
Huang, P. George
1991-01-01
An ongoing research effort designed to apply the best possible second-moment-closure model to simulate complex hypersonic flows is presented. The baseline model under consideration is the Launder-Reece-Rodi Reynolds stress transport turbulence model. Two add-ons accounting for wall effects, namely, the Launder-Shima low-Reynolds-number model and the compressible wall-function technique, are tested. Results are reported for flow over a flat plate, both adiabatic-wall and cooled-wall cases. It has been found that further improvements of the existing models are necessary to achieve accurate prediction in high Mach number flow range.
A PDF closure model for compressible turbulent chemically reacting flows
NASA Technical Reports Server (NTRS)
Kollmann, W.
1992-01-01
The objective of the proposed research project was the analysis of single point closures based on probability density function (pdf) and characteristic functions and the development of a prediction method for the joint velocity-scalar pdf in turbulent reacting flows. Turbulent flows of boundary layer type and stagnation point flows with and without chemical reactions were be calculated as principal applications. Pdf methods for compressible reacting flows were developed and tested in comparison with available experimental data. The research work carried in this project was concentrated on the closure of pdf equations for incompressible and compressible turbulent flows with and without chemical reactions.
Development of Turbulent Biological Closure Parameterizations
2011-09-30
the role of TIBI term in the ADR equation a simple example, that of upwelling of seed nutrients and phytoplankton into a turbulent optically active...overall role that turbulence plays in determining the mean phytoplankton profile and in contributing to total phytoplankton production . As indicated... nutrients , phytoplankton , and zooplankton embedded in the turbulent field. Contrast the TIBI terms with the biological turbulent flux terms ’ , ’ , ’i
Nonlinear closures for scale separation in supersonic magnetohydrodynamic turbulence
NASA Astrophysics Data System (ADS)
Grete, Philipp; Vlaykov, Dimitar G.; Schmidt, Wolfram; Schleicher, Dominik R. G.; Federrath, Christoph
2015-02-01
Turbulence in compressible plasma plays a key role in many areas of astrophysics and engineering. The extreme plasma parameters in these environments, e.g. high Reynolds numbers, supersonic and super-Alfvenic flows, however, make direct numerical simulations computationally intractable even for the simplest treatment—magnetohydrodynamics (MHD). To overcome this problem one can use subgrid-scale (SGS) closures—models for the influence of unresolved, subgrid-scales on the resolved ones. In this work we propose and validate a set of constant coefficient closures for the resolved, compressible, ideal MHD equations. The SGS energies are modeled by Smagorinsky-like equilibrium closures. The turbulent stresses and the electromotive force (EMF) are described by expressions that are nonlinear in terms of large scale velocity and magnetic field gradients. To verify the closures we conduct a priori tests over 137 simulation snapshots from two different codes with varying ratios of thermal to magnetic pressure ({{β }p}=0.25,1,2.5,5,25) and sonic Mach numbers ({{M}s}=2,2.5,4). Furthermore, we make a comparison to traditional, phenomenological eddy-viscosity and α -β -γ closures. We find only mediocre performance of the kinetic eddy-viscosity and α -β -γ closures, and that the magnetic eddy-viscosity closure is poorly correlated with the simulation data. Moreover, three of five coefficients of the traditional closures exhibit a significant spread in values. In contrast, our new closures demonstrate consistently high correlations and constant coefficient values over time and over the wide range of parameters tested. Important aspects in compressible MHD turbulence such as the bi-directional energy cascade, turbulent magnetic pressure and proper alignment of the EMF are well described by our new closures.
Validity conditions for moment closure approximations in stochastic chemical kinetics
Schnoerr, David; Sanguinetti, Guido; Grima, Ramon
2014-08-28
Approximations based on moment-closure (MA) are commonly used to obtain estimates of the mean molecule numbers and of the variance of fluctuations in the number of molecules of chemical systems. The advantage of this approach is that it can be far less computationally expensive than exact stochastic simulations of the chemical master equation. Here, we numerically study the conditions under which the MA equations yield results reflecting the true stochastic dynamics of the system. We show that for bistable and oscillatory chemical systems with deterministic initial conditions, the solution of the MA equations can be interpreted as a valid approximation to the true moments of the chemical master equation, only when the steady-state mean molecule numbers obtained from the chemical master equation fall within a certain finite range. The same validity criterion for monostable systems implies that the steady-state mean molecule numbers obtained from the chemical master equation must be above a certain threshold. For mean molecule numbers outside of this range of validity, the MA equations lead to either qualitatively wrong oscillatory dynamics or to unphysical predictions such as negative variances in the molecule numbers or multiple steady-state moments of the stationary distribution as the initial conditions are varied. Our results clarify the range of validity of the MA approach and show that pitfalls in the interpretation of the results can only be overcome through the systematic comparison of the solutions of the MA equations of a certain order with those of higher orders.
The closure problem for turbulence in meteorology and oceanography
NASA Technical Reports Server (NTRS)
Pierson, W. J., Jr.
1985-01-01
The dependent variables used for computer based meteorological predictions and in plans for oceanographic predictions are wave number and frequency filtered values that retain only scales resolvable by the model. Scales unresolvable by the grid in use become 'turbulence'. Whether or not properly processed data are used for initial values is important, especially for sparce data. Fickian diffusion with a constant eddy diffusion is used as a closure for many of the present models. A physically realistic closure based on more modern turbulence concepts, especially one with a reverse cascade at the right times and places, could help improve predictions.
Modeling near wall effects in second moment closures by elliptic relaxation
NASA Technical Reports Server (NTRS)
Laurence, D.; Durbin, P.
1994-01-01
The elliptic relaxation model of Durbin (1993) for modeling near-wall turbulence using second moment closures (SMC) is compared to DNS data for a channel flow at Re(sub t) = 395. The agreement for second order statistics and even the terms in their balance equation is quite satisfactory, confirming that very little viscous effects (via Kolmogoroff scales) need to be added to the high Reynolds versions of SMC for near-wall-turbulence. The essential near-wall feature is thus the kinematic blocking effect that a solid wall exerts on the turbulence through the fluctuating pressure, which is best modeled by an elliptic operator. Above the transition layer, the effect of the original elliptic operator decays rapidly, and it is suggested that the log-layer is better reproduced by adding a non-homogeneous reduction of the return to isotropy, the gradient of the turbulent length scale being used as a measure of the inhomogeneity of the log-layer. The elliptic operator was quite easily applied to the non-linear Craft & Launder pressure-strain model yielding an improved distinction between the spanwise and wall normal stresses, although at higher Reynolds number (Re) and away from the wall, the streamwise component is severely underpredicted, as well as the transition in the mean velocity from the log to the wake profiles. In this area a significant change of behavior was observed in the DNS pressure-strain term, entirely ignored in the models.
NASA Astrophysics Data System (ADS)
Fisher, A. W.; Sanford, L. P.; Scully, M. E.
2016-12-01
Coherent wave-driven turbulence generated through wave breaking or nonlinear wave-current interactions, e.g. Langmuir turbulence (LT), can significantly enhance the downward transfer of momentum, kinetic energy, and dissolved gases in the oceanic surface layer. There are few observations of these processes in the estuarine or coastal environments, where wind-driven mixing may co-occur with energetic tidal mixing and strong density stratification. This presents a major challenge for evaluating vertical mixing parameterizations used in modeling estuarine and coastal dynamics. We carried out a large, multi-investigator study of wind-driven estuarine dynamics in the middle reaches of Chesapeake Bay, USA, during 2012-2013. The center of the observational array was an instrumented turbulence tower with both atmospheric and marine turbulence sensors as well as rapidly sampled temperature and conductivity sensors. For this paper, we examined the impacts of surface gravity waves on vertical profiles of turbulent mixing and compared our results to second-moment turbulence closure predictions. Wave and turbulence measurements collected from the vertical array of Acoustic Doppler Velocimeters (ADVs) provided direct estimates of the dominant terms in the TKE budget and the surface wave field. Observed dissipation rates, TKE levels, and turbulent length scales are compared to published scaling relations and used in the calculation of second-moment nonequilibrium stability functions. Results indicate that in the surface layer of the estuary, where elevated dissipation is balanced by vertical divergence in TKE flux, existing nonequilibrium stability functions underpredict observed eddy viscosities. The influences of wave breaking and coherent wave-driven turbulence on modeled and observed stability functions will be discussed further in the context of turbulent length scales, TKE and dissipation profiles, and the depth at which the wave-dominated turbulent transport layer
New Results on the Realizability of Reynolds Stress Turbulence Closures
1993-10-01
NASA Contractor Report 191548 Un - ICASE Report No. 93-76 Ml ICASE U NEW RESULTS ON THE REALIZABILITY OF REYNOLDS STRESS TURBULENCE CLOSURES DTIC F...Av’i7 ibL ii.y Cdes - Avaii a. dlor Dist Special DTI / I -3 1,’DTIC qUALrfM Ui--M ID3 NEW RESULTS ON THE REALIZABILITY OF REYNOLDS STRESS TURBULENCE...realizability of Reynolds stress models in homogeneous turbulence is critically as- sessed from a theoretical standpoint. It is proven that a well known
Compressibility Corrections to Closure Approximations for Turbulent Flow Simulations
Cloutman, L D
2003-02-01
We summarize some modifications to the usual closure approximations for statistical models of turbulence that are necessary for use with compressible fluids at all Mach numbers. We concentrate here on the gradient-flu approximation for the turbulent heat flux, on the buoyancy production of turbulence kinetic energy, and on a modification of the Smagorinsky model to include buoyancy. In all cases, there are pressure gradient terms that do not appear in the incompressible models and are usually omitted in compressible-flow models. Omission of these terms allows unphysical rates of entropy change.
Turbulent fluid motion IV-averages, Reynolds decomposition, and the closure problem
NASA Technical Reports Server (NTRS)
Deissler, Robert G.
1992-01-01
Ensemble, time, and space averages as applied to turbulent quantities are discussed, and pertinent properties of the averages are obtained. Those properties, together with Reynolds decomposition, are used to derive the averaged equations of motion and the one- and two-point moment or correlation equations. The terms in the various equations are interpreted. The closure problem of the averaged equations is discussed, and possible closure schemes are considered. Those schemes usually require an input of supplemental information unless the averaged equations are closed by calculating their terms by a numerical solution of the original unaveraged equations. The law of the wall for velocities and temperatures, the velocity- and temperature-defect laws, and the logarithmic laws for velocities and temperatures are derived. Various notions of randomness and their relation to turbulence are considered in light of ergodic theory.
New results on the realizability of Reynolds stress turbulence closures
NASA Technical Reports Server (NTRS)
Speziale, Charles G.; Abid, Ridha; Durbin, Paul A.
1993-01-01
The realizability of Reynolds stress models in homogeneous turbulence is critically assessed from a theoretical standpoint. It is proven that a well known second-order closure formulated by Shih and Lumley using the strong realizability constraints of Schumann is, in fact, not a realizable model. The problem arises from the failure to properly satisfy the necessary positive second time derivative constraint when a principal Reynolds stress vanishes - a fatal flaw that becomes apparent when the non-analytic terms in their model are made single-valued as required on physical grounds. It is furthermore shown that the centrifugal acceleration generated by rotations of the principal axes of the Reynolds stress tensor can make the second derivative singular at the most extreme limits of realizable turbulence. This previously overlooked effect appears to make it impossible to identically satisfy the strong form of realizability in any version of the present generation of second-order closures. On the other hand, models properly formulated to satisfy the weak form of realizability - wherein states of one or two component turbulence are not accessible in finite time are found to be realizable. However, unlike the simpler and more commonly used second order closures, these models can be ill-behaved near the extreme limits of realizable turbulence due to the way that higher-degree nonlinearities are often unnecessarily introduced to satisfy realizability. Illustrative computations of homogeneous shear flows are presented to demonstrate these points which can have important implications for turbulence modeling.
On the relation between the conditional moment closure and unsteady flamelets
NASA Astrophysics Data System (ADS)
Klimenko, A. Y.
2001-09-01
We consider the relation between the conditional moment closure (CMC) and the unsteady flamelet model (FM). The CMC equations were originally constructed as global equations, while FM was derived asymptotically for a thin reaction zone. The recent tendency is to use FM-type equations as global equations. We investigate the possible consequences and suggest a new version of FM: coordinate-invariant FM (CIFM). Unlike FM, CIFM complies with conditional properties of the exact transport equations which are used effectively in CMC. We analyse the assumptions needed to obtain another global version of FM: representative interactive flamelets (RIF), from original FM and demonstrate that, in homogeneous turbulence, one of these assumptions is equivalent to the main CMC hypothesis.
Visibility moments and power spectrum of turbulence velocity
NASA Astrophysics Data System (ADS)
Dutta, Prasun
2016-02-01
Here we introduce moments of visibility function and discuss how those can be used to estimate the power spectrum of the turbulent velocity of external spiral galaxies. We perform numerical simulation to confirm the credibility of this method and found that for galaxies with lower inclination angles it works fine. The estimator outlined here is unbiased and has the potential to recover the turbulent velocity spectrum completely from radio interferometric observations.
Second order closure modeling of turbulent buoyant wall plumes
NASA Technical Reports Server (NTRS)
Zhu, Gang; Lai, Ming-Chia; Shih, Tsan-Hsing
1992-01-01
Non-intrusive measurements of scalar and momentum transport in turbulent wall plumes, using a combined technique of laser Doppler anemometry and laser-induced fluorescence, has shown some interesting features not present in the free jet or plumes. First, buoyancy-generation of turbulence is shown to be important throughout the flow field. Combined with low-Reynolds-number turbulence and near-wall effect, this may raise the anisotropic turbulence structure beyond the prediction of eddy-viscosity models. Second, the transverse scalar fluxes do not correspond only to the mean scalar gradients, as would be expected from gradient-diffusion modeling. Third, higher-order velocity-scalar correlations which describe turbulent transport phenomena could not be predicted using simple turbulence models. A second-order closure simulation of turbulent adiabatic wall plumes, taking into account the recent progress in scalar transport, near-wall effect and buoyancy, is reported in the current study to compare with the non-intrusive measurements. In spite of the small velocity scale of the wall plumes, the results showed that low-Reynolds-number correction is not critically important to predict the adiabatic cases tested and cannot be applied beyond the maximum velocity location. The mean and turbulent velocity profiles are very closely predicted by the second-order closure models. but the scalar field is less satisfactory, with the scalar fluctuation level underpredicted. Strong intermittency of the low-Reynolds-number flow field is suspected of these discrepancies. The trends in second- and third-order velocity-scalar correlations, which describe turbulent transport phenomena, are also predicted in general, with the cross-streamwise correlations better than the streamwise one. Buoyancy terms modeling the pressure-correlation are shown to improve the prediction slightly. The effects of equilibrium time-scale ratio and boundary condition are also discussed.
NASA Astrophysics Data System (ADS)
Yu, R.; Lipatnikov, A. N.; Bai, X. S.
2014-08-01
In order to gain further insight into (i) the use of conditioned quantities for characterizing turbulence within a premixed flame brush and (ii) the influence of front propagation on turbulent scalar transport, a 3D Direct Numerical Simulation (DNS) study of an infinitely thin front that self-propagates in statistically stationary, homogeneous, isotropic, forced turbulence was performed by numerically integrating Navier-Stokes and level set equations. While this study was motivated by issues relevant to premixed combustion, the density was assumed to be constant in order (i) to avoid the influence of the front on the flow and, therefore, to know the true turbulence characteristics as reference quantities for assessment of conditioned moments and (ii) to separate the influence of front propagation on turbulent transport from the influence of pressure gradient induced by heat release. Numerical simulations were performed for two turbulence Reynolds numbers (50 and 100) and four ratios (1, 2, 5, and 10) of the rms turbulent velocity to the front speed. Obtained results show that, first, the mean front thickness is decreased when a ratio of the rms turbulent velocity to the front speed is decreased. Second, although the gradient diffusion closure yields the right direction of turbulent scalar flux obtained in the DNS, the diffusion coefficient Dt determined using the DNS data depends on the mean progress variable. Moreover, Dt is decreased when the front speed is increased, thus, indicating that the front propagation affects turbulent scalar transport even in a constant-density case. Third, conditioned moments of the velocity field differ from counterpart mean moments, thus, disputing the use of conditioned velocity moments for characterizing turbulence when modeling premixed turbulent combustion. Fourth, computed conditioned enstrophies are close to the mean enstrophy in all studied cases, thus, suggesting the use of conditioned enstrophy for characterizing turbulence
Prediction of the turbulent wake with second-order closure
NASA Technical Reports Server (NTRS)
Taulbee, D. B.; Lumley, J. L.
1981-01-01
A turbulence was envisioned whose energy containing scales would be Gaussian in the absence of inhomogeneity, gravity, etc. An equation was constructed for a function equivalent to the probability density, the second moment of which corresponded to the accepted modeled form of the Reynolds stress equation. The third moment equations obtained from this were simplified by the assumption of weak inhomogeneity. Calculations are presented with this model as well as interpretations of the results.
Conditional Moment Closure Schemes for Studying Stochastic Dynamics of Genetic Circuits.
Soltani, Mohammad; Vargas-Garcia, Cesar Augusto; Singh, Abhyudai
2015-08-01
Inside individual cells, stochastic expression drives random fluctuations in gene product copy numbers, which corrupts functioning of both natural and synthetic genetic circuits. Dynamic models of genetic circuits are formulated stochastically using the chemical master equation framework. Since obtaining probability distributions can be computationally expensive in these models, noise is typically investigated through lower-order statistical moments (mean, variance, correlation, skewness, etc.) of mRNA/proteins levels. However, due to the nonlinearities in genetic circuits, this moment dynamics is typically not closed, in the sense that the time derivative of the lower-order statistical moments depends on high-order moments. Moment equations are closed by expressing higher-order moments as nonlinear functions of lower-order moments, a technique commonly referred to as moment closure. We provide a new moment closure scheme for studying stochastic dynamics of genetic circuits, where genes randomly toggle between transcriptionally active and inactive states. The method is based on conditioning protein levels on active states of genes and then expressing higher-order moments as functions of lower-order conditional moments. The conditional closure scheme is illustrated on different circuit motifs and found to outperform existing closure techniques. Rapid computation of stochasticity through closure methods will enable improved characterization and design of synthetic circuits that exhibit robust performance in spite of noisy expression of underlying genes.
NASA Astrophysics Data System (ADS)
Madadi-Kandjani, E.; Fox, R. O.; Passalacqua, A.
2017-06-01
An extended quadrature method of moments using the β kernel density function (β -EQMOM) is used to approximate solutions to the evolution equation for univariate and bivariate composition probability distribution functions (PDFs) of a passive scalar for binary and ternary mixing. The key element of interest is the molecular mixing term, which is described using the Fokker-Planck (FP) molecular mixing model. The direct numerical simulations (DNSs) of Eswaran and Pope ["Direct numerical simulations of the turbulent mixing of a passive scalar," Phys. Fluids 31, 506 (1988)] and the amplitude mapping closure (AMC) of Pope ["Mapping closures for turbulent mixing and reaction," Theor. Comput. Fluid Dyn. 2, 255 (1991)] are taken as reference solutions to establish the accuracy of the FP model in the case of binary mixing. The DNSs of Juneja and Pope ["A DNS study of turbulent mixing of two passive scalars," Phys. Fluids 8, 2161 (1996)] are used to validate the results obtained for ternary mixing. Simulations are performed with both the conditional scalar dissipation rate (CSDR) proposed by Fox [Computational Methods for Turbulent Reacting Flows (Cambridge University Press, 2003)] and the CSDR from AMC, with the scalar dissipation rate provided as input and obtained from the DNS. Using scalar moments up to fourth order, the ability of the FP model to capture the evolution of the shape of the PDF, important in turbulent mixing problems, is demonstrated. Compared to the widely used assumed β -PDF model [S. S. Girimaji, "Assumed β-pdf model for turbulent mixing: Validation and extension to multiple scalar mixing," Combust. Sci. Technol. 78, 177 (1991)], the β -EQMOM solution to the FP model more accurately describes the initial mixing process with a relatively small increase in computational cost.
Second moment closure analysis of the backstep flow database
NASA Technical Reports Server (NTRS)
Parneix, S.; Laurence, D.; Durbin, P.
1996-01-01
A Second Moment Closure computation (SMC) is compared in detail with the Direct Numerical Simulation (DNS) data of Le and Moin for the backstep flow at Re = 5,000 in an attempt to understand why the intensity of the backflow and, consequently, the friction coefficient in the recirculation bubble are severely underestimated. The data show that this recirculation bubble is far from being laminar except in the very near wall layer. A novel 'differential a priori' procedure was used, in which the full transport equation for one isolated component of the Reynolds stress tensor was solved using DNS data as input. Conclusions are then different from what would have been deduced by comparing a full simulation to a DNS. One cause of discrepancy was traced back to insufficient transfer of energy to the normal stress by pressure strain, but was not cured. A significant finding, confirmed by the DNS data in the core region of a channel flow, is that the coefficient that controls destruction of dissipation, C epsilon(sub 2), should be decreased by a factor of 2 when production is vanishing. This is also the case in the recirculation bubble, and a new formulation has cured 25% of the backflow discrepancy.
Modeling evaporation effects in conditional moment closure for spray autoignition
NASA Astrophysics Data System (ADS)
Borghesi, Giulio; Mastorakos, Epaminondas; Devaud, Cécile B.; Bilger, Robert W.
2011-10-01
Simulations of an n-heptane spray autoigniting under conditions relevant to a diesel engine are performed using two-dimensional, first-order conditional moment closure (CMC) with full treatment of spray terms in the mixture fraction variance and CMC equations. The conditional evaporation term in the CMC equations is closed assuming interphase exchange to occur at the droplet saturation mixture fraction values only. Modeling of the unclosed terms in the mixture fraction variance equation is done accordingly. Comparison with experimental data for a range of ambient oxygen concentrations shows that the ignition delay is overpredicted. The trend of increasing ignition delay with decreasing oxygen concentration, however, is correctly captured. Good agreement is found between the computed and measured flame lift-off height for all conditions investigated. Analysis of source terms in the CMC temperature equation reveals that a convective-reactive balance sets in at the flame base, with spatial diffusion terms being important, but not as important as in lifted jet flames in cold air. Inclusion of droplet terms in the governing equations is found to affect the mixture fraction variance field in the region where evaporation is the strongest, and to slightly increase the ignition delay time due to the cooling associated with the evaporation. Both flame propagation and stabilization mechanisms, however, remain unaffected.
Interpolative Hyperbolic Realizable Moment Closures for Non-Equilibrium Flows with Heat Transfer
NASA Astrophysics Data System (ADS)
Tensuda, Boone Rudy
The predictive capabilities of a novel, 14-moment, maximum-entropy-based, interpolative closure are explored for multi-dimensional non-equilibrium flows of a monatomic gas with heat transfer. Unlike the maximum-entropy closure on which it is based, the interpolative closure provides closed-form expressions for the closing fluxes while retaining a large region of hyperbolicity. Properties of the moment system are explored via a dispersion analysis and an implicit finite-volume solution procedure is proposed. Multi-dimensional applications of the closure are then examined for several canonical non-equilibrium flow problems in order to provide an assessment of its capabilities. The predictive capabilities of the closure were found to surpass those of the 10-moment Gaussian closure. It was also found to predict interesting non-equilibrium phenomena, such as counter-gradient heat flux. The proposed implicit solver showed improved computational performance compared to the previously studied semi-implicit technique.
Some Results Relevant to Statistical Closures for Compressible Turbulence
NASA Technical Reports Server (NTRS)
Ristorcelli, J. R.
1998-01-01
For weakly compressible turbulent fluctuations there exists a small parameter, the square of the fluctuating Mach number, that allows an investigation using a perturbative treatment. The consequences of such a perturbative analysis in three different subject areas are described: 1) initial conditions in direct numerical simulations, 2) an explanation for the oscillations seen in the compressible pressure in the direct numerical simulations of homogeneous shear, and 3) for turbulence closures accounting for the compressibility of velocity fluctuations. Initial conditions consistent with small turbulent Mach number asymptotics are constructed. The importance of consistent initial conditions in the direct numerical simulation of compressible turbulence is dramatically illustrated: spurious oscillations associated with inconsistent initial conditions are avoided, and the fluctuating dilatational field is some two orders of magnitude smaller for a compressible isotropic turbulence. For the isotropic decay it is shown that the choice of initial conditions can change the scaling law for the compressible dissipation. A two-time expansion of the Navier-Stokes equations is used to distinguish compressible acoustic and compressible advective modes. A simple conceptual model for weakly compressible turbulence - a forced linear oscillator is described. It is shown that the evolution equations for the compressible portions of turbulence can be understood as a forced wave equation with refraction. Acoustic modes of the flow can be amplified by refraction and are able to manifest themselves in large fluctuations of the compressible pressure.
Assessment of Higher-Order RANS Closures in a Decelerated Planar Wall-Bounded Turbulent Flow
NASA Technical Reports Server (NTRS)
Jeyapaul, Elbert; Coleman, Gary N.; Rumsey, Christopher L.
2014-01-01
A reference DNS database is presented, which includes third- and fourth-order moment budgets for unstrained and strained planar channel flow. Existing RANS closure models for third- and fourth-order terms are surveyed, and new model ideas are introduced. The various models are then compared with the DNS data term by term using a priori testing of the higher-order budgets of turbulence transport, velocity-pressure-gradient, and dissipation for both the unstrained and strained databases. Generally, the models for the velocity-pressure-gradient terms are most in need of improvement.
Derivation of the conditional moment closure equations for spray combustion
Mortensen, Mikael; Bilger, Robert W.
2009-01-15
In this work we derive the fundamental equations for conditional moment closure (CMC) modelling of individual phases set in a two-phase flow. The derivation is based on the instantaneous transport equations for the single phase that involve a level set/indicator function technique for accounting for interfaces. Special emphasis is put on spray combustion with the CMC equations formulated for the gas phase. The CMC equations are to be viewed as an adjunct to existing methods for the modelling of the dynamics of sprays: they provide a refinement of the modelling of chemical reactions in the gas phase. The resulting CMC equations differ significantly from those already in use in the literature. They contain, of course, unclosed terms that need to be modelled. Investigation of the unclosed terms associated with evaporation at the droplet surface is well beyond the capabilities of laboratory measurement or direct numerical simulation. It is proposed that modelling of these terms be based on the well-established 'laws' of similarity between heat and mass transfer: an example is detailed for one example of the general modelling of the spray dynamics. Other unclosed terms are important throughout the gas phase. Models used for these terms in single-phase flows are reviewed and it is proposed that any modifications needed for these models be investigated by DNS of suitable model problems having good resolution of the flow and mixing in the inter-droplet space. It is proposed that a spray analogue of the scalar mixing layer that has been widely studied in single-phase flows be used as the model problem for such DNS studies and also for LES and RANS modelling. (author)
Ocean Turbulence I: One-Point Closure Model Momentum and Heat Vertical Diffusivities
NASA Technical Reports Server (NTRS)
Canuto, V. M.; Howard, A.; Cheng, Y.; Dubovikov, M. S.
1999-01-01
Since the early forties, one-point turbulence closure models have been the canonical tools used to describe turbulent flows in many fields. In geophysics, Mellor and Yamada applied such models using the 1980 state-of-the art. Since then, no improvements were introduced to alleviate two major difficulties: 1) closure of the pressure correlations, which affects the correct determination of the critical Richardson number Ri(sub cr) above which turbulent mixing is no longer possible and 2) the need to express the non-local third-order moments (TOM) in terms of lower order moments rather than via the down-gradient approximation as done thus far, since the latter seriously underestimates the TOMs. Since 1) and 2) are still being dealt with adjustable parameters which weaken the credibility of the models, alternative models, not based on turbulence modeling, have been suggested. The aim of this paper is to show that new information, partly derived from the newest 2-point closure model discussed, can be used to solve these shortcomings. The new one-point closure model, which in its simplest form is algebraic and thus simple to implement, is first shown to reproduce a variety of data. Then, it is used in a Ocean-General Circulation Model (O-GCM) where it reproduces well a large variety of ocean data. While phenomenological models are specifically tuned to ocean turbulence, the present model is not. It is first tested against laboratory data on stably stratified flows and then used in an O-GCM. It is more general, more predictive and more resilient, e.g., it can incorporate phenomena like wave-breaking at the surface, salinity diffusivity, non-locality, etc. One important feature that naturally comes out of the new model is that the predicted Richardson critical value Ri(sub cr) is Ri (sub cr approx. = 1) in agreement with both Large Eddy Simulations (LES) and empirical evidence while all previous models predicted Ri (sub cr approx. = 0.2) which led to a considerable
Conditional Second Order Closure for Turbulent Shear Flows.
1985-07-22
measurements in several shear flows and satisfactory agreement between calculation and experiment is obtained. S Ps *s ~ J j~~- p .’* % LX- W-Vvw.n W...which allows calculation of the intermittency factor and statistical moments characterizing the fluctuations in the individual zones. The closure model...The resulting model is then compared with measurements in several shear flows and satisfactory agreement between calculation and experiment is
Magnetic moment conservation and particles acceleration in turbulence
NASA Astrophysics Data System (ADS)
Dalena, S.; Greco, A.; Matthaeus, W. H.
2010-12-01
The present work concerns the study of particle magnetic moment conservation in the presence of turbulent magnetic fields. As we know from the particle orbit theory, for slow temporal and spatial magnetic field variations(i.e. if their characteristic length and time are greater than the particle orbit diameter and the time spent by a particle to execute one orbit, respectively), the magnetic moment, defined as μ = (v^2⊥ /B) (averaged over the particle gyroperiod) is an adiabatic invariant and remains constant during particle motion. But in presence of a well developed magnetic turbulence μ can undergo rapid variations and might not be constant anymore. Of course, this fact could influence particle acceleration and could have a considerable implications in many astrophysical problems, such as coronal heating. In order to reproduce and extend some of the results obtained by Karimabadi et al. 1992, we study the interaction between ions and a single or a couple of electromagnetic waves. We varied both the wave frequency and the cosine of pitch angle at which particles are injected, in order to observe in this very simple case which is the limit for magnetic moment conservation. We also will reconsider the results of Dmitruk and Matthaeus (2006) regarding particle acceleration in turbulence, taking into account statistics of the magnetic moment (see also Lehe et al., 2010). Later we will add more waves to obtain a complete turbulent spectrum. The final aim of this research work is the understanding the behavior of particles magnetic moment during magnetic reconnection phenomena. H. Karimabadi, D. Krauss-Varban and T. Teresawa, JGR, 97, 13853, 1992. P. Dmitruk and W. H. Matthaeus, JGR, 11, A12110, 2006. R. Lehe, I. J. Parrish and E. Quataert, Astrophys. J. 707, 404, 2009.
Non-local Second Order Closure Scheme for Boundary Layer Turbulence and Convection
NASA Astrophysics Data System (ADS)
Meyer, Bettina; Schneider, Tapio
2017-04-01
There has been scientific consensus that the uncertainty in the cloud feedback remains the largest source of uncertainty in the prediction of climate parameters like climate sensitivity. To narrow down this uncertainty, not only a better physical understanding of cloud and boundary layer processes is required, but specifically the representation of boundary layer processes in models has to be improved. General climate models use separate parameterisation schemes to model the different boundary layer processes like small-scale turbulence, shallow and deep convection. Small scale turbulence is usually modelled by local diffusive parameterisation schemes, which truncate the hierarchy of moment equations at first order and use second-order equations only to estimate closure parameters. In contrast, the representation of convection requires higher order statistical moments to capture their more complex structure, such as narrow updrafts in a quasi-steady environment. Truncations of moment equations at second order may lead to more accurate parameterizations. At the same time, they offer an opportunity to take spatially correlated structures (e.g., plumes) into account, which are known to be important for convective dynamics. In this project, we study the potential and limits of local and non-local second order closure schemes. A truncation of the momentum equations at second order represents the same dynamics as a quasi-linear version of the equations of motion. We study the three-dimensional quasi-linear dynamics in dry and moist convection by implementing it in a LES model (PyCLES) and compare it to a fully non-linear LES. In the quasi-linear LES, interactions among turbulent eddies are suppressed but nonlinear eddy—mean flow interactions are retained, as they are in the second order closure. In physical terms, suppressing eddy—eddy interactions amounts to suppressing, e.g., interactions among convective plumes, while retaining interactions between plumes and the
Relationships between energy balance closure and turbulent transport of energy
NASA Astrophysics Data System (ADS)
Banerjee, Tirtha; Zeeman, Matthias; Brugger, Peter; De Roo, Frederik; Mauder, Matthias
2017-04-01
The energy balance residual (EBR), defined as the difference between the available energy (sum of net radiation and ground heat flux) and the turbulent fluxes of latent and sensible heat, is often found to have a large positive value. Several land surface experiments and flux networks report an average energy balance closure of approximately 80%. Although different factors can influence the energy balance closure across measurement campaigns, a significant EBR even when sites are horizontally with short canopies indicates of a systematic bias resulting from the general underestimation of the aerodynamic transport of energy, especially horizontal divergence of the mean advective fluxes and transport by low-frequency motions generally called 'secondary circulations'. These low frequency local transports can occur from various processes such as coherent large scale organized motions, convective cells and even significant transient changes. Thus, we decided to study the budget of the turbulent kinetic energy (TKE) in conjunction with the energy balance closure and the turbulent fluxes associated with nonlocal motions, advection and flux divergence. In the current work, this interdependency has been investigated using surface flux (Eddy Covariance) at the TERENO sites Fendt, Graswang and Rottenbuch in Southern Germany (with gentle topography. Statistical methods for dimensional reduction techniques has been used to extract the effects and significance of aforementioned processes towards explaining the observed annual average EBR of about 50 Wm-2. Initial results indicate a high correlation between EBR and the TKE dissipation rate, as well as the skewness of vertical velocity and the turbulent fluxes associated with flux divergence, confirming the role of secondary circulations. Overall, improved understanding of such connections between the fundamental mechanisms of TKE transport and the energy balance likely advances the knowledge towards constraining the modeling
Variational approach to the closure problem of turbulence theory
NASA Astrophysics Data System (ADS)
Qian, J.
1983-08-01
A new method is proposed to solve the closure problem of turbulence theory and to drive the Kolmogorov law in an Eulerian framework. Instead of using complex Fourier components of velocity field as modal parameters, a complete set of independent real parameters and dynamic equations are worked out to describe the dynamic states of a turbulence. Classical statistical mechanics is used to study the statistical behavior of the turbulence. An approximate stationary solution of the Liouville equation is obtained by a perturbation method based on a Langevin-Fokker-Planck (LFP) model. The dynamic damping coefficient eta of the LFP model is treated as an optimum control parameter to minimize the error of the perturbation solution; this leads to a convergent integral equation for eta to replace the divergent response equation of Kraichnan's direct-interaction (DI) approximation, thereby solving the closure problem without appealing to a Lagrangian formulation. The Kolmogorov constant Ko is evaluated numerically, obtaining Ko = 1.2, which is compatible with the experimental data given by Gibson and Schwartz, (1963).
Multi-dimensional validation of a maximum-entropy-based interpolative moment closure
NASA Astrophysics Data System (ADS)
Tensuda, Boone R.; McDonald, James G.; Groth, Clinton P. T.
2016-11-01
The performance of a novel maximum-entropy-based 14-moment interpolative closure is examined for multi-dimensional flows via validation of the closure for several established benchmark problems. Despite its consideration of heat transfer, this 14-moment closure contains closed-form expressions for the closing fluxes, unlike the maximum-entropy models on which it is based. While still retaining singular behaviour in some regions of realizable moment space, the interpolative closure proves to have a large region of hyperbolicity while remaining computationally tractable. Furthermore, the singular nature has been shown to be advantageous for practical simulations. The multi-dimensional cases considered here include Couette flow, heat transfer between infinite parallel plates, subsonic flow past a circular cylinder, and lid-driven cavity flow. The 14-moment predictions are compared to analytical, DSMC, and experimental results as well the results of other closures. For each case, a range of Knudsen numbers are explored in order to assess the validity and accuracy of the closure in different regimes. For Couette flow and heat transfer between flat plates, it is shown that the closure predictions are consistent with the expected analytical solutions in all regimes. In the cases of flow past a circular cylinder and lid-driven cavity flow, the closure is found to give more accurate results than the related lower-order maximum-entropy Gaussian and maximum-entropy-based regularized Gaussian closures. The ability to predict important non-equilibrium phenomena, such as a counter-gradient heat flux, is also established.
Evolution of a turbulent pycnocline within the framework of a modified model of turbulent closure
NASA Astrophysics Data System (ADS)
Soustova, Irina; Troitskaya, Yuliya; Ezhova, Ekaterina; Rybushkina, Galina; Zilitinkevich, Sergej
2015-04-01
The formation and evolution of a turbulent pycnocline generated by internal wave breaking were investigated within the framework of a modified model of turbulent closure. Numerical computation based on closed Reynolds equations using closure hypotheses obtained in the framework of the kinetic approach showed a strong dependence of vertical distributions corresponding to hydrodynamic parameters on the anisotropy of turbulence and speed of pycnocline motion. Strongly anisotropic motion is characterized by the presence of stepwise variations in the vertical profiles of buoyancy frequency, turbulence scale, and kinetic and potential energy as compared to the known analytical solution obtained earlier without allowance for a non-steady-state term in the kinetic energy balance equation. In the case of a weaker anisotropy, no sharp changes are observed in spatial and energy characteristics of turbulence and the qualitative shape of their profiles in the pycnolcline region coincides with the known analytical dependences. The obtained result is important for development of numerical climatic models of the interaction between the atmosphere and the ocean. This work was supported by the Russian Foundation of Basic Research (13-05-00865, 14-05-91767, 15-45-02580).
NASA Technical Reports Server (NTRS)
Ristorcelli, J. R.
1993-01-01
The turbulent mass flux, or equivalently the fluctuating Favre velocity mean, appears in the first and second moment equations of compressible kappa-epsilon and Reynolds stress closures. Mathematically it is the difference between the unweighted and density-weighted averages of the velocity field and is therefore a measure of the effects of compressibility through variations in density. It appears to be fundamental to an inhomogeneous compressible turbulence, in which it characterizes the effects of the mean density gradients, in the same way the anisotropy tensor characterizes the effects of the mean velocity gradients. An evolution equation for the turbulent mass flux is derived. A truncation of this equation produces an algebraic expression for the mass flux. The mass flux is found to be proportional to the mean density gradients with a tensor eddy-viscosity that depends on both the mean deformation and the Reynolds stresses. The model is tested in a wall bounded DNS at Mach 4.5 with notable results.
Application of Gaussian Moment Closures to Three-Dimensional Micro-Scale Flows
NASA Astrophysics Data System (ADS)
Lam, Christopher
A parallel, implicit, adaptive mesh refinement (AMR), finite-volume scheme is described for the solution of the standard and regularized Gaussian moment closures on three-dimensional, multi-block, body-fitted, hexahedral meshes. The standard Gaussian closure has been shown to accurately predict non-equilibrium phenomena at moderate Knudsen numbers through an anisotropic treatment of pressure. The regularized closure builds on these advantages and includes the effects of non-equilibrium heat transfer by means of a first-order correction to the standard Gaussian closure. The combined moment closure treatment / numerical method is applied to the prediction of three-dimensional, non-equilibrium, micro-scale, gaseous flows. Unlike other regularized moment closures, the underlying closure is the standard maximum-entropy Gaussian closure which provides a fully-realizable and strictly hyperbolic description of non-equilibrium gaseous flows that is valid from the continuum limit, through the transition regime, and up to the free-molecular flow limit. The proposed finite-volume scheme uses Riemann-solver-based flux functions and limited linear reconstruction to provide accurate and monotonic solutions, even in the presence of large solution gradients and/or under-resolved solution content. A rather effective and highly scalable parallel implicit time-marching scheme based on a Jacobian-free inexact Newton-Krylov-Schwarz (NKS) approach with additive Schwarz preconditioning and domain partitioning following from the multi-block AMR mesh is used to obtain solutions to the non-linear ordinary-differential equations that result from finite-volume spatial discretization procedure. Details are given of the standard and regularized Gaussian closure, extensions for diatomic gases, and slip-flow boundary treatment. Numerical results for several canonical flow problems demonstrate the potential of the closures, that when combined with an efficient parallel solution method, provide an
NASA Astrophysics Data System (ADS)
Wright, Y. M.; Bolla, M.; Boulouchos, K.; Borghesi, G.; Mastorakos, E.
2015-01-01
Energy conversion devices of practical interest such as engines or combustors operate in highly turbulent flow regimes. Due to the nature of the hydrocarbon fuels employed, the oxidation chemistry involves a broad range of time-scales some of which cannot be decoupled from the flow. Among the approaches utilised to tackle the modelling of turbulent combustion, Conditional Moment Closure (CMC), belonging to the computationally efficient class of presumed PDF methods, has shown great potential. For single-phase flows it has been demonstrated on non-premixed turbulent lifted and opposed jets, lifted flames and auto-igniting jets. Here we seek to review recent advances in both modelling and application of CMC for auto-ignition of fuel sprays. The experiments chosen for code validation and model improvement include generic spray test rigs with dimensions of passenger car as well as large two-stroke marine engines. Data for a broad range of operating conditions of a heavy-duty truck engine is additionally employed to assess the predictive capability of the model with respect to NOx emissions. An outlook on future enhancements including e.g. LES-CMC formulation also for two-phase flows as well as developments in the field of soot emissions are summarised briefly.
Complete hierarchies of SIR models on arbitrary networks with exact and approximate moment closure.
Sharkey, Kieran J; Wilkinson, Robert R
2015-06-01
We first generalise ideas discussed by Kiss et al. (2015) to prove a theorem for generating exact closures (here expressing joint probabilities in terms of their constituent marginal probabilities) for susceptible-infectious-removed (SIR) dynamics on arbitrary graphs (networks). For Poisson transmission and removal processes, this enables us to obtain a systematic reduction in the number of differential equations needed for an exact 'moment closure' representation of the underlying stochastic model. We define 'transmission blocks' as a possible extension of the block concept in graph theory and show that the order at which the exact moment closure representation is curtailed is the size of the largest transmission block. More generally, approximate closures of the hierarchy of moment equations for these dynamics are typically defined for the first and second order yielding mean-field and pairwise models respectively. It is frequently implied that, in principle, closed models can be written down at arbitrary order if only we had the time and patience to do this. However, for epidemic dynamics on networks, these higher-order models have not been defined explicitly. Here we unambiguously define hierarchies of approximate closed models that can utilise subsystem states of any order, and show how well-known models are special cases of these hierarchies.
NASA Astrophysics Data System (ADS)
Cheng, A.; Xu, K.
2012-12-01
This presentation describes the implementation and testing of a higher-order turbulence closure, an intermediately-prognostic higher-order turbulence closure (IPHOC), into the Community Atmosphere Model (CAM) version 5 (CAM5). The third-order turbulence closure introduces a joint double-Gaussian distribution of liquid water potential temperature, total water mixing ratio, and vertical velocity to represent any skewed turbulence circulations. The distribution is inferred from the first-, second-, and third-order moments of the variables given above and is used to diagnose cloud fraction and grid-mean liquid water mixing ratio, as well as the buoyancy term and fourth-order terms in the equations describing the evolution of the second- and third-order moments. In addition, a prognostic planetary boundary layer (PBL) height approach has been incorporated in IPHOC in order to resolve the strong inversion above PBL for the coarse general circulation model (GCM) vertical grid-spacing. The IPHOC replaces PBL, shallow convection, and cloud macrophysics parameterizations in CAM5. The coupling of CAM5 with IPHOC (CAM5-IPHOC) represents a more unified treatment of boundary layer and shallow convective processes. Results from global simulations are presented and suggest that CAM5-IPHOC can provide a better treatment of boundary layer clouds and processes, when compared to CAM5. At the GCSS/WGNE Pacific Cross-Section Intercomparison (GPCI) cross section, CAM5-IPHOC tends to correct the underestimate of the stratocumulus and shallow cumulus clouds both in cloud cover and liquid water path by CAM5. The decoupling of stratocumulus clouds and the associated transition from stratocumulus-to-shallow cumulus clouds are also more realistic and reasonable.
Efficient algorithms and implementations of entropy-based moment closures for rarefied gases
NASA Astrophysics Data System (ADS)
Schaerer, Roman Pascal; Bansal, Pratyuksh; Torrilhon, Manuel
2017-07-01
We present efficient algorithms and implementations of the 35-moment system equipped with the maximum-entropy closure in the context of rarefied gases. While closures based on the principle of entropy maximization have been shown to yield very promising results for moderately rarefied gas flows, the computational cost of these closures is in general much higher than for closure theories with explicit closed-form expressions of the closing fluxes, such as Grad's classical closure. Following a similar approach as Garrett et al. (2015) [13], we investigate efficient implementations of the computationally expensive numerical quadrature method used for the moment evaluations of the maximum-entropy distribution by exploiting its inherent fine-grained parallelism with the parallelism offered by multi-core processors and graphics cards. We show that using a single graphics card as an accelerator allows speed-ups of two orders of magnitude when compared to a serial CPU implementation. To accelerate the time-to-solution for steady-state problems, we propose a new semi-implicit time discretization scheme. The resulting nonlinear system of equations is solved with a Newton type method in the Lagrange multipliers of the dual optimization problem in order to reduce the computational cost. Additionally, fully explicit time-stepping schemes of first and second order accuracy are presented. We investigate the accuracy and efficiency of the numerical schemes for several numerical test cases, including a steady-state shock-structure problem.
NASA Technical Reports Server (NTRS)
Cheng, A.; Xu, K.-M.; Golaz, J.-C.
2004-01-01
A hierarchy of third-order turbulence closure models are used to simulate boundary-layer cumuli in this study. An unrealistically strong liquid-water oscillation (LWO) is found in the fully prognostic model, which predicts all third moments. The LWO propagates from cloud base to cloud top with a speed of 1 m/s. The period of the oscillation is about 1000 s. Liquid-water buoyancy terms in the third-moment equations contribute to the LWO. The LWO mainly affects the vertical profiles of cloud fraction, mean liquid-water mixing ratio and the fluxes of liquid-water potential temperature and total water, but has less impact on the vertical profiles of other second-moments and third-moments. In order to minimize the LWO, a moderate large diffusion coefficient and a large turbulent dissipation at its originating level are needed. However, this approach distorts the vertical distributions of cloud fraction and liquid-water mixing ratio. A better approach is to parameterize liquid-water buoyancy more reasonably. A minimally prognostic model, which diagnoses all third moments except for vertical velocity, is shown to produce better results, compared to a fully prognostic model.
NASA Technical Reports Server (NTRS)
Cheng, A.; Xu, K.-M.; Golaz, J.-C.
2004-01-01
A hierarchy of third-order turbulence closure models are used to simulate boundary-layer cumuli in this study. An unrealistically strong liquid-water oscillation (LWO) is found in the fully prognostic model, which predicts all third moments. The LWO propagates from cloud base to cloud top with a speed of 1 m/s. The period of the oscillation is about 1000 s. Liquid-water buoyancy terms in the third-moment equations contribute to the LWO. The LWO mainly affects the vertical profiles of cloud fraction, mean liquid-water mixing ratio and the fluxes of liquid-water potential temperature and total water, but has less impact on the vertical profiles of other second-moments and third-moments. In order to minimize the LWO, a moderate large diffusion coefficient and a large turbulent dissipation at its originating level are needed. However, this approach distorts the vertical distributions of cloud fraction and liquid-water mixing ratio. A better approach is to parameterize liquid-water buoyancy more reasonably. A minimally prognostic model, which diagnoses all third moments except for vertical velocity, is shown to produce better results, compared to a fully prognostic model.
Autonomic Closure in Reynolds-Averaged Navier-Stokes (RANS) Simulations of Turbulent Flows
NASA Astrophysics Data System (ADS)
Ahlf, Rick J.
Reynolds-averaged Navier-Stokes (RANS) simulation is the industry standard for computing practical turbulent flows - since large eddy simulation (LES) and direct numerical simulation (DNS) require comparatively massive computational power to simulate even relatively simple flows. RANS, like LES, requires that a user specify a "closure model" for the underlying turbulence physics. However, despite more than 60 years of research into turbulence modeling, current models remain largely unable to accurately predict key aspects of the complex turbulent flows frequently encountered in practical engineering applications. Recently a new approach, termed "autonomic closure", has been developed for LES that avoids the need to specify any prescribed turbulence model. Autonomic closure is a fully-adaptive, self-optimizing approach to the closure problem, in which the simulation itself determines the optimal local, instantaneous relation between any unclosed term and the simulation variables via solution of a nonlinear, nonparametric system identification problem. In principle, it should be possible to extend autonomic closure from LES to RANS simulations, and this thesis is the initial exploration of such an extension. A RANS implementation of autonomic closure would have far-reaching impacts on the ability to simulate practical engineering applications that involve turbulent flows. This thesis has developed the formal connection between autonomic closure for LES and its counterpart for RANS simulations, and provides a priori results from FLUENT simulations of the turbulent flow over a backward-facing step to evaluate the performance of an initial implementation of autonomic closure for RANS. Key aspects of these results lay the groundwork on which future efforts to extend autonomic closure to RANS simulations can be based.
An alternative assessment of second-order closure models in turbulent shear flows
NASA Technical Reports Server (NTRS)
Speziale, Charles G.; Gatski, Thomas B.
1994-01-01
The performance of three recently proposed second-order closure models is tested in benchmark turbulent shear flows. Both homogeneous shear flow and the log-layer of an equilibrium turbulent boundary layer are considered for this purpose. An objective analysis of the results leads to an assessment of these models that stands in contrast to that recently published by other authors. A variety of pitfalls in the formulation and testing of second-order closure models are uncovered by this analysis.
Comparison of different moment-closure approximations for stochastic chemical kinetics
Schnoerr, David; Sanguinetti, Guido; Grima, Ramon
2015-11-14
In recent years, moment-closure approximations (MAs) of the chemical master equation have become a popular method for the study of stochastic effects in chemical reaction systems. Several different MA methods have been proposed and applied in the literature, but it remains unclear how they perform with respect to each other. In this paper, we study the normal, Poisson, log-normal, and central-moment-neglect MAs by applying them to understand the stochastic properties of chemical systems whose deterministic rate equations show the properties of bistability, ultrasensitivity, and oscillatory behaviour. Our results suggest that the normal MA is favourable over the other studied MAs. In particular, we found that (i) the size of the region of parameter space where a closure gives physically meaningful results, e.g., positive mean and variance, is considerably larger for the normal closure than for the other three closures, (ii) the accuracy of the predictions of the four closures (relative to simulations using the stochastic simulation algorithm) is comparable in those regions of parameter space where all closures give physically meaningful results, and (iii) the Poisson and log-normal MAs are not uniquely defined for systems involving conservation laws in molecule numbers. We also describe the new software package MOCA which enables the automated numerical analysis of various MA methods in a graphical user interface and which was used to perform the comparative analysis presented in this paper. MOCA allows the user to develop novel closure methods and can treat polynomial, non-polynomial, as well as time-dependent propensity functions, thus being applicable to virtually any chemical reaction system.
A k-{\\varepsilon} turbulence closure model of an isothermal dry granular dense matter
NASA Astrophysics Data System (ADS)
Fang, Chung
2016-07-01
The turbulent flow characteristics of an isothermal dry granular dense matter with incompressible grains are investigated by the proposed first-order k-{\\varepsilon} turbulence closure model. Reynolds-filter process is applied to obtain the balance equations of the mean fields with two kinematic equations describing the time evolutions of the turbulent kinetic energy and dissipation. The first and second laws of thermodynamics are used to derive the equilibrium closure relations satisfying turbulence realizability conditions, with the dynamic responses postulated by a quasi-linear theory. The established closure model is applied to analyses of a gravity-driven stationary flow down an inclined moving plane. While the mean velocity decreases monotonically from its value on the moving plane toward the free surface, the mean porosity increases exponentially; the turbulent kinetic energy and dissipation evolve, respectively, from their minimum and maximum values on the plane toward their maximum and minimum values on the free surface. The evaluated mean velocity and porosity correspond to the experimental outcomes, while the turbulent dissipation distribution demonstrates a similarity to that of Newtonian fluids in turbulent shear flows. When compared to the zero-order model, the turbulent eddy evolution tends to enhance the transfer of the turbulent kinetic energy and plane shearing across the flow layer, resulting in more intensive turbulent fluctuation in the upper part of the flow. Solid boundary as energy source and sink of the turbulent kinetic energy becomes more apparent in the established first-order model.
NASA Astrophysics Data System (ADS)
Kadantsev, Evgeny; Fortelius, Carl; Druzhinin, Oleg; Mortikov, Evgeny; Glazunov, Andrey; Zilitinkevich, Sergej
2016-04-01
We examine and validate the EFB turbulence closure model (Zilitinkevich et al., 2013), which is based on the budget equations for basic second moments, namely, two energies: turbulent kinetic energy EK and turbulent potential energy EP, and vertical turbulent fluxes of momentum and potential temperature, τi (i = 1, 2) and Fz. Instead of traditional postulation of down-gradient turbulent transport, the EFB closure determines the eddy viscosity and eddy conductivity from the steady-state version of the budget equations for τi and Fz. Furthermore, the EFB closure involves new prognostic equation for turbulent dissipation time scale tT, and extends the theory to non-steady turbulence regimes accounting for non-gradient and non-local turbulent transports (when the traditional concepts of eddy viscosity and eddy conductivity become generally inconsistent). Our special interest is in asymptotic behavior of the EFB closure in strongly stable stratification. For this purpose, we consider plane Couette flow, namely, the flow between two infinite parallel plates, one of which is moving relative to another. We use a set of Direct Numerical Simulation (DNS) experiments at the highest possible Reynolds numbers for different bulk Richardson numbers (Druzhinin et al., 2015). To demonstrate potential improvements in Numerical Weather Prediction models, we test the new closure model in various idealized cases, varying stratification from the neutral and conventionally neutral to stable (GABLS1) running a test RANS model and HARMONIE/AROME model in single-column mode. Results are compared with DNS and LES (Large Eddy Simulation) runs and different numerical weather prediction models.
Using field inversion to quantify functional errors in turbulence closures
NASA Astrophysics Data System (ADS)
Singh, Anand Pratap; Duraisamy, Karthik
2016-04-01
A data-informed approach is presented with the objective of quantifying errors and uncertainties in the functional forms of turbulence closure models. The approach creates modeling information from higher-fidelity simulations and experimental data. Specifically, a Bayesian formalism is adopted to infer discrepancies in the source terms of transport equations. A key enabling idea is the transformation of the functional inversion procedure (which is inherently infinite-dimensional) into a finite-dimensional problem in which the distribution of the unknown function is estimated at discrete mesh locations in the computational domain. This allows for the use of an efficient adjoint-driven inversion procedure. The output of the inversion is a full-field of discrepancy that provides hitherto inaccessible modeling information. The utility of the approach is demonstrated by applying it to a number of problems including channel flow, shock-boundary layer interactions, and flows with curvature and separation. In all these cases, the posterior model correlates well with the data. Furthermore, it is shown that even if limited data (such as surface pressures) are used, the accuracy of the inferred solution is improved over the entire computational domain. The results suggest that, by directly addressing the connection between physical data and model discrepancies, the field inversion approach materially enhances the value of computational and experimental data for model improvement. The resulting information can be used by the modeler as a guiding tool to design more accurate model forms, or serve as input to machine learning algorithms to directly replace deficient modeling terms.
Direct numerical simulation-based Reynolds-averaged closure for bubble-induced turbulence
NASA Astrophysics Data System (ADS)
Ma, Tian; Santarelli, Claudio; Ziegenhein, Thomas; Lucas, Dirk; Fröhlich, Jochen
2017-03-01
Budgets of the turbulent kinetic energy from direct numerical simulations (DNSs) of disperse bubbly channel flows are used to develop a model for bubble-induced turbulence in the Euler-Euler Reynolds-averaged framework. First, an appropriate time scale is selected. Second, links between the unclosed terms in the transport equations of the turbulence quantities and the DNS data for small bubbles are established. Third, a suitably chosen iterative procedure employing the full Reynolds-averaged model provides suitable coefficients for the closure of the terms resulting from bubble-induced turbulence while largely removing the influence of others. At the same time these results validate the closure, exhibiting very good agreement with the DNS and better performance than the standard closures. The model is now ready for use and can be employed in practical Euler-Euler simulations.
NASA Astrophysics Data System (ADS)
Helfand, H. M.; Labraga, J. C.
1988-01-01
The behavior of the Mellor and Yamada Level 2.5 second-order turbulence closure model is analyzed over its entire domain of definition on the Ri × q2/qe2 plane, where Ri is the Richardson number of the mean flow and where q2/qe2 is the ratio of the turbulent kinetic energy predicted by the model to that which would obtain in a state of local equilibrium. The Level 2.5 model is reasonably accurate over the subdomain q2/qe2 1, but it becomes unrealistic and pathological for the case of decaying turbulence (q2/qe2 < 1).The model is modified for the case of growing turbulence to rectify some of its physical shortcomings for that case, and to remove the pathologies that prohibit its use in a general circulation model. The modified model attempts to take into account the effects of the growth rate, advection and vertical turbulent diffusion terms in the balance equations for all of the second moments, as well as the effects of the rapid return-to-isotropy or scrambling terms in the equations for the anisotropic components of the moments.The performance of the modified Level 2.5 model has been tested and compared to the performance of various other modified versions of the model through the numerical simulation of a growing convective planetary boundary layer. The modified Level 2.5 model gives a realistic-looking simulation of the evolution of the second turbulent moments at the 300 m level. The scheme approaches the same asymptotic state as does the turbulent kinetic energy adjustment scheme, but the modified Level 2.5 model predicts a longer period of transience. The TKE-adjustment scheme reduces to the Level 2 model during the growth phase of turbulence. The other schemes, with one exception, either cause the integration to blow up or to result in an obviously nonphysical simulation of the planetary boundary layer dynamics.The modified Level 2.5 model is proposed as a viable candidate for the prediction of turbulence and the simulation of the planetary boundary layer
Optimization and large scale computation of an entropy-based moment closure
Hauck, Cory D.; Hill, Judith C.; Garrett, C. Kristopher
2015-09-10
We present computational advances and results in the implementation of an entropy-based moment closure, M_{N}, in the context of linear kinetic equations, with an emphasis on heterogeneous and large-scale computing platforms. Entropy-based closures are known in several cases to yield more accurate results than closures based on standard spectral approximations, such as P_{N}, but the computational cost is generally much higher and often prohibitive. Several optimizations are introduced to improve the performance of entropy-based algorithms over previous implementations. These optimizations include the use of GPU acceleration and the exploitation of the mathematical properties of spherical harmonics, which are used as test functions in the moment formulation. To test the emerging high-performance computing paradigm of communication bound simulations, we present timing results at the largest computational scales currently available. Lastly, these results show, in particular, load balancing issues in scaling the M_{N} algorithm that do not appear for the P_{N} algorithm. We also observe that in weak scaling tests, the ratio in time to solution of M_{N} to P_{N} decreases.
Optimization and large scale computation of an entropy-based moment closure
Hauck, Cory D.; Hill, Judith C.; Garrett, C. Kristopher
2015-09-10
We present computational advances and results in the implementation of an entropy-based moment closure, MN, in the context of linear kinetic equations, with an emphasis on heterogeneous and large-scale computing platforms. Entropy-based closures are known in several cases to yield more accurate results than closures based on standard spectral approximations, such as PN, but the computational cost is generally much higher and often prohibitive. Several optimizations are introduced to improve the performance of entropy-based algorithms over previous implementations. These optimizations include the use of GPU acceleration and the exploitation of the mathematical properties of spherical harmonics, which are used asmore » test functions in the moment formulation. To test the emerging high-performance computing paradigm of communication bound simulations, we present timing results at the largest computational scales currently available. Lastly, these results show, in particular, load balancing issues in scaling the MN algorithm that do not appear for the PN algorithm. We also observe that in weak scaling tests, the ratio in time to solution of MN to PN decreases.« less
Optimization and large scale computation of an entropy-based moment closure
NASA Astrophysics Data System (ADS)
Kristopher Garrett, C.; Hauck, Cory; Hill, Judith
2015-12-01
We present computational advances and results in the implementation of an entropy-based moment closure, MN, in the context of linear kinetic equations, with an emphasis on heterogeneous and large-scale computing platforms. Entropy-based closures are known in several cases to yield more accurate results than closures based on standard spectral approximations, such as PN, but the computational cost is generally much higher and often prohibitive. Several optimizations are introduced to improve the performance of entropy-based algorithms over previous implementations. These optimizations include the use of GPU acceleration and the exploitation of the mathematical properties of spherical harmonics, which are used as test functions in the moment formulation. To test the emerging high-performance computing paradigm of communication bound simulations, we present timing results at the largest computational scales currently available. These results show, in particular, load balancing issues in scaling the MN algorithm that do not appear for the PN algorithm. We also observe that in weak scaling tests, the ratio in time to solution of MN to PN decreases.
Simulations of Nocturnal Drainage Flows by a q2l Turbulence Closure Model.
NASA Astrophysics Data System (ADS)
Yamada, T.
1983-01-01
Nocturnal drainage flows observed over a nearly two-dimensional ridge called Rattlesnake Hills near Richland, Washington are simulated by using a simplified turbulence closure model in which only turbulence kinetic energy and turbulence length scale equations are solved prognostically. The present model is slightly simpler than a level 2.5 model which has been extensively used in previous simulations of various atmospheric boundary layer phenomena. Wind and temperature profiles computed by the present model are generally in excellent agreement with observations made by towers erected on the slope of Rattlesnake Hills. Strong coupling between the mean and turbulence variables is also demonstrated.
Simulations of nocturnal drainage flows by a q/sup 2/l turbulence closure model
Yamada, T.
1983-01-01
Nocturnal drainage flows observed over a nearly two-dimensional ridge called Rattlesnake Hills near Richland, Washington are simulated by using a simplified turbulence closure model in which only turbulence kinetic energy and turbulence length scale equations are solved prognostically. The present model is slightly simpler than a level 2.5 model which has been extensively used in previous simulations of various atmospheric boundary layer phenomena. Wind and temperature profiles computed by the present model are generally in excellent agreement with observations made by towers erected on the slope of Rattlesnake Hills. Strong coupling between the mean and turbulence variables is also demonstrated.
NASA Astrophysics Data System (ADS)
Hendrickson, Kelli; Yue, Dick
2016-11-01
This work presents the development and a priori testing of closure models for the incompressible highly-variable density turbulent (IHVDT) flow in the near wake region of a transom stern. This complex, three-dimensional flow includes three regions with distinctly different flow behavior: (i) the convergent corner waves that originate from the body and collide on the ship center plane; (ii) the "rooster tail" that forms from the collision; and (iii) the diverging wave train. The characteristics of these regions involve violent free-surface flows and breaking waves with significant turbulent mass flux (TMF) at Atwood number At = (ρ2 -ρ1) / (ρ2 +ρ1) 1 for which there is little guidance in turbulence closure modeling for the momentum and scalar transport along the wake. Utilizing datasets from high-resolution simulations of the near wake of a canonical three-dimensional transom stern using conservative Volume-of-Fluid (cVOF), implicit Large Eddy Simulation (iLES), and Boundary Data Immersion Method (BDIM), we develop explicit algebraic turbulent mass flux closure models that incorporate the most relevant physical processes. Performance of these models in predicting the turbulent mass flux in all three regions of the wake will be presented. Office of Naval Research.
Elliptic blending model: A new near-wall Reynolds-stress turbulence closure
NASA Astrophysics Data System (ADS)
Manceau, Rémi; Hanjalić, Kemal
2002-02-01
A new approach to modeling the effects of a solid wall in one-point second-moment (Reynolds-stress) turbulence closures is presented. The model is based on the relaxation of an inhomogeneous (near-wall) formulation of the pressure-strain tensor towards the chosen conventional homogeneous (far-from-a-wall) form using the blending function α, for which an elliptic equation is solved. The approach preserves the main features of Durbin's Reynolds-stress model, but instead of six elliptic equations (for each stress component), it involves only one, scalar elliptic equation. The model, called "the elliptic blending model," offers significant simplification, while still complying with the basic physical rationale for the elliptic relaxation concept. In addition to model validation against direct numerical simulation in a plane channel for Reτ=590, the model was applied in the computation of the channel flow at a "real-life" Reynolds number of 106, showing a good prediction of the logarithmic profile of the mean velocity.
Measurements of turbulence moments in boundary layers over transversely grooved surfaces
NASA Technical Reports Server (NTRS)
Bandyopadhyay, P. R.; Watson, R. D.
1987-01-01
Wind tunnel measurements of second, third, and fourth order turbulence moments in turbulent boundary layers over d-types and k-types of grooved and smooth surfaces are discussed. The near-wall turbulence structure is found to vary with the spanwise aspect ratio. For decreasing height, the third moment of the normal velocity fluctuations is shown to become negative over crop canopies and model plant canopies, although not in smooth, two-dimensional, sandgrain or gravel roughness. The instantaneous motions related to the flux of shear stress near the wall in smooth and transversely grooved surfaces are shown to be opposite in sign to those in three-dimensional roughness.
NASA Astrophysics Data System (ADS)
Laplante, Jérémie; Groth, Clinton P. T.
2016-11-01
The Navier-Stokes-Fourier (NSF) equations are conventionally used to model continuum flow near local thermodynamic equilibrium. In the presence of more rarefied flows, there exists a transitional regime in which the NSF equations no longer hold, and where particle-based methods become too expensive for practical problems. To close this gap, moment closure techniques having the potential of being both valid and computationally tractable for these applications are sought. In this study, a number of five-moment closures for a model one-dimensional kinetic equation are assessed and compared. In particular, four different moment closures are applied to the solution of stationary shocks. The first of these is a Grad-type moment closure, which is known to fail for moderate departures from equilibrium. The second is an interpolative closure based on maximization of thermodynamic entropy which has previously been shown to provide excellent results for 1D gaskinetic theory. Additionally, two quadrature methods of moments (QMOM) are considered. One method is based on the representation of the distribution function in terms of a combination of three Dirac delta functions. The second method, an extended QMOM (EQMOM), extends the quadrature-based approach by assuming a bi-Maxwellian representation of the distribution function. The closing fluxes are analyzed in each case and the region of physical realizability is examined for the closures. Numerical simulations of stationary shock structures as predicted by each moment closure are compared to reference kinetic and the corresponding NSF-like equation solutions. It is shown that the bi-Maxwellian and interpolative maximum-entropy-based moment closures are able to closely reproduce the results of the true maximum-entropy distribution closure for this case very well, whereas the other methods do not. For moderate departures from local thermodynamic equilibrium, the Grad-type and QMOM closures produced unphysical subshocks and were
Uncertainty Quantification of Turbulence Model Closure Coefficients for Transonic Wall-Bounded Flows
NASA Technical Reports Server (NTRS)
Schaefer, John; West, Thomas; Hosder, Serhat; Rumsey, Christopher; Carlson, Jan-Renee; Kleb, William
2015-01-01
The goal of this work was to quantify the uncertainty and sensitivity of commonly used turbulence models in Reynolds-Averaged Navier-Stokes codes due to uncertainty in the values of closure coefficients for transonic, wall-bounded flows and to rank the contribution of each coefficient to uncertainty in various output flow quantities of interest. Specifically, uncertainty quantification of turbulence model closure coefficients was performed for transonic flow over an axisymmetric bump at zero degrees angle of attack and the RAE 2822 transonic airfoil at a lift coefficient of 0.744. Three turbulence models were considered: the Spalart-Allmaras Model, Wilcox (2006) k-w Model, and the Menter Shear-Stress Trans- port Model. The FUN3D code developed by NASA Langley Research Center was used as the flow solver. The uncertainty quantification analysis employed stochastic expansions based on non-intrusive polynomial chaos as an efficient means of uncertainty propagation. Several integrated and point-quantities are considered as uncertain outputs for both CFD problems. All closure coefficients were treated as epistemic uncertain variables represented with intervals. Sobol indices were used to rank the relative contributions of each closure coefficient to the total uncertainty in the output quantities of interest. This study identified a number of closure coefficients for each turbulence model for which more information will reduce the amount of uncertainty in the output significantly for transonic, wall-bounded flows.
Allam, A.M.; Crichlow, H.B.; Soliman, M.Y.
1981-01-01
A numerical technique for analyzing the behavior of a fractured gas reservoir system is presented. The reservoir is simulated by a fully implicit three-dimensional model that incorporates the effects of turbulent flow and closure stress in a finite conductivity fracture. The model utilizes the real gas pseudo-pressure, two-point upstream transmissibilities and a stable iterative process based on a sparse matrix approach to solving the equation systems. This paper presents a description of the model and applications to various reservoirs to illustrate the effects of fracture heights, turbulence and closure pressure on well performance. 16 refs.
Analytical methods for the development of Reynolds stress closures in turbulence
NASA Technical Reports Server (NTRS)
Speziale, Charles G.
1990-01-01
Analytical methods for the development of Reynolds stress models in turbulence are reviewed in detail. Zero, one and two equation models are discussed along with second-order closures. A strong case is made for the superior predictive capabilities of second-order closure models in comparison to the simpler models. The central points are illustrated by examples from both homogeneous and inhomogeneous turbulence. A discussion of the author's views concerning the progress made in Reynolds stress modeling is also provided along with a brief history of the subject.
NASA Astrophysics Data System (ADS)
Fabijonas, Bruce R.; Holm, Darryl D.
2004-04-01
The Craik-Criminale class of exact solutions is examined for a nonlinear-reactive fluids theory that includes a family of turbulence closure models. These may be formally regarded as either large eddy simulation or Reynolds-averaged Navier-Stokes models of turbulence. All of the turbulence closure models in the class under investigation preserve the existence of elliptic instability, although they shift its angle of critical stability as a function of the rotation rate Ω of the coordinate system, the wave number β of the Kelvin wave, and the model parameter α, the turbulence correlation length. Elliptic instability allows a comparison among the properties of these models. It is emphasized that the physical mechanism for this instability is not wave-wave interaction, but rather wave, mean-flow interaction as governed by the choice of a model's nonlinearity.
Closure of a kinetic model of plasma in strong turbulence by relaxation
NASA Technical Reports Server (NTRS)
Tchen, C. M.
1978-01-01
A Fokker-Planck kinetic equation for a turbulent plasma is derived by a repeated cascade decomposition. Calculation of the propagator and the kinetic equation determine the transport coefficients (diffusivity and turbulent viscosity) by means of a closure based on a relaxation procedure governing the approach to equilibrium. The k to the minus third power spectral law is obtained, which governs the coupling between the velocity and the electrostatic field fluctuations.
Fluid simulation of tokamak ion temperature gradient turbulence with zonal flow closure model
NASA Astrophysics Data System (ADS)
Yamagishi, Osamu; Sugama, Hideo
2016-03-01
Nonlinear fluid simulation of turbulence driven by ion temperature gradient modes in the tokamak fluxtube configuration is performed by combining two different closure models. One model is a gyrofluid model by Beer and Hammett [Phys. Plasmas 3, 4046 (1996)], and the other is a closure model to reproduce the kinetic zonal flow response [Sugama et al., Phys. Plasmas 14, 022502 (2007)]. By including the zonal flow closure, generation of zonal flows, significant reduction in energy transport, reproduction of the gyrokinetic transport level, and nonlinear upshift on the critical value of gradient scale length are observed.
Fluid simulation of tokamak ion temperature gradient turbulence with zonal flow closure model
Yamagishi, Osamu Sugama, Hideo
2016-03-15
Nonlinear fluid simulation of turbulence driven by ion temperature gradient modes in the tokamak fluxtube configuration is performed by combining two different closure models. One model is a gyrofluid model by Beer and Hammett [Phys. Plasmas 3, 4046 (1996)], and the other is a closure model to reproduce the kinetic zonal flow response [Sugama et al., Phys. Plasmas 14, 022502 (2007)]. By including the zonal flow closure, generation of zonal flows, significant reduction in energy transport, reproduction of the gyrokinetic transport level, and nonlinear upshift on the critical value of gradient scale length are observed.
Puleo, J.A.; Mouraenko, O.; Hanes, D.M.
2004-01-01
Six one-dimensional-vertical wave bottom boundary layer models are analyzed based on different methods for estimating the turbulent eddy viscosity: Laminar, linear, parabolic, k—one equation turbulence closure, k−ε—two equation turbulence closure, and k−ω—two equation turbulence closure. Resultant velocity profiles, bed shear stresses, and turbulent kinetic energy are compared to laboratory data of oscillatory flow over smooth and rough beds. Bed shear stress estimates for the smooth bed case were most closely predicted by the k−ω model. Normalized errors between model predictions and measurements of velocity profiles over the entire computational domain collected at 15° intervals for one-half a wave cycle show that overall the linear model was most accurate. The least accurate were the laminar and k−ε models. Normalized errors between model predictions and turbulence kinetic energy profiles showed that the k−ω model was most accurate. Based on these findings, when the smallest overall velocity profile prediction error is required, the processing requirements and error analysis suggest that the linear eddy viscosity model is adequate. However, if accurate estimates of bed shear stress and TKE are required then, of the models tested, the k−ω model should be used.
Second-order closure PBL model with new third-order moments: Comparison with LES data
NASA Technical Reports Server (NTRS)
Canuto, V. M.; Minotti, F.; Ronchi, C.; Ypma, R. M.; Zeman, O.
1994-01-01
This paper contains two parts. In the first part, a new set of diagnostic equations is derived for the third-order moments for a buoyancy-driven flow, by exact inversion of the prognostic equations for the third-order moment equations in the stationary case. The third-order moments exhibit a universal structure: they all are a linear combination of the derivatives of all the second-order moments, bar-w(exp 2), bar-w theta, bar-theta(exp 2), and bar-q(exp 2). Each term of the sum contains a turbulent diffusivity D(sub t), which also exhibits a universal structure of the form D(sub t) = a nu(sub t) + b bar-w theta. Since the sign of the convective flux changes depending on stable or unstable stratification, D(sub t) varies according to the type of stratification. Here nu(sub t) approximately equal to wl (l is a mixing length and w is an rms velocity) represents the 'mechanical' part, while the 'buoyancy' part is represented by the convective flux bar-w theta. The quantities a and b are functions of the variable N(sub tau)(exp 2), where N(exp 2) = g alpha derivative of Theta with respect to z and tau is the turbulence time scale. The new expressions for the third-order moments generalize those of Zeman and Lumley, which were subsequently adopted by Sun and Ogura, Chen and Cotton, and Finger and Schmidt in their treatments of the convective boundary layer. In the second part, the new expressions for the third-order moments are used to solve the ensemble average equations describing a purely convective boundary laye r heated from below at a constant rate. The computed second- and third-order moments are then compared with the corresponding Large Eddy Simulation (LES) results, most of which are obtained by running a new LES code, and part of which are taken from published results. The ensemble average results compare favorably with the LES data.
Second-order closure PBL model with new third-order moments: Comparison with LES data
NASA Technical Reports Server (NTRS)
Canuto, V. M.; Minotti, F.; Ronchi, C.; Ypma, R. M.; Zeman, O.
1994-01-01
This paper contains two parts. In the first part, a new set of diagnostic equations is derived for the third-order moments for a buoyancy-driven flow, by exact inversion of the prognostic equations for the third-order moment equations in the stationary case. The third-order moments exhibit a universal structure: they all are a linear combination of the derivatives of all the second-order moments, bar-w(exp 2), bar-w theta, bar-theta(exp 2), and bar-q(exp 2). Each term of the sum contains a turbulent diffusivity D(sub t), which also exhibits a universal structure of the form D(sub t) = a nu(sub t) + b bar-w theta. Since the sign of the convective flux changes depending on stable or unstable stratification, D(sub t) varies according to the type of stratification. Here nu(sub t) approximately equal to wl (l is a mixing length and w is an rms velocity) represents the 'mechanical' part, while the 'buoyancy' part is represented by the convective flux bar-w theta. The quantities a and b are functions of the variable N(sub tau)(exp 2), where N(exp 2) = g alpha derivative of Theta with respect to z and tau is the turbulence time scale. The new expressions for the third-order moments generalize those of Zeman and Lumley, which were subsequently adopted by Sun and Ogura, Chen and Cotton, and Finger and Schmidt in their treatments of the convective boundary layer. In the second part, the new expressions for the third-order moments are used to solve the ensemble average equations describing a purely convective boundary laye r heated from below at a constant rate. The computed second- and third-order moments are then compared with the corresponding Large Eddy Simulation (LES) results, most of which are obtained by running a new LES code, and part of which are taken from published results. The ensemble average results compare favorably with the LES data.
Hamiltonian fluid closures of the Vlasov-Ampère equations: From water-bags to N moment models
Perin, M.; Chandre, C.; Tassi, E.; Morrison, P. J.
2015-09-15
Moment closures of the Vlasov-Ampère system, whereby higher moments are represented as functions of lower moments with the constraint that the resulting fluid system remains Hamiltonian, are investigated by using water-bag theory. The link between the water-bag formalism and fluid models that involve density, fluid velocity, pressure and higher moments is established by introducing suitable thermodynamic variables. The cases of one, two, and three water-bags are treated and their Hamiltonian structures are provided. In each case, we give the associated fluid closures and we discuss their Casimir invariants. We show how the method can be extended to an arbitrary number of fields, i.e., an arbitrary number of water-bags and associated moments. The thermodynamic interpretation of the resulting models is discussed. Finally, a general procedure to derive Hamiltonian N-field fluid models is proposed.
Three-dimensional structures and turbulence closure of the wake developing in a wall shear layer
NASA Technical Reports Server (NTRS)
Hah, C.
1981-01-01
The turbulent wake interacting with the rotating wall shear layer is investigated analytically and numerically. The turbulent wakes of the rotating blades in a compressor which are interacting with the rotating hub-wall boundary layer are analyzed. A modified version of the closure model of the pressure-strain correlation term in the Reynolds stress transport equation is developed to predict the effect of rotation, which is appreciable for the present flow because the thick hub-wall boundary layer is interacting with the rotor wake. It is noted that the Poisson type equation for the pressure-strain correlation has an extra rotation term when the entire flow field is rotating. This extra rotation term is modeled to accommodate the effect of rotation. In addition, the standard correction for the wall effect is incorporated for the utilized Reynolds stress closure model. The rotation-modified Reynolds stress closure model is used to predict the present flow, and the predictions are compared with the experimental data. The experimental data reveal that the characteristics of the three-dimensional turbulent wake interacting with the wall shear layer are considerably altered by the effects of the wall and the rotation. These features are predicted with good accuracy by the turbulence closure model developed.
USDA-ARS?s Scientific Manuscript database
The lack of energy closure has been a longstanding issue with Eddy Covariance (EC). Multiple mechanisms have been proposed to explain the discrepancies in energy balance including diurnal energy storage changes, advection of energy, and larger scale turbulent processes that cannot be resolved by fi...
Navier-Stokes computation of compressible turbulent flows with a second order closure, part 1
NASA Technical Reports Server (NTRS)
Haminh, Hieu; Kollmann, Wolfgang; Vandromme, Dany
1990-01-01
A second order closure turbulence model for compressible flows is developed and implemented in a 2D Reynolds-averaged Navier-Stokes solver. From the beginning where a kappa-epsilon turbulence model was implemented in the bidiagonal implicit method of MACCORMACK (referred to as the MAC3 code) to the final stage of implementing a full second order closure in the efficient line Gauss-Seidel algorithm, numerous work was done, individually and collectively. Besides the collaboration itself, the final product of this work is a second order closure derived from the Launder, Reece, and Rodi model to account for near wall effects, which has been called FRAME model, which stands for FRench-AMerican-Effort. During the reporting period, two different problems were worked out. The first was to provide Ames researchers with a reliable compressible boundary layer code including a wide collection of turbulence models for quick testing of new terms, both in two equations and in second order closure (LRR and FRAME). The second topic was to complete the implementation of the FRAME model in the MAC5 code. The work related to these two different contributions is reported. dilatation in presence of stron shocks. This work, which has been conducted during a work at the Center for Turbulence Research with Zeman aimed also to cros-check earlier assumptions by Rubesin and Vandromme.
USDA-ARS?s Scientific Manuscript database
The lack of energy closure has been a longstanding issue with Eddy Covariance (EC). Multiple mechanisms have been proposed to explain the discrepancies in energy balance including diurnal energy storage changes, advection of energy, and larger scale turbulent processes that cannot be resolved by fi...
About the coupling of turbulence closure models with averaged Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Vandromme, D.; Ha Minh, H.
1986-01-01
The MacCormack implicit predictor-corrector model (1981) for numerical solution of the coupled Navier-Stokes equations for turbulent flows is extended to nonconservative multiequation turbulence models, as well as the inclusion of second-order Reynolds stress turbulence closure. A scalar effective pressure turbulent contribution to the pressure field is defined to approximate the effects of the Reynolds stress in strongly sheared flows. The Jacobian matrices of the transport equations are diagonalized to reduce the required computer memory and run time. Techniques are defined for including turbulence in the diagonalization. Application of the method is demonstrated with solutions generated for transonic nozzle flow and for the interaction between a supersonic flat plate boundary layer and a 12 deg compression-expansion ramp.
About the coupling of turbulence closure models with averaged Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Vandromme, D.; Ha Minh, H.
1986-01-01
The MacCormack implicit predictor-corrector model (1981) for numerical solution of the coupled Navier-Stokes equations for turbulent flows is extended to nonconservative multiequation turbulence models, as well as the inclusion of second-order Reynolds stress turbulence closure. A scalar effective pressure turbulent contribution to the pressure field is defined to approximate the effects of the Reynolds stress in strongly sheared flows. The Jacobian matrices of the transport equations are diagonalized to reduce the required computer memory and run time. Techniques are defined for including turbulence in the diagonalization. Application of the method is demonstrated with solutions generated for transonic nozzle flow and for the interaction between a supersonic flat plate boundary layer and a 12 deg compression-expansion ramp.
LES-Modeling of a Partially Premixed Flame using a Deconvolution Turbulence Closure
NASA Astrophysics Data System (ADS)
Wang, Qing; Wu, Hao; Ihme, Matthias
2015-11-01
The modeling of the turbulence/chemistry interaction in partially premixed and multi-stream combustion remains an outstanding issue. By extending a recently developed constrained minimum mean-square error deconvolution (CMMSED) method, to objective of this work is to develop a source-term closure for turbulent multi-stream combustion. In this method, the chemical source term is obtained from a three-stream flamelet model, and CMMSED is used as closure model, thereby eliminating the need for presumed PDF-modeling. The model is applied to LES of a piloted turbulent jet flame with inhomogeneous inlets, and simulation results are compared with experiments. Comparisons with presumed PDF-methods are performed, and issues regarding resolution and conservation of the CMMSED method are examined. The author would like to acknowledge the support of funding from Stanford Graduate Fellowship.
Prediction of High-Lift Flows using Turbulent Closure Models
NASA Technical Reports Server (NTRS)
Rumsey, Christopher L.; Gatski, Thomas B.; Ying, Susan X.; Bertelrud, Arild
1997-01-01
The flow over two different multi-element airfoil configurations is computed using linear eddy viscosity turbulence models and a nonlinear explicit algebraic stress model. A subset of recently-measured transition locations using hot film on a McDonnell Douglas configuration is presented, and the effect of transition location on the computed solutions is explored. Deficiencies in wake profile computations are found to be attributable in large part to poor boundary layer prediction on the generating element, and not necessarily inadequate turbulence modeling in the wake. Using measured transition locations for the main element improves the prediction of its boundary layer thickness, skin friction, and wake profile shape. However, using measured transition locations on the slat still yields poor slat wake predictions. The computation of the slat flow field represents a key roadblock to successful predictions of multi-element flows. In general, the nonlinear explicit algebraic stress turbulence model gives very similar results to the linear eddy viscosity models.
Performance of four turbulence closure models implemented using a generic length scale method
Warner, J.C.; Sherwood, C.R.; Arango, H.G.; Signell, R.P.
2005-01-01
A two-equation turbulence model (one equation for turbulence kinetic energy and a second for a generic turbulence length-scale quantity) proposed by Umlauf and Burchard [J. Marine Research 61 (2003) 235] is implemented in a three-dimensional oceanographic model (Regional Oceanographic Modeling System; ROMS v2.0). These two equations, along with several stability functions, can represent many popular turbulence closures, including the k-kl (Mellor-Yamada Level 2.5), k-??, and k-?? schemes. The implementation adds flexibility to the model by providing an unprecedented range of turbulence closure selections in a single 3D oceanographic model and allows comparison and evaluation of turbulence models in an otherwise identical numerical environment. This also allows evaluation of the effect of turbulence models on other processes such as suspended-sediment distribution or ecological processes. Performance of the turbulence models and sediment-transport schemes is investigated with three test cases for (1) steady barotropic flow in a rectangular channel, (2) wind-induced surface mixed-layer deepening in a stratified fluid, and (3) oscillatory stratified pressure-gradient driven flow (estuarine circulation) in a rectangular channel. Results from k-??, k-??, and gen (a new closure proposed by Umlauf and Burchard [J. Marine Research 61 (2003) 235]) are very similar for these cases, but the k-kl closure results depend on a wall-proximity function that must be chosen to suit the flow. Greater variations appear in simulations of suspended-sediment concentrations than in salinity simulations because the transport of suspended-sediment amplifies minor variations in the methods. The amplification is caused by the added physics of a vertical settling rate, bottom stress dependent resuspension, and diffusive transport of sediment in regions of well mixed salt and temperature. Despite the amplified sensitivity of sediment to turbulence models in the estuary test case, the four
Inference of turbulence parameters from a ROMS simulation using the k-ε closure scheme
NASA Astrophysics Data System (ADS)
Thyng, Kristen M.; Riley, James J.; Thomson, Jim
2013-12-01
Comparisons between high resolution turbulence data from Admiralty Inlet, WA (USA), and a 65-meter horizontal grid resolution simulation using the hydrostatic ocean modelling code, Regional Ocean Modeling System (ROMS), show that the model's k-ε turbulence closure scheme performs reasonably well. Turbulent dissipation rates and Reynolds stresses agree within a factor of two, on average. Turbulent kinetic energy (TKE) also agrees within a factor of two, but only for motions within the observed inertial sub-range of frequencies (i.e., classic approximately isotropic turbulence). TKE spectra from the observations indicate that there is significant energy at lower frequencies than the inertial sub-range; these scales are not captured by the model closure scheme nor the model grid resolution. To account for scales not present in the model, the inertial sub-range is extrapolated to lower frequencies and then integrated to obtain an inferred, diagnostic total TKE, with improved agreement with the observed total TKE. The realistic behavior of the dissipation rate and Reynolds stress, combined with the adjusted total TKE, imply that ROMS simulations can be used to understand and predict spatial and temporal variations in turbulence. The results are suggested for application to siting tidal current turbines.
Modeling of turbulent chemical reaction
NASA Technical Reports Server (NTRS)
Chen, J.-Y.
1995-01-01
Viewgraphs are presented on modeling turbulent reacting flows, regimes of turbulent combustion, regimes of premixed and regimes of non-premixed turbulent combustion, chemical closure models, flamelet model, conditional moment closure (CMC), NO(x) emissions from turbulent H2 jet flames, probability density function (PDF), departures from chemical equilibrium, mixing models for PDF methods, comparison of predicted and measured H2O mass fractions in turbulent nonpremixed jet flames, experimental evidence of preferential diffusion in turbulent jet flames, and computation of turbulent reacting flows.
NASA Astrophysics Data System (ADS)
Anderson, R. G.; Wang, D.
2012-12-01
Eddy Covariance (EC) is widely used for direct, non-invasive observations of land-atmosphere energy and mass fluxes. However, EC observations of available energy fluxes are usually less than fluxes inferred from radiometer and soil heat flux observations; thus introducing additional uncertainty in using and interpreting EC flux measurements. We compare EC observations from two towers established over sugarcane (Saccharum officinarum L.) in Hawai'i, USA under similar cultivation, temperature, sunlight, and precipitation, but drastically different wind conditions due to orographic effects. At a daily scale, we find that energy closure for both towers occurs on days when the entire 24 hours has sufficient turbulence. At our windier site, this turbulence condition occurs over 60% of the time, which contributes to substantially better daily energy closure (~98%) than at the calmer site (~75%). At our windy site, we then invert the daily energy closure for continuously windy days to calculate canopy energy storage. At full canopy, peak daily canopy energy storage fluxes (200-400 Wm-2) are approximately an order of magnitude larger than soil heat flux (20-40 Wm-2). As a fraction of net radiation, canopy energy storage appears to vary seasonally and shows substantially greater variability than soil heat flux. The results illustrate the importance of sustained turbulence for accurate, direct measurement of land-atmosphere fluxes. As increasing number of EC towers are established in complex terrain, these results indicate the need for preliminary wind studies to optimize tower placement where orography enhances, rather than suppresses, turbulence.
A compressible Navier-Stokes solver with two-equation and Reynolds stress turbulence closure models
NASA Technical Reports Server (NTRS)
Morrison, Joseph H.
1992-01-01
This report outlines the development of a general purpose aerodynamic solver for compressible turbulent flows. Turbulent closure is achieved using either two equation or Reynolds stress transportation equations. The applicable equation set consists of Favre-averaged conservation equations for the mass, momentum and total energy, and transport equations for the turbulent stresses and turbulent dissipation rate. In order to develop a scheme with good shock capturing capabilities, good accuracy and general geometric capabilities, a multi-block cell centered finite volume approach is used. Viscous fluxes are discretized using a finite volume representation of a central difference operator and the source terms are treated as an integral over the control volume. The methodology is validated by testing the algorithm on both two and three dimensional flows. Both the two equation and Reynolds stress models are used on a two dimensional 10 degree compression ramp at Mach 3, and the two equation model is used on the three dimensional flow over a cone at angle of attack at Mach 3.5. With the development of this algorithm, it is now possible to compute complex, compressible high speed flow fields using both two equation and Reynolds stress turbulent closure models, with the capability of eventually evaluating their predictive performance.
Two-Point Turbulence Closure Applied to Variable Resolution Modeling
NASA Technical Reports Server (NTRS)
Girimaji, Sharath S.; Rubinstein, Robert
2011-01-01
Variable resolution methods have become frontline CFD tools, but in order to take full advantage of this promising new technology, more formal theoretical development is desirable. Two general classes of variable resolution methods can be identified: hybrid or zonal methods in which RANS and LES models are solved in different flow regions, and bridging or seamless models which interpolate smoothly between RANS and LES. This paper considers the formulation of bridging methods using methods of two-point closure theory. The fundamental problem is to derive a subgrid two-equation model. We compare and reconcile two different approaches to this goal: the Partially Integrated Transport Model, and the Partially Averaged Navier-Stokes method.
NASA Astrophysics Data System (ADS)
Ralston, David K.; Cowles, Geoffrey W.; Geyer, W. Rockwell; Holleman, Rusty C.
2017-01-01
The Connecticut River is a tidal salt wedge estuary, where advection of sharp salinity gradients through channel constrictions and over steeply sloping bathymetry leads to spatially heterogeneous stratification and mixing. A 3-D unstructured grid finite-volume hydrodynamic model (FVCOM) was evaluated against shipboard and moored observations, and mixing by both the turbulent closure and numerical diffusion were calculated. Excessive numerical mixing in regions with strong velocities, sharp salinity gradients, and steep bathymetry reduced model skill for salinity. Model calibration was improved by optimizing both the bottom roughness (z0), based on comparison with the barotropic tidal propagation, and the mixing threshold in the turbulence closure (steady state Richardson number, Rist), based on comparison with salinity. Whereas a large body of evidence supports a value of Rist ˜ 0.25, model skill for salinity improved with Rist ˜ 0.1. With Rist = 0.25, numerical mixing contributed about 1/2 the total mixing, while with Rist = 0.10 it accounted for ˜2/3, but salinity structure was more accurately reproduced. The combined contributions of numerical and turbulent mixing were quantitatively consistent with high-resolution measurements of turbulent mixing. A coarser grid had increased numerical mixing, requiring further reductions in turbulent mixing and greater bed friction to optimize skill. The optimal Rist for the fine grid case was closer to 0.25 than for the coarse grid, suggesting that additional grid refinement might correspond with Rist approaching the theoretical limit. Numerical mixing is rarely assessed in realistic models, but comparisons with high-resolution observations in this study suggest it is an important factor.
On the consistency of Reynolds stress turbulence closures with hydrodynamic stability theory
NASA Technical Reports Server (NTRS)
Speziale, Charles G.; Abid, Ridha; Blaisdell, Gregory A.
1995-01-01
The consistency of second-order closure models with results from hydrodynamic stability theory is analyzed for the simplified case of homogeneous turbulence. In a recent study, Speziale, Gatski, and MacGiolla Mhuiris showed that second-order closures are capable of yielding results that are consistent with hydrodynamic stability theory for the case of homogeneous shear flow in a rotating frame. It is demonstrated in this paper that this success is due to the fact that the stability boundaries for rotating homogeneous shear flow are not dependent on the details of the spatial structure of the disturbances. For those instances where they are -- such as in the case of elliptical flows where the instability mechanism is more subtle -- the results are not so favorable. The origins and extent of this modeling problem are examined in detail along with a possible resolution based on rapid distortion theory (RDT) and its implications for turbulence modeling.
Critical examination of two-equation turbulence closure models
NASA Technical Reports Server (NTRS)
Chambers, T. L.; Wilcox, D. C.
1976-01-01
Comparison of the Jones-Launder, Ng-Spalding, Saffman-Wilcox, and Wilcox-Traci two-equation turbulence models has been conducted. It was shown that the Saffman-Wilcox and Wilcox-Traci dissipation-rate formulations admit straightforward integration through the viscous sublayer, whereas integration through the viscous sublayer is a more difficult issue with the Jones-Launder dissipation-function and the Ng-Spalding length-scale formulations. Numerical computations were conducted in which the models were applied to four equilibrium boundary layer flows including adverse, zero, and favorable pressure gradients. Computations of zero pressure gradient flow over a convex wall composed the final part of the comparison.
NASA Astrophysics Data System (ADS)
Wang, Minghuai; Larson, Vincent E.; Ghan, Steven; Ovchinnikov, Mikhail; Schanen, David P.; Xiao, Heng; Liu, Xiaohong; Rasch, Philip; Guo, Zhun
2015-06-01
In this study, a higher-order turbulence closure scheme, called Cloud Layers Unified By Binormals (CLUBB), is implemented into a Multiscale Modeling Framework (MMF) model to improve low-cloud simulations. The performance of CLUBB in MMF simulations with two different microphysics configurations (one-moment cloud microphysics without aerosol treatment and two-moment cloud microphysics coupled with aerosol treatment) is evaluated against observations and further compared with results from the Community Atmosphere Model, Version 5 (CAM5) with conventional cloud parameterizations. CLUBB is found to improve low-cloud simulations in the MMF, and the improvement is particularly evident in the stratocumulus-to-cumulus transition regions. Compared to the single-moment cloud microphysics, CLUBB with two-moment microphysics produces clouds that are closer to the coast and agrees better with observations. In the stratocumulus-to-cumulus transition regions, CLUBB with two-moment cloud microphysics produces short-wave cloud forcing in better agreement with observations, while CLUBB with single-moment cloud microphysics overestimates short-wave cloud forcing. CLUBB is further found to produce quantitatively similar improvements in the MMF and CAM5, with slightly better performance in the MMF simulations (e.g., MMF with CLUBB generally produces low clouds that are closer to the coast than CAM5 with CLUBB). Improved low-cloud simulations in MMF make it an even more attractive tool for studying aerosol-cloud-precipitation interactions.
Wang, Minghuai; Larson, Vincent E.; Ghan, Steven; ...
2015-04-18
In this study, a higher-order turbulence closure scheme, called Cloud Layers Unified by Binormals (CLUBB), is implemented into a Multi-scale Modeling Framework (MMF) model to improve low cloud simulations. The performance of CLUBB in MMF simulations with two different microphysics configurations (one-moment cloud microphysics without aerosol treatment and two-moment cloud microphysics coupled with aerosol treatment) is evaluated against observations and further compared with results from the Community Atmosphere Model, Version 5 (CAM5) with conventional cloud parameterizations. CLUBB is found to improve low cloud simulations in the MMF, and the improvement is particularly evident in the stratocumulus-to-cumulus transition regions. Compared tomore » the single-moment cloud microphysics, CLUBB with two-moment microphysics produces clouds that are closer to the coast, and agrees better with observations. In the stratocumulus-to cumulus transition regions, CLUBB with two-moment cloud microphysics produces shortwave cloud forcing in better agreement with observations, while CLUBB with single moment cloud microphysics overestimates shortwave cloud forcing. CLUBB is further found to produce quantitatively similar improvements in the MMF and CAM5, with slightly better performance in the MMF simulations (e.g., MMF with CLUBB generally produces low clouds that are closer to the coast than CAM5 with CLUBB). As a result, improved low cloud simulations in MMF make it an even more attractive tool for studying aerosol-cloud-precipitation interactions.« less
Mao, Haidan; Zhao, Daomu
2010-01-18
Based on the intensity moments and Wigner distribution function, the second-order moments for broadband partially coherent flat-topped (BPCFT) beams in atmospheric turbulence are studied. The beam width of BPCFT beams in atmospheric turbulence is larger than that in free space. The beam width of BPCFT beams in atmospheric turbulence is larger than that of broadband fully coherent flat-topped (BFCFT) beams in atmospheric turbulence. The broader the bandwidth is, the larger the beam width of BPCFT beams becomes. Similar conclusion can be obtained by analyzing the divergence angle and beam propagation factor of BPCFT beams. The beam width of BPCFT beams in atmospheric turbulence is less affected by the broad spectral bandwidth than that in free space. The beam width of BFCFT beams in atmospheric turbulence is less affected by the broad spectral bandwidth than that of BPCFT beams in atmospheric turbulence.
NASA Astrophysics Data System (ADS)
Soltani, Mohsen; Mauder, Matthias; Laux, Patrick; Kunstmann, Harald
2017-07-01
The temporal multiscale variability of the surface heat fluxes is assessed by the analysis of the turbulent heat and moisture fluxes using the eddy covariance (EC) technique at the TERrestrial ENvironmental Observatories (TERENO) prealpine region. The fast and slow response variables from three EC sites located at Fendt, Rottenbuch, and Graswang are gathered for the period of 2013 to 2014. Here, the main goals are to characterize the multiscale variations and drivers of the turbulent fluxes, as well as to quantify the energy balance closure (EBC) and analyze the possible reasons for the lack of EBC at the EC sites. To achieve these goals, we conducted a principal component analysis (PCA) and a climatological turbulent flux footprint analysis. The results show significant differences in the mean diurnal variations of the sensible heat (H) and latent heat (LE) fluxes, because of variations in the solar radiation, precipitation patterns, soil moisture, and the vegetation fraction throughout the year. LE was the main consumer of net radiation. Based on the first principal component (PC1), the radiation and temperature components with a total mean contribution of 29.5 and 41.3%, respectively, were found to be the main drivers of the turbulent fluxes at the study EC sites. A general lack of EBC is observed, where the energy imbalance values amount 35, 44, and 35% at the Fendt, Rottenbuch, and Graswang sites, respectively. An average energy balance ratio (EBR) of 0.65 is obtained in the region. The best closure occurred in the afternoon peaking shortly before sunset with a different pattern and intensity between the study sites. The size and shape of the annual mean half-hourly turbulent flux footprint climatology was analyzed. On average, 80% of the flux footprint was emitted from a radius of approximately 250 m around the EC stations. Moreover, the overall shape of the flux footprints was in good agreement with the prevailing wind direction for all three TERENO EC sites.
Three-Dimensional Shallow Water Adaptive Hydraulics (ADH-SW3): Turbulence Closure
2015-06-01
ER D C/ CH L CR -1 5- 1 Three-Dimensional Shallow Water Adaptive Hydraulics (ADH-SW3): Turbulence Closure Co as ta l a nd H yd ra ul ic...military engineering, geospatial sciences, water resources, and environmental sciences for the Army, the Department of Defense, civilian agencies, and our...library at http://acwc.sdp.sirsi.net/client/default. ERDC/CHL CR-15-1 June 2015 Three-Dimensional Shallow Water Adaptive Hydraulics (ADH-SW3
A second-order closure analysis of turbulent diffusion flames. [combustion physics
NASA Technical Reports Server (NTRS)
Varma, A. K.; Fishburne, E. S.; Beddini, R. A.
1977-01-01
A complete second-order closure computer program for the investigation of compressible, turbulent, reacting shear layers was developed. The equations for the means and the second order correlations were derived from the time-averaged Navier-Stokes equations and contain third order and higher order correlations, which have to be modeled in terms of the lower-order correlations to close the system of equations. In addition to fluid mechanical turbulence models and parameters used in previous studies of a variety of incompressible and compressible shear flows, a number of additional scalar correlations were modeled for chemically reacting flows, and a typical eddy model developed for the joint probability density function for all the scalars. The program which is capable of handling multi-species, multistep chemical reactions, was used to calculate nonreacting and reacting flows in a hydrogen-air diffusion flame.
A critique of some recent second-order turbulence closure models for compressible boundary layers
NASA Technical Reports Server (NTRS)
Rubesin, M. W.; Crisalli, A. J.; Horstman, C. C.; Acharya, M.; Lanfranco, M. J.
1977-01-01
Computations based on two recently developed second-order turbulence closure models are compared with a series of boundary-layer experiments and with predictions of these experiments using an algebraic mixing length model. One of the models employs an eddy viscosity, whereas the other evaluates components of the Reynolds stress tensor. For flat plates, the computations are compared with the van Driest skin-friction transformation to assess the handling of compressibility. For boundary layers in pressure gradients, four experiments at Mach 4 and one at Mach 6.7 are used as the bases for comparison. In general, both models represent mean velocities and skin friction reasonably well, but represent the turbulence shear stress less accurately.
A comparison of turbulence closure models for transonic flows about airfoils
NASA Technical Reports Server (NTRS)
King, Lyndell S.
1987-01-01
Navier-Stokes transonic airfoil calculations using three different turbulence closure models are presented and compared with available experimental data. Two of the models, Cebeci-Smith and Baldwin-Lomax, are equilibrium models in the sense that the turbulent shear stress is assumed to depend only on the local properties of the mean flow. The third model, Johnson and King, is a nonequilibrium model in which an ordinary differential equation is employed to account for the streamwise development of the maximum Reynolds shear stress. An eddy viscosity distribution across the boundary layer is assumed which is functionally dependent on this stress. For attached flows with little inviscid-viscous interaction, little difference in the results with the different models is noted. With stronger interactions and with separation occurring on the airfoils, the nonequilibrium model is shown to perform better.
NASA Technical Reports Server (NTRS)
Fichtl, G. H.
1972-01-01
Results of recent measurements of the distribution function of wind shear and the associated third and fourth standardized moments. Emphasis is placed on the vertical variation of the longitudinal component of turbulence, i.e., the component of turbulence along the mean wind vector. The data source consists of 11 sets of longitudinal turbulent velocity fluctuation time histories digitized at 0.2-sec intervals with approximately 18,000 data points per history.
Anomalous scaling from controlled closure in a shell model of turbulence
NASA Astrophysics Data System (ADS)
L'vov, Victor S.; Pierotti, Daniela; Pomyalov, Anna; Procaccia, Itamar
2000-04-01
We present a model of hydrodynamic turbulence for which the program of computing the scaling exponents from first principles can be developed in a controlled fashion. The model consists of N suitably coupled copies of the "Sabra" shell model of turbulence. The couplings are chosen to include two components: random and deterministic, with a relative importance that is characterized by a parameter called ɛ. It is demonstrated, using numerical simulations of up to 25 copies and 28 shells that in the N→∞ limit but for 0<ɛ⩽1 this model exhibits correlation functions whose scaling exponents are anomalous. The theoretical calculation of the scaling exponents follows verbatim the closure procedure suggested recently for the Navier-Stokes problem, with the additional advantage that in the N→∞ limit the parameter ɛ can be used to regularize the closure procedure. The main result of this paper is a finite and closed set of scale-invariant equations for the 2nd and 3rd order statistical objects of the theory. This set of equations takes into account terms up to order ɛ4 and neglects terms of order ɛ6. Preliminary analysis of this set of equations indicates a K41 normal scaling at ɛ=0, with a birth of anomalous exponents at larger values of ɛ, in agreement with the numerical simulations.
NASA Technical Reports Server (NTRS)
Eggleston, John M; Diederich, Franklin W
1957-01-01
The correlation functions and power spectra of the rolling and yawing moments on an airplane wing due to the three components of continuous random turbulence are calculated. The rolling moments to the longitudinal (horizontal) and normal (vertical) components depend on the spanwise distributions of instantaneous gust intensity, which are taken into account by using the inherent properties of symmetry of isotropic turbulence. The results consist of expressions for correlation functions or spectra of the rolling moment in terms of the point correlation functions of the two components of turbulence. Specific numerical calculations are made for a pair of correlation functions given by simple analytic expressions which fit available experimental data quite well. Calculations are made for four lift distributions. Comparison is made with the results of previous analyses which assumed random turbulence along the flight path and linear variations of gust velocity across the span.
Second moments of optical degradation due to a thin turbulent layer
NASA Technical Reports Server (NTRS)
Steinmetz, W. J.
1980-01-01
The effect of the thin turbulent layers, including boundary layers and shear layers, on light propagation is examined from a theoretical point of view. In particular, a mathematical model is developed to describe the interaction between the aerodynamic or, more precisely, the density fluctuations and the electromagnetic field. It is assumed that the turbulence induces a normally distributed phase aberration which is a homogenous random function in the plane of the aperture. The optical degradation is described in terms of the optical transfer function and the Strehl ratio which are random. Expressions for the first and second moments of these two parameters are developed from the definitions. Asymptotic (large aperture) approximations to these expressions are derived and discussed. Finally, the exact approximate results are compared for several typical values of the ratios of aperture diameter to scale of density fluctuations and rms phase aberration to wave length respectively.
Zhou, Ye; Schilling, Oleg; Ghosh, Sanjoy
2002-08-01
The spectral eddy and backscatter viscosity and the spectral eddy and backscatter resistivity for incompressible, three-dimensional, isotropic, nonhelical magnetohydrodynamic (MHD) turbulence are constructed using the eddy-damped quasinormal Markovian statistical closure model developed by Pouquet, Frisch, and Léorat [J. Fluid Mech. 77, 321 (1976)] in terms of primitive variables. The approach used is an extension of the methodology developed by Leslie and Quarini [J. Fluid Mech. 91, 65 (1979)] for fluid turbulence to MHD turbulence. The eddy and backscatter viscosities and the eddy and backscatter resistivities are calculated numerically for assumed kinetic and magnetic energy spectra, E(v)(k) and E(B)(k), with a production subrange and a k(-5/3) inertial subrange for the two cases r(A)=1 and r(A)=1 / 2, where r(A)=E(v)(k)/E(B)(k) is the Alfvén ratio. It is shown that the effects of the unresolved subgrid scales on the resolved-scale velocity and magnetic field consist of an eddy damping and backscatter. The eddy viscosity and resistivity, and the backscatter viscosity and resistivity (the correlation function of the stochastic velocity and magnetic backscatter force) are shown to have a dependence on k/k(c), where k(c) is the cutoff wave number, which is very similar to the dependence calculated in the pure (i.e., nonmagnetic) Navier-Stokes turbulence case. The eddy viscosity and resistivity, and the backscatter viscosity and resistivity numerically calculated here can be used to develop improved subgrid-scale parametrizations for spectral large-eddy simulations of homogenous MHD turbulence.
Applying an economical scale-aware PDF-based turbulence closure model in NOAA NCEP GCMs
NASA Astrophysics Data System (ADS)
Belochitski, A.; Krueger, S. K.; Moorthi, S.; Bogenschutz, P.; Pincus, R.
2016-12-01
A novel unified representation of sub-grid scale (SGS) turbulence, cloudiness, and shallow convection is being implemented into the NOAA NCEP Global Forecasting System (GFS) general circulation model. The approach, known as Simplified High Order Closure (SHOC), is based on predicting a joint PDF of SGS thermodynamic variables and vertical velocity and using it to diagnose turbulent diffusion coefficients, SGS fluxes, condensation and cloudiness. Unlike other similar methods, only one new prognostic variable, turbulent kinetic energy (TKE), needs to be intoduced, making the technique computationally efficient.SHOC is now incorporated into a version of GFS, as well as into the next generation of the NCEP global model - NOAA Environmental Modeling System (NEMS). Turbulent diffusion coefficients computed by SHOC are now used in place of those produced by the boundary layer turbulence and shallow convection parameterizations. Large scale microphysics scheme is no longer used to calculate cloud fraction or the large-scale condensation/deposition. Instead, SHOC provides these variables. Radiative transfer parameterization uses cloudiness computed by SHOC.Outstanding problems include high level tropical cloud fraction being too high in SHOC runs, possibly related to the interaction of SHOC with condensate detrained from deep convection.Future work will consist of evaluating model performance and tuning the physics if necessary, by performing medium-range NWP forecasts with prescribed initial conditions, and AMIP-type climate tests with prescribed SSTs. Depending on the results, the model will be tuned or parameterizations modified. Next, SHOC will be implemented in the NCEP CFS, and tuned and evaluated for climate applications - seasonal prediction and long coupled climate runs. Impact of new physics on ENSO, MJO, ISO, monsoon variability, etc will be examined.
NASA Technical Reports Server (NTRS)
Johnson, D. A.; King, L. S.
1984-01-01
A new turbulence closure model designed specifically to treat two-dimensional, turbulent boundary layers with strong adverse pressure gradients and attendant separation, is presented. The influence of history effects are modeled by using an ordinary differential equation (ODE) derived from the turbulence kinetic-energy equation, to describe the streamwise development of the maximum Reynolds shear stress in conjunction with an assumed eddy-viscosity distribution which has as its velocity scale the maximum Reynolds shear stress. In the outer part of the boundary layer, the eddy viscosity is treated as a free parameter which is adjusted in order to satisfy the ODE for the maximum shear stress. Because of this, the model s not simply an eddy-viscosity model, but contains features of a Reynolds-stress model. Comparisons with experiments are presented which clearly show the proposed model to be superior to the Cebeci-Smith model in treating strongly retarded and separated flows. In contrast to two-equation, eddy-viscosity models, it requires only slightly more computational effort than simple models like the Cebeci-Smith model.
NASA Astrophysics Data System (ADS)
Hong, Liu; Yang, Zaibao; Zhu, Yi; Yong, Wen-An
2015-12-01
In this article, we propose a novel approach to construct macroscopic balance equations and constitutive equations describing various irreversible phenomena. It is based on the general principles of non-equilibrium thermodynamics and consists of four basic steps: picking suitable state variables, choosing a strictly concave entropy function, properly separating entropy fluxes and production rates, and determining a dissipation matrix. Our approach takes advantage of both extended irreversible thermodynamics and GENERIC formalisms and shows a direct correspondence with Levermore's moment-closure hierarchies for the Boltzmann equation. As a direct application, a new ten-moment model beyond the classical hierarchies is constructed and is shown to recover the Euler equations in the equilibrium state. These interesting results may put various macroscopic modeling approaches, starting from the general principles of non-equilibrium thermodynamics, on a solid microscopic foundation based on the Boltzmann equation.
NASA Astrophysics Data System (ADS)
Tassi, Emanuele
2014-07-01
We address the problem of the existence of the Hamiltonian structure for an electrostatic drift-kinetic model and for the related fluid models describing the evolution of the first two moments of the distribution function with respect to the parallel velocity. The drift-kinetic model, which accounts for background density and temperature gradients as well as polarization effects, is shown to possess a noncanonical Hamiltonian structure. The corresponding Poisson bracket is expressed in terms of the fluid moments and it is found that the set of functionals of the zero order moment forms a sub-algebra, thus automatically leading to a class of one-moment Hamiltonian fluid models. In particular, in the limit of weak spatial variations of the background quantities, the Charney-Hasegawa-Mima equation, with its Hamiltonian structure, is recovered. For the set of functionals of the first two moments, which, unlike the case of the Vlasov equation, turns out not to form a sub-algebra, we look for closures that lead to a closed Poisson bracket restricted to this set of functionals. The constraint of the Jacobi identity turns out to select the adiabatic equation of state for an ideal gas with one-degree-of-freedom molecules, as the only admissible closure in this sense. When the so called δf ordering is applied to the model, on the other hand, a Poisson bracket is obtained if the second order moment is a linear combination of the first two moments of the total distribution function. By means of this procedure, three-dimensional Hamiltonian fluid models that couple a generalized Charney-Hasegawa-Mima equation with an evolution equation for the parallel velocity are derived. Among these, a model adopted by Meiss and Horton [Phys. Fluids 26, 990 (1983)] to describe drift waves coupled to ion-acoustic waves, is obtained and its Hamiltonian structure is provided explicitly. Contribution to the Topical Issue "Theory and Applications of the Vlasov Equation", edited by Francesco
Experimental Investigation of Statistical Moments of Travel Time in Grid-Generated Turbulence
NASA Astrophysics Data System (ADS)
Durgin, William; Meleschi, Shangari; Andreeva, Tatiana
2003-11-01
Experimental Investigation of Statistical Moments of Travel Time in Grid-Generated Turbulence W.W. Durgin, S.B. Meleschi and T.A. Andreeva ABSTRACT. An experimental technique for investigation of the behavior of acoustic waves propagation through a turbulent medium is discussed. The present study utilizes the ultrasonic travel-time technique to diagnose a grid-generated turbulence. The statistics of the travel-time variations of ultrasonic wave propagation along a path are used to determine some metrics of the turbulence. Experimental investigation is performed under well-controlled laboratory conditions using a data acquisition and control system featuring a high-speed analog to digital conversion card that enables fine resolution of ultrasonic signals. Experimental data confirm numerical and theoretical predictions of a nonlinear increase of the first-order travel time variance with propagation distance. This behavior seems to be closely related to the occurrence of first caustics [Kulkarny and White, Blanc-Benon et al, 1991, 1995]. With increased turbulent intensity the distance at which the first caustic occurs, decreases. Numerically the phenomena was explored by Blanc-Benon and Juvé [1990], Juvé et al, 1991; Karweit et al [1991]; and their probability of appearance in a random field theoretically by Kulkarny and White [1982], Klyatskin [1993], Blanc-Benon et al, [1995]. Current work seeks to illustrate the correspondence between flow parameters and the first appearance of non-linearity in the travel time variance. Expansion of experimental controls to include flow temperature references and rigid transducer supports adds to the integrity of the determined travel times.
Raghib, Michael; Hill, Nicholas A; Dieckmann, Ulf
2011-05-01
The prevalence of structure in biological populations challenges fundamental assumptions at the heart of continuum models of population dynamics based only on mean densities (local or global). Individual-based models (IBMs) were introduced during the last decade in an attempt to overcome this limitation by following explicitly each individual in the population. Although the IBM approach has been quite useful, the capability to follow each individual usually comes at the expense of analytical tract ability, which limits the generality of the statements that can be made. For the specific case of spatial structure in populations of sessile (and identical) organisms, space-time point processes with local regulation seem to cover the middle ground between analytical tract ability and a higher degree of biological realism. This approach has shown that simplified representations of fecundity, local dispersal and density-dependent mortality weighted by the local competitive environment are sufficient to generate spatial patterns that mimic field observations. Continuum approximations of these stochastic processes try to distill their fundamental properties, and they keep track of not only mean densities, but also higher order spatial correlations. However, due to the non-linearities involved they result in infinite hierarchies of moment equations. This leads to the problem of finding a 'moment closure'; that is, an appropriate order of (lower order) truncation, together with a method of expressing the highest order density not explicitly modelled in the truncated hierarchy in terms of the lower order densities. We use the principle of constrained maximum entropy to derive a closure relationship for truncation at second order using normalisation and the product densities of first and second orders as constraints, and apply it to one such hierarchy. The resulting 'maxent' closure is similar to the Kirkwood superposition approximation, or 'power-3' closure, but it is
Fast Maximum Entropy Moment Closure Approach to Solving the Boltzmann Equation
NASA Astrophysics Data System (ADS)
Summy, Dustin; Pullin, Dale
2015-11-01
We describe a method for a moment-based solution of the Boltzmann Equation (BE). This is applicable to an arbitrary set of velocity moments whose transport is governed by partial-differential equations (PDEs) derived from the BE. The equations are unclosed, containing both higher-order moments and molecular-collision terms. These are evaluated using a maximum-entropy reconstruction of the velocity distribution function f (c , x , t) , from the known moments, within a finite-box domain of single-particle velocity (c) space. Use of a finite-domain alleviates known problems (Junk and Unterreiter, Continuum Mech. Thermodyn., 2002) concerning existence and uniqueness of the reconstruction. Unclosed moments are evaluated with quadrature while collision terms are calculated using any desired method. This allows integration of the moment PDEs in time. The high computational cost of the general method is greatly reduced by careful choice of the velocity moments, allowing the necessary integrals to be reduced from three- to one-dimensional in the case of strictly 1D flows. A method to extend this enhancement to fully 3D flows is discussed. Comparison with relaxation and shock-wave problems using the DSMC method will be presented. Partially supported by NSF grant DMS-1418903.
Third-Moment Studies of Cascade Dynamics in Solar Wind Turbulence (Invited)
NASA Astrophysics Data System (ADS)
Smith, C. W.; Stawarz, J. E.; Vasquez, B. J.; Forman, M. A.; MacBride, B. T.
2010-12-01
Kolmogorov [1941] and Yaglom [1949] showed that the incompressible hydrodynamic equations governing fluid turbulence could be manipulated to yield a rigorous third-order structure function expression for the energy cascade at inertial range scales. In that derivation the structure function scales linearly with separation distance and the proportionality constant is a factor of the energy cascade rate. For decades it has been argued that the most commonly studied spatial scales for magnetic and velocity fluctuations in the solar wind form an inertial range in an MHD analogy to hydrodynamic turbulence. Politano and Pouquet [1998a,b] and Podesta [2008] derived third-moment expressions for the inertial range cascade in MHD in direct analogy with the earlier hydrodynamic results. We have been exploring the use of these expressions for both isotropic and anisotropic solar wind turbulence [MacBride 2005, 2008; Stawarz 2009, 2010; Smith 2009, 2010; Forman 2010a,b] and find (1) the measured third moments do scale linearly with separation and (2) the resulting estimate for the energy cascade rate accurately account for the energy cascade budget required for turbulence to heat the solar wind. In addition, the anisotropic formalism shows preferential cascade perpendicular to the mean magnetic field. Recent results show the unexpected backward transfer of energy associated with the dominant outward-propagating component when the cross-helicity < δ V \\cdot δ B > is large. The latter behavior is thought to exist over only a limited range of heliocentric distances forming a transient turbulent dynamic near 1 AU. We will include some important comments about the need to monitor convergence and error analyses when using solar wind data. Kolmogorov, 1941, Dokl. Akad. Nauk SSSR, 32, 16. Forman, et al., 2010a, Physical Review Letters, 104, 189001. Forman, et al., 2010b, Solar Wind 12, 176. MacBride, et al., 2005, Solar Wind 11, 613. MacBride, et al., 2008, The Astrophysical Journal
Modelling complex draft-tube flows using near-wall turbulence closures
Ventikos, Y.; Sotiropoulos, F.; Patel, V.C.
1996-12-31
This paper presents a finite-volume method for simulating flows through complex hydroturbine draft-tube configurations using near-wall turbulence closures. The method employs the artificial-compressibility pressure-velocity coupling approach in conjunction with multigrid acceleration for fast convergence on very fine grids. Calculations are carried out for a draft tube with two downstream piers on a computational mesh consisting of 1.2x10{sup 6} nodes. Comparisons of the computed results with measurements demonstrate the ability of the method to capture most experimental trends with reasonable accuracy. Calculated three-dimensional particle traces reveal very complex flow features in the vicinity of the piers, including horse-shoe longitudinal vortices and and regions of flow reversal.
Generalized higher order two-point moments in turbulent boundary layers.
NASA Astrophysics Data System (ADS)
Yang, Xiang; Marusic, Ivan; Meneveau, Charles
2015-11-01
Generalized higher order two-point moments such as
NASA Astrophysics Data System (ADS)
Xu, Yonggen; Li, Yude; Dan, Youquan; Du, Quan; Wang, Shijian
2016-07-01
The Wigner distribution function (WDF) has been used to study the propagation properties of partially coherent Laguerre Gaussian (PCLG) beams through atmospheric turbulence. Based on the extended Huygens-Fresnel principle, an analytical formula of the propagation matrixes in terms of the second-order moments of the WDF for PCLG Beams in the receiving plane is derived. And then the analytical formulae for the curvature radii of PCLG Beams propagating in turbulence are given by the second-order moments of the WDF. The numerical results indicate that the curvature radius of PCLG Beams changes more rapidly in turbulence than that in the free space. The influence of the transverse coherence width and the beam waist width on the curvature radius of PCLG Beams is obvious, while the laser wavelength and the inner scale of turbulence have a slight effect. The study results may be useful for remote sensing and free space optical communications.
Eigenspace perturbations for uncertainty estimation of single-point turbulence closures
NASA Astrophysics Data System (ADS)
Iaccarino, Gianluca; Mishra, Aashwin Ananda; Ghili, Saman
2017-02-01
Reynolds-averaged Navier-Stokes (RANS) models represent the workhorse for predicting turbulent flows in complex industrial applications. However, RANS closures introduce a significant degree of epistemic uncertainty in predictions due to the potential lack of validity of the assumptions utilized in model formulation. Estimating this uncertainty is a fundamental requirement for building confidence in such predictions. We outline a methodology to estimate this structural uncertainty, incorporating perturbations to the eigenvalues and the eigenvectors of the modeled Reynolds stress tensor. The mathematical foundations of this framework are derived and explicated. Thence, this framework is applied to a set of separated turbulent flows, while compared to numerical and experimental data and contrasted against the predictions of the eigenvalue-only perturbation methodology. It is exhibited that for separated flows, this framework is able to yield significant enhancement over the established eigenvalue perturbation methodology in explaining the discrepancy against experimental observations and high-fidelity simulations. Furthermore, uncertainty bounds of potential engineering utility can be estimated by performing five specific RANS simulations, reducing the computational expenditure on such an exercise.
NASA Technical Reports Server (NTRS)
Canuto, V. M.; Dubovikov, M. S.; Howard, A.; Cheng, Y.
1999-01-01
In papers 1 and 2 we have presented the results of the most updated 1-point closure model for the turbulent vertical diffusivities of momentum, heat and salt, K(sub m,h,s). In this paper, we derive the analytic expressions for K(sub m,h,s) using a new 2-point closure model that has recently been developed and successfully tested against some approx. 80 turbulence statistics for different flows. The new model has no free parameters. The expressions for K(sub m, h. s) are analytical functions of two stability parameters: the Turner number R(sub rho) (salinity gradient/temperature gradient) and the Richardson number R(sub i) (temperature gradient/shear). The turbulent kinetic energy K and its rate of dissipation may be taken local or non-local (K-epsilon model). Contrary to all previous models that to describe turbulent mixing below the mixed layer (ML) have adopted three adjustable "background diffusivities" for momentum. heat and salt, we propose a model that avoids such adjustable diffusivities. We assume that below the ML, K(sub m,h,s) have the same functional dependence on R(sub i) and R(sub rho) derived from the turbulence model. However, in order to compute R(sub i) below the ML, we use data of vertical shear due to wave-breaking measured by Gargett et al. (1981). The procedure frees the model from adjustable background diffusivities and indeed we use the same model throughout the entire vertical extent of the ocean. Using the new K(sub m,h, s), we run an O-GCM and present a variety of results that we compare with Levitus and the KPP model. Since the traditional 1-point (used in papers 1 and 2) and the new 2-point closure models used here represent different modeling philosophies and procedures, testing them in an O-GCM is indispensable. The basic motivation is to show that the new 2-point closure model gives results that are overall superior to the 1-point closure in spite of the fact that the latter rely on several adjustable parameters while the new 2-point
Applying an economical scale-aware PDF-based turbulence closure model in NOAA NCEP GCMs.
NASA Astrophysics Data System (ADS)
Krueger, S. K.; Belochitski, A.; Moorthi, S.; Bogenschutz, P.; Pincus, R.
2015-12-01
A novel unified representation of sub-grid scale (SGS) turbulence, cloudiness, and shallow convection is being implemented into the NOAA NCEP Global Forecasting System (GFS) general circulation model. The approach, known as Simplified High Order Closure (SHOC), is based on predicting a joint PDF of SGS thermodynamic variables and vertical velocity and using it to diagnose turbulent diffusion coefficients, SGS fluxes, condensation and cloudiness. Unlike other similar methods, only one new prognostic variable, turbulent kinetic energy (TKE), needs to be intoduced, making the technique computationally efficient.SHOC code was adopted for a global model environment from its origins in a cloud resolving model, and incorporated into NCEP GFS. SHOC was first tested in a non-interactive mode, a configuration where SHOC receives inputs from the host model, but its outputs are not returned to the GFS. In this configuration: a) SGS TKE values produced by GFS SHOC are consistent with those produced by SHOC in a CRM, b) SGS TKE in GFS SHOC exhibits a well defined diurnal cycle, c) there's enhanced boundary layer turbulence in the subtropical stratocumulus and tropical transition-to-cumulus areas d) buoyancy flux diagnosed from the assumed PDF is consistent with independently calculated Brunt-Vaisala frequency in identifying stable and unstable regions.Next, SHOC was coupled to GFS, namely turbulent diffusion coefficients computed by SHOC are now used in place of those currently produced by the GFS boundary layer and shallow convection schemes (Han and Pan, 2011), as well as condensation and cloud fraction diagnosed from the SGS PDF replace those calculated in the current large-scale cloudines scheme (Zhao and Carr, 1997). Ongoing activities consist of debugging the fully coupled GFS/SHOC.Future work will consist of evaluating model performance and tuning the physics if necessary, by performing medium-range NWP forecasts with prescribed initial conditions, and AMIP-type climate
Smith, W.S.; Kao, C.Y.J.
1996-01-01
A high-resolution one-dimensional version of a second-order turbulence closure radiative-convective model, developed at Los Alamos National Laboratory, is used to simulate the interactions among turbulence, radiation, and bulk cloud parameters in stratiform clouds observed during the Arctic Stratus Experiment conducted during June 1980 over the Beaufort Sea. The fidelity of the model to the underlying physics is assessed by comparing the modeled evolution of the cloud-capped boundary layer against data reported for two particular days of observations. Over the period encompassed by these observations, the boundary layer evolved from a well-mixed cloud-capped boundary layer overlying a stable cloudy surface layer to a shallower well-mixed boundary layer with a single upper cloud deck and a clear, diminished, stable surface layer. The model was able to reproduce the observed profiles of the liquid water content, cloud-base height, radiative heating rates, and the mean and turbulence variables over the period of observation fairly well. The formation and eventual dissipation of the surface cloud feature over the period of the simulation was found to be caused by the formation of a stable surface layer as the modeled air mass moved over the relatively cold Beaufort Sea region. Condensation occurred as heat in the surface layer was transported downward toward the sea surface. Eventual dissipation of the surface cloud layer resulted from the transport of moisture in the surface layer downward toward the sea surface. The results show that the subsidence was the major influence on the evolution of the cloud-top height but was not a major factor for dissipation of either cloud layer during the simulation. 17 refs., 9 figs.
Analysis of Highly-Resolved Simulations of 2-D Humps Toward Improvement of Second-Moment Closures
NASA Technical Reports Server (NTRS)
Jeyapaul, Elbert; Rumsey Christopher
2013-01-01
Fully resolved simulation data of flow separation over 2-D humps has been used to analyze the modeling terms in second-moment closures of the Reynolds-averaged Navier- Stokes equations. Existing models for the pressure-strain and dissipation terms have been analyzed using a priori calculations. All pressure-strain models are incorrect in the high-strain region near separation, although a better match is observed downstream, well into the separated-flow region. Near-wall inhomogeneity causes pressure-strain models to predict incorrect signs for the normal components close to the wall. In a posteriori computations, full Reynolds stress and explicit algebraic Reynolds stress models predict the separation point with varying degrees of success. However, as with one- and two-equation models, the separation bubble size is invariably over-predicted.
NASA Astrophysics Data System (ADS)
Paterson, William R.; Giles, Barbara L.; Avanov, Levon A.; Barrie, Alex C.; Boardsen, Scott A.; Dorelli, John C.; Gershman, Daniel J.; Mackler, David A.; El-Alaoui, Mostafa; Burch, James L.; Russell, Christopher T.; Torbert, Roy B.
2017-04-01
The Fast Plasma Instrumentation for the Magnetospheric Multiscale mission measures the velocity distributions of electrons and ions with energies several eV to 30 keV. In its fast survey mode of operation, velocity distributions are acquired every 30 ms for the electrons and every 150 ms for the ions. Due to telemetry limitations, only a small subset of these distributions can be transmitted to the ground. To facilitate selection of intervals with high potential for addressing magnetic reconnection, a compact set of approximate plasma moments is computed onboard the spacecraft and sent to the ground at the full temporal resolution of the instrumentation. Although these moments were not intended for direct use in scientific investigations, they have the advantage of being the only FPI data product that is available at high time resolution across the entire scientific region of interest. In this presentation we report on prospects for using these data to address scientific questions, with emphasis on studies of turbulence.
From Markovian to pairwise epidemic models and the performance of moment closure approximations.
Taylor, Michael; Simon, Péter L; Green, Darren M; House, Thomas; Kiss, Istvan Z
2012-05-01
Many if not all models of disease transmission on networks can be linked to the exact state-based Markovian formulation. However the large number of equations for any system of realistic size limits their applicability to small populations. As a result, most modelling work relies on simulation and pairwise models. In this paper, for a simple SIS dynamics on an arbitrary network, we formalise the link between a well known pairwise model and the exact Markovian formulation. This involves the rigorous derivation of the exact ODE model at the level of pairs in terms of the expected number of pairs and triples. The exact system is then closed using two different closures, one well established and one that has been recently proposed. A new interpretation of both closures is presented, which explains several of their previously observed properties. The closed dynamical systems are solved numerically and the results are compared to output from individual-based stochastic simulations. This is done for a range of networks with the same average degree and clustering coefficient but generated using different algorithms. It is shown that the ability of the pairwise system to accurately model an epidemic is fundamentally dependent on the underlying large-scale network structure. We show that the existing pairwise models are a good fit for certain types of network but have to be used with caution as higher-order network structures may compromise their effectiveness.
Allam, A.M.
1982-01-01
Although techniques for designing a fracture treatment are available, the intended results of these techniques are often not attained. The evaluation of fracturing treatments on low permeability gas wells is required to both optimize the fracturing design and form prediction calculations of a treatments effect. This study primarily investigates the effect of fracture height on the performance of vertically fractured wells. The effects of layered media, turbulance, and closure pressure are included in this work. Consider that a well, intercepted by a vertical fracture, is in the center of a squared drainage system with closed outer boundary. Any increase in well productivity will be determined by fracture parameters, which are: fracture length, height, fracture conductivity, and location of the fracture in the formaton. On the basis of the analysis of fluid flow in porous media, the problem solving technique used in this study is the numerical method. A three-dimensional finite difference fully implicit model was written for this. In addition, the Sparse Matrix technique was used as a solver. Furthermore, Slices Source Over Relaxation was used as an iterative method for solving routines. Presented here are the numerical results of the three-dimensional model for a well intercepting a vertical fracture wth finite conductivity. The results are presented in the general form of dimensionless variables. Type curves considering the effect of fracture height on well performance are included. In addition, type curves for turbulent flow in the fracture are also obtained. Finally, other important contributions of this work are the data showing the effect of layered formation on fractured well performance.
NASA Technical Reports Server (NTRS)
Cheng, Anning; Xu, Kuan-Man
2006-01-01
The abilities of cloud-resolving models (CRMs) with the double-Gaussian based and the single-Gaussian based third-order closures (TOCs) to simulate the shallow cumuli and their transition to deep convective clouds are compared in this study. The single-Gaussian based TOC is fully prognostic (FP), while the double-Gaussian based TOC is partially prognostic (PP). The latter only predicts three important third-order moments while the former predicts all the thirdorder moments. A shallow cumulus case is simulated by single-column versions of the FP and PP TOC models. The PP TOC improves the simulation of shallow cumulus greatly over the FP TOC by producing more realistic cloud structures. Large differences between the FP and PP TOC simulations appear in the cloud layer of the second- and third-order moments, which are related mainly to the underestimate of the cloud height in the FP TOC simulation. Sensitivity experiments and analysis of probability density functions (PDFs) used in the TOCs show that both the turbulence-scale condensation and higher-order moments are important to realistic simulations of the boundary-layer shallow cumuli. A shallow to deep convective cloud transition case is also simulated by the 2-D versions of the FP and PP TOC models. Both CRMs can capture the transition from the shallow cumuli to deep convective clouds. The PP simulations produce more and deeper shallow cumuli than the FP simulations, but the FP simulations produce larger and wider convective clouds than the PP simulations. The temporal evolutions of cloud and precipitation are closely related to the turbulent transport, the cold pool and the cloud-scale circulation. The large amount of turbulent mixing associated with the shallow cumuli slows down the increase of the convective available potential energy and inhibits the early transition to deep convective clouds in the PP simulation. When the deep convective clouds fully develop and the precipitation is produced, the cold pools
A second-order closure model for the effect of averaging time on turbulent plume dispersion
Sykes, R.I.; Gabruk, R.S.
1996-12-31
Turbulent dispersion in the atmosphere is a result of chaotic advection by a wide spectrum of eddy motions. In genera, the larger scale motions behave like a time-dependent, spatially inhomogeneous mean wind and produce coherent meandering of a pollutant cloud or plume, while the smaller scale motions act to diffuse the pollutant and mix it with the ambient air. The distinction between the two types of motion is dependent on both the sampling procedure and the scale of the pollutant cloud. For the case of a continuous plume of material, the duration of the sampling time (the time average period) determines the effective size of the plume. The objective is the development of a practical scheme for representing the effect of time-averaging on plume width. The model must describe relative dispersion in the limit of short-term averages, and give the absolute, or ensemble, dispersion rate for long-term sampling. The authors shall generalize the second-order closure ensemble dispersion model of Sykes et al. to include the effect of time-averaging, so they first briefly review the basic model.
NASA Astrophysics Data System (ADS)
Talamelli, Alessandro; Segalini, Antonio; Örlü, Ramis; Schlatter, Philipp; Alfredsson, P. Henrik
2013-04-01
Spatial averaging, resulting from the finite size of a hot-wire probe, significantly affects the accuracy of velocity measurements in turbulent flows close to walls. Here, we extend the theoretical model, introduced in Segalini et al. (Meas Sci Technol 22:104508, 2011) quantifying the effect of a linear spatial filter of hot-wire probes on the mean and the variance of the streamwise velocity in turbulent wall-bounded flows, to describe the effect of the spatial filtering on the third- and fourth-order moments of the same velocity component. The model, based on the three-(four) point velocity-correlation function for the third-(fourth-) order moment, shows that the filtering can be related to a characteristic length scale which is an equivalent of the Taylor transverse microscale for the second-order moment. The capacity of the model to accurately describe the attenuation is validated against direct numerical simulation (DNS) data of a zero pressure-gradient turbulent boundary layer. The DNS data allow the filtering effect to be appraised for different wire lengths and for the different moments. The model shows good accuracy except for the third-order moment in the region where a zero-crossing of the third-order function is observed and where the equations become ill-conditioned. An "a posteriori" correction procedure, based on the developed model, to correct the measured third- and fourth-order velocity moments is also presented. This procedure, based on combining the measured data by two single hot-wire sensors with different wire lengths, is a natural extension of the one introduced by Segalini et al. (Exp Fluids 51:693-700, 2011) to evaluate both the turbulence intensity and the transverse Taylor microscale in turbulent flows. The technique is validated against spatially averaged simulation data showing a good capacity to correct the actual profiles over the entire height of the boundary layer except, as expected, for the third-order moment in the region where
NASA Technical Reports Server (NTRS)
Lichtenstein, J. H.
1978-01-01
An analytical method of computing the averaging effect of wing-span size on the loading of a wing induced by random turbulence was adapted for use on a digital electronic computer. The turbulence input was assumed to have a Dryden power spectral density. The computations were made for lift, rolling moment, and bending moment for two span load distributions, rectangular and elliptic. Data are presented to show the wing-span averaging effect for wing-span ratios encompassing current airplane sizes. The rectangular wing-span loading showed a slightly greater averaging effect than did the elliptic loading. In the frequency range most bothersome to airplane passengers, the wing-span averaging effect can reduce the normal lift load, and thus the acceleration, by about 7 percent for a typical medium-sized transport. Some calculations were made to evaluate the effect of using a Von Karman turbulence representation. These results showed that using the Von Karman representation generally resulted in a span averaging effect about 3 percent larger.
Podesta, J. J.; Forman, M. A.; Smith, C. W.
2007-09-15
Laws governing the behavior of statistical third-order moments in the inertial range are among the few rigorous results in the theory of statistically homogeneous incompressible magnetohydrodynamic turbulence. These fundamental laws apply to both isotropic and anisotropic turbulence. Assuming that the turbulence is stationary in time and statistically axisymmetric under proper rotations about the direction of the mean magnetic field, it is shown that the general mathematical form of the tensor quantities appearing in these laws is constrained by symmetry to have a particular form. Using these forms, the general solutions of the law for the vector and pseudovector third-order moments F and F{sub C} are obtained in the limit of large kinetic Reynolds number and large magnetic Reynolds number. The physical meaning of the different terms in F and F{sub C} are investigated and a method for obtaining the cascade rates of energy {epsilon} and cross-helicity {epsilon}{sub C} from experimental data is described. The results show that the measurement of the cascade rates goes hand-in-hand with the measurement of the spatial anisotropy of the third-order moments F and F{sub C}. The theory developed here can be applied to measure the turbulent cascade rates of energy and cross-helicity in laboratory plasma experiments, numerical simulations, and the solar wind.
NASA Technical Reports Server (NTRS)
Xu, Kuan-Man
2015-01-01
Low-level clouds cover nearly half of the Earth and play a critical role in regulating the energy and hydrological cycle. Despite the fact that a great effort has been put to advance the modeling and observational capability in recent years, low-level clouds remains one of the largest uncertainties in the projection of future climate change. Low-level cloud feedbacks dominate the uncertainty in the total cloud feedback in climate sensitivity and projection studies. These clouds are notoriously difficult to simulate in climate models due to its complicated interactions with aerosols, cloud microphysics, boundary-layer turbulence and cloud dynamics. The biases in both low cloud coverage/water content and cloud radiative effects (CREs) remain large. A simultaneous reduction in both cloud and CRE biases remains elusive. This presentation first reviews the effort of implementing the higher-order turbulence closure (HOC) approach to representing subgrid-scale turbulence and low-level cloud processes in climate models. There are two HOCs that have been implemented in climate models. They differ in how many three-order moments are used. The CLUBB are implemented in both CAM5 and GDFL models, which are compared with IPHOC that is implemented in CAM5 by our group. IPHOC uses three third-order moments while CLUBB only uses one third-order moment while both use a joint double-Gaussian distribution to represent the subgrid-scale variability. Despite that HOC is more physically consistent and produces more realistic low-cloud geographic distributions and transitions between cumulus and stratocumulus regimes, GCMs with traditional cloud parameterizations outperform in CREs because tuning of this type of models is more extensively performed than those with HOCs. We perform several tuning experiments with CAM5 implemented with IPHOC in an attempt to produce the nearly balanced global radiative budgets without deteriorating the low-cloud simulation. One of the issues in CAM5-IPHOC
NASA Astrophysics Data System (ADS)
Ezhova, E. V.; Zilitinkevitch, S. S.; Rybushkina, G. V.; Soustova, I. A.; Troitskaya, Yu. I.
2016-05-01
The self-similar turbulent density jump evolution has been studied in the scope of a turbulence closure modernized theory which takes into account the anisotropy and mutual transformation of the turbulent fluctuation kinetic and potential energy for a stably stratified fluid. The numerical calculation, performed using the equations for the average density and kinetic and potential energies of turbulent fluctuations, indicates that the vertical profiles of the buoyancy frequency, turbulence scale, and kinetic and potential energies drastically change when the turbulence anisotropy is strong. The vertical profiles of the corresponding energy and spatial discontinuity parameters, calculated at a weaker anisotropy, indicate that similar drastic changes are absent and a qualitative agreement exists with the known analytical solution, which describes the density jump evolution in a freshwater basin and was obtained previously [5, 8] in the scope of a turbulence local-similarity hypothesis applied in combination with the budget equation for the turbulent fluctuation kinetic energy.
NASA Astrophysics Data System (ADS)
Newell, Alan C.; Rumpf, Benno
2011-01-01
In this article, we state and review the premises on which a successful asymptotic closure of the moment equations of wave turbulence is based, describe how and why this closure obtains, and examine the nature of solutions of the kinetic equation. We discuss obstacles that limit the theory's validity and suggest how the theory might then be modified. We also compare the experimental evidence with the theory's predictions in a range of applications. Finally, and most importantly, we suggest open challenges and encourage the reader to apply and explore wave turbulence with confidence. The narrative is terse but, we hope, delivered at a speed more akin to the crisp pace of a Hemingway story than the wordjumblingtumbling rate of a Joycean novel.
NASA Technical Reports Server (NTRS)
Canuto, V. M.; Howard, A.; Cheng, Y.; Dubovikov, M. S.
1999-01-01
We develop and test a 1-point closure turbulence model with the following features: 1) we include the salinity field and derive the expression for the vertical turbulent diffusivities of momentum K(sub m) , heat K(sub h) and salt K(sub s) as a function of two stability parameters: the Richardson number R(sub i) (stratification vs. shear) and the Turner number R(sub rho) (salinity gradient vs. temperature gradient). 2) to describe turbulent mixing below the mixed layer (ML), all previous models have adopted three adjustable "background diffusivities" for momentum, heat and salt. We propose a model that avoids such adjustable diffusivities. We assume that below the ML, the three diffusivities have the same functional dependence on R( sub i) and R(sub rho) as derived from the turbulence model. However, in order to compute R(sub i) below the ML, we use data of vertical shear due to wave-breaking.measured by Gargett et al. The procedure frees the model from adjustable background diffusivities and indeed we employ the same model throughout the entire vertical extent of the ocean. 3) in the local model, the turbulent diffusivities K(sub m,h,s) are given as analytical functions of R(sub i) and R(sub rho). 5) the model is used in an O-GCM and several results are presented to exhibit the effect of double diffusion processes. 6) the code is available upon request.
Two-point closure method for turbulence with reacting and mixing chemical elements of type A+B→ C
NASA Astrophysics Data System (ADS)
Meshram, M. C.
2010-12-01
Turbulence with reacting and mixing chemical elements of type A+B→C was investigated by using the two-point closure method, For implementation of this method, two-point correlation functions and two-point triple correlation functions are defined first. Equations describing the turbulence under study that describe the dynamical behaviour are written in terms of two-point correlation functions and two-point triple correlation functions. These describe the dynamical behaviour of two-point double-reactant fluctuation correlation functions. In each of these equations, two-point triple correlation functions appear. Thus, the characteristic difficulty of indeterminacy in turbulence theory is noticed in these equations too. A simple closure hypothesis for two-point triple correlation functions is proposed with a view to overcoming the indeterminacy. This hypothesis enables one to obtain the closed set of equations for double correlation functions, as desired. The resulting equations for double correlation functions provide theoretical information about the turbulence under investigation. Having obtained the closed set of equations for double correlation functions, the relationships for reactants' eddy diffusivity functions are derived. Also, the reactants' energy and transfer functions in fluid space are obtained. Having expressed the Karman-Howarth equations for the present investigation in dimensionless form, these are rewritten in terms of energy functions in fluid space. The system of equations for scales of segregation related to reactants A and B is derived. Various length scales involved in this study can be evaluated on integration of these equations, which in turn generates theoretical information about the turbulence under investigation.
Workshop on Engineering Turbulence Modeling
NASA Technical Reports Server (NTRS)
Povinelli, Louis A. (Editor); Liou, W. W. (Editor); Shabbir, A. (Editor); Shih, T.-H. (Editor)
1992-01-01
Discussed here is the future direction of various levels of engineering turbulence modeling related to computational fluid dynamics (CFD) computations for propulsion. For each level of computation, there are a few turbulence models which represent the state-of-the-art for that level. However, it is important to know their capabilities as well as their deficiencies in order to help engineers select and implement the appropriate models in their real world engineering calculations. This will also help turbulence modelers perceive the future directions for improving turbulence models. The focus is on one-point closure models (i.e., from algebraic models to higher order moment closure schemes and partial differential equation methods) which can be applied to CFD computations. However, other schemes helpful in developing one-point closure models, are also discussed.
Navier-Stokes computation of compressible turbulent flows with a second order closure
NASA Technical Reports Server (NTRS)
Dingus, C.; Kollmann, W.
1991-01-01
The objective was the development of a complete second order closure for wall bounded flows, including all components of the dissipation rate tensor and a numerical solution procedure for the resulting system of equations. The main topics discussed are the closure of the pressure correlations and the viscous destruction terms in the dissipation rate equations and the numerical solution scheme based on a block-tridiagonal solver for the nine equations required for the prediction of plane or axisymmetric flows.
NASA Astrophysics Data System (ADS)
Piest, Jürgen
1989-06-01
This is the first of a series of three papers which report on an theoretical turbulence investigation. In the present part, the Reynolds equation for the mean velocity field in turbulent shear flow is derived in a systematic way starting from established physical knowledge. A basic problem of contemporary turbulence theory is that, at the hydrodynamic level, there seems to be no way presently to derive systematically the initial probability distribution of the fluctuating momentum density. For this reason, N-particle statistical mechanics is employed in this investigation. The closure problem of continuum turbulence theory is avoided by this method. The technique of deriving transport equations from the Liouville equation by projection operator methods is used for the derivation. Stationary constant density/temperature processes are considered only. The dissipative term of the momemtum transport equation is analyzed in order to obtain the formulas for the laminar and turbulent friction forces. The latter is obtained as a second-order convolution in the mean velocity field. The kernel function is a time integral of an equilibrium triple correlation function; it constitutes a physical “constant” of the fluid which is needed in addition to the viscosity constant. Its calculation has been the object of a separate investigation which will be reported in the second paper. The third paper describes the numerical evaluation and comparison with experiment for the spherical case of the circular jet. In the present state, the theoretical formula does not reproduce the experimental data. This is considered a preliminary result which, in view of the systematic nature of the derivation, offers the possibility to trace it back to the spots where the theoretical structure is still not adequate.
Modeling flows over gravel beds by a drag force method and a modified S-A turbulence closure
NASA Astrophysics Data System (ADS)
Zeng, C.; Li, C. W.
2012-09-01
A double-averaged Navier-Stokes equations (DANS) model has been developed for depth-limited open channel flows over gravels. Three test cases are used to validate the model: an open-channel flow over a densely packed gravel bed with small-scale uniform roughness (D/d50 ˜ 13, d50 = median diameter of roughness elements, D = water depth), open-channel flows over large-scale sparsely distributed roughness elements (D/Δ ˜ 2.3-8.7, Δ = roughness height) and steep slope gravel-bed river flows with D/d50 ˜ 7-25. Various methods of treatment of the gravel-induced resistance effect have been investigated. The results show that the wall function approach (WFA) is successful in simulating flows over small gravels but is not appropriate for large gravels since the vertical profile of the longitudinal velocity does not follow the logarithmic-linear relationship. The drag force method (DFM) performs better but the non-logarithmic velocity distribution generated by sparsely distributed gravels cannot be simulated accurately. Noting that the turbulence length scale within the gravel layer is governed by the gravel size, the DANS model incorporating the DFM and a modified Spalart-Allmaras (S-A) turbulence closure is proposed. The turbulence length scale parameter in the S-A model is modified to address the change in the turbulence structure within the gravel layer. The computed velocity profiles agree well with the corresponding measured profiles in all cases. Particularly, the model reproduces the S-shape velocity profile for sparsely distributed large size roughness elements. The modeling methodology is robust and can be easily integrated into the existing numerical models.
NASA Astrophysics Data System (ADS)
Belen'kii, Mikhail S.; Hughes, Kevin; Brinkley, Timothy J.; Oldenettel, Jerry R.
2002-12-01
Fourier Telescopy is an active laser-based imaging method for high-resolution imaging of dim objects in Geosynchronous (GEO) orbit. The Geo Light Imaging National Testbed will be buit to demonstrate new powerful imaging capability. Several processes including laser speckle, atmospheric turbulence on the downlink and 1-km horizontal path, as well as Poisson shot noise can contribute to the measurement error of the Fourier phase of the object and thus degrade the reconstructed image. We investigated the impact of three processes including laser speckle, turbulence, and Poisson shot noise on the measurement error of the Fourier phase. We introduced the concept of power-in-the-bucket receiver and applied this concept to the receiver in the Fourier telescopy system. We found that the power-in-the-bucket receiver cancels the effects of turbulence on the horizontal path on the Fourier telescopy system. We evaluated variance of the real and imaginary parts of the triple product, as well as variance of the Fourier phase of the object by using a numercal simulation code. The twelfth moment of the optcal filed was calculated in the resenceof laser speckle, atmospheric turbulence, and Poisson shot noise. Simulation results confirmed that Fourier telescopy system is immune to the efects of turbulence on the horizontal path. It also showed that the effect of turbulence on the downlink path on the triple product is small. Laser speckle contributes strongly to the variations of the real part of the triple product and weakly to the imaginary part. Statistical properties of the triple product depend on the noise source. Poisson shot noise and laser speckle poduce the main contribution to the variance of the triple product and measurement error of the object Fourier pase. Phase variance reduces with increasing the number of heliostats, number of pulses, fringe visibility, and fringe signal-to-noise ratio. For 40 heliostat receivers, 100 averaged pulses, and all considered fringe SNRs
NASA Technical Reports Server (NTRS)
Cheng, Anning; Xu, Kuan-Man
2015-01-01
Five-year simulation experiments with a multi-scale modeling Framework (MMF) with a advanced intermediately prognostic higher-order turbulence closure (IPHOC) in its cloud resolving model (CRM) component, also known as SPCAM-IPHOC (super parameterized Community Atmospheric Model), are performed to understand the fast tropical (30S-30N) cloud response to an instantaneous doubling of CO2 concentration with SST held fixed at present-day values. SPCAM-IPHOC has substantially improved the low-level representation compared with SPCAM. It is expected that the cloud responses to greenhouse warming in SPCAM-IPHOC is more realistic. The change of rising motion, surface precipitation, cloud cover, and shortwave and longwave cloud radiative forcing in SPCAM-IPHOC from the greenhouse warming will be presented in the presentation.
Osman, K T; Wan, M; Matthaeus, W H; Weygand, J M; Dasso, S
2011-10-14
The first direct determination of the inertial range energy cascade rate, using an anisotropic form of Yaglom's law for magnetohydrodynamic turbulence, is obtained in the solar wind with multispacecraft measurements. The two-point mixed third-order structure functions of Elsässer fluctuations are integrated over a sphere in magnetic field-aligned coordinates, and the result is consistent with a linear scaling. Therefore, volume integrated heating and cascade rates are obtained that, unlike previous studies, make only limited assumptions about the underlying spectral geometry of solar wind turbulence. These results confirm the turbulent nature of magnetic and velocity field fluctuations in the low frequency limit, and could supply the energy necessary to account for the nonadiabatic heating of the solar wind.
NASA Astrophysics Data System (ADS)
Bou-Zeid, Elie; Huang, Jing; Golaz, Jean-Christophe
2011-11-01
A disconnect remains between our improved physical understanding of boundary layers stabilized by buoyancy and how we parameterize them in coarse atmospheric models. Most operational climate models require excessive turbulence mixing in such conditions to prevent decoupling of the atmospheric component from the land component, but the performance of such a model is unlikely to be satisfactory under weakly and moderately stable conditions. Using Large-eddy simulation, we revisit some of the basic challenges in parameterizing stable atmospheric boundary layers: eddy-viscosity closure is found to be more reliable due to an improved alignment of vertical Reynolds stresses and mean strains under stable conditions, but the dependence of the magnitude of the eddy viscosity on stability is not well represented by several models tested here. Thus, we propose a new closure that reproduces the different stability regimes better. Subsequently, tests of this model in the GFDL's single-column model (SCM) are found to yield good agreement with LES results in idealized steady-stability cases, as well as in cases with gradual and sharp changes of stability with time.
A hybrid Reynolds averaged/PDF closure model for supersonic turbulent combustion
NASA Technical Reports Server (NTRS)
Frankel, Steven H.; Hassan, H. A.; Drummond, J. Philip
1990-01-01
A hybrid Reynolds averaged/assumed pdf approach has been developed and applied to the study of turbulent combustion in a supersonic mixing layer. This approach is used to address the 'laminar-like' treatment of the thermochemical terms that appear in the conservation equations. Calculations were carried out for two experiments involving H2-air supersonic turbulent mixing. Two different forms of the pdf were implemented. In general, the results show modest improvement from previous calculations. Moreover, the results appear to be somewhat independent of the form of the assumed pdf.
Comparison of a correlation term-discard closure for decaying homogeneous turbulence with experiment
NASA Technical Reports Server (NTRS)
Deissler, R. G.
1979-01-01
Turbulence decay is calculated by using experimental initial conditions and discarding quadruple-correlation terms in the correlation equations. Agreement with experiment is good only for moderately small times, but there are no perceptible negative spectral energies even at large times.
Third-moment descriptions of the interplanetary turbulent cascade, intermittency and back transfer
Coburn, Jesse T.; Forman, Miriam A.; Smith, Charles W.; Vasquez, Bernard J.; Stawarz, Julia E.
2015-01-01
We review some aspects of solar wind turbulence with an emphasis on the ability of the turbulence to account for the observed heating of the solar wind. Particular attention is paid to the use of structure functions in computing energy cascade rates and their general agreement with the measured thermal proton heating. We then examine the use of 1 h data samples that are comparable in length to the correlation length for the fluctuations to obtain insights into local inertial range dynamics and find evidence for intermittency in the computed energy cascade rates. When the magnetic energy dominates the kinetic energy, there is evidence of anti-correlation in the cascade of energy associated with the outward- and inward-propagating components that we can only partially explain. PMID:25848079
NASA Technical Reports Server (NTRS)
Xu, Kuan-Man; Cheng, Anning
2007-01-01
The effects of subgrid-scale condensation and transport become more important as the grid spacings increase from those typically used in large-eddy simulation (LES) to those typically used in cloud-resolving models (CRMs). Incorporation of these effects can be achieved by a joint probability density function approach that utilizes higher-order moments of thermodynamic and dynamic variables. This study examines how well shallow cumulus and stratocumulus clouds are simulated by two versions of a CRM that is implemented with low-order and third-order turbulence closures (LOC and TOC) when a typical CRM horizontal resolution is used and what roles the subgrid-scale and resolved-scale processes play as the horizontal grid spacing of the CRM becomes finer. Cumulus clouds were mostly produced through subgrid-scale transport processes while stratocumulus clouds were produced through both subgrid-scale and resolved-scale processes in the TOC version of the CRM when a typical CRM grid spacing is used. The LOC version of the CRM relied upon resolved-scale circulations to produce both cumulus and stratocumulus clouds, due to small subgrid-scale transports. The mean profiles of thermodynamic variables, cloud fraction and liquid water content exhibit significant differences between the two versions of the CRM, with the TOC results agreeing better with the LES than the LOC results. The characteristics, temporal evolution and mean profiles of shallow cumulus and stratocumulus clouds are weakly dependent upon the horizontal grid spacing used in the TOC CRM. However, the ratio of the subgrid-scale to resolved-scale fluxes becomes smaller as the horizontal grid spacing decreases. The subcloud-layer fluxes are mostly due to the resolved scales when a grid spacing less than or equal to 1 km is used. The overall results of the TOC simulations suggest that a 1-km grid spacing is a good choice for CRM simulation of shallow cumulus and stratocumulus.
Turbulent Transport in Fusion Plasmas, Effects of Toroidicity and Fluid Closure
Weiland, Jan
2009-11-10
Basic aspects of turbulent transport in toroidal magnetized plasmas are discussed. In particular Kadomtsev's mixing length estimate is found to work well for the Cyclone base case at the experimental gradient. Generalizations to include non-Markovian effects and off diagonal fluxes are given. The importance of toroidal effects is stressed These enter particularly strongly in convective or off diagonal fluxes. This feature applies also to momentum ttransport.
NASA Technical Reports Server (NTRS)
Eisfeld, Bernhard; Rumsey, Chris; Togiti, Vamshi
2015-01-01
The implementation of the SSG/LRR-omega differential Reynolds stress model into the NASA flow solvers CFL3D and FUN3D and the DLR flow solver TAU is verified by studying the grid convergence of the solution of three different test cases from the Turbulence Modeling Resource Website. The model's predictive capabilities are assessed based on four basic and four extended validation cases also provided on this website, involving attached and separated boundary layer flows, effects of streamline curvature and secondary flow. Simulation results are compared against experimental data and predictions by the eddy-viscosity models of Spalart-Allmaras (SA) and Menter's Shear Stress Transport (SST).
NASA Astrophysics Data System (ADS)
Macole, Sabat; Vié, Aymeric; Larat, Adam; Doisneau, Francois; Chalons, Christophe; Massot, Marc
2014-11-01
The simulation of particle-laden flows is a challenging topic due to their multiscale character. Lagrangian particle tracking methods are classically used. However, for high performance computing, such approaches deteriorate with the disperse phase inhomogeneities. Moment methods bypass this issue through an Eulerian framework allowing to use the same parallelization paradigm as the gas phase. We present recent developments for DNS and LES based on a Kinetic-Based Moment Method. The moment system is closed by assuming a presumed shape for the NDF. The selected NDF is an Anisotropic Gaussian giving the following properties: 1/hyperbolicity; 2/realizability of the moments; 3/maximization of entropy; 4/H-theorem. The method is evaluated on configurations of increasing complexity that exhibit its potential and drawbacks. This method extends towards LES by means of a full kinetic-based filtering technique instead of filtering the moment equations. Thus realizability conditions are easily derived, and the main properties of the DNS system are preserved. The subgrid terms are closed following the work of Zaichik et al. 2009. The resulting LES strategy is evaluated based on filtered DNS results.
NASA Astrophysics Data System (ADS)
Dunn, Dennis; Squires, Kyle
2015-11-01
Modeling dispersions of particles in multiphase flows is especially challenging in gas-solid suspensions. Lagrangian methods are suitable for dilute particle mediums, but are not cost effective at denser concentrations and impose additional modeling challenges. A moderately dense particle phase is neither sufficiently dense for a continuum limit assumption (collisional equilibrium) nor sufficiently dilute for a Lagrangian method, and resides in the intermediate regime under consideration in the current work. A quadrature-based moment method (QBMM) is chosen to simulate a particle-laden turbulent channel flow considering inter-particle collision effects. In quadrature-based approaches similarly behaving particles may be grouped together and treated in a stochastic manner within an Eulerian framework. Specifically, the Conditional Quadrature Method of Moments (CQMOM) is implemented to discretize a fully 3-D velocity space and capture particle trajectory crossing (PTC). This has the potential for large computational savings as compared to Lagrangian methods, especially when dense collisions are prominent. The probability density function is discretized with a two-point-quadrature in each dimension - the minimum requirement to capture PTC and enforce collisions. Predictions of the channel flow demonstrate that the collision treatment leads to the expected effects (e.g., redistribution of kinetic energy) and also offer improved accuracy relative to simpler approaches.
NASA Technical Reports Server (NTRS)
Shabbir, Aamir
1991-01-01
The heat flux and Reynolds stress budgets are presented for a buoyant plume. The terms involving pressure correlations are obtained as the closing terms in these budgets. Despite certain measurement errors, these budgets provide useful information about how various phenomena contribute to the transport of second moments. These experimental results are used to assess the local equilibrium assumption and to investigate why the mechanical to thermal time scale ratio for a buoyant plume is different than the commonly recommended value. Analysis show that this departure is a consequence of the local equilibrium assumption being not satisfied in the present experiment.
A numerical method for prediction of compressible turbulent flows with closure models
NASA Technical Reports Server (NTRS)
Huang, P. G.
1990-01-01
A new computer code to solve the time averaged Navier-Stokes equations is developed. Many of the state-of-the-art numerical techniques and algorithms have been tested and implemented in the program in order to achieve a better numerical accuracy and code efficiency. Various turbulence models are tested for a wide range of flows. The initial focus has been on two-equation eddy-viscosity models, which are the most advanced available in current compressible flow codes. The long term goal will be to test Reynolds-Stress models and to explore their performance in the high Mach number range. Although testing and improvement of turbulence models for supersonic and hypersonic flows is the primary objective of this research, part of the effort has been devoted to analyzing the vortex breakdown phenomena using new computer programs. Some preliminary results on the breakdown of a vortex flow in a tube are reported. Present calculations are restricted to two dimensional flow geometry.
Mean velocity and moments of turbulent velocity fluctuations in the wake of a model ship propulsor
NASA Astrophysics Data System (ADS)
Pêgo, J. P.; Lienhart, H.; Durst, F.
2007-08-01
; Schneekluth and Bertram in Ship design for efficiency and economy, 1998), the co-rotating propellers model showed a much stronger swirl in the wake of the propulsor. The anisotropy of turbulence was analyzed using the anisotropy tensor introduced by Lumley and Newman (J Fluid Mech 82(1):161-178, 1977). The invariants of the anisotropy tensor of the wake flow were computed and were plotted in the Lumley-Newman-diagram. These measurements revealed that the anisotropy tensor in the wake of ship propellers is located near to the borders of the invariant map, showing a large degree of anisotropy. They will be presented and will be discussed with respect to applications of turbulence models to predict swirling flows.
NASA Technical Reports Server (NTRS)
1996-01-01
Topics considered include: New approach to turbulence modeling; Second moment closure analysis of the backstep flow database; Prediction of the backflow and recovery regions in the backward facing step at various Reynolds numbers; Turbulent flame propagation in partially premixed flames; Ensemble averaged dynamic modeling. Also included a study of the turbulence structures of wall-bounded shear flows; Simulation and modeling of the elliptic streamline flow.
Yoshimatsu, Katsunori
2012-06-01
The four-fifths law for third-order longitudinal moments is examined, using direct numerical simulation (DNS) data on three-dimensional (3D) forced incompressible magnetohydrodynamic (MHD) turbulence without a uniformly imposed magnetic field in a periodic box. The magnetic Prandtl number is set to one, and the number of grid points is 512(3). A generalized Kármán-Howarth-Kolmogorov equation for second-order velocity moments in isotropic MHD turbulence is extended to anisotropic MHD turbulence by means of a spherical average over the direction of r. Here, r is a separation vector. The viscous, forcing, anisotropic and nonstationary terms in the generalized equation are quantified. It is found that the influence of the anisotropic terms on the four-fifths law is negligible at small scales, compared to that of the viscous term. However, the influence of the directional anisotropy, which is measured by the departure of the third-order moments in a particular direction of r from the spherically averaged ones, on the four-fifths law is suggested to be substantial, at least in the case studied here.
NASA Astrophysics Data System (ADS)
Yang, X. I. A.; Meneveau, C.; Marusic, I.; Biferale, L.
2016-08-01
In wall-bounded turbulence, the moment generating functions (MGFs) of the streamwise velocity fluctuations
NASA Technical Reports Server (NTRS)
Xu, Kuan-Man; Cheng, Anning
2010-01-01
This study presents preliminary results from a multiscale modeling framework (MMF) with an advanced third-order turbulence closure in its cloud-resolving model (CRM) component. In the original MMF, the Community Atmosphere Model (CAM3.5) is used as the host general circulation model (GCM), and the System for Atmospheric Modeling with a first-order turbulence closure is used as the CRM for representing cloud processes in each grid box of the GCM. The results of annual and seasonal means and diurnal variability are compared between the modified and original MMFs and the CAM3.5. The global distributions of low-level cloud amounts and precipitation and the amounts of low-level clouds in the subtropics and middle-level clouds in mid-latitude storm track regions in the modified MMF show substantial improvement relative to the original MMF when both are compared to observations. Some improvements can also be seen in the diurnal variability of precipitation.
NASA Technical Reports Server (NTRS)
Wang, Shouping; Wang, Qing
1994-01-01
This study focuses on the effects of drizzle in a one-dimensional third-order turbulence closure model of the nocturnal stratus-topped marine boundary layer. When the simulated drizzle rate is relatively small (maximum approximately equal to 0.6 mm/day), steady-state solutions are obtained. The boundary layer stabilizes essentially because drizzle causes evaporative cooling of the subcloud layer. This stabilization considerably reduces the buoyancy flux and turbulence kinetic energy below the stratus cloud. Thus, drizzle tends to decouple the cloud from the subcloud layer in the model, as suggested by many observational studies. In addition, the evaporation of drizzle in the subcloud layer creates small scattered clouds, which are likely to represent cumulus clouds, below the solid stratus cloud in the model. The sensitivity experiments show that these scattered clouds help maintain a coupled boundary layer. When the drizzle rate is relatively large (maximum approximately equal to 0.9 mm/day), the response of the model becomes transient with bursts in turbulent fluxes. This phenomenon is related to the formation of the scattered cloud layer below the solid stratus cloud. It appears that the model is inadequate to represent the heat and moisture transport by strong updrafts covering a small fractional area in cumulus convection.
Ihme, Matthias; Pitsch, Heinz
2008-10-15
Previously conducted studies of the flamelet/progress variable model for the prediction of nonpremixed turbulent combustion processes identified two areas for model improvements: the modeling of the presumed probability density function (PDF) for the reaction progress parameter and the consideration of unsteady effects [Ihme et al., Proc. Combust. Inst. 30 (2005) 793]. These effects are of particular importance during local flame extinction and subsequent reignition. Here, the models for the presumed PDFs for conserved and reactive scalars are re-examined and a statistically most likely distribution (SMLD) is employed and tested in a priori studies using direct numerical simulation (DNS) data and experimental results from the Sandia flame series. In the first part of the paper, the SMLD model is employed for a reactive scalar distribution. Modeling aspects of the a priori PDF, accounting for the bias in composition space, are discussed. The convergence of the SMLD with increasing number of enforced moments is demonstrated. It is concluded that information about more than two moments is beneficial to accurately represent the reactive scalar distribution in turbulent flames with strong extinction and reignition. In addition to the reactive scalar analysis, the potential of the SMLD for the representation of conserved scalar distributions is also analyzed. In the a priori study using DNS data it is found that the conventionally employed beta distribution provides a better representation for the scalar distribution. This is attributed to the fact that the beta-PDF implicitly enforces higher moment information that is in excellent agreement with the DNS data. However, the SMLD outperforms the beta distribution in free shear flow applications, which are typically characterized by strongly skewed scalar distributions, in the case where higher moment information can be enforced. (author)
NASA Astrophysics Data System (ADS)
Frisch, Uriel
1996-01-01
Written five centuries after the first studies of Leonardo da Vinci and half a century after A.N. Kolmogorov's first attempt to predict the properties of flow, this textbook presents a modern account of turbulence, one of the greatest challenges in physics. "Fully developed turbulence" is ubiquitous in both cosmic and natural environments, in engineering applications and in everyday life. Elementary presentations of dynamical systems ideas, probabilistic methods (including the theory of large deviations) and fractal geometry make this a self-contained textbook. This is the first book on turbulence to use modern ideas from chaos and symmetry breaking. The book will appeal to first-year graduate students in mathematics, physics, astrophysics, geosciences and engineering, as well as professional scientists and engineers.
Turbulence modelling in CFD: Present status, future prospects
NASA Technical Reports Server (NTRS)
Launder, Brian E.
1992-01-01
Information is given in viewgraph form for turbulence modeling in computational fluid dynamics (CFD). The Eddy Viscosity Models (EVM), Algebraic Second Moment Closures (ASM), and Differential Second-Moment Closures (DSM) are considered. It is concluded that EVM's, ASM's, and DSM's will remain in use, though with a steady decline in importance of EVM's and ASM's in favor of DSM's. Improved versions of low-Re two-equation EVM's should lead to more reliable predictions of separated flows than are achievable at present. Further refinement of sub-models in second moment closures can be expected throughout this decade. There will be increasing attention given to interfacing SMC with higher order approaches such as LES, and an increased use of two-time-scale schemes providing distinct time scales for large and fairly small eddies.
Turbulence modelling in CFD: Present status, future prospects
NASA Technical Reports Server (NTRS)
Launder, Brian E.
1992-01-01
Information is given in viewgraph form for turbulence modeling in computational fluid dynamics (CFD). The Eddy Viscosity Models (EVM), Algebraic Second Moment Closures (ASM), and Differential Second-Moment Closures (DSM) are considered. It is concluded that EVM's, ASM's, and DSM's will remain in use, though with a steady decline in importance of EVM's and ASM's in favor of DSM's. Improved versions of low-Re two-equation EVM's should lead to more reliable predictions of separated flows than are achievable at present. Further refinement of sub-models in second moment closures can be expected throughout this decade. There will be increasing attention given to interfacing SMC with higher order approaches such as LES, and an increased use of two-time-scale schemes providing distinct time scales for large and fairly small eddies.
Systematic study of Reynolds stress closure models in the computations of plane channel flows
NASA Technical Reports Server (NTRS)
Demuren, A. O.; Sarkar, S.
1992-01-01
The roles of pressure-strain and turbulent diffusion models in the numerical calculation of turbulent plane channel flows with second-moment closure models are investigated. Three turbulent diffusion and five pressure-strain models are utilized in the computations. The main characteristics of the mean flow and the turbulent fields are compared against experimental data. All the features of the mean flow are correctly predicted by all but one of the Reynolds stress closure models. The Reynolds stress anisotropies in the log layer are predicted to varying degrees of accuracy (good to fair) by the models. None of the models could predict correctly the extent of relaxation towards isotropy in the wake region near the center of the channel. Results from the directional numerical simulation are used to further clarify this behavior of the models.
NASA Astrophysics Data System (ADS)
Manickam, B.; Franke, J.; Muppala, S. P. R.; Dinkelacker, F.
In this LES study, an algebraic flame surface wrinkling model based on the progress variable gradient approach is validated for lean premixed turbulent propane/air flames measured on VOLVO test rig. These combustion results are analyzed for uncertainty in the solution using two quality assessment techniques.
Turbulence modeling for separated flow
NASA Technical Reports Server (NTRS)
Durbin, Paul A.
1994-01-01
Two projects are described in this report. The first involves assessing turbulence models in separated flow. The second addresses the anomalous behavior of certain turbulence models in stagnation point flow. The primary motivation for developing turbulent transport models is to provide tools for computing non-equilibrium, or complex, turbulent flows. Simple flows can be analyzed using data correlations or algebraic eddy viscosities, but in more complicated flows such as a massively separated boundary layer, a more elaborate level of modeling is required. It is widely believed that at least a two-equation transport model is required in such cases. The transport equations determine the evolution of suitable velocity and time-scales of the turbulence. The present study included assessment of second-moment closures in several separated flows, including sharp edge separation; smooth wall, pressure driven separation; and unsteady vortex shedding. Flows with mean swirl are of interest for their role in enhancing mixing both by turbulent and mean motion. The swirl can have a stabilizing effect on the turbulence. An axi-symmetric extension to the INS-2D computer program was written adding the capability of computing swirling flow. High swirl can produce vortex breakdown on the centerline of the jet and it occurs in various combustors.
NASA Astrophysics Data System (ADS)
Behrendt, A.; Wulfmeyer, V.; Hammann, E.; Muppa, S. K.; Pal, S.
2015-05-01
The rotational Raman lidar (RRL) of the University of Hohenheim (UHOH) measures atmospheric temperature profiles with high resolution (10 s, 109 m). The data contain low-noise errors even in daytime due to the use of strong UV laser light (355 nm, 10 W, 50 Hz) and a very efficient interference-filter-based polychromator. In this paper, the first profiling of the second- to fourth-order moments of turbulent temperature fluctuations is presented. Furthermore, skewness profiles and kurtosis profiles in the convective planetary boundary layer (CBL) including the interfacial layer (IL) are discussed. The results demonstrate that the UHOH RRL resolves the vertical structure of these moments. The data set which is used for this case study was collected in western Germany (50°53'50.56'' N, 6°27'50.39'' E; 110 m a.s.l.) on 24 April 2013 during the Intensive Observations Period (IOP) 6 of the HD(CP)2 (High-Definition Clouds and Precipitation for advancing Climate Prediction) Observational Prototype Experiment (HOPE). We used the data between 11:00 and 12:00 UTC corresponding to 1 h around local noon (the highest position of the Sun was at 11:33 UTC). First, we investigated profiles of the total noise error of the temperature measurements and compared them with estimates of the temperature measurement uncertainty due to shot noise derived with Poisson statistics. The comparison confirms that the major contribution to the total statistical uncertainty of the temperature measurements originates from shot noise. The total statistical uncertainty of a 20 min temperature measurement is lower than 0.1 K up to 1050 m a.g.l. (above ground level) at noontime; even for single 10 s temperature profiles, it is smaller than 1 K up to 1020 m a.g.l. Autocovariance and spectral analyses of the atmospheric temperature fluctuations confirm that a temporal resolution of 10 s was sufficient to resolve the turbulence down to the inertial subrange. This is also indicated by the integral scale of
NASA Astrophysics Data System (ADS)
Mochizuki, Shinsuke; Osaka, Hideo
1989-10-01
Some properties associated with the large eddy structures of a d-type rough wall turbulent boundary layer at a momentum thickness Reynolds number R sub theta = 800 have been examined experimentally. The higher order moments and the contribution of violent events to the Reynolds shear stress are measured and compared with the results of both smooth and k-type rough wall flow as well as a d-type rough wall flow at a high Reynolds number R sub theta = 5000. The low Reynolds number effect in the outer layer, which in general enlarges the contorted surface of the viscous super-layer, is found even in the present rough wall flow.
Mechanics of Turbulence of Multicomponent Gases
NASA Astrophysics Data System (ADS)
Marov, Mikhail Ya.; Kolesnichenko, Aleksander V.
2002-02-01
Turbulence in multicomponent reacting gas mixtures is an important mechanism underlying numerous natural phenomena closely related to the study of our space environment. This book develops a new mathematical approach for modelling multicomponent gas turbulence that adequately describes the combined processes of dynamics and heat and mass transfer when chemical kinetics and turbulent mixing are equally important. The developed models include the evolutionary transfer equations for the single-point second correlation moments of turbulent fluctuations of thermohydrodynamical parameters. The phenomenological approach to the closure problem in hydrodynamic equations of mean motion at the level of the first order moments is based on the thermodynamics of irreversible processes and enables defining relationships in a more general form as compared to those conventionally deduced using the mixing path concept. Based on the developed approach, turbulent exchange factors for a planetary upper atmosphere are evaluated, and a turbulent model of a protoplanetary accretion gas-dust disk involving heat and mass transfer and coagulation is also considered. As compared to previously published books on the problem of turbulence, this book deals, for the first time, with the complicated models of reacting gas mixtures. It is intended for graduate and postgraduate students in the fields of fluid gas dynamics, astrophysics, space physics, planetary sciences, and aeronomy, and especially for those dealing with computer modelling of the processes in such natural media. The book may also be of interest to specialists in the relevant fields of ecology, engineering, and material processing.
NASA Astrophysics Data System (ADS)
Behrendt, A.; Wulfmeyer, V.; Hammann, E.; Muppa, S. K.; Pal, S.
2014-11-01
The rotational Raman lidar of the University of Hohenheim (UHOH) measures atmospheric temperature profiles during daytime with high resolution (10 s, 109 m). The data contain low noise errors even in daytime due to the use of strong UV laser light (355 nm, 10 W, 50 Hz) and a very efficient interference-filter-based polychromator. In this paper, we present the first profiling of the second- to forth-order moments of turbulent temperature fluctuations as well as of skewness and kurtosis in the convective boundary layer (CBL) including the interfacial layer (IL). The results demonstrate that the UHOH RRL resolves the vertical structure of these moments. The data set which is used for this case study was collected in western Germany (50°53'50.56'' N, 6°27'50.39'' E, 110 m a.s.l.) within one hour around local noon on 24 April 2013 during the Intensive Observations Period (IOP) 6 of the HD(CP)2 Observational Prototype Experiment (HOPE), which is embedded in the German project HD(CP)2 (High-Definition Clouds and Precipitation for advancing Climate Prediction). First, we investigated profiles of the noise variance and compared it with estimates of the statistical temperature measurement uncertainty Δ T based on Poisson statistics. The agreement confirms that photon count numbers obtained from extrapolated analog signal intensities provide a lower estimate of the statistical errors. The total statistical uncertainty of a 20 min temperature measurement is lower than 0.1 K up to 1050 m a.g.l. at noontime; even for single 10 s temperature profiles, it is smaller than 1 K up to 1000 m a.g.l.. Then we confirmed by autocovariance and spectral analyses of the atmospheric temperature fluctuations that a temporal resolution of 10 s was sufficient to resolve the turbulence down to the inertial subrange. This is also indicated by the profile of the integral scale of the temperature fluctuations, which was in the range of 40 to 120 s in the CBL. Analyzing then profiles of the second
Ahmed, Khurshid; Munawar, Muhammad; Chakraborty, Rabin; Hartono, Beny; Yusri, Achmad
2015-01-01
Rupture of sinus of Valsalva (SV) is a rare occurrence with a wide spectrum of presentation, ranging from an asymptomatic murmur to cardiogenic shock or even sudden cardiac death. We hereby report a case which was successfully closed by transcatheter technique. In this case, ruptured SV was entered from the aorta, an arteriovenous loop was created and device was implanted using a venous approach. The procedure was safe, effective and uncomplicated, obviating the need for surgery. In this case, the authors report for the first time the use of echo color Doppler turbulent flow jet diameter as a reference value for sizing the device.
Research activities at the Center for Modeling of Turbulence and Transition
NASA Technical Reports Server (NTRS)
Shih, Tsan-Hsing
1993-01-01
The main research activities at the Center for Modeling of Turbulence and Transition (CMOTT) are described. The research objective of CMOTT is to improve and/or develop turbulence and transition models for propulsion systems. The flows of interest in propulsion systems can be both compressible and incompressible, three dimensional, bounded by complex wall geometries, chemically reacting, and involve 'bypass' transition. The most relevant turbulence and transition models for the above flows are one- and two-equation eddy viscosity models, Reynolds stress algebraic- and transport-equation models, pdf models, and multiple-scale models. All these models are classified as one-point closure schemes since only one-point (in time and space) turbulent correlations, such as second moments (Reynolds stresses and turbulent heat fluxes) and third moments, are involved. In computational fluid dynamics, all turbulent quantities are one-point correlations. Therefore, the study of one-point turbulent closure schemes is the focus of our turbulence research. However, other research, such as the renormalization group theory, the direct interaction approximation method, and numerical simulations are also pursued to support the development of turbulence modeling.
PDF modeling of turbulence-radiation interactions
Mazumder, S.; Modest, M.F.
1997-07-01
The interactions between turbulence and radiation, although acknowledged and qualitatively understood over the last several decades, are extremely difficult to model. Traditional Eulerian turbulence models are incapable of addressing the closure problem for any realistic reactive flow situation, because of the large number of unknown turbulent moments that need to be modeled. A novel approach, based on the velocity-composition joint probability density function (PDF) method, is presented. This approach is Lagrangian in nature and provides an elegant and feasible alternative to turbulence closure. A mixed Monte Carlo/finite-volume technique is used to simulate a bluff-body-stabilized methane-air diffusion flame in a two-dimensional planar recirculating combustor, and enables treatment of turbulence in recirculating flows, finite-rate chemistry, and multiple-band radiation calculations within the CPU limitations of a standard single-processor workstation. Results demonstrate the role of radiation and turbulence-radiation interactions in altering the overall flame structure, the wall heat loads, and the overall heat emission by the flame at various Reynolds numbers and equivalence ratios.
Turbulence modeling and experiments
NASA Technical Reports Server (NTRS)
Shabbir, Aamir
1992-01-01
The best way of verifying turbulence is to do a direct comparison between the various terms and their models. The success of this approach depends upon the availability of the data for the exact correlations (both experimental and DNS). The other approach involves numerically solving the differential equations and then comparing the results with the data. The results of such a computation will depend upon the accuracy of all the modeled terms and constants. Because of this it is sometimes difficult to find the cause of a poor performance by a model. However, such a calculation is still meaningful in other ways as it shows how a complete Reynolds stress model performs. Thirteen homogeneous flows are numerically computed using the second order closure models. We concentrate only on those models which use a linear (or quasi-linear) model for the rapid term. This, therefore, includes the Launder, Reece and Rodi (LRR) model; the isotropization of production (IP) model; and the Speziale, Sarkar, and Gatski (SSG) model. Which of the three models performs better is examined along with what are their weaknesses, if any. The other work reported deal with the experimental balances of the second moment equations for a buoyant plume. Despite the tremendous amount of activity toward the second order closure modeling of turbulence, very little experimental information is available about the budgets of the second moment equations. Part of the problem stems from our inability to measure the pressure correlations. However, if everything else appearing in these equations is known from the experiment, pressure correlations can be obtained as the closing terms. This is the closest we can come to in obtaining these terms from experiment, and despite the measurement errors which might be present in such balances, the resulting information will be extremely useful for the turbulence modelers. The purpose of this part of the work was to provide such balances of the Reynolds stress and heat
NASA Astrophysics Data System (ADS)
Leitch, A. S.; Nesic, Z.; Christen, A.; Black, T. A.
2010-12-01
opposing gradient in manual chamber-measured soil CO2 effluxes. The additional CO2 difference measurement period at the 2.6-m height (with IRGAs measuring at 2 Hz) also included 5 CSAT3 sonic anemometers measuring at the same locations at 10 Hz. The setup permits back-of-the-envelope calculation of horizontal turbulent CO2 flux divergence along the 73.5-m transect, a term in the scalar conservation equation which has received much interest but little quantification in the literature. The IRGAs also measured high frequency water vapour concentrations, permitting the calculation of (horizontal) turbulent and (horizontal and vertical) advective H2O fluxes. H2O fluxes other than the vertical turbulent flux are not routinely calculated, but may have the potential to shed light on the energy-balance closure problem in the same manner as advective CO2 fluxes comment on the friction velocity correction procedure. Horizontal turbulent carbon dioxide flux divergence and energy balance closure will be discussed, along with final conclusions for advective carbon dioxide fluxes at DF49.
CFD Simulation of the Turbulent Flow and Heat Transfer in a Bare Rod Bundle
In, W.K.; Shin, C.H.; Oh, D.S.; Chun, T.H.
2004-07-01
A computational fluid dynamics(CFD) analysis has been performed to investigate the turbulent flow and heat transfer in a triangular rod bundle with pitch-to-diameter ratios(P/D) of 1.06 and 1.12. The CFD predictions using various turbulence models were compared with the experimental results. Anisotropic turbulence models(nonlinear k - {epsilon} and second-moment closure models) predicted the turbulence-driven secondary flow in the triangular subchannel and the distributions of the time mean velocity and temperature showing a significantly improved agreement with the measurements from the linear standard k - {epsilon} model. The anisotropic turbulence models predicted the turbulence structure for a rod bundle with a large P/D fairly well but could not predict the very high turbulent intensity of the azimuthal velocity observed in the narrow flow region(gap) for a rod bundle with a small P/D. (authors)
Scalar Dispersion Inside Plant Canopies: The Role of Turbulence Intermittency
NASA Astrophysics Data System (ADS)
Chamecki, M.; Zhang, K.; Pan, Y.; Gleicher, S.; Isard, S.
2012-12-01
Turbulent dispersion of scalar quantities such as heat, water vapor, carbon dioxide, biogenic volatile organic compounds and pathogenic spores within plant canopies play a major role in many problems of practical interest. The non-Gaussian, strongly skewed, highly organized, and vertically heterogeneous turbulence produced by the interactions between the flow and the plant canopy and the complex spatial distribution of sources and sinks of these scalars give rise to one of the most challenging problems in atmospheric turbulence. Given this complex scenario, the failure of standard eddy-diffusivity models in predicting the turbulent fluxes of scalars within plant canopies should be no surprise. The usual alternative is to use second-order closure models to determine the scalar fluxes, requiring eddy-diffusivity type closures for third-order moments. In this work we revisit the problem of scalar dispersion within a plant canopy using a combination of experimental data obtained in a cornfield, numerical experiments using large eddy simulation, and simple Lagrangian models of particle dispersion. In particular, we focus on the effects of intermittency and higher-order moments of the vertical velocity on the turbulent fluxes of passive scalars. We show that the skewness of the vertical velocity fluctuations, which is associated with uneven distribution of timescales of sweeps and ejections, plays an important role in determining the vertical scalar fluxes. In addition, connections between the distribution of turbulence time scales and the residence time of scalars within the canopy region will be discussed.
NASA Astrophysics Data System (ADS)
Bogenschutz, P. A.; Gettelman, A.; Morrison, H.; Larson, V. E.; Schanen, D. P.; Meyer, N. R.; Craig, C.
2012-07-01
This paper describes the coupling of the Community Atmosphere Model (CAM) version 5 with a unified multi-variate probability density function (PDF) parameterization, Cloud Layers Unified by Binormals (CLUBB). CLUBB replaces the planetary boundary layer (PBL), shallow convection, and cloud macrophysics schemes in CAM5 with a higher-order turbulence closure based on an assumed PDF. Comparisons of single-column versions of CAM5 and CAM-CLUBB are provided in this paper for several boundary layer regimes. As compared to Large Eddy Simulations (LES), CAM-CLUBB and CAM5 simulate marine stratocumulus regimes with similar accuracy. For shallow convective regimes, CAM-CLUBB improves the representation of cloud cover and liquid water path (LWP). In addition, for shallow convection CAM-CLUBB offers better fidelity for sub-grid scale vertical velocity, which is an important input for aerosol activation. Finally, CAM-CLUBB results are more robust to changes in vertical and temporal resolution when compared to CAM5.
NASA Astrophysics Data System (ADS)
Bogenschutz, P. A.; Gettelman, A.; Morrison, H.; Larson, V. E.; Schanen, D. P.; Meyer, N. R.; Craig, C.
2012-11-01
This paper describes the coupling of the Community Atmosphere Model (CAM) version 5 with a unified multi-variate probability density function (PDF) parameterization, Cloud Layers Unified by Binormals (CLUBB). CLUBB replaces the planetary boundary layer (PBL), shallow convection, and cloud macrophysics schemes in CAM5 with a higher-order turbulence closure based on an assumed PDF. Comparisons of single-column versions of CAM5 and CAM-CLUBB are provided in this paper for several boundary layer regimes. As compared to large eddy simulations (LESs), CAM-CLUBB and CAM5 simulate marine stratocumulus regimes with similar accuracy. For shallow convective regimes, CAM-CLUBB improves the representation of cloud cover and liquid water path (LWP). In addition, for shallow convection CAM-CLUBB offers better fidelity for subgrid-scale vertical velocity, which is an important input for aerosol activation. Finally, CAM-CLUBB results are more robust to changes in vertical and temporal resolution when compared to CAM5.
NASA Astrophysics Data System (ADS)
Ji, Jeong-Young; Lee, Hankyu Q.; Held, Eric D.
2017-02-01
Ion parallel closures are obtained for arbitrary atomic weights and charge numbers. For arbitrary collisionality, the heat flow and viscosity are expressed as kernel-weighted integrals of the temperature and flow-velocity gradients. Simple, fitted kernel functions are obtained from the 1600 parallel moment solution and the asymptotic behavior in the collisionless limit. The fitted kernel parameters are tabulated for various temperature ratios of ions to electrons. The closures can be used conveniently without solving the kinetic equation or higher order moment equations in closing ion fluid equations.
Analytical theories of turbulence and the epsilon expansion
NASA Astrophysics Data System (ADS)
Dannevik, William P.; Yakhot, Victor; Orszag, Steven A.
1987-07-01
The fixed-point form of hydrodynamic equations emerging from renormalization group (RNG) analysis of strong turbulence is analyzed using perturbation expansion in powers of the renormalized coupling constant. The stochastic models adopted to describe the universality of small scales and the basics of the RNG analysis are outlined. The properties of the analytical closures for the moment hierarchy derived by simple perturbation expansion are explored, and the Kolmogorov constant is computed. The procedure for diffusion of a passive scalar is outlined, and the derivation of turbulent diffusivity and the Batchelor constant is presented.
Modeling of Turbulent Swirling Flows
NASA Technical Reports Server (NTRS)
Shih, Tsan-Hsing; Zhu, Jiang; Liou, William; Chen, Kuo-Huey; Liu, Nan-Suey; Lumley, John L.
1997-01-01
Aircraft engine combustors generally involve turbulent swirling flows in order to enhance fuel-air mixing and flame stabilization. It has long been recognized that eddy viscosity turbulence models are unable to appropriately model swirling flows. Therefore, it has been suggested that, for the modeling of these flows, a second order closure scheme should be considered because of its ability in the modeling of rotational and curvature effects. However, this scheme will require solution of many complicated second moment transport equations (six Reynolds stresses plus other scalar fluxes and variances), which is a difficult task for any CFD implementations. Also, this scheme will require a large amount of computer resources for a general combustor swirling flow. This report is devoted to the development of a cubic Reynolds stress-strain model for turbulent swirling flows, and was inspired by the work of Launder's group at UMIST. Using this type of model, one only needs to solve two turbulence equations, one for the turbulent kinetic energy k and the other for the dissipation rate epsilon. The cubic model developed in this report is based on a general Reynolds stress-strain relationship. Two flows have been chosen for model evaluation. One is a fully developed rotating pipe flow, and the other is a more complex flow with swirl and recirculation.
Mizuno, Y; Ohi, K; Sogabe, T; Yamamoto, Y; Kaneda, Y
2010-09-01
A numerical analysis is made on the four-point correlation function in a similarity range of a model of two-dimensional passive scalar field ψ advected by a turbulent velocity field with infinitely small correlation time. The model yields an exact closure equation for the four-point correlation Ψ{4} of ψ, which may be casted into the form of an eigenvalue problem in the similarity range. The analysis of the eigenvalue problem gives not only the scale dependence of Ψ{4} , but also the dependence on the configuration of the four points. The numerical analysis gives S4(R)∝R{ζ{4}} in the similarity range in which S2(R)∝R{ζ{2}} , where S_{N} is the structure function defined by S{N}(R)≡⟨[ψ(x+R)-ψ(x)]{N} and ζ{4}≠2ζ{2} . The estimate of ζ_{4} by the numerical analysis of the eigenvalue problem is in good agreement with numerical simulations so far reported. The agreement supports the idea of universality of the exponent ζ{4} in the sense that ζ_{4} is insensitive to conditions of ψ outside the similarity range. The numerical analysis also shows that the correlation C(R,r)≡[ψ(x+R)-ψ(x)]{2}[ψ(x+r)-ψ(x)]{2}> is stronger than that given by the joint-normal approximation, and scales like C(R,r)∝(r/R){χ} for r/R<1 with R and r in the similarity range, where χ is a constant depending on the angle between R and r .
Methods of separation of variables in turbulence theory
NASA Technical Reports Server (NTRS)
Tsuge, S.
1978-01-01
Two schemes of closing turbulent moment equations are proposed both of which make double correlation equations separated into single-point equations. The first is based on neglected triple correlation, leading to an equation differing from small perturbed gasdynamic equations where the separation constant appears as the frequency. Grid-produced turbulence is described in this light as time-independent, cylindrically-isotropic turbulence. Application to wall turbulence guided by a new asymptotic method for the Orr-Sommerfeld equation reveals a neutrally stable mode of essentially three dimensional nature. The second closure scheme is based on an assumption of identity of the separated variables through which triple and quadruple correlations are formed. The resulting equation adds, to its equivalent of the first scheme, an integral of nonlinear convolution in the frequency describing a role due to triple correlation of direct energy-cascading.
A Study of Turbulence-Chemistry-Soot-Radiation Interaction in Luminous Turbulent Jet Flames
NASA Astrophysics Data System (ADS)
Roy, Somesh; Haworth, Daniel
2013-11-01
A detailed soot model based on method of moments with interpolative closure (MOMIC) is used in RANS simulations of luminous turbulent jet flames using OpenFOAM. A detailed chemical mechanism has been used to describe the chemistry of key soot precursors, and a transported probability density function (tPDF) method has been used to capture the turbulence-chemistry-soot-radiation interactions. The results from the detailed soot model have been compared with those from a semi-empirical, two-equation soot model for accuracy and performance. The effects of turbulence-chemistry-radiation interactions on soot dynamics are isolated and quantified. This work has been supported by NASA under cooperative agreement NNX07AB40A and by NSF under grant OCI-0904649.
On recontamination and directional-bias problems in Monte Carlo simulation of PDF turbulence models
NASA Technical Reports Server (NTRS)
Hsu, Andrew T.
1991-01-01
Turbulent combustion can not be simulated adequately by conventional moment closure turbulence models. The difficulty lies in the fact that the reaction rate is in general an exponential function of the temperature, and the higher order correlations in the conventional moment closure models of the chemical source term can not be neglected, making the applications of such models impractical. The probability density function (pdf) method offers an attractive alternative: in a pdf model, the chemical source terms are closed and do not require additional models. A grid dependent Monte Carlo scheme was studied, since it is a logical alternative, wherein the number of computer operations increases only linearly with the increase of number of independent variables, as compared to the exponential increase in a conventional finite difference scheme. A new algorithm was devised that satisfies a restriction in the case of pure diffusion or uniform flow problems. Although for nonuniform flows absolute conservation seems impossible, the present scheme has reduced the error considerably.
Predicting aerodynamic sound utilizing a two-point, two-time turbulence theory
NASA Technical Reports Server (NTRS)
Hecht, A. M.; Teske, M. E.; Bilanin, A. J.
1981-01-01
The feasibility of determining two-point, two-time turbulent velocity correlations based on extending closure models for one-point, one-time turbulence correlations is demonstrated. The procedure used is based on a spatial moment integral formulation of the governing equations using approximate, parameterized trial functions for the two-point, two-time velocity correlations. Solution of the equations is shown to give a set of anisotropic length scales and the separation-time-dependent decorrelation of the ensemble averaged turbulent velocities. The analysis is simplified using the assumption of homogeneous stationary turbulence and a constant shear, unidirectional mean flow. It is shown that the anisotropic behavior of measured turbulence correlations can be characterized through this technique.
Some Basic Laws of Isotropic Turbulent Flow
NASA Technical Reports Server (NTRS)
Loitsianskii, L. G.
1945-01-01
An Investigation is made of the diffusion of artificially produced turbulence behind screens or other turbulence producers. The method is based on the author's concept of disturbance moment as a certain theoretically well-founded measure of turbulent disturbances.
NASA Technical Reports Server (NTRS)
Bingham, G. J.; Noonan, K. W.
1974-01-01
An investigation was conducted in a low-turbulence pressure tunnel to determine the two-dimensional lift and pitching-moment characteristics of an NACA 6716 and an NACA 4416 airfoil with 35-percent-chord single-slotted flaps. Both models were tested with flaps deflected from 0 deg to 45 deg, at angles of attack from minus 6 deg to several degrees past stall, at Reynolds numbers from 3.0 million to 13.8 million, and primarily at a Mach number of 0.23. Tests were also made to determine the effect of several slot entry shapes on performance.
NASA Astrophysics Data System (ADS)
Varma, A. K.; Sandri, G.; Donaldson, C. Dup.
1980-01-01
Models for the scalar probability density function (pdf) have to be developed to achieve closure of turbulent transport equations for mixing and reacting flows. The best statistical bounds on a number of moments for two and three species flows have been derived and have been used to construct and test a delta function 'typical eddy' pdf model. It has been proven that for two species a rational pdf composed only of delta functions can always be constructed at any point within the statistically valid moment space. The delta function model and a canonical pdf model have been directly compared to experimental pdf measurements and both the models show good agreement for higher-order moments, but the delta function model is simpler to construct and is recommended for closure of the transport equations for mixing flows.
Center for Modeling of Turbulence and Transition (CMOTT). Research briefs: 1990
NASA Technical Reports Server (NTRS)
Povinelli, Louis A. (Compiler); Liou, Meng-Sing (Compiler); Shih, Tsan-Hsing (Compiler)
1991-01-01
Brief progress reports of the Center for Modeling of Turbulence and Transition (CMOTT) research staff from May 1990 to May 1991 are given. The objectives of the CMOTT are to develop, validate, and implement the models for turbulence and boundary layer transition in the practical engineering flows. The flows of interest are three dimensional, incompressible, and compressible flows with chemistry. The schemes being studied include the two-equation and algebraic Reynolds stress models, the full Reynolds stress (or second moment closure) models, the probability density function models, the Renormalization Group Theory (RNG) and Interaction Approximation (DIA), the Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS).
Center for Modeling of Turbulence and Transition (CMOTT): Research Briefs, 1992
NASA Technical Reports Server (NTRS)
Liou, William W. (Editor)
1992-01-01
The progress is reported of the Center for Modeling of Turbulence and Transition (CMOTT). The main objective of the CMOTT is to develop, validate and implement the turbulence and transition models for practical engineering flows. The flows of interest are three-dimensional, incompressible and compressible flows with chemical reaction. The research covers two-equation (e.g., k-e) and algebraic Reynolds-stress models, second moment closure models, probability density function (pdf) models, Renormalization Group Theory (RNG), Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS).
Statistical turbulence theory and turbulence phenomenology
NASA Technical Reports Server (NTRS)
Herring, J. R.
1973-01-01
The application of deductive turbulence theory for validity determination of turbulence phenomenology at the level of second-order, single-point moments is considered. Particular emphasis is placed on the phenomenological formula relating the dissipation to the turbulence energy and the Rotta-type formula for the return to isotropy. Methods which deal directly with most or all the scales of motion explicitly are reviewed briefly. The statistical theory of turbulence is presented as an expansion about randomness. Two concepts are involved: (1) a modeling of the turbulence as nearly multipoint Gaussian, and (2) a simultaneous introduction of a generalized eddy viscosity operator.
PDF methods for turbulent reactive flows
NASA Technical Reports Server (NTRS)
Hsu, Andrew T.
1995-01-01
Viewgraphs are presented on computation of turbulent combustion, governing equations, closure problem, PDF modeling of turbulent reactive flows, validation cases, current projects, and collaboration with industry and technology transfer.
Detailed modeling of soot formation and turbulence-radiation interactions in turbulent jet flames
NASA Astrophysics Data System (ADS)
Mehta, Ranjan S.
Detailed radiation modeling of turbulent sooting flames faces a number of challenges. Principal among these have been been a lack of good models for predicting soot formation and effective means to capture turbulence-chemistry interactions in soot subprocesses. Uncertainties in measurement and prediction of soot properties has also been a problem. Radiative heat transfer becomes important in combustion environments due to the very high temperatures encountered and has not yet been studied in sufficient detail in the case of luminous (i.e., sooting) flames. A comprehensive approach for modeling turbulent reacting flows, including detailed chemistry, radiation and soot models with detailed closures for turbulence-chemistry interactions (TCI) and turbulence-radiation interactions (TRI) is developed in this work. A review of up-to-date literature on turbulent combustion modeling, turbulence-radiation interactions and soot modeling is given. A transported probability density function (PDF) approach is used to model turbulence-chemistry interactions and extended to include soot formation. Nongray gas and soot radiation is modeled using a photon Monte Carlo (PMC) method coupled with the PDF method. Soot formation is modeled based on the method of moments (MOM) approach with interpolative closure. Optimal soot submodel parameters are identified based on comparison of model predictions with experimental data from various laminar premixed and (opposed) diffusion flames. These parameters (including gas-phase chemistry) are applied to turbulent flames without further "tuning." Six turbulent jet flames with Reynolds numbers varying from 6700 to 15000, varying fuel types---pure ethylene, 90% methane-10% ethylene blend and different oxygen concentrations in the oxidizer stream from 21%O2 (air) to 55%O 2, are simulated. The predicted soot volume fractions, temperature and radiative wall fluxes (when available) are compared with experiments. All the simulations are carried out with
Moment Closure for the Stochastic Logistic Model
2006-01-16
for Collaborative Biotech- nologies through grant DAAD19-03-D-0004 from the U.S. Army Research Office and by the National Science Foundation under Grant...No. CCR-0311084. 2 abhi@engineering.ucsb.edu, hespanha@ece.ucsb.edu Preprint submitted to Elsevier Science 16 January 2006 Report Documentation Page...Comput. Science . Springer-Verlag, Berlin, pp. 387–401. Hespanha, J. P., Singh, A., 2005. Stochastic models for chemically reacting systems using
Simulating a Cold-Air Outbreak with SHOC (Simplified Higher-Order Closure)
NASA Astrophysics Data System (ADS)
Krueger, S. K.; Bogenschutz, P.
2013-12-01
The Grey Zone Project aims to systematically explore convective transport and cloud processes in weather and climate models at various resolutions, ranging from high resolution turbulent resolving scales all the way to coarse resolutions that require full parameterized descriptions of these processes. The first Grey Zone intercomparison case is based on observations of a cold air outbreak during the CONSTRAIN field campaign. The purpose of the intercomparison is two-fold: First, through systematically varying the horizontal resolution, the intercomparison will aim to assess the relative contributions of the resolved and the subgrid-scale (SGS) cloud and convective processes in the Grey Zone for the present CONSTRAIN case. Second, the intercomparison is interesting in its own right as it is the first time that a comprehensive mid-latitude cold-air outbreak case has been organized. We will participate by using a version of a cloud-resolving model, SAM (System for Atmospheric Modeling), that includes SHOC (Simplified Higher-Order Closure, Bogenschutz and Krueger 2013) which combines several existing components: A prognostic SGS turbulence kinetic energy (TKE) equation, an assumed double-Gaussian PDF following Golaz et al. (2002), the diagnostic second-moment closure of Redelsperger and Sommeria (1986), the diagnostic closure for
Lattice Boltzmann Representations of MHD Turbulence
NASA Astrophysics Data System (ADS)
Vahala, George; Vahala, Linda; Soe, Min; Flint, Christopher
2013-10-01
Lattice Botlzmann algorithms are an ideally parallelized method for the solutions of macroscopic nonlinear equations of physics - like resistive MHD. In its simplest LB representation one introduces a scalar distribution for the density-velocity fields and a vector distribution for the magnetic field. An important feature is that gradients of certain macroscopic fields can be represented by local moments of the mesoscopic distribution functions. In particular, div B = 0 can be exactly enforced to machine accuracy, without any divergence cleaning. One of the problems facing the explicit LB code is numerical instabilities. Methods to permit strong turbulence simulations include: (a) moving from a single BGK to multiple collisional relaxation, (b) quasi-equilibria and central moment enhanced LB representations. The LB turbulence modeling of Ansumali et al. to Navier-Stokes turbulence will be extended to MHD in which in its noted that filtering and Chapman-Enskog limits do not commute. In the NS-case, it leads to unique Samgorinsky closure scheme, with definite filter width.
Conditional statistics in a turbulent premixed flame derived from direct numerical simulation
NASA Technical Reports Server (NTRS)
Mantel, Thierry; Bilger, Robert W.
1994-01-01
The objective of this paper is to briefly introduce conditional moment closure (CMC) methods for premixed systems and to derive the transport equation for the conditional species mass fraction conditioned on the progress variable based on the enthalpy. Our statistical analysis will be based on the 3-D DNS database of Trouve and Poinsot available at the Center for Turbulence Research. The initial conditions and characteristics (turbulence, thermo-diffusive properties) as well as the numerical method utilized in the DNS of Trouve and Poinsot are presented, and some details concerning our statistical analysis are also given. From the analysis of DNS results, the effects of the position in the flame brush, of the Damkoehler and Lewis numbers on the conditional mean scalar dissipation, and conditional mean velocity are presented and discussed. Information concerning unconditional turbulent fluxes are also presented. The anomaly found in previous studies of counter-gradient diffusion for the turbulent flux of the progress variable is investigated.
ERIC Educational Resources Information Center
Williams, Kate
2012-01-01
The informatics moment is the moment when a person seeks help in using some digital technology that is new to him or her. This article examines the informatics moment in people's everyday lives as they sought help at a branch public library. Four types of literacy were involved: basic literacy (reading and writing), computer literacy (use of a…
ERIC Educational Resources Information Center
Williams, Kate
2012-01-01
The informatics moment is the moment when a person seeks help in using some digital technology that is new to him or her. This article examines the informatics moment in people's everyday lives as they sought help at a branch public library. Four types of literacy were involved: basic literacy (reading and writing), computer literacy (use of a…
Characteristics of 3D turbulent jets in crossflow
NASA Technical Reports Server (NTRS)
Demuren, A. O.
1991-01-01
Three dimensional turbulent jets in crossflow at low to medium jet-to-crossflow velocity ratios are computed with a finite volume numerical procedure which utilizes a second-moment closure model to approximate the Reynolds stresses. A multigrid method is used to accelerate the convergence rate of the procedure. Comparison of the computations to measured data show good qualitative agreement. All trends are correctly predicted, though there is some uncertainty on the height of penetration of the jet. The evolution of the vorticity field is used to explore the jet-crossflow interaction.
NASA Technical Reports Server (NTRS)
Ristorcelli, J. R.
1995-01-01
The mathematical consequences of a few simple scaling assumptions about the effects of compressibility are explored using a simple singular perturbation idea and the methods of statistical fluid mechanics. Representations for the pressure-dilation and dilatational dissipation covariances appearing in single-point moment closures for compressible turbulence are obtained. While the results are expressed in the context of a second-order statistical closure they provide some interesting and very clear physical metaphors for the effects of compressibility that have not been seen using more traditional linear stability methods. In the limit of homogeneous turbulence with quasi-normal large-scales the expressions derived are - in the low turbulent Mach number limit - asymptotically exact. The expressions obtained are functions of the rate of change of the turbulence energy, its correlation length scale, and the relative time scale of the cascade rate. The expressions for the dilatational covariances contain constants which have a precise and definite physical significance; they are related to various integrals of the longitudinal velocity correlation. The pressure-dilation covariance is found to be a nonequilibrium phenomena related to the time rate of change of the internal energy and the kinetic energy of the turbulence. Also of interest is the fact that the representation for the dilatational dissipation in turbulence, with or without shear, features a dependence on the Reynolds number. This article is a documentation of an analytical investigation of the implications of a pseudo-sound theory for the effects of compressibility.
NASA Technical Reports Server (NTRS)
Kim, S.-W.; Chen, C.-P.
1988-01-01
The paper presents a multiple-time-scale turbulence model of a single point closure and a simplified split-spectrum method. Consideration is given to a class of turbulent boundary layer flows and of separated and/or swirling elliptic turbulent flows. For the separated and/or swirling turbulent flows, the present turbulence model yielded significantly improved computational results over those obtained with the standard k-epsilon turbulence model.
NASA Technical Reports Server (NTRS)
Kim, S.-W.; Chen, C.-P.
1988-01-01
The paper presents a multiple-time-scale turbulence model of a single point closure and a simplified split-spectrum method. Consideration is given to a class of turbulent boundary layer flows and of separated and/or swirling elliptic turbulent flows. For the separated and/or swirling turbulent flows, the present turbulence model yielded significantly improved computational results over those obtained with the standard k-epsilon turbulence model.
Group-kinetic theory of turbulence
NASA Technical Reports Server (NTRS)
Tchen, C. M.
1986-01-01
The two phases are governed by two coupled systems of Navier-Stokes equations. The couplings are nonlinear. These equations describe the microdynamical state of turbulence, and are transformed into a master equation. By scaling, a kinetic hierarchy is generated in the form of groups, representing the spectral evolution, the diffusivity and the relaxation. The loss of memory in formulating the relaxation yields the closure. The network of sub-distributions that participates in the relaxation is simulated by a self-consistent porous medium, so that the average effect on the diffusivity is to make it approach equilibrium. The kinetic equation of turbulence is derived. The method of moments reverts it to the continuum. The equation of spectral evolution is obtained and the transport properties are calculated. In inertia turbulence, the Kolmogoroff law for weak coupling and the spectrum for the strong coupling are found. As the fluid analog, the nonlinear Schrodinger equation has a driving force in the form of emission of solitons by velocity fluctuations, and is used to describe the microdynamical state of turbulence. In order for the emission together with the modulation to participate in the transport processes, the non-homogeneous Schrodinger equation is transformed into a homogeneous master equation. By group-scaling, the master equation is decomposed into a system of transport equations, replacing the Bogoliubov system of equations of many-particle distributions. It is in the relaxation that the memory is lost when the ensemble of higher-order distributions is simulated by an effective porous medium. The closure is thus found. The kinetic equation is derived and transformed into the equation of spectral flow.
Tieszen, Sheldon Robert; Domino, Stefan Paul; Black, Amalia Rebecca
2005-06-01
A validation study has been conducted for a turbulence model used to close the temporally filtered Navier Stokes (TFNS) equations. A turbulence model was purposely built to support fire simulations under the Accelerated Strategic Computing (ASC) program. The model was developed so that fire transients could be simulated and it has been implemented in SIERRA/Fuego. The model is validated using helium plume data acquired for the Weapon System Certification Campaign (C6) program in the Fire Laboratory for Model Accreditation and Experiments (FLAME). The helium plume experiments were chosen as the first validation problem for SIERRA/Fuego because they embody the first pair-wise coupling of scalar and momentum fields found in fire plumes. The validation study includes solution verification through grid and time step refinement studies. A formal statistical comparison is used to assess the model uncertainty. The metric uses the centerline vertical velocity of the plume. The results indicate that the simple model is within the 95% confidence interval of the data for elevations greater than 0.4 meters and is never more than twice the confidence interval from the data. The model clearly captures the dominant puffing mode in the fire but under resolves the vorticity field. Grid dependency of the model is noted.
Closure phase and lucky imaging.
Rhodes, William T
2009-01-01
Since its introduction by Jennison in 1958, the closure-phase method for removing the effects of electrical path-length errors in radio astronomy and of atmospheric turbulence in optical astronomy has been based on the non-redundant-spacing triple interferometer. It is shown that through application of lucky imaging concepts it is possible to relax this condition, making closure-phase methods possible with redundantly spaced interferometer configurations and thereby widening their range of application. In particular, a quadruple-interferometer can, under lucky imaging conditions, be treated as though it were a triple interferometer. The slit-annulus aperture is investigated as a special case.
Turbulence program for propulsion systems
NASA Technical Reports Server (NTRS)
Shih, Tsan-Hsing
1995-01-01
Program goals at the Center for Modeling of Turbulence and Transition (CMOTT), NASA Lewis Research Center, are (1) to develop reliable turbulence (including bypass transition) and combustion models for complex flows in propulsion systems and (2) to integrate developed models into deliverable CFD tools for propulsion systems in collaboration with industry. This viewgraph presentation covers the following topics: development of turbulence and combustion models; collaboration with industry and technology transfer; isotropic eddy viscosity models; algebraic Reynolds stress models; scalar turbulence models; second order closure models; multiple scale k-epsilon models; and PDF modeling of turbulent reacting flows.
Zhang, T.; Ladeinde, F.; Zhang, H.; Prasad, V.
1996-12-31
This study examines the relative performance of four turbulence models for their possible application in simulating turbulent flow and heat transfer in the Czochralski crystal growth process. These are the standard {kappa}-{epsilon} model with wall function, the low-Reynolds-number {kappa}-{epsilon} model proposed by Abe and Kondoh, the renormalization group {kappa}-{epsilon} model of Yakhot et al. and the algebraic stress model by Gatski and Speziale. Attention was given to the renormalization group {kappa}-{epsilon} model (RNG) and particularly the algebraic stress model (ASM) because of its nonlinear and nonisotropic properties. In fact, the latter model has been reported to give comparable results to full-scale second moment closures for complicated systems with rotation, body force and mild inhomogeneity. Some of the comparisons were made with experimental measurements of turbulent, high Rayleigh number flows. The RNG and ASM results agree better with the experimental data of Cheesewright et al. for the vertical velocity distribution.
Randall, David A.; Cheng, Anning; Ghan, Steve; Khairoutdinov, Marat; Larson, Vince; Moeng, Chin-Hoh
2015-07-27
The intermediately-prognostic higher-order turbulence closure (IPHOC) introduces a joint double-Gaussian distribution of liquid water potential temperature (θ_{l} ), total water mixing ratio (q_{t }), and vertical velocity (w ) to represent any skewed turbulence circulations .The distribution is inferred from the first-, second-, and third-order moments of the variables given above, and is used to diagnose cloud fraction and grid-mean liquid water mixing ratio, as well as the buoyancy and fourth-order terms in the equations describing the evolution of the second- and third-order moments. Only three third-order moments (those of θ_{l} , q_{t }, and w ) are predicted in the IPHOC.
Computing aerodynamic sound using advanced statistical turbulence theories
NASA Technical Reports Server (NTRS)
Hecht, A. M.; Teske, M. E.; Bilanin, A. J.
1981-01-01
It is noted that the calculation of turbulence-generated aerodynamic sound requires knowledge of the spatial and temporal variation of Q sub ij (xi sub k, tau), the two-point, two-time turbulent velocity correlations. A technique is presented to obtain an approximate form of these correlations based on closure of the Reynolds stress equations by modeling of higher order terms. The governing equations for Q sub ij are first developed for a general flow. The case of homogeneous, stationary turbulence in a unidirectional constant shear mean flow is then assumed. The required closure form for Q sub ij is selected which is capable of qualitatively reproducing experimentally observed behavior. This form contains separation time dependent scale factors as parameters and depends explicitly on spatial separation. The approximate forms of Q sub ij are used in the differential equations and integral moments are taken over the spatial domain. The velocity correlations are used in the Lighthill theory of aerodynamic sound by assuming normal joint probability.
ERIC Educational Resources Information Center
Groffman, Sidney
An experimental test of visual closure based on an information-theory concept of perception was devised to test the ability to discriminate visual stimuli with reduced cues. The test is to be administered in a timed individual situation in which the subject is presented with sets of incomplete drawings of simple objects that he is required to name…
Dynamics and structure of turbulent premixed flames
NASA Technical Reports Server (NTRS)
Bilger, R. W.; Swaminathan, N.; Ruetsch, G. R.; Smith, N. S. A.
1995-01-01
In earlier work (Mantel & Bilger, 1994) the structure of the turbulent premixed flame was investigated using statistics based on conditional averaging with the reaction progress variable as the conditioning variable. The DNS data base of Trouve and Poinsot (1994) was used in this investigation. Attention was focused on the conditional dissipation and conditional axial velocity in the flame with a view to modeling these quantities for use in the conditional moment closure (CMC) approach to analysis of kinetics in premixed flames (Bilger, 1993). Two remarkable findings were made: there was almost no acceleration of the axial velocity in the flame front itself; and the conditional scalar dissipation remained as high, or higher, than that found in laminar premixed flames. The first finding was surprising since in laminar flames all the fluid acceleration occurs through the flame front, and this could be expected also for turbulent premixed flames at the flamelet limit. The finding gave hope of inventing a new approach to the dynamics of turbulent premixed flames through use of rapid distortion theory or an unsteady Bernoulli equation. This could lead to a new second order closure for turbulent premixed flames. The second finding was contrary to our measurements with laser diagnostics in lean hydrocarbon flames where it is found that conditional scalar dissipation drops dramatically below that for laminar flamelets when the turbulence intensity becomes high. Such behavior was not explainable with a one-step kinetic model, even at non-unity Lewis number. It could be due to depletion of H2 from the reaction zone by preferential diffusion. The capacity of the flame to generate radicals is critically dependent on the levels of H2 present (Bilger, et al., 1991). It seemed that a DNS computation with a multistep reduced mechanism would be worthwhile if a way could be found to make this feasible. Truly innovative approaches to complex problems often come only when there is the
Scaling laws for homogeneous turbulent shear flows in a rotating frame
NASA Technical Reports Server (NTRS)
Speziale, Charles G.; Mhuiris, Nessan Macgiolla
1988-01-01
The scaling properties of plane homogeneous turbulent shear flows in a rotating frame are examined mathematically by a direct analysis of the Navier-Stokes equations. It is proved that two such shear flows are dynamically similar if and only if their initial dimensionless energy spectrum E star (k star, 0), initial dimensionless shear rate SK sub 0/epsilon sub 0, initial Reynolds number K squared sub 0/nu epsilon sub 0, and the ration of the rotation rate to the shear rate omega/S are identical. Consequently, if universal equilibrium states exist, at high Reynolds numbers, they will only depend on the single parameter omega/S. The commonly assumed dependence of such equilibrium states on omega/S through the Richardson number Ri=-2(omega/S)(1-2 omega/S) is proven to be inconsistent with the full Navier-Stokes equations and to constitute no more than a weak approximation. To be more specific, Richardson number similarity is shown to only rigorously apply to certain low-order truncations of the Navier-Stokes equations (i.e., to certain second-order closure models) wherein closure is achieved at the second-moment level by assuming that the higher-order moments are a small perturbation of their isotropic states. The physical dependence of rotating turbulent shear flows on omega/S is discussed in detail along with the implications for turbulence modeling.
Vowell, Kennison L.
1987-01-01
A closure for an inclined duct having an open upper end and defining downwardly extending passageway. The closure includes a cap for sealing engagement with the open upper end of the duct. Associated with the cap are an array of vertically aligned plug members, each of which has a cross-sectional area substantially conforming to the cross-sectional area of the passageway at least adjacent the upper end of the passageway. The plug members are interconnected in a manner to provide for free movement only in the plane in which the duct is inclined. The uppermost plug member is attached to the cap means and the cap means is in turn connected to a hoist means which is located directly over the open end of the duct.
Sable, D. E.
1985-06-11
A closure device connectible to a well head through which the polished rod of a rod string extends into a well tubing for operating pump means for moving well fluids to a surface flow conductor, the closure device having a tubular ram provided with a packing or plug for closing an annular passage between the polished rod and a tubular body connected to the well head above a lateral port of the tubular body, the tubular ram and the tubular body having thread means for moving the plug between an operative lower position wherein it closes the annular passage when the rod string is stationary and on inoperative upper position; seal means between the ram and the polished rod spaced above the plug; and a plurality of independent seal means between the ram and the tubular body operative when the plug is in its inoperative position. The plug of the closure device is especially adapted to operate under high temperature and pressure conditions of the well, as during steam injection operations when the rod string is stationary, to protect the seal means from high pressures and temperatures as well as any fluids which may be corrosive or otherwise deleterious to the substance of which the seal means are made.
Towards a mesoscale eddy closure
NASA Astrophysics Data System (ADS)
Eden, Carsten; Greatbatch, Richard J.
A turbulence closure for the effect of mesoscale eddies in non-eddy-resolving ocean models is proposed. The closure consists of a prognostic equation for the eddy kinetic energy (EKE) that is integrated as an additional model equation, and a diagnostic relation for an eddy length scale ( L), which is given by the minimum of Rhines scale and Rossby radius. Combining EKE and L using a standard mixing length assumption gives a diffusivity ( K), corresponding to the thickness diffusivity in the [Gent, P.R., McWilliams, J.C. 1990. Isopycnal mixing in ocean circulation models. J. Phys. Oceanogr. 20, 150-155] parameterisation. Assuming downgradient mixing of potential vorticity with identical diffusivity shows how K is related to horizontal and vertical mixing processes in the horizontal momentum equation, and also enables us to parameterise the source of EKE related to eddy momentum fluxes. The mesoscale eddy closure is evaluated using synthetic data from two different eddy-resolving models covering the North Atlantic Ocean and the Southern Ocean, respectively. The diagnosis shows that the mixing length assumption together with the definition of eddy length scales is valid within certain limitations. Furthermore, implementation of the closure in non-eddy-resolving models of the North Atlantic and the Southern Ocean shows consistently that the closure has skill at reproducing the results of the eddy-resolving model versions in terms of EKE and K.
LES, DNS and RANS for the analysis of high-speed turbulent reacting flows
NASA Technical Reports Server (NTRS)
Adumitroaie, V.; Colucci, P. J.; Taulbee, D. B.; Givi, P.
1995-01-01
The purpose of this research is to continue our efforts in advancing the state of knowledge in large eddy simulation (LES), direct numerical simulation (DNS), and Reynolds averaged Navier Stokes (RANS) methods for the computational analysis of high-speed reacting turbulent flows. In the second phase of this work, covering the period 1 Aug. 1994 - 31 Jul. 1995, we have focused our efforts on two programs: (1) developments of explicit algebraic moment closures for statistical descriptions of compressible reacting flows and (2) development of Monte Carlo numerical methods for LES of chemically reacting flows.
NASA Astrophysics Data System (ADS)
Krueger, S. K.; Lesage, A. T.; Bogenschutz, P.
2014-12-01
We are using a cloud-resolving model, SAM (System for Atmospheric Modeling) to examine the sensitivity of our simulations of an evolving mixed-phase cloud-topped boundary layer during a cold-air outbreak over the North Atlantic Ocean to the representations of the SGS turbulence and cloudiness and of the microphysics. Our version of SAM includes SHOC (Simplified Higher-Order Closure, Bogenschutz and Krueger 2013) which combines several existing components: A prognostic SGS turbulence kinetic energy (TKE) equation, an assumed double-Gaussian PDF following Golaz et al. (2002), the diagnostic second-moment closure of Redelsperger and Sommeria (1986), the diagnostic closure for the third moment of vertical velocity by Canuto et al. (2001), and a turbulence length scale related to the SGS TKE (Teixeira and Cheinet 2004) and to eddy length scales. Cold-air outbreaks typically produce an evolving cloud-topped boundary layer whose structure is influenced by strong surface fluxes of sensible and latent heat, mixed-phase microphysics, cloud-top radiative cooling, and cloud-top entrainment. By systematically varying the horizontal resolution from 1 to 100 km and comparing the results to a benchmark large-eddy simulation of the case, we will assess the ability of SHOC to represent this type of boundary layer. The image shows the cloud water path from a large-eddy simulation of the CONSTRAIN case. The domain size is 64 km by 64 km. Such simulations are used as benchmarks for coarse-grid simulations that use SHOC.
BOOK REVIEW: Statistical Mechanics of Turbulent Flows
NASA Astrophysics Data System (ADS)
Cambon, C.
2004-10-01
This is a handbook for a computational approach to reacting flows, including background material on statistical mechanics. In this sense, the title is somewhat misleading with respect to other books dedicated to the statistical theory of turbulence (e.g. Monin and Yaglom). In the present book, emphasis is placed on modelling (engineering closures) for computational fluid dynamics. The probabilistic (pdf) approach is applied to the local scalar field, motivated first by the nonlinearity of chemical source terms which appear in the transport equations of reacting species. The probabilistic and stochastic approaches are also used for the velocity field and particle position; nevertheless they are essentially limited to Lagrangian models for a local vector, with only single-point statistics, as for the scalar. Accordingly, conventional techniques, such as single-point closures for RANS (Reynolds-averaged Navier-Stokes) and subgrid-scale models for LES (large-eddy simulations), are described and in some cases reformulated using underlying Langevin models and filtered pdfs. Even if the theoretical approach to turbulence is not discussed in general, the essentials of probabilistic and stochastic-processes methods are described, with a useful reminder concerning statistics at the molecular level. The book comprises 7 chapters. Chapter 1 briefly states the goals and contents, with a very clear synoptic scheme on page 2. Chapter 2 presents definitions and examples of pdfs and related statistical moments. Chapter 3 deals with stochastic processes, pdf transport equations, from Kramer-Moyal to Fokker-Planck (for Markov processes), and moments equations. Stochastic differential equations are introduced and their relationship to pdfs described. This chapter ends with a discussion of stochastic modelling. The equations of fluid mechanics and thermodynamics are addressed in chapter 4. Classical conservation equations (mass, velocity, internal energy) are derived from their
Direct numerical simulation of soot formation and transport in turbulent nonpremixed ethylene flames
NASA Astrophysics Data System (ADS)
Lignell, David Owen
Combustion is central to society and accounts for the majority of the world's energy production. Soot formation, transport, and emission from turbulent flames are an important process in nonpremixed combustion. Soot is a major air pollutant with adverse health effects; its emission reduces combustion efficiencies associated with unburned fuel; and soot interacts strongly with the composition and temperature fields of flames, contributing to the bulk of radiative heat transfer. Simulation of combustion is an important and emerging discipline that compliments theoretical and experimental investigations and can provide fundamental insight into turbulent combustion environments and aid in engineering design of practical equipment. Simulations of practical combustion environments cannot fully resolve all flow and chemical phenomena due to the wide range of timescales and lengthscales present and must rely on models to capture the effects of unresolved turbulent transport and turbulence-chemistry interactions. Very little is know about soot formation in turbulent flames due to the difficulty of experimental measurements and the computational cost of simulation. Direct numerical simulation (DNS) resolves all relevant flow and chemical structures in turbulent flames, requiring no turbulence closure models. DNS of soot formation with realistic combustion chemistry and soot formation is presented in this dissertation. A series of increasingly complex flow configurations is investigated including one-dimensional relaxing diffusion flames, two-dimensional mixing layers and decaying turbulence simulations, and a three-dimensional temporally evolving jet flame. A reduced ethylene mechanism consisting of 19 transported species is coupled to a four-step soot model using the method of moments. The DNS are used to quantify soot formation and transport in turbulent flames. The proximity of soot to a flame is important, as this impacts the soot reaction and radiation rates
Experience with turbulence interaction and turbulence-chemistry models at Fluent Inc.
NASA Technical Reports Server (NTRS)
Choudhury, D.; Kim, S. E.; Tselepidakis, D. P.; Missaghi, M.
1995-01-01
This viewgraph presentation discusses (1) turbulence modeling: challenges in turbulence modeling, desirable attributes of turbulence models, turbulence models in FLUENT, and examples using FLUENT; and (2) combustion modeling: turbulence-chemistry interaction and FLUENT equilibrium model. As of now, three turbulence models are provided: the conventional k-epsilon model, the renormalization group model, and the Reynolds-stress model. The renormalization group k-epsilon model has broadened the range of applicability of two-equation turbulence models. The Reynolds-stress model has proved useful for strongly anisotropic flows such as those encountered in cyclones, swirlers, and combustors. Issues remain, such as near-wall closure, with all classes of models.
Progress in the development of PDF turbulence models for combustion
NASA Technical Reports Server (NTRS)
Hsu, Andrew T.
1991-01-01
A combined Monte Carlo-computational fluid dynamic (CFD) algorithm was developed recently at Lewis Research Center (LeRC) for turbulent reacting flows. In this algorithm, conventional CFD schemes are employed to obtain the velocity field and other velocity related turbulent quantities, and a Monte Carlo scheme is used to solve the evolution equation for the probability density function (pdf) of species mass fraction and temperature. In combustion computations, the predictions of chemical reaction rates (the source terms in the species conservation equation) are poor if conventional turbulence modles are used. The main difficulty lies in the fact that the reaction rate is highly nonlinear, and the use of averaged temperature produces excessively large errors. Moment closure models for the source terms have attained only limited success. The probability density function (pdf) method seems to be the only alternative at the present time that uses local instantaneous values of the temperature, density, etc., in predicting chemical reaction rates, and thus may be the only viable approach for more accurate turbulent combustion calculations. Assumed pdf's are useful in simple problems; however, for more general combustion problems, the solution of an evolution equation for the pdf is necessary.
Parallel Simulation of Unsteady Turbulent Flames
NASA Technical Reports Server (NTRS)
Menon, Suresh
1996-01-01
Time-accurate simulation of turbulent flames in high Reynolds number flows is a challenging task since both fluid dynamics and combustion must be modeled accurately. To numerically simulate this phenomenon, very large computer resources (both time and memory) are required. Although current vector supercomputers are capable of providing adequate resources for simulations of this nature, the high cost and their limited availability, makes practical use of such machines less than satisfactory. At the same time, the explicit time integration algorithms used in unsteady flow simulations often possess a very high degree of parallelism, making them very amenable to efficient implementation on large-scale parallel computers. Under these circumstances, distributed memory parallel computers offer an excellent near-term solution for greatly increased computational speed and memory, at a cost that may render the unsteady simulations of the type discussed above more feasible and affordable.This paper discusses the study of unsteady turbulent flames using a simulation algorithm that is capable of retaining high parallel efficiency on distributed memory parallel architectures. Numerical studies are carried out using large-eddy simulation (LES). In LES, the scales larger than the grid are computed using a time- and space-accurate scheme, while the unresolved small scales are modeled using eddy viscosity based subgrid models. This is acceptable for the moment/energy closure since the small scales primarily provide a dissipative mechanism for the energy transferred from the large scales. However, for combustion to occur, the species must first undergo mixing at the small scales and then come into molecular contact. Therefore, global models cannot be used. Recently, a new model for turbulent combustion was developed, in which the combustion is modeled, within the subgrid (small-scales) using a methodology that simulates the mixing and the molecular transport and the chemical kinetics
On the modelling of non-reactive and reactive turbulent combustor flows
NASA Technical Reports Server (NTRS)
Nikjooy, Mohammad; So, Ronald M. C.
1987-01-01
A study of non-reactive and reactive axisymmetric combustor flows with and without swirl is presented. Closure of the Reynolds equations is achieved by three models: kappa-epsilon, algebraic stress and Reynolds stress closure. Performance of two locally nonequilibrium and one equilibrium algebraic stress models is analyzed assuming four pressure strain models. A comparison is also made of the performance of a high and a low Reynolds number model for combustor flow calculations using Reynolds stress closures. Effects of diffusion and pressure-strain models on these closures are also investigated. Two models for the scalar transport are presented. One employs the second-moment closure which solves the transport equations for the scalar fluxes, while the other solves the algebraic equations for the scalar fluxes. In addition, two cases of non-premixed and one case of premixed combustion are considered. Fast- and finite-rate chemistry models are applied to non-premixed combustion. Both show promise for application in gas turbine combustors. However, finite rate chemistry models need to be examined to establish a suitable coupling of the heat release effects on turbulence field and rate constants.
Autonomic Closure for Large Eddy Simulation
NASA Astrophysics Data System (ADS)
King, Ryan; Hamlington, Peter; Dahm, Werner J. A.
2015-11-01
A new autonomic subgrid-scale closure has been developed for large eddy simulation (LES). The approach poses a supervised learning problem that captures nonlinear, nonlocal, and nonequilibrium turbulence effects without specifying a predefined turbulence model. By solving a regularized optimization problem on test filter scale quantities, the autonomic approach identifies a nonparametric function that represents the best local relation between subgrid stresses and resolved state variables. The optimized function is then applied at the grid scale to determine unknown LES subgrid stresses by invoking scale similarity in the inertial range. A priori tests of the autonomic approach on homogeneous isotropic turbulence show that the new approach is amenable to powerful optimization and machine learning methods and is successful for a wide range of filter scales in the inertial range. In these a priori tests, the autonomic closure substantially improves upon the dynamic Smagorinsky model in capturing the instantaneous, statistical, and energy transfer properties of the subgrid stress field.
Linzell, S.M.; Dorcy, D.J.
1958-08-26
A quick opening type of stuffing box employing two banks of rotatable shoes, each of which has a caraming action that forces a neoprene sealing surface against a pipe or rod where it passes through a wall is presented. A ring having a handle or wrench attached is placed eccentric to and between the two banks of shoes. Head bolts from the shoes fit into slots in this ring, which are so arranged that when the ring is rotated a quarter turn in one direction the shoes are thrust inwardly to cramp the neopnrene about the pipe, malting a tight seal. Moving the ring in the reverse direction moves the shoes outwardly and frees the pipe which then may be readily removed from the stuffing box. This device has particular application as a closure for the end of a coolant tube of a neutronic reactor.
A nonlocal fluid closure for antiparallel reconnection
NASA Astrophysics Data System (ADS)
Ng, J.; Hakim, A.; Bhattacharjee, A.
2016-12-01
The integration of kinetic effects in fluid models is an important problem in global simulations of the Earth's magnetosphere and space weather modelling. In particular, it has been shown that ion kinetics play an important role in the dynamics of large reconnecting systems, and that fluid models can account of some of these effects[1,2] . Here we introduce a new fluid model and closure for collisionless magnetic reconnection and more general applications. Taking moments of the kinetic equation, we evolve the full pressure tensor for electrons and ions, which includes the off diagonal terms necessary for reconnection. Kinetic effects are recovered by using a nonlocal heat flux closure, which approximates linear Landau damping in the fluid framework [3]. Using the island coalescence problem as a test, we show how the nonlocal ion closure improves on the typical collisional closures used for ten-moment models and circumvents the need for a colllisional free parameter. Finally, we extend the closure to study guide-field reconnection and discuss the implementation of a twenty-moment model.[1] A. Stanier et al. Phys Rev Lett (2015)[2] J. Ng et al. Phys Plasmas (2015)[3] G. Hammett et al. Phys Rev Lett (1990)
A nonlocal fluid closure for antiparallel reconnection
NASA Astrophysics Data System (ADS)
Ng, Jonathan; Hakim, A.; Bhattacharjee, A.
2016-10-01
The integration of kinetic effects in fluid models is an important problem in global simulations of the Earth's magnetosphere and space weather modelling. In particular, it has been shown that ion kinetics play an important role in the dynamics of large reconnecting systems, and that fluid models can account of some of these effects. Here we introduce a new fluid model and closure for collisionless magnetic reconnection and more general applications. Taking moments of the kinetic equation, we evolve the full pressure tensor for electrons and ions, which includes the off diagonal terms necessary for reconnection. Kinetic effects are recovered by using a nonlocal heat flux closure, which approximates linear Landau damping in the fluid framework. Using the island coalescence problem as a test, we show how the nonlocal ion closure improves on the typical collisional closures used for ten-moment models and circumvents the need for a colllisional free parameter. Finally, we extend the closure to study guide-field reconnection and discuss the implementation of a twenty-moment model. Supported by: NSF Grant No. AGS-1338944, DOE Contract DE-AC02-09CH11466.
Turbulent transport across invariant canonical flux surfaces
Hollenberg, J.B.; Callen, J.D.
1994-07-01
Net transport due to a combination of Coulomb collisions and turbulence effects in a plasma is investigated using a fluid moment description that allows for kinetic and nonlinear effects via closure relations. The model considered allows for ``ideal`` turbulent fluctuations that distort but preserve the topology of species-dependent canonical flux surfaces {psi}{sub {number_sign},s} {triple_bond} {integral} dF {center_dot} B{sub {number_sign},s} {triple_bond} {gradient} {times} [A + (m{sub s}/q{sub s})u{sub s}] in which u{sub s} is the flow velocity of the fluid species. Equations for the net transport relative to these surfaces due to ``nonideal`` dissipative processes are found for the total number of particles and total entropy enclosed by a moving canonical flux surface. The corresponding particle transport flux is calculated using a toroidal axisymmetry approximation of the ideal surfaces. The resulting Lagrangian transport flux includes classical, neoclassical-like, and anomalous contributions and shows for the first time how these various contributions should be summed to obtain the total particle transport flux.
Physics-Preserving Turbulent Closure Models
2001-08-01
REQUIREMENTS (2) AND (3) 2.1.1. q - v relation Theorem 1. f is independent of v. Proof From the principle of observer transformations ( Geankoplis 1983...constraints on large-eddy simulations, Theoret. Comput. Fluid Dynamics, 9, 85-102. Geankoplis , C. J. (1983) Transport Processes: Momentum, Heat, and Mass
LES, DNS and RANS for the analysis of high-speed turbulent reacting flows
NASA Technical Reports Server (NTRS)
Givi, Peyman; Taulbee, Dale B.; Adumitroaie, Virgil; Sabini, George J.; Shieh, Geoffrey S.
1994-01-01
The purpose of this research is to continue our efforts in advancing the state of knowledge in large eddy simulation (LES), direct numerical simulation (DNS), and Reynolds averaged Navier Stokes (RANS) methods for the computational analysis of high-speed reacting turbulent flows. In the second phase of this work, covering the period 1 Sep. 1993 - 1 Sep. 1994, we have focused our efforts on two research problems: (1) developments of 'algebraic' moment closures for statistical descriptions of nonpremixed reacting systems, and (2) assessments of the Dirichlet frequency in presumed scalar probability density function (PDF) methods in stochastic description of turbulent reacting flows. This report provides a complete description of our efforts during this past year as supported by the NASA Langley Research Center under Grant NAG1-1122.
Angular distribution of turbulence in wave space
NASA Technical Reports Server (NTRS)
Coleman, G.; Ferziger, J. H.; Bertoglio, J. P.
1987-01-01
An alternative to the one-point closure model for turbulence, the large eddy simulation (LES), together with its more exact relative, direct numerical simulation (DNS) are discussed. These methods are beginning to serve as partial substitutes for turbulence experiments. The eddy damped quasi-normal Markovian (EDQNM) theory is reviewed. Angular distribution of the converted data was examined in relationship to EDQNM.
Kinetic Electron Closures for Electromagnetic Simulation of Drift and Shear-Alfven Waves (II)
Cohen, B I; Dimits, A M; Nevins, W M; Chen, Y; Parker, S
2001-10-11
An electromagnetic hybrid scheme (fluid electrons and gyrokinetic ions) is elaborated in example calculations and extended to toroidal geometry. The scheme includes a kinetic electron closure valid for {beta}{sub e} > m{sub e}/m{sub i} ({beta}{sub e} is the ratio of the plasma electron pressure to the magnetic field energy density). The new scheme incorporates partially linearized ({delta}f) drift-kinetic electrons whose pressure and number density moments are used to close the fluid momentum equation for the electron fluid (Ohm's law). The test cases used are small-amplitude kinetic shear-Alfven waves with electron Landau damping, the ion-temperature-gradient instability, and the collisionless drift instability (universal mode) in an unsheared slab as a function of the plasma {beta}{sub e}. Attention is given to resolution and convergence issues in simulations of turbulent steady states.
Lacunarity and intermittency in fluid turbulence
NASA Technical Reports Server (NTRS)
Smith, L. A.; Fournier, J.-D.; Spiegel, E. A.
1986-01-01
It is shown that oscillations in the high-order moments of turbulent velocity fields are inherent to the fractal character of intermittent turbulence and are a feature of the lacunarity of fractal sets. Oscillations in simple Cantor sets are described, and a single parameter to measure lacunarity is identified. The connection between oscillations in fractals and in the turbulent velocity correlations is discussed using the phenomenological beta model of intermittent turbulence (Frisch et al., 1978).
Lacunarity and intermittency in fluid turbulence
NASA Technical Reports Server (NTRS)
Smith, L. A.; Fournier, J.-D.; Spiegel, E. A.
1986-01-01
It is shown that oscillations in the high-order moments of turbulent velocity fields are inherent to the fractal character of intermittent turbulence and are a feature of the lacunarity of fractal sets. Oscillations in simple Cantor sets are described, and a single parameter to measure lacunarity is identified. The connection between oscillations in fractals and in the turbulent velocity correlations is discussed using the phenomenological beta model of intermittent turbulence (Frisch et al., 1978).
Filtering skill for turbulent signals for a suite of nonlinear and linear extended Kalman filters
NASA Astrophysics Data System (ADS)
Branicki, M.; Gershgorin, B.; Majda, A. J.
2012-02-01
The filtering skill for turbulent signals from nature is often limited by errors due to utilizing an imperfect forecast model. In particular, real-time filtering and prediction when very limited or no a posteriori analysis is possible (e.g. spread of pollutants, storm surges, tsunami detection, etc.) introduces a number of additional challenges to the problem. Here, a suite of filters implementing stochastic parameter estimation for mitigating model error through additive and multiplicative bias correction is examined on a nonlinear, exactly solvable, stochastic test model mimicking turbulent signals in regimes ranging from configurations with strongly intermittent, transient instabilities associated with positive finite-time Lyapunov exponents to laminar behavior. Stochastic Parameterization Extended Kalman Filter (SPEKF), used as a benchmark here, involves exact formulas for propagating the mean and covariance of the augmented forecast model including the unresolved parameters. The remaining filters use the same nonlinear forecast model but they introduce model error through different moment closure approximations and/or linear tangent approximation used for computing the second-order statistics of the augmented stochastic forecast model. A comprehensive study of filter performance is carried out in the presence of various moment closure errors which are enhanced by additional model errors due to incorrect parameters inducing additive and multiplicative stochastic biases. The estimation skill of the unresolved stochastic parameters is also discussed and it is shown that the linear tangent filter, despite its popularity, is completely unreliable in many turbulent regimes for both parameter estimation and filtering; moreover, regimes of filter divergence for the linear tangent filter are identified. The results presented here provide useful guidelines for filtering turbulent, high-dimensional, spatially extended systems with more general model errors, as well as
Numerical Simulation of High-Speed Turbulent Reacting Flows
NASA Technical Reports Server (NTRS)
Givi, P.; Taulbee, D. B.; Madnia, C. K.; Jaberi, F. A.; Colucci, P. J.; Gicquel, L. Y. M.; Adumitroaie, V.; James, S.
1999-01-01
The objectives of this research are: (1) to develop and implement a new methodology for large eddy simulation of (LES) of high-speed reacting turbulent flows. (2) To develop algebraic turbulence closures for statistical description of chemically reacting turbulent flows.
Calculation methods for compressible turbulent boundary layers, 1976
NASA Technical Reports Server (NTRS)
Bushnell, D. M.; Cary, A. M., Jr.; Harris, J. E.
1977-01-01
Equations and closure methods for compressible turbulent boundary layers are discussed. Flow phenomena peculiar to calculation of these boundary layers were considered, along with calculations of three dimensional compressible turbulent boundary layers. Procedures for ascertaining nonsimilar two and three dimensional compressible turbulent boundary layers were appended, including finite difference, finite element, and mass-weighted residual methods.
Numerical simulation of the nocturnal turbulence characteristics over Rattlesnake Mountain
W.E. Heilman; E.S. Takle
1991-01-01
A two-dimensional second-order turbulence-closure model based on Mellor-Yamada level 3 is used to examine the nocturnal turbulence characteristics over Rattlesnake Mountain in Washington. Simulations of mean horizontal velocities and potential temperatures agree well with data. The equations for the components of the turbulent kinetic energy (TKE) show that anisotropy...
On the coalescence-dispersion modeling of turbulent molecular mixing
NASA Technical Reports Server (NTRS)
Givi, Peyman; Kosaly, George
1987-01-01
The general coalescence-dispersion (C/D) closure provides phenomenological modeling of turbulent molecular mixing. The models of Curl and Dopazo and O'Brien appear as two limiting C/D models that bracket the range of results one can obtain by various models. This finding is used to investigate the sensitivtiy of the results to the choice of the model. Inert scalar mixing is found to be less model-sensitive than mixing accompanied by chemical reaction. Infinitely fast chemistry approximation is used to relate the C/D approach to Toor's earlier results. Pure mixing and infinite rate chemistry calculations are compared to study further a recent result of Hsieh and O'Brien who found that higher concentration moments are not sensitive to chemistry.
Analytic closures for M1 neutrino transport
Murchikova, E. M.; Abdikamalov, E.; Urbatsch, T.
2017-04-25
Carefully accounting for neutrino transport is an essential component of many astrophysical studies. Solving the full transport equation is too expensive for most realistic applications, especially those involving multiple spatial dimensions. For such cases, resorting to approximations is often the only viable option for obtaining solutions. One such approximation, which recently became popular, is the M1 method. It utilizes the system of the lowest two moments of the transport equation and closes the system with an ad hoc closure relation. The accuracy of the M1 solution depends on the quality of the closure. Several closures have been proposed in themore » literature and have been used in various studies. We carry out an extensive study of these closures by comparing the results of M1 calculations with precise Monte Carlo calculations of the radiation field around spherically symmetric protoneutron star models. We find that no closure performs consistently better or worse than others in all cases. The level of accuracy that a given closure yields depends on the matter configuration, neutrino type and neutrino energy. As a result, given this limitation, the maximum entropy closure by Minerbo on average yields relatively accurate results in the broadest set of cases considered in this work.« less
Analytic closures for M1 neutrino transport
NASA Astrophysics Data System (ADS)
Murchikova, E. M.; Abdikamalov, E.; Urbatsch, T.
2017-08-01
Carefully accounting for neutrino transport is an essential component of many astrophysical studies. Solving the full transport equation is too expensive for most realistic applications, especially those involving multiple spatial dimensions. For such cases, resorting to approximations is often the only viable option for obtaining solutions. One such approximation, which recently became popular, is the M1 method. It utilizes the system of the lowest two moments of the transport equation and closes the system with an ad hoc closure relation. The accuracy of the M1 solution depends on the quality of the closure. Several closures have been proposed in the literature and have been used in various studies. We carry out an extensive study of these closures by comparing the results of M1 calculations with precise Monte Carlo calculations of the radiation field around spherically symmetric protoneutron star models. We find that no closure performs consistently better or worse than others in all cases. The level of accuracy that a given closure yields depends on the matter configuration, neutrino type and neutrino energy. Given this limitation, the maximum entropy closure by Minerbo on average yields relatively accurate results in the broadest set of cases considered in this work.
Calculation methods for compressible turbulent boundary layers
NASA Technical Reports Server (NTRS)
Bushnell, D. M.; Cary, A. M., Jr.; Harris, J. E.
1976-01-01
Calculation procedures for non-reacting compressible two- and three-dimensional turbulent boundary layers were reviewed. Integral, transformation and correlation methods, as well as finite difference solutions of the complete boundary layer equations summarized. Alternative numerical solution procedures were examined, and both mean field and mean turbulence field closure models were considered. Physics and related calculation problems peculiar to compressible turbulent boundary layers are described. A catalog of available solution procedures of the finite difference, finite element, and method of weighted residuals genre is included. Influence of compressibility, low Reynolds number, wall blowing, and pressure gradient upon mean field closure constants are reported.
Multilevel turbulence simulations
Tziperman, E.
1994-12-31
The authors propose a novel method for the simulation of turbulent flows, that is motivated by and based on the Multigrid (MG) formalism. The method, called Multilevel Turbulence Simulations (MTS), is potentially more efficient and more accurate than LES. In many physical problems one is interested in the effects of the small scales on the larger ones, or in a typical realization of the flow, and not in the detailed time history of each small scale feature. MTS takes advantage of the fact that the detailed simulation of small scales is not needed at all times, in order to make the calculation significantly more efficient, while accurately accounting for the effects of the small scales on the larger scale of interest. In MTS, models of several resolutions are used to represent the turbulent flow. The model equations in each coarse level incorporate a closure term roughly corresponding to the tau correction in the MG formalism that accounts for the effects of the unresolvable scales on that grid. The finer resolution grids are used only a small portion of the simulation time in order to evaluate the closure terms for the coarser grids, while the coarse resolution grids are then used to accurately and efficiently calculate the evolution of the larger scales. The methods efficiency relative to direct simulations is of the order of the ratio of required integration time to the smallest eddies turnover time, potentially resulting in orders of magnitude improvement for a large class of turbulence problems.
Exact statistical results for binary mixing and reaction in variable density turbulence
NASA Astrophysics Data System (ADS)
Ristorcelli, J. R.
2017-02-01
We report a number of rigorous statistical results on binary active scalar mixing in variable density turbulence. The study is motivated by mixing between pure fluids with very different densities and whose density intensity is of order unity. Our primary focus is the derivation of exact mathematical results for mixing in variable density turbulence and we do point out the potential fields of application of the results. A binary one step reaction is invoked to derive a metric to asses the state of mixing. The mean reaction rate in variable density turbulent mixing can be expressed, in closed form, using the first order Favre mean variables and the Reynolds averaged density variance, ⟨ρ2⟩ . We show that the normalized density variance, ⟨ρ2⟩ , reflects the reduction of the reaction due to mixing and is a mix metric. The result is mathematically rigorous. The result is the variable density analog, the normalized mass fraction variance ⟨c2⟩ used in constant density turbulent mixing. As a consequence, we demonstrate that use of the analogous normalized Favre variance of the mass fraction, c″ 2˜ , as a mix metric is not theoretically justified in variable density turbulence. We additionally derive expressions relating various second order moments of the mass fraction, specific volume, and density fields. The central role of the density specific volume covariance ⟨ρ v ⟩ is highlighted; it is a key quantity with considerable dynamical significance linking various second order statistics. For laboratory experiments, we have developed exact relations between the Reynolds scalar variance ⟨c2⟩ its Favre analog c″ 2˜ , and various second moments including ⟨ρ v ⟩ . For moment closure models that evolve ⟨ρ v ⟩ and not ⟨ρ2⟩ , we provide a novel expression for ⟨ρ2⟩ in terms of a rational function of ⟨ρ v ⟩ that avoids recourse to Taylor series methods (which do not converge for large density differences). We have derived
Hinton, F. L.; Waltz, R. E.
2006-10-15
Expressions for particle and energy fluxes and heating rates due to turbulence are derived. These fluxes and heating rates are identified from moments of an extended drift-kinetic equation for the equilibrium distribution function. These include neoclassical as well as turbulent diffusion and heating. Phase-space conservation is demonstrated, allowing the drift-kinetic equation to be expressed in conservative form. This facilitates taking moments with few approximations, mainly those consistent with drift kinetics for the equilibrium distribution function and the relative smallness of the fluctuations. The turbulent heating is uniquely defined by choosing the standard gyrokinetic definition for the energy flux. With this definition, most of the heating can be expressed in the form of ohmic heating from turbulent parallel and perpendicular current density perturbations. The latter current is identified with grad-B and curvature drifts, plus terms involving magnetic perturbations (which are smaller for low beta). A small contribution to the heating comes from the divergence of an energy flux that is dependent on the finite gyroradius of the ions. The fluxes and heating rates are expressed in a form that can be easily evaluated from gyrokinetic turbulence simulations.
Stirring turbulence with turbulence
NASA Astrophysics Data System (ADS)
Cekli, Hakki Ergun; Joosten, René; van de Water, Willem
2015-12-01
We stir wind-tunnel turbulence with an active grid that consists of rods with attached vanes. The time-varying angle of these rods is controlled by random numbers. We study the response of turbulence on the statistical properties of these random numbers. The random numbers are generated by the Gledzer-Ohkitani-Yamada shell model, which is a simple dynamical model of turbulence that produces a velocity field displaying inertial-range scaling behavior. The range of scales can be adjusted by selection of shells. We find that the largest energy input and the smallest anisotropy are reached when the time scale of the random numbers matches that of the largest eddies of the wind-tunnel turbulence. A large mismatch of these times creates a highly intermittent random flow with interesting but quite anomalous statistics.
Turbulence Heating Observer - Thor
NASA Astrophysics Data System (ADS)
Retino, A.; Vaivads, A.; Escoubet, C. P.; Khotyaintsev, Y. V.; Soucek, J.; Valentini, F.; Chen, C. H. K.; Fazakerley, A. N.; Lavraud, B.; Marcucci, M. F.; Narita, Y.; Vainio, R. O.; Gehler, M.; Voirin, T.; Wielders, A.; Boudin, N.; Osuna, P.
2016-12-01
Turbulent fluctuations are ubiquitous in astrophysical plasmas and reach up scales as large as stars, bubbles and clouds blown out by stellar winds as well as entire galaxies. However, most of the irreversible energy dissipation associated to turbulent fluctuations occurs at very small scales, the so-called kinetic scales, where the plasma no longer behaves as a fluid and the properties of individual plasma species (electrons, protons, and other ions) become important. The heating of different plasma species as well as the acceleration of particles to high energies are governed by kinetic processes which determine how the turbulent electromagnetic fluctuations dissipate. Thus, processes at kinetic scales directly affect the large-scale properties of astrophysical plasmas. Turbulence Heating ObserveR (THOR) is one of the three candidates for selection as the next ESA M-class mission (M4). THOR will be the first mission ever flown in space that is fully dedicated to study plasma turbulent fluctuations and associated energization mechanisms. It will explore the kinetic plasma processes that determine the fundamental behavior of the majority of baryonic matter in the universe, and will lead to an understanding of the basic plasma heating and particle acceleration mechanisms, of their effect on different plasma species and of their relative importance in different turbulent regimes. THOR will provide closure of these fundamental questions by making detailed in situ measurements of the closest available dilute and turbulent magnetized plasmas - the Near-Earth's space - at unprecedented temporal and spatial resolution. THOR focuses on particular regions in space: the pristine solar wind, the Earth's bow shock and interplanetary shocks, and the compressed solar wind regions downstream of shocks. These regions are selected because of their different turbulence properties and reflect the properties of a number of distant astrophysical environments. Here we present THOR
Novafil. A dynamic suture for wound closure.
Rodeheaver, G T; Nesbit, W S; Edlich, R F
1986-01-01
Abdominal wound dehiscence was quantitatively studied in a rat model. Polybutester suture is a new monofilament nonabsorbable suture that has unique stress-strain properties that are potentially beneficial for abdominal wound closure. The abdominal volume at the moment of wound dehiscence was correlated with the extensibility of the suture material used for closure. Interrupted sutures of polybutester cut through the tissues at a mean abdominal volume of 212 +/- 3 ml. This volume was significantly (p less than or equal to 0.005) greater than the mean volumes reached with nylon (197 +/- 3 ml) or polyglycolic acid (187 +/- 4 ml). Closure of abdomens with continuous polybutester suture resulted in a mean rupture volume of 218 +/- 3 ml, which was significantly (p less than or equal to 0.005) greater than that achieved with the same suture employed as simple interrupted sutures (212 +/- 4 ml). The influence of width of tissue bite, suture size, and needle configuration was also evaluated. PMID:3017248
Discussion of turbulence modelling: Past and future
NASA Technical Reports Server (NTRS)
Speziale, Charles G.
1989-01-01
The full text of a paper presented at the Whither Turbulence Workshop (Cornell University, March 22-24, 1989) on past and future trends in turbulence modeling is provided. It is argued that Reynolds stress models are likely to remain the preferred approach for technological applications for at least the next few decades. In general agreement with the Launder position paper, it is further argued that among the variety of Reynolds stress models in use, second-order closures constitute by far the most promising approach. However, some needed improvements in the specification of the turbulent length scale are emphasized. The central points of the paper are illustrated by examples from homogeneous turbulence.
Assembling Transgender Moments
ERIC Educational Resources Information Center
Greteman, Adam J.
2017-01-01
In this article, the author seeks to assemble moments--scholarly, popular, and aesthetic--in order to explore the possibilities that emerge as moments collect in education's encounters with the needs, struggles, and possibilities of transgender lives and practices. Assembling moments, the author argues, illustrates the value of "moments"…
Evolution equations for the joint probability of several compositions in turbulent combustion
Bakosi, Jozsef
2010-01-01
One-point statistical simulations of turbulent combustion require models to represent the molecular mixing of species mass fractions, which then determine the reaction rates. For multi-species mixing the Dirichlet distribution has been used to characterize the assumed joint probability density function (PDF) of several scalars, parametrized by solving modeled evolution equations for their means and the sum of their variances. The PDF is then used to represent the mixing state and to obtain the chemical reactions source terms in moment closures or large eddy simulation. We extend the Dirichlet PDF approach to transported PDF methods by developing its governing stochastic differential equation (SDE). The transport equation, as opposed to parametrizing the assumed PDF, enables (1) the direct numerical computation of the joint PDF (and therefore the mixing model to directly account for the flow dynamics (e.g. reaction) on the shape of the evolving PDF), and (2) the individual specification of the mixing timescales of each species. From the SDE, systems of equations are derived that govern the first two moments, based on which constraints are established that provide consistency conditions for material mixing. A SDE whose solution is the generalized Dirichlet PDF is also developed and some of its properties from the viewpoint of material mixing are investigated. The generalized Dirichlet distribution has the following advantages over the standard Dirichlet distribution due to its more general covariance structure: (1) its ability to represent differential diffusion (i.e. skewness) without affecting the scalar means, and (2) it can represent both negatively and positively correlated scalars. The resulting development is a useful representation of the joint PDF of inert or reactive scalars in turbulent flows: (1) In moment closures, the mixing physics can be consistently represented by one underlying modeling principle, the Dirichlet or the generalized Dirichlet PDF, and
Turbulence Model Discovery with Data-Driven Learning and Optimization
NASA Astrophysics Data System (ADS)
King, Ryan; Hamlington, Peter
2016-11-01
Data-driven techniques have emerged as a useful tool for model development in applications where first-principles approaches are intractable. In this talk, data-driven multi-task learning techniques are used to discover flow-specific optimal turbulence closure models. We use the recently introduced autonomic closure technique to pose an online supervised learning problem created by test filtering turbulent flows in the self-similar inertial range. The autonomic closure is modified to solve the learning problem for all stress components simultaneously with multi-task learning techniques. The closure is further augmented with a feature extraction step that learns a set of orthogonal modes that are optimal at predicting the turbulent stresses. We demonstrate that these modes can be severely truncated to enable drastic reductions in computational costs without compromising the model accuracy. Furthermore, we discuss the potential universality of the extracted features and implications for reduced order modeling of other turbulent flows.
A closure scheme for chemical master equations.
Smadbeck, Patrick; Kaznessis, Yiannis N
2013-08-27
Probability reigns in biology, with random molecular events dictating the fate of individual organisms, and propelling populations of species through evolution. In principle, the master probability equation provides the most complete model of probabilistic behavior in biomolecular networks. In practice, master equations describing complex reaction networks have remained unsolved for over 70 years. This practical challenge is a reason why master equations, for all their potential, have not inspired biological discovery. Herein, we present a closure scheme that solves the master probability equation of networks of chemical or biochemical reactions. We cast the master equation in terms of ordinary differential equations that describe the time evolution of probability distribution moments. We postulate that a finite number of moments capture all of the necessary information, and compute the probability distribution and higher-order moments by maximizing the information entropy of the system. An accurate order closure is selected, and the dynamic evolution of molecular populations is simulated. Comparison with kinetic Monte Carlo simulations, which merely sample the probability distribution, demonstrates this closure scheme is accurate for several small reaction networks. The importance of this result notwithstanding, a most striking finding is that the steady state of stochastic reaction networks can now be readily computed in a single-step calculation, without the need to simulate the evolution of the probability distribution in time.
A closure scheme for chemical master equations
Smadbeck, Patrick; Kaznessis, Yiannis N.
2013-01-01
Probability reigns in biology, with random molecular events dictating the fate of individual organisms, and propelling populations of species through evolution. In principle, the master probability equation provides the most complete model of probabilistic behavior in biomolecular networks. In practice, master equations describing complex reaction networks have remained unsolved for over 70 years. This practical challenge is a reason why master equations, for all their potential, have not inspired biological discovery. Herein, we present a closure scheme that solves the master probability equation of networks of chemical or biochemical reactions. We cast the master equation in terms of ordinary differential equations that describe the time evolution of probability distribution moments. We postulate that a finite number of moments capture all of the necessary information, and compute the probability distribution and higher-order moments by maximizing the information entropy of the system. An accurate order closure is selected, and the dynamic evolution of molecular populations is simulated. Comparison with kinetic Monte Carlo simulations, which merely sample the probability distribution, demonstrates this closure scheme is accurate for several small reaction networks. The importance of this result notwithstanding, a most striking finding is that the steady state of stochastic reaction networks can now be readily computed in a single-step calculation, without the need to simulate the evolution of the probability distribution in time. PMID:23940327
Bumblebee Flight in Heavy Turbulence
NASA Astrophysics Data System (ADS)
Engels, T.; Kolomenskiy, D.; Schneider, K.; Lehmann, F.-O.; Sesterhenn, J.
2016-01-01
High-resolution numerical simulations of a tethered model bumblebee in forward flight are performed superimposing homogeneous isotropic turbulent fluctuations to the uniform inflow. Despite tremendous variation in turbulence intensity, between 17% and 99% with respect to the mean flow, we do not find significant changes in cycle-averaged aerodynamic forces, moments, or flight power when averaged over realizations, compared to laminar inflow conditions. The variance of aerodynamic measures, however, significantly increases with increasing turbulence intensity, which may explain flight instabilities observed in freely flying bees.
A comparison of three algebraic stress closures for combustor flow calculations
NASA Technical Reports Server (NTRS)
Nikjooy, M.; So, R. M. C.; Hwang, B. C.
1985-01-01
A comparison is made of the performance of two locally nonequilibrium and one equilibrium algebraic stress closures in calculating combustor flows. Effects of four different pressure-strain models on these closure models are also analyzed. The results show that the pressure-strain models have a much greater influence on the calculated mean velocity and turbulence field than the algebraic stress closures, and that the best mean strain model for the pressure-strain terms is that proposed by Launder, Reece and Rodi (1975). However, the equilibrium algebraic stress closure with the Rotta return-to-isotropy model (1951) for the pressure-strain terms gives as good a correlation with measurements as when the Launder et al. mean strain model is included in the pressure-strain model. Finally, comparison of the calculations with the standard k-epsilon closure results show that the algebraic stress closures are better suited for simple turbulent flow calculations.
Magnetohydrodynamic Turbulence and the Geodynamo
NASA Technical Reports Server (NTRS)
Shebalin, John V.
2016-01-01
Recent research results concerning forced, dissipative, rotating magnetohydrodynamic (MHD) turbulence will be discussed. In particular, we present new results from long-time Fourier method (periodic box) simulations in which forcing contains varying amounts of magnetic and kinetic helicity. Numerical results indicate that if MHD turbulence is forced so as to produce a state of relatively constant energy, then the largest-scale components are dominant and quasistationary, and in fact, have an effective dipole moment vector that aligns closely with the rotation axis. The relationship of this work to established results in ideal MHD turbulence, as well as to models of MHD turbulence in a spherical shell will also be presented. These results appear to be very pertinent to understanding the Geodynamo and the origin of its dominant dipole component. Our conclusion is that MHD turbulence, per se, may well contain the origin of the Earth's dipole magnetic field.
Energy transfer in compressible turbulence
NASA Technical Reports Server (NTRS)
Bataille, Francoise; Zhou, YE; Bertoglio, Jean-Pierre
1995-01-01
This letter investigates the compressible energy transfer process. We extend a methodology developed originally for incompressible turbulence and use databases from numerical simulations of a weak compressible turbulence based on Eddy-Damped-Quasi-Normal-Markovian (EDQNM) closure. In order to analyze the compressible mode directly, the well known Helmholtz decomposition is used. While the compressible component has very little influence on the solenoidal part, we found that almost all of the compressible turbulence energy is received from its solenoidal counterpart. We focus on the most fundamental building block of the energy transfer process, the triadic interactions. This analysis leads us to conclude that, at low turbulent Mach number, the compressible energy transfer process is dominated by a local radiative transfer (absorption) in both inertial and energy containing ranges.
Moment-to-Moment Emotions during Reading
ERIC Educational Resources Information Center
Graesser, Arthur C.; D'Mello, Sidney
2012-01-01
Moment-to-moment emotions are affective states that dynamically change during reading and potentially influence comprehension. Researchers have recently identified these emotions and the emotion trajectories in reading, tutoring, and problem solving. The primary learning-centered emotions are boredom, frustration, confusion, flow (engagement),…
Moment-to-Moment Emotions during Reading
ERIC Educational Resources Information Center
Graesser, Arthur C.; D'Mello, Sidney
2012-01-01
Moment-to-moment emotions are affective states that dynamically change during reading and potentially influence comprehension. Researchers have recently identified these emotions and the emotion trajectories in reading, tutoring, and problem solving. The primary learning-centered emotions are boredom, frustration, confusion, flow (engagement),…
A BBGKY framework for fluid turbulence
NASA Technical Reports Server (NTRS)
Montgomery, D.
1976-01-01
A framework is presented for a systematic kinetic theory of turbulence originating from the Liouville equation for the Fourier coefficients of fluid variables. The real and imaginary parts of these Fourier coefficients play the role that particle coordinates (positions and momenta) play in the BBGKY theory. The basic relations of the problem are the incompressible Navier-Stokes equations in two dimensions with zero viscosity, with the probability distributions of Fourier coefficients rather than moments being the basic variables of the theory. A kinetic equation is derived and shown to possess a number of requirements that any reasonable kinetic equation must have: conservation laws, positive-definite spectral densities, and an H-theorem. The major lack in the theory is any reliable information on the relaxation predicted by the complicated linear operator H. Closure of the hierarchy is achieved by the hypothesis that the five-coefficient correlation function is negligible. Problems associated with inclusion of viscosity and external driving forces are discussed.
Partial moment entropy approximation to radiative heat transfer
Frank, Martin . E-mail: frank@mathematik.uni-kl.de; Dubroca, Bruno . E-mail: Bruno.Dubroca@math.u-bordeaux.fr; Klar, Axel . E-mail: klar@mathematik.uni-kl.de
2006-10-10
We extend the half moment entropy closure for the radiative heat transfer equations presented in Dubroca and Klar [B. Dubroca, A. Klar, Half moment closure for radiative transfer equations, J. Comput. Phys. 180 (2002) 584-596] and Turpault et al. [R. Turpault, M. Frank, B. Dubroca, A. Klar, Multigroup half space moment approximations to the radiative heat transfer equations, J. Comput. Phys. 198 (2004) 363-371] to multi-D. To that end, we consider a partial moment system with general partitions of the unit sphere closed by an entropy minimization principle. We give physical and mathematical reasons for this choice of model and study its properties. Several numerical examples in different physical regimes are presented.
NASA Astrophysics Data System (ADS)
Fox, Rodney O.; Vie, Aymeric; Laurent, Frederique; Chalons, Christophe; Massot, Marc
2012-11-01
Numerous applications involve a disperse phase carried by a gaseous flow. To simulate such flows, one can resort to a number density function (NDF) governed a kinetic equation. Traditionally, Lagrangian Monte-Carlo methods are used to solve for the NDF, but are expensive as the number of numerical particles needed must be large to control statistical errors. Moreover, such methods are not well adapted to high-performance computing because of the intrinsic inhomogeneity of the NDF. To overcome these issues, Eulerian methods can be used to solve for the moments of the NDF resulting in an unclosed Eulerian system of hyperbolic conservation laws. To obtain closure, in this work a multivariate bi-Gaussian quadrature is used, which can account for particle trajectory crossing (PTC) over a large range of Stokes numbers. This closure uses up to four quadrature points in 2-D velocity phase space to capture large-scale PTC, and an anisotropic Gaussian distribution around each quadrature point to model small-scale PTC. Simulations of 2-D particle-laden isotropic turbulence at different Stokes numbers are employed to validate the Eulerian models against results from the Lagrangian approach. Good agreement is found for the number density fields over the entire range of Stokes numbers tested. Research carried out at the Center for Turbulence Research 2012 Summer Program.
Numerical Investigation of a Statistically Stationary Turbulent Reacting Flow
NASA Astrophysics Data System (ADS)
Overholt, Matthew R.; Pope, Stephen B.
1997-11-01
Direct numerical simulation (DNS) has been very useful in the study of inert scalar mixing in turbulent flows, and has recently become feasible for studies of reacting scalars. We have formulated an accessible inhomogeneous nonpremixed turbulent reactive flow for investigating the effects of mixing on reaction and testing mixing models. The mixture fraction-progress variable approach is used with a model single-step reversible finite-rate thermochemistry, yielding non-trivial stationary solutions corresponding to stable reaction and allowing local extinction to occur. A mean gradient in the mixture fraction gives rise to stationarity without forcing, as well as a flame brush. A range of reaction zone thicknesses and Damkohler numbers are examined, yielding a broad spectrum of behavior, ranging from thick to thin flames, and from local extinction to near equilibrium. Based on this study results from full probability density function (PDF) simulations using the IEM and EMST mixing models are evaluated. Conditional moment closure (CMC) results are evaluated as well.
Theory of strong turbulence by renormalization
NASA Technical Reports Server (NTRS)
Tchen, C. M.
1981-01-01
The hydrodynamical equations of turbulent motions are inhomogeneous and nonlinear in their inertia and force terms and will generate a hierarchy. A kinetic method was developed to transform the hydrodynamic equations into a master equation governing the velocity distribution, as a function of the time, the position and the velocity as an independent variable. The master equation presents the advantage of being homogeneous and having fewer nonlinear terms and is therefore simpler for the investigation of closure. After the closure by means of a cascade scaling procedure, the kinetic equation is derived and possesses a memory which represents the nonMarkovian character of turbulence. The kinetic equation is transformed back to the hydrodynamical form to yield an energy balance in the cascade form. Normal and anomalous transports are analyzed. The theory is described for incompressible, compressible and plasma turbulence. Applications of the method to problems relating to sound generation and the propagation of light in a nonfrozen turbulence are considered.
A Stochastic Model for the Relative Motion of High Stokes Number Particles in Isotropic Turbulence
NASA Astrophysics Data System (ADS)
Dhariwal, Rohit; Rani, Sarma; Koch, Donald
2014-11-01
In the current study, a novel analytical closure for the diffusion current in the PDF equation is presented that is applicable to high-inertia particle pairs with Stokes numbers Str >> 1 . Here Str is a Stokes number based on the time-scale τr of eddies whose size scales with pair separation r. Using this closure, Langevin equations were solved to evolve particle-pair relative velocities and separations in stationary isotropic turbulence. The Langevin equation approach enables the simulation of the full PDF of pair relative motion, instead of only the first few moments of the PDF as is the case in a moments-based approach. Accordingly, PDFs Ω (U | r) and Ω (Ur | r) are computed for various separations r, where the former is the PDF of relative velocity U and the latter is the PDF of the radial component of relative velocity Ur, both conditioned upon the separation r. Consistent with the DNS study of Sundaram & Collins, the Langevin simulations capture the transition of Ω (U | r) from being Gaussian at integral-scale separations to an exponential PDF at Kolmogorov-scale separations. The radial distribution functions (RDFs) computed from these simulations also show reasonable quantitative agreement with those from the DNS of Fevrier et al.
NASA Technical Reports Server (NTRS)
Chandler, C. L.
1987-01-01
In order to forecast turbulence, one needs to have an understanding of the cause of turbulence. Therefore, an attempt is made to show the atmospheric structure that often results when aircraft encounter moderate or greater turbulence. The analysis is based on thousands of hours of observations of flights over the past 39 years of aviation meteorology.
NASA Astrophysics Data System (ADS)
Jin, F.; Pan, L.; Watanabe, M.
2005-05-01
The two-way interaction between synoptic eddy and low-frequency flow (SELF), which we will refer to as the SELF interaction, has been recognized for decades to play an important role in the dynamics of the low-frequency variability of the atmospheric circulation. We propose a new framework for studying the dynamics of the SELF interaction and the low-frequency variability in a stormy background flow. By considering a Gaussian flow as a surrogate for the stormy background flow, we expand the traditional climatological basic flow to a synthetic stochastic basic flow. Its ensemble mean is the observed climatological mean flow while its prescribed variance/covariance fields represent the climatological variance/covariance fields of the observed synoptic eddies. Low-frequency anomalies in the traditional month-to-seasonal mean flow and in the variance/covariance fields of the transient eddy flow are viewed as equivalent to the anomalies in the first and second moments of the quasi-stationary stochastic flow ensemble. The linear dynamics of SELF interaction are described by the coupling among the anomalies in first and second moments. Under the assumption that slow changes in the second moments are in quasi-equilibrium with the anomalies in the first moment, an analytical non-local dynamical closure for SELF interaction is obtained. Using this framework, we show that leading low-frequency modes earn their dominance because they can effective organizing the turbulent synoptic flow such that they get reinforced by positive SELF interaction.
Stochastic superparameterization in quasigeostrophic turbulence
Grooms, Ian; Majda, Andrew J.
2014-08-15
In this article we expand and develop the authors' recent proposed methodology for efficient stochastic superparameterization algorithms for geophysical turbulence. Geophysical turbulence is characterized by significant intermittent cascades of energy from the unresolved to the resolved scales resulting in complex patterns of waves, jets, and vortices. Conventional superparameterization simulates large scale dynamics on a coarse grid in a physical domain, and couples these dynamics to high-resolution simulations on periodic domains embedded in the coarse grid. Stochastic superparameterization replaces the nonlinear, deterministic eddy equations on periodic embedded domains by quasilinear stochastic approximations on formally infinite embedded domains. The result is a seamless algorithm which never uses a small scale grid and is far cheaper than conventional SP, but with significant success in difficult test problems. Various design choices in the algorithm are investigated in detail here, including decoupling the timescale of evolution on the embedded domains from the length of the time step used on the coarse grid, and sensitivity to certain assumed properties of the eddies (e.g. the shape of the assumed eddy energy spectrum). We present four closures based on stochastic superparameterization which elucidate the properties of the underlying framework: a ‘null hypothesis’ stochastic closure that uncouples the eddies from the mean, a stochastic closure with nonlinearly coupled eddies and mean, a nonlinear deterministic closure, and a stochastic closure based on energy conservation. The different algorithms are compared and contrasted on a stringent test suite for quasigeostrophic turbulence involving two-layer dynamics on a β-plane forced by an imposed background shear. The success of the algorithms developed here suggests that they may be fruitfully applied to more realistic situations. They are expected to be particularly useful in providing accurate and
Turbulence modeling of gas-solid suspension flows
NASA Technical Reports Server (NTRS)
Chen, C. P.
1988-01-01
The purpose here is to discuss and review advances in two-phase turbulent modeling techniques and their applications in various gas-solid suspension flow situations. In addition to the turbulence closures, heat transfer effect, particle dispersion and wall effects are partially covered.
Joint PDF Modelling of Turbulent Flow and Dispersion in an Urban Street Canyon
NASA Astrophysics Data System (ADS)
Bakosi, J.; Franzese, P.; Boybeyi, Z.
2009-05-01
The joint probability density function (PDF) of turbulent velocity and concentration of a passive scalar in an urban street canyon is computed using a newly developed particle-in-cell Monte Carlo method. Compared to moment closures, the PDF methodology provides the full one-point one-time PDF of the underlying fields containing all higher moments and correlations. The small-scale mixing of the scalar released from a concentrated source at the street level is modelled by the interaction by exchange with the conditional mean (IECM) model, with a micro-mixing time scale designed for geometrically complex settings. The boundary layer along no-slip walls (building sides and tops) is fully resolved using an elliptic relaxation technique, which captures the high anisotropy and inhomogeneity of the Reynolds stress tensor in these regions. A less computationally intensive technique based on wall functions to represent the boundary layers and its effect on the solution are also explored. The calculated statistics are compared to experimental data and large-eddy simulation. The present work can be considered as the first example of computation of the full joint PDF of velocity and a transported passive scalar in an urban setting. The methodology proves successful in providing high level statistical information on the turbulence and pollutant concentration fields in complex urban scenarios.
Optimal prediction for moment models: crescendo diffusion and reordered equations
NASA Astrophysics Data System (ADS)
Seibold, Benjamin; Frank, Martin
2009-12-01
A direct numerical solution of the radiative transfer equation or any kinetic equation is typically expensive, since the radiative intensity depends on time, space and direction. An expansion in the direction variables yields an equivalent system of infinitely many moments. A fundamental problem is how to truncate the system. Various closures have been presented in the literature. We want to generally study the moment closure within the framework of optimal prediction, a strategy to approximate the mean solution of a large system by a smaller system, for radiation moment systems. We apply this strategy to radiative transfer and show that several closures can be re-derived within this framework, such as P N , diffusion, and diffusion correction closures. In addition, the formalism gives rise to new parabolic systems, the reordered P N equations, that are similar to the simplified P N equations. Furthermore, we propose a modification to existing closures. Although simple and with no extra cost, this newly derived crescendo diffusion yields better approximations in numerical tests.
PDF approach for turbulent scalar field: Some recent developments
NASA Technical Reports Server (NTRS)
Gao, Feng
1993-01-01
The probability density function (PDF) method has been proven a very useful approach in turbulence research. It has been particularly effective in simulating turbulent reacting flows and in studying some detailed statistical properties generated by a turbulent field There are, however, some important questions that have yet to be answered in PDF studies. Our efforts in the past year have been focused on two areas. First, a simple mixing model suitable for Monte Carlo simulations has been developed based on the mapping closure. Secondly, the mechanism of turbulent transport has been analyzed in order to understand the recently observed abnormal PDF's of turbulent temperature fields generated by linear heat sources.
Studying Turbulence Using Numerical Simulation Databases. Proceedings of the 1987 Summer Program
NASA Technical Reports Server (NTRS)
Moin, Parviz (Editor); Reynolds, William C. (Editor); Kim, John (Editor)
1987-01-01
The focus was on the use of databases obtained from direct numerical simulations of turbulent flows, for study of turbulence physics and modeling. Topics addressed included: stochastic decomposition/chaos/bifurcation; two-point closure (or k-space) modeling; scalar transport/reacting flows; Reynolds stress modeling; and structure of turbulent boundary layers.
NASA Astrophysics Data System (ADS)
Lecoustre, Vivien; Arias, Paul; Roy, Somesh; Wang, Wei; Luo, Zhaoyu; Haworth, Dan; Im, Hong; Lu, Tianfeng; Ma, Kwan-Liu; Sankaran, Ramanan; Trouve, Arnaud
2011-11-01
Direct numerical simulations of 2D temporally-evolving luminous turbulent ethylene-air jet diffusion flames are performed using a high-order compressible Navier-Stokes solver. The simulations use a reduced mechanism derived from a detailed ethylene-air chemical kinetic mechanism that includes the reaction pathways for the formation of polycyclic aromatic hydrocarbons. The gas-phase chemistry is coupled with a detailed soot particle model based on the method of moments with interpolative closure that accounts for soot nucleation, coagulation, surface growth through HACA mechanism, and oxidation. Radiative heat transfer of CO2, H2O, and soot is treated by solving the radiative transfer equation using the discrete transfer method. This work presents preliminary results of radiation effects on soot dynamics at the tip of a jet diffusion flame with a particular focus on soot formation/oxidation.
A B-B-G-K-Y framework for fluid turbulence
NASA Technical Reports Server (NTRS)
Montgomery, D.
1975-01-01
A kinetic theory for fluid turbulence is developed from the Liouville equation and the associated BBGKY hierarchy. Real and imaginary parts of Fourier coefficients of fluid variables play the roles of particles. Closure is achieved by the assumption of negligible five-coefficient correlation functions and probability distributions of Fourier coefficients are the basic variables of the theory. An additional approximation leads to a closed-moment description similar to the so-called eddy-damped Markovian approximation. A kinetic equation is derived for which conservation laws and an H-theorem can be rigorously established, the H-theorem implying relaxation of the absolute equilibrium of Kraichnan. The equation can be cast in the Fokker-Planck form, and relaxation times estimated from its friction and diffusion coefficients. An undetermined parameter in the theory is the free decay time for triplet correlations. Some attention is given to the inclusion of viscous damping and external driving forces.
Large-eddy simulation of compressible turbulence
NASA Technical Reports Server (NTRS)
Squires, Kyle D.
1991-01-01
The increase in the range of length scales with increasing Reynolds number limits the direct simulation of turbulent flows to relatively simple geometries and low Reynolds numbers. However, since most flows of engineering interest occur at much higher Reynolds number than is currently within the capabilities of full simulation, prediction of these flow fields can only be obtained by solving some suitably-averaged set of governing equations. In the traditional Reynolds-averaged approach, the Navier-Stokes equations are averaged over time. This in turn yields correlations between various turbulence fluctuations. It is these terms, e.g. the Reynolds stresses, for which a turbulence model must be derived. Turbulence modeling of incompressible flows has received a great amount of attention in the literature. An area of research that has received comparatively less attention is the modeling of compressible turbulent flows. An approach to simulating compressible turbulence at high Reynolds numbers is through the use of Large-Eddy Simulation (LES). In LES the dependent variables are decomposed into a large-scale (resolved) component and a sub-grid scale component. It is the small-scale components of the velocity field which are presumably more homogeneous than the large scales and, therefore, more easily modeled. Thus, it seems plausible that simpler models, which should be more universal in character than those employed in second-order closure schemes, may be developed for LES of compressible turbulence. The objective of the present research, therefore, is to explore models for the Large-Eddy Simulation of compressible turbulent flows. Given the recent successes of Zeman in second order closure modeling of compressible turbulence, model development was guided by principals employed in second-order closures.
Novak, Thomas E
2011-05-01
Children with bladder exstrophy present a formidable surgical challenge. Like all major reconstructive surgeries, the best hope for a favorable outcome lies in achieving success in the first operative attempt. Regardless of the surgical approach, however, complications do occur. A failed exstrophy closure is a major complication with significant implications on the long-term surgical outcome and ultimate fate of the urinary tract. Successful repeat exstrophy closure can be accomplished in most cases when performed in conjunction with pelvic osteotomy and proper postoperative immobilization. Modern staged repair of exstrophy, complete primary repair of exstrophy, and immediate continent urinary diversion have been advocated by different groups in the management of a failed exstrophy closure. It is apparent that compared with children who undergo successful primary closure, a failed closure with subsequent successful repeat closure makes the child much less likely to achieve sufficient bladder growth to be considered for bladder neck reconstruction, and furthermore, makes them less likely to have a successful bladder neck reconstruction even when they are an acceptable candidate. Although acceptable dryness rates after repeat closure can ultimately be obtained, they are typically at the expense of a commitment to intermittent catheterization and continent diversion. Published by Elsevier Inc.
Numerical Simulation of High-Speed Turbulent Reacting Flows
NASA Technical Reports Server (NTRS)
Givi, P.; Taulbee, D. B.; Madnia, C. K.; Jaberi, F. A.; Colucci, P. J.; Gicquel, L. Y. M.; Adumitroaie, V.; James, S.
1999-01-01
The objectives of this research are: (1) to develop and implement a new methodology for large eddy simulation of (LES) of high-speed reacting turbulent flows. (2) To develop algebraic turbulence closures for statistical description of chemically reacting turbulent flows. We have just completed the third year of Phase III of this research. This is the Final Report of our activities on this research sponsored by the NASA LaRC.
NASA Astrophysics Data System (ADS)
Yunardi, Y.; Darmadi, D.; Hisbullah, H.; Fairweather, M.
2011-12-01
This paper presents the results of an application of a first-order conditional moment closure (CMC) approach coupled with a semi-empirical soot model to investigate the effect of various detailed combustion chemistry schemes on soot formation and destruction in turbulent non-premixed flames. A two-equation soot model representing soot particle nucleation, growth, coagulation and oxidation, was incorporated into the CMC model. The turbulent flow-field of both flames is described using the Favre-averaged fluid-flow equations, applying a standard k-ɛ turbulence model. A number of five reaction kinetic mechanisms having 50-100 species and 200-1000 elementary reactions called ABF, Miller-Bowman, GRI-Mech3.0, Warnatz, and Qin were employed to study the effect of combustion chemistry schemes on soot predictions. The results showed that of various kinetic schemes being studied, each yields similar accuracy in temperature prediction when compared with experimental data. With respect to soot prediction, the kinetic scheme containing benzene elementary reactions tends to result in a better prediction on soot concentrations in comparison to those contain no benzene elementary reactions. Among five kinetic mechanisms being studied, the Qin combustion scheme mechanism turned to yield the best prediction on both flame temperature and soot levels.
Cascade modeling of single and two-phase turbulence
NASA Astrophysics Data System (ADS)
Bolotnov, Igor A.
The analysis of turbulent two-phase flows requires closure models in order to perform reliable computational multiphase fluid dynamics (CFMD) analyses. A turbulence cascade model, which tracks the evolution of the turbulent kinetic energy between the various eddy sizes, has been developed for the analysis of the single and bubbly two-phase turbulence. Various flows are considered including the decay of isotropic grid-induced turbulence, uniform shear flow and turbulent channel flow. The model has been developed using a "building block" approach by moving from modeling of simpler turbulent flows (i.e., homogeneous, isotropic decay) to more involved turbulent flows (i.e., non-homogeneous channel flow). The spectral cascade-transport model's performance has been assessed against a number of experimental and direct numerical simulation (DNS) results.
Parallel closures in an inhomogeneous magnetic field
NASA Astrophysics Data System (ADS)
Lee, Hankyu; Ji, Jeong-Young
2016-10-01
We solve a reduced drift kinetic equation with a Krook-type model collision operator to obtain parallel closures. Grid points in the velocity space are chosen for Gauss-Laguerre quadrature to take closure moments. For trapped and passing regimes, analytical solutions are expressed as kernel-weighted integrals of thermodynamic drives. The analytical sloutions are compared to numerical solutions obtained from a finite difference method. Inverting the free streaming operator near a bouncing point is investigated to improve accuracy of solutions. Research supported by the U.S. DOE under Grant Nos. DE-SC0014033, DE-FG02-04ER54746, DE-FC02-04ER54798, and DE-FC02-05ER54812.
A CLASS OF PHYSICALLY MOTIVATED CLOSURES FOR RADIATION HYDRODYNAMICS
Chan, Chi-kwan
2011-02-01
Radiative transfer and radiation hydrodynamics use the relativistic Boltzmann equation to describe the kinetics of photons. It is difficult to solve the six-dimensional time-dependent transfer equation unless the problem is highly symmetric or in equilibrium. When the radiation field is smooth, it is natural to take angular moments of the transfer equation to reduce the degrees of freedom. However, low order moment equations contain terms that depend on higher order moments. To close the system of moment equations, approximations are made to truncate this hierarchy. Popular closures used in astrophysics include flux-limited diffusion and the M{sub 1} closure, which are rather ad hoc and do not necessarily capture the correct physics. In this paper, we propose a new class of closures for radiative transfer and radiation hydrodynamics. We start from a different perspective and highlight the consistency of a fully relativistic formalism. We present a generic framework to approximate radiative transfer based on relativistic Grad's moment method. We then derive a 14-field method that minimizes unphysical photon self-interaction.
Sternal exploration or closure
... Chronic pain Decreased lung function Increased risk of death More infections Need to repeat or revise the procedure Alternative Names VAC - vacuum-assisted closure - sternal wound; Sternal dehiscence; Sternal infection References ...
NASA Technical Reports Server (NTRS)
Ahmed, S.; Tannehill, J. C.
1990-01-01
A new nonequilibrium turbulence closure model has been developed for computing wall bounded two-dimensional turbulent flows. This two-layer eddy viscosity model was motivated by the success of the Johnson-King model in separated flow regions. The influence of history effects are described by an ordinary differential equation developed from the turbulent kinetic energy equation. The performance of the present model has been evaluated by solving the flow around three airfoils using the Reynolds time-averaged Navier-Stokes equations. Excellent results were obtained for both attached and separated turbulent flows about the NACA 0012 airfoil, the RAE 2822 airfoil, and the Integrated Technology A 153W airfoil. Based on the comparison of the numerical solutions with the available experimental data, it is concluded that the new nonequilibrium turbulence model accurately captures the history effects of convection and diffusion on turbulence.
NASA Astrophysics Data System (ADS)
Bogenschutz, Peter A.
Over the past few years a new type of general circulation model (GCM) has emerged that is known as the multiscale modeling framework (MMF). The Colorado State University (CSU) MMF represents a coupling between the Community Atmosphere Model (CAM) GCM and the System of Atmospheric Modeling (SAM) cloud resolving model (CRM). Within this MMF the embedded CRM replaces the traditionally used parameterized moist physics in CAM to represent subgrid-scale (SGS) convection. However, due to substantial increases of computational burden associated with the MMF, the embedded CRM is typically run with a horizontal grid size of 4 km. With a horizontal grid size of 4 km, a low-order closure CRM cannot adequately represent shallow convective processes, such as trade-wind cumulus or stratocumulus. A computationally inexpensive parameterization of turbulence and clouds is presented in this dissertation. An extensive a priori test is performed to determine which functional form of an assumed PDF is best suited for coarse-grid CRMs for both deep shallow and deep convection. The diagnostic approach to determine the input moments needed for the assumed PDFs uses the subgrid-scale (SGS) turbulent kinetic energy (TKE) as the basis for the parameterization. The term known as the turbulent length scale (L) is examined, as it is needed to parameterize the dissipation of turbulence and therefore is needed to better balance the budgets of SGS TKE. A new formulation of this term is added to the model code which appears to be able to partition resolved and SGS TKE fairly accurately. Results from "offline" tests of the simple diagnostic closure within SAM shows that the cloud and turbulence properties of shallow convection can be adequately represented when compared to large eddy simulation (LES) benchmark simulations. Results are greatly improved when compared to the standard version of SAM. The preliminary test of the scheme within the embedded CRM of the MMF shows promising results with the
SONAR SIGNALS, *UNDERWATER SOUND SIGNALS, SHOCK WAVES, TURBULENCE, WAVE PROPAGATION, SOUND TRANSMISSION, ACOUSTIC ATTENUATION, AMPLITUDE, UNDERWATER EXPLOSIONS, ACOUSTIC REFLECTION, SOUND RANGING, BOTTOM LOSS, BOTTOM BOUNCE .
NASA Technical Reports Server (NTRS)
White, III, Dorsey E. (Inventor); Updike, deceased, Benjamin T. (Inventor); Allred, Johnny W. (Inventor)
1989-01-01
A quick actuating closure for a pressure vessel 80 in which a wedge ring 30 with a conical outer surface 31 is moved forward to force shear blocks 40, with conical inner surfaces 41, radially outward to lock an end closure plug 70 within an opening 81 in the pressure vessel 80. A seal ring 60 and a preload ramp 50 sit between the shear blocks 40 and the end closure plug 70 to provide a backup sealing capability. Conical surfaces 44 and 55 of the preload ramp 50 and the shear blocks 40 interact to force the seal ring 60 into shoulders 73 and 85 in the end closure plug 70 and opening 81 to form a tight seal. The end closure plug 70 is unlocked by moving the wedge ring 30 rearward, which causes T-bars 32 of the wedge ring 30 riding within T -slots 42 of the shear blocks 40 to force them radially inward. The end closure plug 70 is then removed, allowing access to the interior of the pressure vessel 80.
Single point modeling of rotating turbulent flows
NASA Technical Reports Server (NTRS)
Hadid, A. H.; Mansour, N. N.; Zeman, O.
1994-01-01
A model for the effects of rotation on turbulence is proposed and tested. These effects which influence mainly the rate of turbulence decay are modeled in a modified turbulent energy dissipation rate equation that has explicit dependence on the mean rotation rate. An appropriate definition of the rotation rate derived from critical point theory and based on the invariants of the deformation tensor is proposed. The modeled dissipation rate equation is numerically well behaved and can be used in conjunction with any level of turbulence closure. The model is applied to the two-equation kappa-epsilon turbulence model and is used to compute separated flows in a backward-facing step and an axisymmetric swirling coaxial jets into a sudden expansion. In general, the rotation modified dissipation rate model shows some improvements over the standard kappa-epsilon model.
Turbulence kinetic energy equation for dilute suspensions
NASA Technical Reports Server (NTRS)
Abou-Arab, T. W.; Roco, M. C.
1989-01-01
A multiphase turbulence closure model is presented which employs one transport equation, namely the turbulence kinetic energy equation. The proposed form of this equation is different from the earlier formulations in some aspects. The power spectrum of the carrier fluid is divided into two regions, which interact in different ways and at different rates with the suspended particles as a function of the particle-eddy size ratio and density ratio. The length scale is described algebraically. A mass/time averaging procedure for the momentum and kinetic energy equations is adopted. The resulting turbulence correlations are modeled under less retrictive assumptions comparative to previous work. The closures for the momentum and kinetic energy equations are given. Comparisons of the predictions with experimental results on liquid-solid jet and gas-solid pipe flow show satisfactory agreement.
Michael Ramsey-Musolf; Wick Haxton; Ching-Pang Liu
2002-03-29
Nuclear anapole moments are parity-odd, time-reversal-even E1 moments of the electromagnetic current operator. Although the existence of this moment was recognized theoretically soon after the discovery of parity nonconservation (PNC), its experimental isolation was achieved only recently, when a new level of precision was reached in a measurement of the hyperfine dependence of atomic PNC in 133Cs. An important anapole moment bound in 205Tl also exists. In this paper, we present the details of the first calculation of these anapole moments in the framework commonly used in other studies of hadronic PNC, a meson exchange potential that includes long-range pion exchange and enough degrees of freedom to describe the five independent S-P amplitudes induced by short-range interactions. The resulting contributions of pi-, rho-, and omega-exchange to the single-nucleon anapole moment, to parity admixtures in the nuclear ground state, and to PNC exchange currents are evaluated, using configuration-mixed shell-model wave functions. The experimental anapole moment constraints on the PNC meson-nucleon coupling constants are derived and compared with those from other tests of the hadronic weak interaction. While the bounds obtained from the anapole moment results are consistent with the broad ''reasonable ranges'' defined by theory, they are not in good agreement with the constraints from the other experiments. We explore possible explanations for the discrepancy and comment on the potential importance of new experiments.
The higher moments in the Lundgren model conform with Kolmogorov scaling
NASA Astrophysics Data System (ADS)
Segel, Daniel
1995-12-01
We calculate the structure functions of the higher moments of the vorticity in the framework of Lundgren's spiral model of turbulence. We show that they conform to the scaling expected from Kolmogorov's scaling hypothesis of 1941, and explain the result.
ODT Based Closure Model for Non-Premixed Combustion LES
NASA Astrophysics Data System (ADS)
Miles, Jeffery Scott
An LES closure method for turbulent non-premixed combustion using data from standalone ODT simulations is developed and validated. An ODT simulation provides a complete view of turbulent combustion including detailed chemistry within a single dimension through spatially (in 1D) and temporally resolved solutions for thermo chemical scalars and a stochastic description of turbulent advection. A unique closure technique removes the limitations associated with prescribed FDF distributions by using the resolved ODT statistics to construct joint scalar distributions needed for LES closure. These distributions are combined with other ODT statistics to construct closure tables for filtered variables such as density and chemical source terms. The tabulated closure follows the classical integration over state-space combining joint distributions with statistics from dependent variables. The temperature and mixture fraction are considered for this joint FDF as they can be combined to provide a complete view of the chemical and thermal state of the overall system within a non-premixed combustion problem. The ODT simulations are used to extract filtered and unfiltered correlations representing FDF distributions for each of the state-defining scalars; and kernel density functions are used to convert the sample datasets into smooth distributions that represent FDFs found within ODT statistics. A stand-alone ODT simulation is configured to generate the statistics and data needed for the closure model construction. The ODT domain selected to match the target problem domain is a one-dimensional axisymmetric piloted jet. This configuration is capable of capturing many of the features of a turbulent jet diffusion flame much like a spatially resolved DNS simulation but at a fraction of the cost. For each realization, the state variables are filtered and stored in vector form with the "instantaneous" values for each term included in the unclosed set required in the LES domain. Model
Pandit, Narendra; Singh, Harjeet; Kumar, Hemanth; Gupta, Rajesh; Verma, G R
2016-11-01
Intestinal loop stoma is a common surgical procedure performed for various benign and malignant abdominal problems, but it rarely undergoes spontaneous closure, without surgical intervention. Two male patients presented to our emergency surgical department with acute abdominal pain. One of them was diagnosed as having rectosigmoid perforation and underwent diversion sigmoid loop colostomy after primary closure of the perforation. The other was a known case of carcinoma of the rectum who had already undergone low anterior resection with covering loop ileostomy; the patient underwent second loop ileostomy, this time for complicated intestinal obstruction. To our surprise, both the loop colostomy and ileostomy closed spontaneously at 8 weeks and 6 weeks, respectively, without any consequences. Spontaneous stoma closure is a rare and interesting event. The exact etiology for spontaneous closure remains unknown, but it may be hypothesized to result from slow retraction of the stoma, added to the concept of a tendency towards spontaneous closure of enterocutaneous fistula. © The Author(s) 2015. Published by Oxford University Press and the Digestive Science Publishing Co. Limited.
Moment inference from tomograms
Day-Lewis, F. D.; Chen, Y.; Singha, K.
2007-01-01
Time-lapse geophysical tomography can provide valuable qualitative insights into hydrologic transport phenomena associated with aquifer dynamics, tracer experiments, and engineered remediation. Increasingly, tomograms are used to infer the spatial and/or temporal moments of solute plumes; these moments provide quantitative information about transport processes (e.g., advection, dispersion, and rate-limited mass transfer) and controlling parameters (e.g., permeability, dispersivity, and rate coefficients). The reliability of moments calculated from tomograms is, however, poorly understood because classic approaches to image appraisal (e.g., the model resolution matrix) are not directly applicable to moment inference. Here, we present a semi-analytical approach to construct a moment resolution matrix based on (1) the classic model resolution matrix and (2) image reconstruction from orthogonal moments. Numerical results for radar and electrical-resistivity imaging of solute plumes demonstrate that moment values calculated from tomograms depend strongly on plume location within the tomogram, survey geometry, regularization criteria, and measurement error. Copyright 2007 by the American Geophysical Union.
Quasisteady turbulence driven by runaway electrons
Muschietti, L.; Appert, K.; Vaclavik, J.
1982-07-01
The evolution of the turbulence driven by runaway electrons has been followed by means of a computer code based on the quasilinear equations. The evolution is not characterized by periodic relaxations as claimed in previous works but ends in a quasisteady turbulent, yet very persistent state, accessible from different initial conditions. This discrepancy is clarified as being due to the excessive stiffness of the moment equations used to demonstrate the relaxations. Moreover, a theory is developed to interpret the quasisteady state found.
Boss, Pauline; Carnes, Donna
2012-12-01
Therapies for grief and loss have traditionally focused on the work of grieving. The goal was to reach an endpoint, now popularly called closure. There are, however, many people who, through no fault of their own, find a loss so unclear that there can be no end to grief. They have not failed in the work of grieving, but rather have suffered ambiguous loss, a type of loss that is inherently open ended. Instead of closure, the therapeutic goal is to help people find meaning despite the lack of definitive information and finality. Hope lies in increasing a family's tolerance for ambiguity, but first, professionals must increase their own comfort with unanswered questions. In this article, the authors, one a poet, the other a family therapist and theorist, offer a unique blending of theory, reflection, and poetry to experientially deepen the process of self-reflection about a kind of loss that defies closure. © FPI, Inc.
Bubble-induced turbulence study in homogeneous turbulent flow using DNS approach
NASA Astrophysics Data System (ADS)
Feng, Jinyong; Bolotnov, Igor
2015-11-01
The effect of a single bubble on the energy transfer to a homogeneous turbulent flow using DNS approach is investigated for various conditions. The single-phase turbulence is numerically generated by pressure-gradient driven uniform flow through a fully resolved turbulence generating grid. The turbulent intensity measured is uniform normal to the flow direction. The decay rate of the turbulent kinetic energy is validated against analytical power law. The collected instantaneous velocity is used as inflow condition for single-bubble simulations to study the bubble-induced turbulence (BIT). In interface-resolved two-phase simulation the bubble is kept at fixed positions by using a proportional-integral-derivative controller. This simulation set allows estimating the turbulent kinetic energy before and after the bubble, quantifying the BIT. Effects of bubble deformability, velocity and turbulent intensity are separately studied. We observe that for a nearly spherical bubble, the bubble-induced turbulence is positive, increasing the level of turbulent kinetic energy in the liquid phase. BIT is influenced by the other studied parameters and the presented work will contribute to the closure BIT model development in multiphase computational fluid dynamics modeling. The work is supported by NSF-CBET-Fluid Dynamics, Award #1333993.
Regularization of turbulence - a comprehensive modeling approach
NASA Astrophysics Data System (ADS)
Geurts, B. J.
2011-12-01
Turbulence readily arises in numerous flows in nature and technology. The large number of degrees of freedom of turbulence poses serious challenges to numerical approaches aimed at simulating and controlling such flows. While the Navier-Stokes equations are commonly accepted to precisely describe fluid turbulence, alternative coarsened descriptions need to be developed to cope with the wide range of length and time scales. These coarsened descriptions are known as large-eddy simulations in which one aims to capture only the primary features of a flow, at considerably reduced computational effort. Such coarsening introduces a closure problem that requires additional phenomenological modeling. A systematic approach to the closure problem, know as regularization modeling, will be reviewed. Its application to multiphase turbulent will be illustrated in which a basic regularization principle is enforced to physically consistently approximate momentum and scalar transport. Examples of Leray and LANS-alpha regularization are discussed in some detail, as are compatible numerical strategies. We illustrate regularization modeling to turbulence under the influence of rotation and buoyancy and investigate the accuracy with which particle-laden flow can be represented. A discussion of the numerical and modeling errors incurred will be given on the basis of homogeneous isotropic turbulence.
Reynolds stress closure modeling in wall-bounded flows
NASA Technical Reports Server (NTRS)
Durbin, Paul A.
1993-01-01
This report describes two projects. Firstly, a Reynolds stress closure for near-wall turbulence is described. It was motivated by the simpler k-epsilon-(v-bar(exp 2)) model described in last year's annual research brief. Direct Numerical Simulation of three-dimensional channel flow shows a curious decrease of the turbulent kinetic energy. The second topic of this report is a model which reproduces this effect. That model is described and used to discuss the relevance of the three dimensional channel flow simulation to swept wing boundary layers.
Second order closure for variable density free shear layer
NASA Astrophysics Data System (ADS)
Vandromme, D.; Kollmann, W.
A full second order closure turbulence model for the prediction of free shear flows with variable density is developed. The importance of density fluctuations due to inhomogeneities in fluid composition is emphasized. Some simplicity is achieved by using density weighted averaging to account implicitly for density fluctuation effects. Transport equations for various second order correlations - such as Reynolds stress, turbulent mass fluxes or density velocity correlations - are derived, modelled and solved, together with the mean equations for momentum and species conservation. Solutions of these equations are compared with the two different sets of experimental data for low speed free mixing layers (helium into nitrogen and freon 12 into air).
Bradburne, John; Patton, Tisha C.
2001-02-25
When Fluor Fernald took over the management of the Fernald Environmental Management Project in 1992, the estimated closure date of the site was more than 25 years into the future. Fluor Fernald, in conjunction with DOE-Fernald, introduced the Accelerated Cleanup Plan, which was designed to substantially shorten that schedule and save taxpayers more than $3 billion. The management of Fluor Fernald believes there are three fundamental concerns that must be addressed by any contractor hoping to achieve closure of a site within the DOE complex. They are relationship management, resource management and contract management. Relationship management refers to the interaction between the site and local residents, regulators, union leadership, the workforce at large, the media, and any other interested stakeholder groups. Resource management is of course related to the effective administration of the site knowledge base and the skills of the workforce, the attraction and retention of qualified a nd competent technical personnel, and the best recognition and use of appropriate new technologies. Perhaps most importantly, resource management must also include a plan for survival in a flat-funding environment. Lastly, creative and disciplined contract management will be essential to effecting the closure of any DOE site. Fluor Fernald, together with DOE-Fernald, is breaking new ground in the closure arena, and ''business as usual'' has become a thing of the past. How Fluor Fernald has managed its work at the site over the last eight years, and how it will manage the new site closure contract in the future, will be an integral part of achieving successful closure at Fernald.
NASA Astrophysics Data System (ADS)
Tsubota, Makoto
2008-11-01
The present article reviews the recent developments in the physics of quantum turbulence. Quantum turbulence (QT) was discovered in superfluid 4He in the 1950s, and the research has tended toward a new direction since the mid 90s. The similarities and differences between quantum and classical turbulence have become an important area of research. QT is comprised of quantized vortices that are definite topological defects, being expected to yield a model of turbulence that is much simpler than the classical model. The general introduction of the issue and a brief review on classical turbulence are followed by a description of the dynamics of quantized vortices. Then, we discuss the energy spectrum of QT at very low temperatures. At low wavenumbers, the energy is transferred through the Richardson cascade of quantized vortices, and the spectrum obeys the Kolmogorov law, which is the most important statistical law in turbulence; this classical region shows the similarity to conventional turbulence. At higher wavenumbers, the energy is transferred by the Kelvin-wave cascade on each vortex. This quantum regime depends strongly on the nature of each quantized vortex. The possible dissipation mechanism is discussed. Finally, important new experimental studies, which include investigations into temperature-dependent transition to QT, dissipation at very low temperatures, QT created by vibrating structures, and visualization of QT, are reviewed. The present article concludes with a brief look at QT in atomic Bose-Einstein condensates.
Finite-element numerical modeling of atmospheric turbulent boundary layer
NASA Technical Reports Server (NTRS)
Lee, H. N.; Kao, S. K.
1979-01-01
A dynamic turbulent boundary-layer model in the neutral atmosphere is constructed, using a dynamic turbulent equation of the eddy viscosity coefficient for momentum derived from the relationship among the turbulent dissipation rate, the turbulent kinetic energy and the eddy viscosity coefficient, with aid of the turbulent second-order closure scheme. A finite-element technique was used for the numerical integration. In preliminary results, the behavior of the neutral planetary boundary layer agrees well with the available data and with the existing elaborate turbulent models, using a finite-difference scheme. The proposed dynamic formulation of the eddy viscosity coefficient for momentum is particularly attractive and can provide a viable alternative approach to study atmospheric turbulence, diffusion and air pollution.
Caldwell, T.B.
1997-04-18
A reducing grout has been developed for closing high level waste tanks at the Savannah River Site in Aiken, South Carolina. The grout has a low redox potential, which minimizes the mobility of Sr{sup 90}, the radionuclide with the highest dose potential after closure. The grout also has a high pH which reduces the solubility of the plutonium isotopes. The grout has a high compressive strength and low permeability, which enhances its ability to limit the migration of contaminants after closure. The grout was designed and tested by Construction Technology Laboratories, Inc. Placement methods were developed by the Savannah River Site personnel.
Entropy production rate as a constraint for collisionless fluid closures
Fleurence, E.; Sarazin, Y.; Garbet, X.; Dif-Pradalier, G.; Ghendrih, Ph.; Grandgirard, V.; Ottaviani, M.
2006-11-30
A novel method is proposed to construct collisionless fluid closures accounting for some kinetic properties. The first dropped fluid moment is assumed to be a linear function of the lower order ones. Optimizing the agreement between the fluid and kinetic entropy production rates is used to constrain the coefficients of the linear development. This procedure is applied to a reduced version of the interchange instability. The closure, involving the absolute value of the wave vector, is non-local in real space. In this case, the linear instability thresholds are the same, and the linear growth rates exhibit similar characteristics. Such a method is applicable to other models and classes of instabilities.
Entropy production rate as a constraint for collisionless fluid closures
NASA Astrophysics Data System (ADS)
Fleurence, E.; Sarazin, Y.; Garbet, X.; Dif-Pradalier, G.; Ghendrih, Ph.; Grandgirard, V.; Ottaviani, M.
2006-11-01
A novel method is proposed to construct collisionless fluid closures accounting for some kinetic properties. The first dropped fluid moment is assumed to be a linear function of the lower order ones. Optimizing the agreement between the fluid and kinetic entropy production rates is used to constrain the coefficients of the linear development. This procedure is applied to a reduced version of the interchange instability. The closure, involving the absolute value of the wave vector, is non-local in real space. In this case, the linear instability thresholds are the same, and the linear growth rates exhibit similar characteristics. Such a method is applicable to other models and classes of instabilities.
NASA Astrophysics Data System (ADS)
Schneider, Florian
2016-10-01
This paper provides a generalization of the realizability-preserving discontinuous-Galerkin scheme given in [3] to general full-moment models that can be closed analytically. It is applied to the class of Kershaw closures, which are able to provide a cheap closure of the moment problem. This results in an efficient algorithm for the underlying linear transport equation. The efficiency of high-order methods is demonstrated using numerical convergence tests and non-smooth benchmark problems.
Chang, D. . Dept. of Physics and Astronomy Fermi National Accelerator Lab., Batavia, IL ); Senjanovic, G. . Dept. of Theoretical Physics)
1990-01-01
We review attempts to achieve a large neutrino magnetic moment ({mu}{sub {nu}} {le} 10{sup {minus}11}{mu}{sub B}), while keeping neutrino light or massless. The application to the solar neutrino puzzle is discussed. 24 refs.
Turbulent transport in premixed flames
NASA Technical Reports Server (NTRS)
Rutland, C. J.; Cant, R. S.
1994-01-01
Simulations of planar, premixed turbulent flames with heat release were used to study turbulent transport. Reynolds stress and Reynolds flux budgets were obtained and used to guide the investigation of important physical effects. Essentially all pressure terms in the transport equations were found to be significant. In the Reynolds flux equations, these terms are the major source of counter-gradient transport. Viscous and molecular terms were also found to be significant, with both dilatational and solenoidal terms contributing to the Reynolds stress dissipation. The BML theory of premixed turbulent combustion was critically examined in detail. The BML bimodal pdf was found to agree well with the DNS data. All BML decompositions, through the third moments, show very good agreement with the DNS results. Several BML models for conditional terms were checked using the DNS data and were found to require more extensive development.
NASA Astrophysics Data System (ADS)
Nazarenko, Sergey
2015-07-01
Wave turbulence is the statistical mechanics of random waves with a broadband spectrum interacting via non-linearity. To understand its difference from non-random well-tuned coherent waves, one could compare the sound of thunder to a piece of classical music. Wave turbulence is surprisingly common and important in a great variety of physical settings, starting with the most familiar ocean waves to waves at quantum scales or to much longer waves in astrophysics. We will provide a basic overview of the wave turbulence ideas, approaches and main results emphasising the physics of the phenomena and using qualitative descriptions avoiding, whenever possible, involved mathematical derivations. In particular, dimensional analysis will be used for obtaining the key scaling solutions in wave turbulence - Kolmogorov-Zakharov (KZ) spectra.
ERIC Educational Resources Information Center
Hanratty, Thomas J.
1980-01-01
This paper gives an account of research on the structure of turbulence close to a solid boundary. Included is a method to study the flow close to the wall of a pipe without interferring with it. (Author/JN)
Mattingly, J.T.
1963-02-12
This invention provides a simple pressure-actuated closure whereby windowless observation ports are opened to the atmosphere at preselected altitudes. The closure comprises a disk which seals a windowless observation port in rocket hull. An evacuated instrument compartment is affixed to the rocket hull adjacent the inner surface of the disk, while the outer disk surface is exposed to the atmosphere through which the rocket is traveling. The pressure differential between the evacuated instrument compartment and the relatively high pressure external atmosphere forces the disk against the edge of the observation port, thereby effecting a tight seai. The instrument compartment is evacuated to a pressure equal to the atmospheric pressure existing at the altitude at which it is desiretl that the closure should open. When the rocket reaches this preselected altitude, the inwardly directed atmospheric force on the disk is just equaled by the residual air pressure force within the instrument compartment. Consequently, the closure disk falls away and uncovers the open observation port. The separation of the disk from the rocket hull actuates a switch which energizes the mechanism of a detecting instrument disposed within the instrument compartment. (AE C)
Lucey, Paula A
2002-01-01
Hospital closures have become more common. The challenges facing a nursing leader in this situation are complex and difficult. This author suggests that looking for new beginnings rather than focusing on endings created an approach to closing a public hospital. The article includes approaches to employee morale, staffing, and patient care.
Evaluation of Two Energy Balance Closure Parametrizations
NASA Astrophysics Data System (ADS)
Eder, Fabian; De Roo, Frederik; Kohnert, Katrin; Desjardins, Raymond L.; Schmid, Hans Peter; Mauder, Matthias
2014-05-01
A general lack of energy balance closure indicates that tower-based eddy-covariance (EC) measurements underestimate turbulent heat fluxes, which calls for robust correction schemes. Two parametrization approaches that can be found in the literature were tested using data from the Canadian Twin Otter research aircraft and from tower-based measurements of the German Terrestrial Environmental Observatories (TERENO) programme. Our analysis shows that the approach of Huang et al. (Boundary-Layer Meteorol 127:273-292, 2008), based on large-eddy simulation, is not applicable to typical near-surface flux measurements because it was developed for heights above the surface layer and over homogeneous terrain. The biggest shortcoming of this parametrization is that the grid resolution of the model was too coarse so that the surface layer, where EC measurements are usually made, is not properly resolved. The empirical approach of Panin and Bernhofer (Izvestiya Atmos Oceanic Phys 44:701-716, 2008) considers landscape-level roughness heterogeneities that induce secondary circulations and at least gives a qualitative estimate of the energy balance closure. However, it does not consider any feature of landscape-scale heterogeneity other than surface roughness, such as surface temperature, surface moisture or topography. The failures of both approaches might indicate that the influence of mesoscale structures is not a sufficient explanation for the energy balance closure problem. However, our analysis of different wind-direction sectors shows that the upwind landscape-scale heterogeneity indeed influences the energy balance closure determined from tower flux data. We also analyzed the aircraft measurements with respect to the partitioning of the "missing energy" between sensible and latent heat fluxes and we could confirm the assumption of scalar similarity only for Bowen ratios 1.
On the Lundgren-Townsend model of turbulent fine scales
NASA Astrophysics Data System (ADS)
Pullin, D. I.; Saffman, P. G.
1993-01-01
Vorticity and velocity-derivative moments for homogeneous isotropic turbulence are calculated using the strained-spiral vortex model of turbulent fine scales given by Lundgren (1982). A specific form of the relaxing spiral vortex is proposed, modeled by a rolling-up vortex layer embedded in a background containing opposite signed vorticity and with zero total circulation at infinity.
Transport Coefficients in Rotating Weakly Compressible Turbulence
NASA Technical Reports Server (NTRS)
Rubinstein, Robert; Zhou, Ye; Erlebacher, Gordon
1998-01-01
Analytical studies of compressible turbulence have found that compressible velocity fluctuations create both effective fluid transport properties and an effective equation of state. This paper investigates the effects of rotation on compressible turbulence. It is shown that rotation modifies the transport properties of compressible turbulence by replacing the turbulence time scale by a rotational time scale, much as rotation modifies the transport properties of incompressible turbulence. But thermal equilibrium properties are modified in a more complex manner. Two regimes are possible: one dominated by incompressible fluctuations, in which the sound speed is modified as it is in non-rotating turbulence, and a rotation dominated regime in which the sound speed enhancement is rotation dependent. The dimensionless parameter which discriminates between regimes is identified. In general, rotation is found to suppress the effects of compressibility. A novel feature of the present analysis is the use of a non-Kolmogorov steady state as the reference state of turbulence. introduction of such steady states expands the power and utility of analytical turbulence closures to a wider range of problems.
NASA Astrophysics Data System (ADS)
Coclite, A.; Pascazio, G.; De Palma, P.; Cutrone, L.
2016-07-01
Flamelet-Progress-Variable (FPV) combustion models allow the evaluation of all thermochemical quantities in a reacting flow by computing only the mixture fraction Z and a progress variable C. When using such a method to predict turbulent combustion in conjunction with a turbulence model, a probability density function (PDF) is required to evaluate statistical averages (e. g., Favre averages) of chemical quantities. The choice of the PDF is a compromise between computational costs and accuracy level. The aim of this paper is to investigate the influence of the PDF choice and its modeling aspects to predict turbulent combustion. Three different models are considered: the standard one, based on the choice of a β-distribution for Z and a Dirac-distribution for C; a model employing a β-distribution for both Z and C; and the third model obtained using a β-distribution for Z and the statistically most likely distribution (SMLD) for C. The standard model, although widely used, does not take into account the interaction between turbulence and chemical kinetics as well as the dependence of the progress variable not only on its mean but also on its variance. The SMLD approach establishes a systematic framework to incorporate informations from an arbitrary number of moments, thus providing an improvement over conventionally employed presumed PDF closure models. The rational behind the choice of the three PDFs is described in some details and the prediction capability of the corresponding models is tested vs. well-known test cases, namely, the Sandia flames, and H2-air supersonic combustion.
Reynold stress closure in jet flows using wave models
NASA Technical Reports Server (NTRS)
Morris, P. J.
1988-01-01
Research program efforts have continued to concentrate on the development of the numerical methods that will form the computational part of the turbulence closure scheme. Studies have continued on the wave model for the two dimensional shear layer. This configuration is being used as a test case for the closure schemes. Several numerical schemes for the solution of the non-separable Rayleigh equation were developed. This solution is required for the closure scheme in more complex geometries. The most efficient method found is a Hybrid scheme that combines both pseudospectral and finite difference techniques. In addition, conformal transformation techniques were developed to transform the arbitrary geometry of the jet to a simple computational domain. The study of the shock structure in arbitrary geometry jets and multiple jets. These developments are described briefly.
Ring closure in actin polymers
NASA Astrophysics Data System (ADS)
Sinha, Supurna; Chattopadhyay, Sebanti
2017-03-01
We present an analysis for the ring closure probability of semiflexible polymers within the pure bend Worm Like Chain (WLC) model. The ring closure probability predicted from our analysis can be tested against fluorescent actin cyclization experiments. We also discuss the effect of ring closure on bend angle fluctuations in actin polymers.
Comments on the present state of second-order closure models for incompressible flows
NASA Technical Reports Server (NTRS)
Speziale, Charles G.
1992-01-01
Second-order closure models account for history and nonlocal effects of the mean velocity gradients on the Reynolds stress tensor. Turbulent flows involving body forces or curvature, Reynolds stress relaxational effects, and counter-gradient transport are usually better described. The topics are presented in viewgraph form and include: (1) the Reynolds stress transport equation; (2) issues in second-order closure modeling; and (3) near wall models.
Large-Eddy Simulation of the Flat-plate Turbulent Boundary Layer at High Reynolds numbers
NASA Astrophysics Data System (ADS)
Inoue, Michio
The near-wall, subgrid-scale (SGS) model [Chung and Pullin, "Large-eddy simulation and wall-modeling of turbulent channel flow'', J. Fluid Mech. 631, 281--309 (2009)] is used to perform large-eddy simulations (LES) of the incompressible developing, smooth-wall, flat-plate turbulent boundary layer. In this model, the stretched-vortex, SGS closure is utilized in conjunction with a tailored, near-wall model designed to incorporate anisotropic vorticity scales in the presence of the wall. The composite SGS-wall model is presently incorporated into a computer code suitable for the LES of developing flat-plate boundary layers. This is then used to study several aspects of zero- and adverse-pressure gradient turbulent boundary layers. First, LES of the zero-pressure gradient turbulent boundary layer are performed at Reynolds numbers Retheta based on the free-stream velocity and the momentum thickness in the range Retheta = 103-1012. Results include the inverse skin friction coefficient, 2/Cf , velocity profiles, the shape factor H, the Karman "constant", and the Coles wake factor as functions of Re theta. Comparisons with some direct numerical simulation (DNS) and experiment are made, including turbulent intensity data from atmospheric-layer measurements at Retheta = O (106). At extremely large Retheta , the empirical Coles-Fernholz relation for skin-friction coefficient provides a reasonable representation of the LES predictions. While the present LES methodology cannot of itself probe the structure of the near-wall region, the present results show turbulence intensities that scale on the wall-friction velocity and on the Clauser length scale over almost all of the outer boundary layer. It is argued that the LES is suggestive of the asymptotic, infinite Reynolds-number limit for the smooth-wall turbulent boundary layer and different ways in which this limit can be approached are discussed. The maximum Retheta of the present simulations appears to be limited by machine
Numerical Simulation of a Convective Turbulence Encounter
NASA Technical Reports Server (NTRS)
Proctor, Fred H.; Hamilton, David W.; Bowles, Roland L.
2002-01-01
A numerical simulation of a convective turbulence event is investigated and compared with observational data. The numerical results show severe turbulence of similar scale and intensity to that encountered during the test flight. This turbulence is associated with buoyant plumes that penetrate the upper-level thunderstorm outflow. The simulated radar reflectivity compares well with that obtained from the aircraft's onboard radar. Resolved scales of motion as small as 50 m are needed in order to accurately diagnose aircraft normal load accelerations. Given this requirement, realistic turbulence fields may be created by merging subgrid-scales of turbulence to a convective-cloud simulation. A hazard algorithm for use with model data sets is demonstrated. The algorithm diagnoses the RMS normal loads from second moments of the vertical velocity field and is independent of aircraft motion.
A stochastic subgrid model for sheared turbulence
NASA Astrophysics Data System (ADS)
Bertoglio, J. P.
A new subgrid model for homogeneous turbulence is proposed. The model is used in a method of Large Eddy Simulation coupled with an E.D.Q.N.M. prediction of the statistical properties of the small scales. The model is stochastic in order to allow a 'disaveraging' of the informations provided by the E.D.Q.N.M. closure. It is based on stochastic amplitude equations for two-point closures. It allows backflow of energy from the small scales, introduces stochasticity into L.E.S., and is well adapted to nonisotropic fields. A few results are presented here.
Moment estimation for chemically reacting systems by extended Kalman filtering.
Ruess, J; Milias-Argeitis, A; Summers, S; Lygeros, J
2011-10-28
In stochastic models of chemically reacting systems that contain bimolecular reactions, the dynamics of the moments of order up to n of the species populations do not form a closed system, in the sense that their time-derivatives depend on moments of order n + 1. To close the dynamics, the moments of order n + 1 are generally approximated by nonlinear functions of the lower order moments. If the molecule counts of some of the species have a high probability of becoming zero, such approximations may lead to imprecise results and stochastic simulation is the only viable alternative for system analysis. Stochastic simulation can produce exact realizations of chemically reacting systems, but tends to become computationally expensive, especially for stiff systems that involve reactions at different time scales. Further, in some systems, important stochastic events can be very rare and many simulations are necessary to obtain accurate estimates. The computational cost of stochastic simulation can then be prohibitively large. In this paper, we propose a novel method for estimating the moments of chemically reacting systems. The method is based on closing the moment dynamics by replacing the moments of order n + 1 by estimates calculated from a small number of stochastic simulation runs. The resulting stochastic system is then used in an extended Kalman filter, where estimates of the moments of order up to n, obtained from the same simulation, serve as outputs of the system. While the initial motivation for the method was improving over the performance of stochastic simulation and moment closure methods, we also demonstrate that it can be used in an experimental setting to estimate moments of species that cannot be measured directly from time course measurements of the moments of other species.
Statistics of High Atwood Number Turbulent Mixing Layers
NASA Astrophysics Data System (ADS)
Baltzer, Jon; Livescu, Daniel
2015-11-01
The statistical properties of incompressible shear-driven planar mixing layers between two miscible streams of fluids with different densities are investigated by means of Direct Numerical Simulations. The simulations begin from a thin interface perturbed by a thin broadband random disturbance, and the mixing layers are allowed to develop to self-similar states. The temporal simulations are performed in unprecedented domain sizes, with grid sizes up to 6144 x 2048 x 1536, which allows turbulent structures to grow and merge naturally. This allows the flow to reach states far-removed from the initial disturbances, thereby enabling high-quality statistics to be obtained for higher moments, pdfs, and other quantities critical to developing closure models. A wide range of Atwood numbers are explored, ranging from nearly constant density to At=0.87. The consequences of increasing the density contrast are investigated for global quantities, such as growth rates, and asymmetries that form in statistical profiles. Additional simulations in smaller domains are performed to study the effects of domain size.
NASA Technical Reports Server (NTRS)
Kim, S.-W.; Chen, C.-P.
1987-01-01
A multiple-time-scale turbulence model of a single point closure and a simplified split-spectrum method is presented. In the model, the effect of the ratio of the production rate to the dissipation rate on eddy viscosity is modeled by use of the multiple-time-scales and a variable partitioning of the turbulent kinetic energy spectrum. The concept of a variable partitioning of the turbulent kinetic energy spectrum and the rest of the model details are based on the previously reported algebraic stress turbulence model. Example problems considered include: a fully developed channel flow, a plane jet exhausting into a moving stream, a wall jet flow, and a weakly coupled wake-boundary layer interaction flow. The computational results compared favorably with those obtained by using the algebraic stress turbulence model as well as experimental data. The present turbulence model, as well as the algebraic stress turbulence model, yielded significantly improved computational results for the complex turbulent boundary layer flows, such as the wall jet flow and the wake boundary layer interaction flow, compared with available computational results obtained by using the standard kappa-epsilon turbulence model.
Small scale dynamics of a shearless turbulent/non-turbulent interface in dilute polymer solutions
NASA Astrophysics Data System (ADS)
Cocconi, G.; De Angelis, E.; Frohnapfel, B.; Baevsky, M.; Liberzon, A.
2017-07-01
We study the physics of the turbulent/non-turbulent interface (TNTI) of an isolated turbulent region in dilute polymer solutions and Newtonian fluids. We designed an experimental setup of a turbulent patch growing in water/dilute polymer solutions, without mean shear and far from the walls. The observations from the experiments are complemented and expanded by simulations performed using a localised homogeneous forcing to generate the turbulent front and the Finitely Extensible Elastic model with the Peterlin closure model for the polymer stress. The comparison, which shows that when Newtonian and viscoelastic TNTIs are fed by the same energy they behave in similar manner both in the experiments and in the simulations, permits to extend the applicability, on a qualitative basis, of single relaxation time polymer models also to turbulent/non-turbulent interfaces. From the detailed analysis offered by the numerical results, the alterations in the dynamics between strain and vorticity help understanding the mechanics of the polymer action on the TNTI without mean shear. The reduced vorticity stretching and increased vorticity compression terms are found to be due to the modified degrees of alignment between vorticity, polymer conformation tensor, and rate-of-strain tensor eigenvectors observed especially near the interface. These alignments at the smallest scales of the non-Newtonian turbulent flow lead to a reduced production of enstrophy and consequently to a reduced entrainment, which in this problem are seen as reduced advancement of a turbulent region.
Separated transonic airfoil flow calculations with a nonequilibrium turbulence model
NASA Technical Reports Server (NTRS)
King, L. S.; Johnson, D. A.
1985-01-01
Navier-Stokes transonic airfoil calculations based on a recently developed nonequilibrium, turbulence closure model are presented for a supercritical airfoil section at transonic cruise conditions and for a conventional airfoil section at shock-induced stall conditions. Comparisons with experimental data are presented which show that this nonequilibrium closure model performs significantly better than the popular Baldwin-Lomax and Cebeci-Smith equilibrium algebraic models when there is boundary-layer separation that results from the inviscid-viscous interactions.
Hospital closure and economic efficiency.
Capps, Cory; Dranove, David; Lindrooth, Richard C
2010-01-01
We present a new framework for assessing the effects of hospital closures on social welfare and the local economy. While patient welfare necessarily declines when patients lose access to a hospital, closures also tend to reduce costs. We study five hospital closures in two states and find that urban hospital bailouts reduce aggregate social welfare: on balance, the cost savings from closures more than offset the reduction in patient welfare. However, because some of the cost savings are shared nationally, total surplus in the local community may decline following a hospital closure.
Numerical experiments in homogeneous turbulence
NASA Technical Reports Server (NTRS)
Rogallo, R. S.
1981-01-01
The direct simulation methods developed by Orszag and Patternson (1972) for isotropic turbulence were extended to homogeneous turbulence in an incompressible fluid subjected to uniform deformation or rotation. The results of simulations for irrotational strain (plane and axisymmetric), shear, rotation, and relaxation toward isotropy following axisymmetric strain are compared with linear theory and experimental data. Emphasis is placed on the shear flow because of its importance and because of the availability of accurate and detailed experimental data. The computed results are used to assess the accuracy of two popular models used in the closure of the Reynolds-stress equations. Data from a variety of the computed fields and the details of the numerical methods used in the simulation are also presented.
Recommendations for managing hospital closure.
van der Wal, R; Bouthillette, F; Havlovic, S J
1998-01-01
An acute care hospital was closed by the British Columbia Ministry of Health in 1993. A research study was conducted to investigate the ways closure of the hospital affected hospital employees and to identify ways to facilitate the closure/reorganization process. Unstructured interviews were conducted with 25 employees around the time of closure and six months after the closure. In the category Living with Closure, six themes arose from the qualitative analysis. They related to (1) provision of information; (2) effect of closure on the working environment and colleagues; (3) perceived stress; (4) recognition of one's worth; (5) provision of support services; and (6) the process of having a new job. The authors offer recommendations stemming from the analysis, which are intended to assist others planning for future hospital reorganizations or closures.
NASA Technical Reports Server (NTRS)
Tchen, C. M.
1986-01-01
Theoretical and numerical works in atmospheric turbulence have used the Navier-Stokes fluid equations exclusively for describing large-scale motions. Controversy over the existence of an average temperature gradient for the very large eddies in the atmosphere suggested that a new theoretical basis for describing large-scale turbulence was necessary. A new soliton formalism as a fluid analogue that generalizes the Schrodinger equation and the Zakharov equations has been developed. This formalism, processing all the nonlinearities including those from modulation provided by the density fluctuations and from convection due to the emission of finite sound waves by velocity fluctuations, treats large-scale turbulence as coalescing and colliding solitons. The new soliton system describes large-scale instabilities more explicitly than the Navier-Stokes system because it has a nonlinearity of the gradient type, while the Navier-Stokes has a nonlinearity of the non-gradient type. The forced Schrodinger equation for strong fluctuations describes the micro-hydrodynamical state of soliton turbulence and is valid for large-scale turbulence in fluids and plasmas where internal waves can interact with velocity fluctuations.
Hybrid Gyrofluid/Gyrokinetic Modeling of Tokamak Turbulence with GryfX
NASA Astrophysics Data System (ADS)
Mandell, Noah; Dorland, Bill; Highcock, Edmund; Hammett, Greg
2016-10-01
Gyrofluid models are more efficient than gyrokinetic models, but have a disadvantage in their potential lack of physics fidelity. Here we present three major improvements to the physics fidelity and speed of gyrofluid models, which we encapsulate in the GryfX gyrofluid turbulence code. First, we implement a new nonlinear closure to model the cascade of free energy simultaneously in k⊥ and v⊥ via nonlinear phase-mixing (NLPM). Second, we use a hybrid algorithm that improves zonal flow physics by simulating zonal flow modes with a fully gyrokinetic model. These two improvements bring heat flux predictions from nonlinear GryfX simulations into agreement with the gyrokinetic code GS2. Third, we implement the equations on modern heterogeneous computing platforms, both as a standalone simulation tool that exploits the power of GPUs and as a component of TRINITY (a transport modeling code for tokamaks). GryfX has a roughly 1,200 times performance advantage over GS2 due to the combination of GPU acceleration and the reduction of hundreds of velocity space grid points to six gyrofluid moments. This makes GryfX ideal for large parameter scans, and enables the use of the TRINITY-GryfX system for efficient multi-scale analysis of tokamak turbulence on transport time scales. Present address: Chalmers University, Gothenburg, Sweden.
Large eddy simulation and direct numerical simulation of high speed turbulent reacting flows
NASA Technical Reports Server (NTRS)
Adumitroaie, V.; Frankel, S. H.; Madnia, C. K.; Givi, P.
1993-01-01
The objective of this research is to make use of Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS) for the computational analyses of high speed reacting flows. Our efforts in the first phase of this research conducted within the past three years have been directed in several issues pertaining to intricate physics of turbulent reacting flows. In our previous 5 semi-annual reports submitted to NASA LaRC, as well as several technical papers in archival journals, the results of our investigations have been fully described. In this progress report which is different in format as compared to our previous documents, we focus only on the issue of LES. The reason for doing so is that LES is the primary issue of interest to our Technical Monitor and that our other findings were needed to support the activities conducted under this prime issue. The outcomes of our related investigations, nevertheless, are included in the appendices accompanying this report. The relevance of the materials in these appendices are, therefore, discussed only briefly within the body of the report. Here, results are presented of a priori and a posterior analyses for validity assessments of assumed Probability Density Function (PDF) methods as potential subgrid scale (SGS) closures for LES of turbulent reacting flows. Simple non-premixed reacting systems involving an isothermal reaction of the type A + B yields Products under both chemical equilibrium and non-equilibrium conditions are considered. A priori analyses are conducted of a homogeneous box flow, and a spatially developing planar mixing layer to investigate the performance of the Pearson Family of PDF's as SGS models. A posteriori analyses are conducted of the mixing layer using a hybrid one-equation Smagorinsky/PDF SGS closure. The Smagorinsky closure augmented by the solution of the subgrid turbulent kinetic energy (TKE) equation is employed to account for hydrodynamic fluctuations, and the PDF is employed for modeling the
Large eddy simulation and direct numerical simulation of high speed turbulent reacting flows
NASA Astrophysics Data System (ADS)
Adumitroaie, V.; Frankel, S. H.; Madnia, C. K.; Givi, P.
The objective of this research is to make use of Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS) for the computational analyses of high speed reacting flows. Our efforts in the first phase of this research conducted within the past three years have been directed in several issues pertaining to intricate physics of turbulent reacting flows. In our previous 5 semi-annual reports submitted to NASA LaRC, as well as several technical papers in archival journals, the results of our investigations have been fully described. In this progress report which is different in format as compared to our previous documents, we focus only on the issue of LES. The reason for doing so is that LES is the primary issue of interest to our Technical Monitor and that our other findings were needed to support the activities conducted under this prime issue. The outcomes of our related investigations, nevertheless, are included in the appendices accompanying this report. The relevance of the materials in these appendices are, therefore, discussed only briefly within the body of the report. Here, results are presented of a priori and a posterior analyses for validity assessments of assumed Probability Density Function (PDF) methods as potential subgrid scale (SGS) closures for LES of turbulent reacting flows. Simple non-premixed reacting systems involving an isothermal reaction of the type A + B yields Products under both chemical equilibrium and non-equilibrium conditions are considered. A priori analyses are conducted of a homogeneous box flow, and a spatially developing planar mixing layer to investigate the performance of the Pearson Family of PDF's as SGS models. A posteriori analyses are conducted of the mixing layer using a hybrid one-equation Smagorinsky/PDF SGS closure. The Smagorinsky closure augmented by the solution of the subgrid turbulent kinetic energy (TKE) equation is employed to account for hydrodynamic fluctuations, and the PDF is employed for modeling the
NASA Technical Reports Server (NTRS)
Webbon, B. W.; Vykukal, H. C. (Inventor)
1978-01-01
A simple, economical and reliable entry closure is described for joining opposite halves of a torso section for a pressure suit in a manner which simplifies self-donning. A single coupling joins coaxially aligned, axially separable, tubular segments of a hard spacesuit along an angulated zone of separation, adapted to be mated in an hermetrically sealing relation. A releasable C section clamp secures the members in their mated relationship.
PDF turbulence modeling and DNS
NASA Technical Reports Server (NTRS)
Hsu, A. T.
1992-01-01
The problem of time discontinuity (or jump condition) in the coalescence/dispersion (C/D) mixing model is addressed in probability density function (pdf). A C/D mixing model continuous in time is introduced. With the continuous mixing model, the process of chemical reaction can be fully coupled with mixing. In the case of homogeneous turbulence decay, the new model predicts a pdf very close to a Gaussian distribution, with finite higher moments also close to that of a Gaussian distribution. Results from the continuous mixing model are compared with both experimental data and numerical results from conventional C/D models. The effect of Coriolis forces on compressible homogeneous turbulence is studied using direct numerical simulation (DNS). The numerical method used in this study is an eight order compact difference scheme. Contrary to the conclusions reached by previous DNS studies on incompressible isotropic turbulence, the present results show that the Coriolis force increases the dissipation rate of turbulent kinetic energy, and that anisotropy develops as the Coriolis force increases. The Taylor-Proudman theory does apply since the derivatives in the direction of the rotation axis vanishes rapidly. A closer analysis reveals that the dissipation rate of the incompressible component of the turbulent kinetic energy indeed decreases with a higher rotation rate, consistent with incompressible flow simulations (Bardina), while the dissipation rate of the compressible part increases; the net gain is positive. Inertial waves are observed in the simulation results.
Efficient Moment Matrix Generation for Arbitrary Chemical Networks
Smadbeck, P.; Kaznessis, Y. N.
2012-01-01
As stochastic simulations become increasingly common in biological research, tools for analysis of such systems are in demand. The deterministic analogue to stochastic models, a set of probability moment equations equivalent to the Chemical Master Equation (CME), offers the possibility of a priori analysis of systems without the need for computationally costly Monte Carlo simulations. Despite the drawbacks of the method, in particular non-linearity in even the simplest of cases, the use of moment equations combined with moment-closure techniques has been used effectively in many fields. The techniques currently available to generate moment equations rely upon analytical expressions that are not efficient upon scaling. Additionally, the resulting moment-dependent matrix is lower diagonal and demands massive memory allocation in extreme cases. Here it is demonstrated that by utilizing factorial moments and the probability generating function (the Z-transform of the probability distribution) a recursive algorithm is produced. The resulting method is scalable and particularly efficient when high-order moments are required. The matrix produced is banded and often demands substantially less memory resources. PMID:23175571
NASA Astrophysics Data System (ADS)
Skrbek, L.
2011-12-01
We review physical properties of quantum fluids He II and 3He-B, where quantum turbulence (QT) has been studied experimentally. Basic properties of QT in these working fluids are discussed within the phenomenological two-fluid model introduced by Landau. We consider counterflows in which the normal and superfluid components flow against each other, as well as co-flows in which the direction of the two fluids is the same. We pay special attention to the important case of zero temperature limit, where QT represents an interesting and probably the simplest prototype of three-dimensional turbulence in fluids. Experimental techniques to explore QT such as second sound attenuation, Andreev reflection, NMR, ion propagation are briefly introduced and results of various experiments on so-called Vinen QT and Kolmogorov QT both in He II and 3He are discussed, emphasizing similarities and differences between classical and quantum turbulence.
Turbulence in Compressible Flows
NASA Technical Reports Server (NTRS)
1997-01-01
Lecture notes for the AGARD Fluid Dynamics Panel (FDP) Special Course on 'Turbulence in Compressible Flows' have been assembled in this report. The following topics were covered: Compressible Turbulent Boundary Layers, Compressible Turbulent Free Shear Layers, Turbulent Combustion, DNS/LES and RANS Simulations of Compressible Turbulent Flows, and Case Studies of Applications of Turbulence Models in Aerospace.
Turbulence in Compressible Flows
NASA Technical Reports Server (NTRS)
1997-01-01
Lecture notes for the AGARD Fluid Dynamics Panel (FDP) Special Course on 'Turbulence in Compressible Flows' have been assembled in this report. The following topics were covered: Compressible Turbulent Boundary Layers, Compressible Turbulent Free Shear Layers, Turbulent Combustion, DNS/LES and RANS Simulations of Compressible Turbulent Flows, and Case Studies of Applications of Turbulence Models in Aerospace.
Turbulent transport modelling of separating and reattaching shear flows
NASA Technical Reports Server (NTRS)
Launder, B. E.
1982-01-01
The improvement of capabilities for computer simulation of turbulent recirculating flows was investigated. Attention has been limited to two dimensional flows and principally to statistically stationary motion. Improvement of turbulence modeling explored the treatment of the near wall sublayer and of the exterior fully turbulent region, working within the framework of turbulence closures requiring the solution of transport equations for the turbulence energy and its dissipation rate. The work on the numerical procedure, based on the Gosman-Pun program TEACH, addressed the problems of incorporating the turbulence model as well as the extension to time dependent flows, the incorporation of a third order approximation of convective transport, and the treatment of non-orthogonal boundaries.
Kinematics of velocity and vorticity correlations in turbulent flow
NASA Technical Reports Server (NTRS)
Bernard, P. S.
1983-01-01
The kinematic problem of calculating second-order velocity moments from given values of the vorticity covariance is examined. Integral representation formulas for second-order velocity moments in terms of the two-point vorticity correlation tensor are derived. The special relationships existing between velocity moments in isotropic turbulence are expressed in terms of the integral formulas yielding several kinematic constraints on the two-point vorticity correlation tensor in isotropic turbulence. Numerical evaluation of these constraints suggests that a Gaussian curve may be the only form of the longitudinal velocity correlation coefficient which is consistent with the requirement of isotropy. It is shown that if this is the case, then a family of exact solutions to the decay of isotropic turbulence may be obtained which contains Batchelor's final period solution as a special case. In addition, the computed results suggest a method of approximating the integral representation formulas in general turbulent shear flows.
Kinematics of velocity and vorticity correlations in turbulent flow
NASA Astrophysics Data System (ADS)
Bernard, P. S.
1983-08-01
The kinematic problem of calculating second-order velocity moments from given values of the vorticity covariance is examined. Integral representation formulas for second-order velocity moments in terms of the two-point vorticity correlation tensor are derived. The special relationships existing between velocity moments in isotropic turbulence are expressed in terms of the integral formulas yielding several kinematic constraints on the two-point vorticity correlation tensor in isotropic turbulence. Numerical evaluation of these constraints suggests that a Gaussian curve may be the only form of the longitudinal velocity correlation coefficient which is consistent with the requirement of isotropy. It is shown that if this is the case, then a family of exact solutions to the decay of isotropic turbulence may be obtained which contains Batchelor's final period solution as a special case. In addition, the computed results suggest a method of approximating the integral representation formulas in general turbulent shear flows.
ERIC Educational Resources Information Center
Espinoza, Roberta
2012-01-01
Educators can have a powerful influence on the future of low-income and minority students whose paths might appear uncertain. By developing trusting relationships, acting as mentors, and sharing information about the education system, teachers, counselors, and other adults can create pivotal moments that transform students' lives. Espinoza shares…
Classroom Ready Teaching Moments
ERIC Educational Resources Information Center
Whalen, D. Joel; Coker, Kesha K.
2017-01-01
This article features thumbnail descriptions of 26 "Teaching Moments" presented at the Society for Marketing Advances 2016 Annual Conference. A wide variety of marketing education interventions are presented, from games that teach marketing fundamentals and enhance faculty effectiveness when counseling students, to visualizing data, and…
ERIC Educational Resources Information Center
Terr, Lenore C.; McDermott, John F.; Benson, Ronald M.; Blos, Peter, Jr.; Deeney, John M.; Rogers, Rita R.; Zrull, Joel P.
2005-01-01
In the summer of 2004, a number of psychotherapists with old ties to the University of Michigan or UCLA decided to write 500-word vignettes that attempted to capture a turning point in one of their child patient's psychotherapies. What did the child and adolescent psychiatrist do to elicit such a moment? Upon receiving seven vignettes, one of us…
ERIC Educational Resources Information Center
Child & Youth Services, 2004
2004-01-01
This chapter presents additional stories and interpretations by John Korsmo, Molly Weingrod, Joseph Stanley, Quinn Wilder, Amy Evans, Rick Flowers, Arcelia Martinez, and Pam Ramsey. The stories and interpretations are presented as teachable moments that are examples of how people are learning to understand youthwork and, as such, are open to…
ERIC Educational Resources Information Center
Goodrow, Mary Ellen
2000-01-01
Details how an unplanned activity involving spinning wool presented a teachable moment for children in a family child care setting. Notes how activities related to farming, spinning wool, and using wool cloth resulted from following the children's lead. Concludes that everyday activities provide opportunities to listen to children, learn about…
ERIC Educational Resources Information Center
Goodrow, Mary Ellen
2000-01-01
Details how an unplanned activity involving spinning wool presented a teachable moment for children in a family child care setting. Notes how activities related to farming, spinning wool, and using wool cloth resulted from following the children's lead. Concludes that everyday activities provide opportunities to listen to children, learn about…
ERIC Educational Resources Information Center
Higgins, Chris
2014-01-01
In "The Humanist Moment," Chris Higgins sets out to recover a tenable, living humanism, rejecting both the version vilified by the anti-humanists and the one sentimentalized by the reactionary nostalgists. Rescuing humanism from such polemics is only the first step, as we find at least nine rival, contemporary definitions of humanism.…
ERIC Educational Resources Information Center
Higgins, Chris
2014-01-01
In "The Humanist Moment," Chris Higgins sets out to recover a tenable, living humanism, rejecting both the version vilified by the anti-humanists and the one sentimentalized by the reactionary nostalgists. Rescuing humanism from such polemics is only the first step, as we find at least nine rival, contemporary definitions of humanism.…
ERIC Educational Resources Information Center
Child & Youth Services, 2004
2004-01-01
This chapter presents additional stories and interpretations by John Korsmo, Molly Weingrod, Joseph Stanley, Quinn Wilder, Amy Evans, Rick Flowers, Arcelia Martinez, and Pam Ramsey. The stories and interpretations are presented as teachable moments that are examples of how people are learning to understand youthwork and, as such, are open to…
Large eddy simulations of compressible magnetohydrodynamic turbulence
NASA Astrophysics Data System (ADS)
Grete, Philipp
2017-02-01
Supersonic, magnetohydrodynamic (MHD) turbulence is thought to play an important role in many processes - especially in astrophysics, where detailed three-dimensional observations are scarce. Simulations can partially fill this gap and help to understand these processes. However, direct simulations with realistic parameters are often not feasible. Consequently, large eddy simulations (LES) have emerged as a viable alternative. In LES the overall complexity is reduced by simulating only large and intermediate scales directly. The smallest scales, usually referred to as subgrid-scales (SGS), are introduced to the simulation by means of an SGS model. Thus, the overall quality of an LES with respect to properly accounting for small-scale physics crucially depends on the quality of the SGS model. While there has been a lot of successful research on SGS models in the hydrodynamic regime for decades, SGS modeling in MHD is a rather recent topic, in particular, in the compressible regime. In this thesis, we derive and validate a new nonlinear MHD SGS model that explicitly takes compressibility effects into account. A filter is used to separate the large and intermediate scales, and it is thought to mimic finite resolution effects. In the derivation, we use a deconvolution approach on the filter kernel. With this approach, we are able to derive nonlinear closures for all SGS terms in MHD: the turbulent Reynolds and Maxwell stresses, and the turbulent electromotive force (EMF). We validate the new closures both a priori and a posteriori. In the a priori tests, we use high-resolution reference data of stationary, homogeneous, isotropic MHD turbulence to compare exact SGS quantities against predictions by the closures. The comparison includes, for example, correlations of turbulent fluxes, the average dissipative behavior, and alignment of SGS vectors such as the EMF. In order to quantify the performance of the new nonlinear closure, this comparison is conducted from the
Streamline curvature effects on turbulent boundary layers
NASA Technical Reports Server (NTRS)
Wilcox, D. C.; Chambers, T. L.
1976-01-01
A theoretical tool has been developed for predicting, in a nonempirical manner, effects of streamline curvature and coordinate-system rotation on turbulent boundary layers. The second-order closure scheme developed by Wilcox and Traci has been generalized for curved streamline flow and for flow in a rotating coordinate system. A physically based straightforward argument shows that curvature/rotation primarily affects the turbulent mixing energy; the argument yields suitable curvature/rotation terms which are added to the mixing-energy equation. Singular-perturbation solutions valid in the wall layer of a curved-wall boundary layer and a fully developed rotating channel flow demonstrate that, with the curvature/rotation terms, the model predicts the curved-wall and the rotating coordinate system laws of the wall. Results of numerical computations of curved-wall boundary layers and of rotating channel flow show that curvature/rotation effects can be computed accurately with second-order closure.
NASA Astrophysics Data System (ADS)
Firl, G. J.; Randall, D. A.
2013-12-01
The so-called "assumed probability density function (PDF)" approach to subgrid-scale (SGS) parameterization has shown to be a promising method for more accurately representing boundary layer cloudiness under a wide range of conditions. A new parameterization has been developed, named the Two-and-a-Half ORder closure (THOR), that combines this approach with a higher-order turbulence closure. THOR predicts the time evolution of the turbulence kinetic energy components, the variance of ice-liquid water potential temperature (θil) and total non-precipitating water mixing ratio (qt) and the covariance between the two, and the vertical fluxes of horizontal momentum, θil, and qt. Ten corresponding third-order moments in addition to the skewnesses of θil and qt are calculated using diagnostic functions assuming negligible time tendencies. The statistical moments are used to define a trivariate double Gaussian PDF among vertical velocity, θil, and qt. The first three statistical moments of each variable are used to estimate the two Gaussian plume means, variances, and weights. Unlike previous similar models, plume variances are not assumed to be equal or zero. Instead, they are parameterized using the idea that the less dominant Gaussian plume (typically representing the updraft-containing portion of a grid cell) has greater variance than the dominant plume (typically representing the "environmental" or slowly subsiding portion of a grid cell). Correlations among the three variables are calculated using the appropriate covariance moments, and both plume correlations are assumed to be equal. The diagnosed PDF in each grid cell is used to calculate SGS condensation, SGS fluxes of cloud water species, SGS buoyancy terms, and to inform other physical parameterizations about SGS variability. SGS condensation is extended from previous similar models to include condensation over both liquid and ice substrates, dependent on the grid cell temperature. Implementations have been
NASA Astrophysics Data System (ADS)
Colucci, Paul John
A methodology termed the "filtered density function" (FDF) is developed and implemented for large eddy simulation (LES) of chemically reacting turbulent flows. In this methodology, the effects of the unresolved scalar fluctuations are taken into account by considering the probability density function (PDF) of the subgrid scale (SGS) scalar quantities. The transport equation governing the evolution of the FDF is derived in which the effect of chemical reaction appears in a closed form. The influences of scalar mixing and convection within the subgrid are modeled. The generalization to variable density flows is made through consideration of the filtered mass density function (FMDF). The FDF and FMDF transport equations are solved numerically via a Lagrangian Monte Carlo scheme in which the solutions of equivalent stochastic differential equations (SDEs) are obtained. The consistency of the approach, the convergence of the Monte Carlo solution, and the performance of the closures employed in the FDF and FMDF transport equations are assessed by comparisons with results obtained by direct numerical simulation (DNS) and by conventional LES procedures in which the first two SGS scalar moments are obtained by a finite difference method (LES-FD). In non-reacting flows, the Monte Carlo solution yields results similar to those via LES-FD for the first two SGS moments. The advantage of the methodology is demonstrated by its use in LES of reacting flows. In the absence of a closure for the SGS scalar fluctuations, the LES-FD results are significantly different from those based on DNS. Comparatively, the FDF and FMDF yield much better agreement with filtered DNS results. The methodology is also tested by comparative assessments against experimental data for a heat releasing hydrogen-fluorine reacting mixing layer.
Analysis of surface energy balance closure over heterogeneous surfaces
NASA Astrophysics Data System (ADS)
Kim, Soojin; Lee, Young-Hee; Kim, Kyu Rang; Park, Young-San
2014-11-01
Surface energy balance closure has been examined using eddy covariance measurements and other observations at one industrial and three agricultural sites near the Nakdong River during daytime. Energy balance closure was evaluated by calculating the long-term averaged energy balance ratio (EBR), the ratio of turbulent energy fluxes to available energy, and the statistical regression of turbulent energy fluxes against available energy using half-hourly data. The EBR of all sites ranges from 0.46 to 0.83 while the coefficient of determination ( R 2) ranges from 0.37 to 0.77. The energy balance closure was relatively poor compared to homogeneous sites, indicating the influence of surface heterogeneity. Unmeasured heat storage terms also seem to play a role in the surface energy budget at the industrial and irrigated sites. The energy balance closure was better in conditions of high wind speed, low downward short wave radiation, and high friction velocity, which suggests the role of heat storage term and surface heterogeneity in surface energy balance at these sites. Spectrum analysis shows a sharp roll-off at the low frequency in co-spectrum, which indicates that low-frequency motions do not significantly contribute to turbulent fluxes. Both the spectra and cospectra in unstable conditions show a broad peak indicating the influence of multiple sizes of large eddies over heterogeneous sites. Most of ogive curves for the kinematic latent and sensible heat fluxes reach an asymptote within 30 minutes regardless of the EBR value, indicating that low frequency motion is not a main factor for energy imbalance. However, stationary eddies due to landscape heterogeneity still remains as a possible cause for energy imbalance.
Two-equation turbulence model for free and bounded two-phase flows
Rizk, M.A.H.T.A.
1985-01-01
A theoretical investigation of turbulent, free and bounded, two-phase flows was conducted. The objective was to develop a two-equation turbulence model which accounts for the interaction between the two phases for two-dimensional, isothermal, free and confined turbulent flows. The two equations describe the conservation turbulence kinetic energy and dissipation rate of that energy for the carrier fluid. The suspension is assumed to be dilute. The dispersed phase is assumed to consist of particles spherical in shape and uniform in size. The physical properties of each phase are assumed to be constant. The two conservation equations are rigorously derived from the momentum equations of the carrier fluid. Closure for high-Reynolds number turbulence is obtained by modeling the turbulent correlations up to third order. Predictions obtained with the high-Reynolds number closure of the model are in very good agreement with available experimental data for the flow of a turbulent round jet laden with spherical, uniform-size solid particles. The high-Reynolds number closure of the model is then extended to enable its use right up to a solid wall by developing a second order closure for low-Reynolds number turbulence which provides a reliable basis for calculating wall-bounded flows.
Talbot, L.; Cheng, R.K.
1993-12-01
Turbulent combustion is the dominant process in heat and power generating systems. Its most significant aspect is to enhance the burning rate and volumetric power density. Turbulent mixing, however, also influences the chemical rates and has a direct effect on the formation of pollutants, flame ignition and extinction. Therefore, research and development of modern combustion systems for power generation, waste incineration and material synthesis must rely on a fundamental understanding of the physical effect of turbulence on combustion to develop theoretical models that can be used as design tools. The overall objective of this program is to investigate, primarily experimentally, the interaction and coupling between turbulence and combustion. These processes are complex and are characterized by scalar and velocity fluctuations with time and length scales spanning several orders of magnitude. They are also influenced by the so-called {open_quotes}field{close_quotes} effects associated with the characteristics of the flow and burner geometries. The authors` approach is to gain a fundamental understanding by investigating idealized laboratory flames. Laboratory flames are amenable to detailed interrogation by laser diagnostics and their flow geometries are chosen to simplify numerical modeling and simulations and to facilitate comparison between experiments and theory.
NASA Technical Reports Server (NTRS)
Bardina, Jorge E.
1995-01-01
The objective of this work is to develop, verify, and incorporate the baseline two-equation turbulence models which account for the effects of compressibility into the three-dimensional Reynolds averaged Navier-Stokes (RANS) code and to provide documented descriptions of the models and their numerical procedures so that they can be implemented into 3-D CFD codes for engineering applications.
Analytical and phenomenological studies of rotating turbulence
NASA Technical Reports Server (NTRS)
Mahalov, Alex; Zhou, YE
1995-01-01
A framework, which combines mathematical analysis, closure theory, and phenomenological treatment, is developed to study the spectral transfer process and reduction of dimensionality in turbulent flows that are subject to rotation. First, we outline a mathematical procedure that is particularly appropriate for problems with two disparate time scales. The approach which is based on the Green's method leads to the Poincare velocity variables and the Poincare transformation when applied to rotating turbulence. The effects of the rotation are now reflected in the modifications to the convolution of a nonlinear term. The Poincare transformed equations are used to obtain a time-dependent analog of the Taylor-Proudman theorem valid in the asymptotic limit when the non-dimensional parameter mu is identical to Omega(t) approaches infinity (Omega is the rotation rate and t is the time). The 'split' of the energy transfer in both direct and inverse directions is established. Secondly, we apply the Eddy-Damped-Quasinormal-Markovian (EDQNM) closure to the Poincare transformed Euler/Navier-Stokes equations. This closure leads to expressions for the spectral energy transfer. In particular, an unique triple velocity decorrelation time is derived with an explicit dependence on the rotation rate. This provides an important input for applying the phenomenological treatment of Zhou. In order to characterize the relative strength of rotation, another non-dimensional number, a spectral Rossby number, which is defined as the ratio of rotation and turbulence time scales, is introduced. Finally, the energy spectrum and the spectral eddy viscosity are deduced.
Closure and ratio correlation analysis of lunar chemical and grain size data
NASA Technical Reports Server (NTRS)
Butler, J. C.
1976-01-01
Major element and major element plus trace element analyses were selected from the lunar data base for Apollo 11, 12 and 15 basalt and regolith samples. Summary statistics for each of the six data sets were compiled, and the effects of closure on the Pearson product moment correlation coefficient were investigated using the Chayes and Kruskal approximation procedure. In general, there are two types of closure effects evident in these data sets: negative correlations of intermediate size which are solely the result of closure, and correlations of small absolute value which depart significantly from their expected closure correlations which are of intermediate size. It is shown that a positive closure correlation will arise only when the product of the coefficients of variation is very small (less than 0.01 for most data sets) and, in general, trace elements in the lunar data sets exhibit relatively large coefficients of variation.
Diagnostic Statistics for the Assessment and Characterization of Complex Turbulent Flows
NASA Technical Reports Server (NTRS)
Ristorcelli, J. R.
1995-01-01
A simple parameterization scheme for a complex turbulent flow using nondimensional parameters coming from the Reynolds stress equations is given. Definitions and brief descriptions of the physical significance of several nondimensional parameters that are used to characterize turbulence from the viewpoint of single-point turbulence closures are given. These nondimensional parameters reflect measures of (1) the spectral band width of the turbulence; (2) deviations from the ideal Kolmogorov behavior; (3) the relative magnitude, orientation, and temporal duration of the deformation to which the turbulence is subjected; (4) one and two-point measures of the large and small scale anisotropy of the turbulence; and (5) inhomogeneity. This is an attempt to create a more systematic methodology for the diagnosis and classification of turbulent flows as well as in the development, validation, and application of turbulence model strategies. The parameters serve also to indicate the adequacy of various assumptions made in single-point turbulence models and in suggesting the appropriate turbulence strategy for a particular complex flow. The compilation will be of interest to experimentalists and to those involved in either computing turbulent flows or whose interests lies in verifying the adequacy of the phenomenological beliefs used in turbulence closures.
Representation of the Essential Flame-Turbulence Dynamics using Specific Flame-Vortex Interactions
NASA Astrophysics Data System (ADS)
Paes, Paulo L. K.; Brasseur, James; Xuan, Yuan
2016-11-01
Many engineering applications involve turbulent reacting flows, where nonlinear, multi-scale turbulence-combustion couplings are important. Directly resolving the complex fluid dynamics involved in these applications is associated with prohibitive computational costs, which makes it necessary to employ turbulent closure models and turbulent combustion models to account for the effects of unresolved scales on resolved scales. Most of these existent closure models rely on some assumptions about the turbulence dynamics and the scale separation between turbulence and the different combustion processes. A better understanding of the turbulence-combustion interactions is required for the development of more accurate, physics-based sub-grid-scale models for turbulent reacting flows. Instead of developing an extreme-resolution, high Reynolds number turbulent flame simulation that is limited to a localized part of the regime diagram, in this work, we propose to develop a series of numerical experiments of simplified interactions between a laminar premixed flame and specified vortex distributions of varying strengths and scales to capture the essential flame-turbulence dynamics over distinct premixed turbulent combustion regimes. The response of the laminar flame to different vortex time and length scales is investigated and the physical relevance of each dataset to practical turbulent premixed flames is discussed.
Nevada Test Site closure program
Shenk, D.P.
1994-08-01
This report is a summary of the history, design and development, procurement, fabrication, installation and operation of the closures used as containment devices on underground nuclear tests at the Nevada Test Site. It also addresses the closure program mothball and start-up procedures. The Closure Program Document Index and equipment inventories, included as appendices, serve as location directories for future document reference and equipment use.
Multigrid acceleration and turbulence models for computations of 3D turbulent jets in crossflow
NASA Technical Reports Server (NTRS)
Demuren, A. O.
1992-01-01
A multigrid method is presented for the calculation of three-dimensional turbulent jets in crossflow. Turbulence closure is achieved with either the standard k-epsilon model or a Reynolds stress model (RSM). Multigrid acceleration enables convergence rates which are far superior to that for a single grid method to be obtained with both turbulence models. With the k-epsilon model the rate approaches that for laminar flow, but with RSM it is somewhat slower. The increased stiffness of the system of equation in the latter may be responsible. Computed results with both turbulence models are compared to experimental data for a pair of opposed jets in crossflow. Both models yield reasonable agreement for the mean flow velocity, but RSM yields better predictions of the Reynolds stresses.
NASA Technical Reports Server (NTRS)
Acres, W. R.
1980-01-01
Safe reentry of the shuttle orbiter requires that the payload bay doors be closed and securely latched. Since a malfunction in the door drive or bulkhead latch systems could make safe reentry impossible, the requirement to provide tools to manually close and secure the doors was implemented. The tools would disconnect a disabled door or latch closure system and close and secure the doors if the normal system failed. The tools required to perform these tasks have evolved into a set that consists of a tubing cutter, a winch, a latching tool, and a bolt extractor. The design, fabrication, and performance tests of each tool are described.
Local isotropy in buoyancy-generated turbulence
NASA Astrophysics Data System (ADS)
Chasnov, Jeffrey R.
1991-12-01
Batchelor et al. (1992) recently considered the turbulent motion generated by buoyancy forces acting on random fluctuations in the density of an infinite fluid. This homogeneous buoyancy-generated flow field with zero mean density gradient was conceived as an idealized system which, like isotropic turbulence, may be useful as a vehicle for the general study of turbulence. The Batchelor et al. study relied partly on theoretical analysis and partly on direct and large-eddy numerical simulations of the flow field. To this mix, we add here a two-point closure study based on the eddy-damped quasi-normal Markovian (EDQNM) closure model applied to axisymmetric turbulence. The EDQNM model has been shown to yield reasonably accurate quantitative results for a variety of problems in homogeneous turbulence (Lesieur 1987). The main advantage here in applying EDQNM to the buoyancy-driven flow field is the wide range of wavenumbers over which a solution of the EDQNM equations may be solved. Whereas a typical large-eddy simulation using 128(exp 3) grid points has a wavenumber range of only 60, the EDQNM calculation can be easily run with a wavenumber range of several decades. Because of the growth in length scales in the buoyancy-driven flow field, this large wavenumber range allows for a solution of the flow field well into its asymptotic regime. Recent comparisons between large-eddy simulations and closure theory (Herring 1990) indicate that a time longer than that attainable by current large-eddy simulations is required to reach flow asymptotics and that conclusions based on large-eddy simulation results may be based only on an intermediate transient state. We briefly introduce the EDQNM equations for the buoyancy-generated flow field. We then present a Kolmogorov-like theoretical argument on the scaling of the small-scale spectra. This scaling is then confirmed by numerical solution of the EDQNM equations. We briefly conclude with possible future research directions.
Astronaut Moments: Randy Bresnik
2017-07-12
Astronaut Moments with NASA astronaut Randy Bresnik. Bresnik and his crewmates, cosmonaut Sergey Ryazanskiy of the Russian space agency Roscosmos and Paolo Nespoli of ESA (European Space Agency), will launch on the Russian Soyuz MS-05 spacecraft at 11:41 a.m. on July 28. They are scheduled to return to Earth in December. The crew members will continue several hundred experiments in biology, biotechnology, physical science and Earth science currently underway and scheduled to take place aboard humanity's only permanently occupied orbiting lab. HD download link: https://archive.org/details/jsc2017m000414_Astronaut-Moments-Randy-Bresnik _______________________________________ FOLLOW THE SPACE STATION! Twitter: https://twitter.com/Space_Station Facebook: https://www.facebook.com/ISS Instagram: https://instagram.com/iss/
Investigations of turbulent scalar fields using probability density function approach
NASA Technical Reports Server (NTRS)
Gao, Feng
1991-01-01
Scalar fields undergoing random advection have attracted much attention from researchers in both the theoretical and practical sectors. Research interest spans from the study of the small scale structures of turbulent scalar fields to the modeling and simulations of turbulent reacting flows. The probability density function (PDF) method is an effective tool in the study of turbulent scalar fields, especially for those which involve chemical reactions. It has been argued that a one-point, joint PDF approach is the one to choose from among many simulation and closure methods for turbulent combustion and chemically reacting flows based on its practical feasibility in the foreseeable future for multiple reactants. Instead of the multi-point PDF, the joint PDF of a scalar and its gradient which represents the roles of both scalar and scalar diffusion is introduced. A proper closure model for the molecular diffusion term in the PDF equation is investigated. Another direction in this research is to study the mapping closure method that has been recently proposed to deal with the PDF's in turbulent fields. This method seems to have captured the physics correctly when applied to diffusion problems. However, if the turbulent stretching is included, the amplitude mapping has to be supplemented by either adjusting the parameters representing turbulent stretching at each time step or by introducing the coordinate mapping. This technique is still under development and seems to be quite promising. The final objective of this project is to understand some fundamental properties of the turbulent scalar fields and to develop practical numerical schemes that are capable of handling turbulent reacting flows.
Modeling turbulent compressible flows - The mass fluctuating velocity and squared density
NASA Technical Reports Server (NTRS)
Taulbee, D.; Vanosdol, J.
1991-01-01
This paper deals with single-point closure theory for compressible turbulent flow, including the effects of compressibility on the turbulence. In particular, the combination of the pressure dilatation and the dilatation dissipation, terms which appear on the turbulent kinetic energy equation, are modeled. Model parameters in these transport equations are determined by comparing predictions with boundary layer measurements. Finally, predictions with a k-epsilon model, including the new formulations, are presented for the compressible shear layer.
Direct Numerical Simulation of Complex Turbulence
NASA Astrophysics Data System (ADS)
Hsieh, Alan
Direct numerical simulations (DNS) of spanwise-rotating turbulent channel flow were conducted. The data base obtained from these DNS simulations were used to investigate the turbulence generation cycle for simple and complex turbulence. For turbulent channel flow, three theoretical models concerning the formation and evolution of sublayer streaks, three-dimensional hairpin vortices and propagating plane waves were validated using visualizations from the present DNS data. The principal orthogonal decomposition (POD) method was used to verify the existence of the propagating plane waves; a new extension of the POD method was derived to demonstrate these plane waves in a spatial channel model. The analyses of coherent structures was extended to complex turbulence and used to determine the proper computational box size for a minimal flow unit (MFU) at Rob < 0.5. Proper realization of Taylor-Gortler vortices in the highly turbulent pressure region was demonstrated to be necessary for acceptably accurate MFU turbulence statistics, which required a minimum spanwise domain length Lz = pi. A dependence of MFU accuracy on Reynolds number was also discovered and MFU models required a larger domain to accurately approximate higher-Reynolds number flows. In addition, the results obtained from the DNS simulations were utilized to evaluate several turbulence closure models for momentum and thermal transport in rotating turbulent channel flow. Four nonlinear eddy viscosity turbulence models were tested and among these, Explicit Algebraic Reynolds Stress Models (EARSM) obtained the Reynolds stress distributions in best agreement with DNS data for rotational flows. The modeled pressure-strain functions of EARSM were shown to have strong influence on the Reynolds stress distributions near the wall. Turbulent heatflux distributions obtained from two explicit algebraic heat flux models consistently displayed increasing disagreement with DNS data with increasing rotation rate. Results
System for closure of a physical anomaly
Bearinger, Jane P; Maitland, Duncan J; Schumann, Daniel L; Wilson, Thomas S
2014-11-11
Systems for closure of a physical anomaly. Closure is accomplished by a closure body with an exterior surface. The exterior surface contacts the opening of the anomaly and closes the anomaly. The closure body has a primary shape for closing the anomaly and a secondary shape for being positioned in the physical anomaly. The closure body preferably comprises a shape memory polymer.
FINAL CLOSURE PLAN SURFACE IMPOUNDMENTS CLOSURE, SITE 300
Lane, J E; Scott, J E; Mathews, S E
2004-09-29
Lawrence Livermore National Laboratory of the University of California (LLNL) operates two Class II surface impoundments that store wastewater that is discharged from a number of buildings located on the Site 300 Facility (Site 300). The wastewater is the by-product of explosives processing. Reduction in the volume of water discharged from these buildings over the past several years has significantly reduced the wastewater storage needs. In addition, the impoundments were constructed in 1984, and the high-density polyethylene (HDPE) geomembrane liners are nearing the end of their service life. The purpose of this project is to clean close the surface impoundments and provide new wastewater storage using portable, above ground storage tanks at six locations. The tanks will be installed prior to closure of the impoundments and will include heaters for allowing evaporation during relatively cool weather. Golder Associates (Golder) has prepared this Final Closure Plan (Closure Plan) on behalf of LLNL to address construction associated with the clean closure of the impoundments. This Closure Plan complies with State Water Resources Control Board (SWRCB) Section 21400 of the California Code of Regulations Title 27 (27 CCR {section}21400). As required by these regulations and guidance, this Plan provides the following information: (1) A site characterization, including the site location, history, current operations, and geology and hydrogeology; (2) The regulatory requirements relevant to clean closure of the impoundments; (3) The closure procedures; and, (4) The procedures for validation and documentation of clean closure.
Helicity statistics in homogeneous and isotropic turbulence and turbulence models
NASA Astrophysics Data System (ADS)
Sahoo, Ganapati; De Pietro, Massimo; Biferale, Luca
2017-02-01
We study the statistical properties of helicity in direct numerical simulations of fully developed homogeneous and isotropic turbulence and in a class of turbulence shell models. We consider correlation functions based on combinations of vorticity and velocity increments that are not invariant under mirror symmetry. We also study the scaling properties of high-order structure functions based on the moments of the velocity increments projected on a subset of modes with either positive or negative helicity (chirality). We show that mirror symmetry is recovered at small scales, i.e., chiral terms are subleading and they are well captured by a dimensional argument plus anomalous corrections. These findings are also supported by a high Reynolds numbers study of helical shell models with the same chiral symmetry of Navier-Stokes equations.
Fracture mechanics analyses of partial crack closure in shell structures
NASA Astrophysics Data System (ADS)
Zhao, Jun
2007-12-01
This thesis presents the theoretical and finite element analyses of crack-face closure behavior in shells and its effect on the stress intensity factor under a bending load condition. Various shell geometries, such as spherical shell, cylindrical shell containing an axial crack, cylindrical shell containing a circumferential crack and shell with double curvatures, are all studied. In addition, the influence of material orthotropy on the crack closure effect in shells is also considered. The theoretical formulation is developed based on the shallow shell theory of Delale and Erdogan, incorporating the effect of crack-face closure at the compressive edges. The line-contact assumption, simulating the crack-face closure at the compressive edges, is employed so that the contact force at the closure edges is introduced, which can be translated to the mid-plane of the shell, accompanied by an additional distributed bending moment. The unknown contact force is computed by solving a mixed-boundary value problem iteratively, that is, along the crack length, either the normal displacement of the crack face at the compressive edges is equal to zero or the contact pressure is equal to zero. It is found that due to the curvature effects crack closure may not always occur on the entire length of the crack, depending on the direction of the bending load and the geometry of the shell. The crack-face closure influences significantly the magnitude of the stress intensity factors; it increases the membrane component but decreases the bending component. The maximum stress intensity factor is reduced by the crack-face closure. The significant influence of geometry and material orthotropy on rack closure behavior in shells is also predicted based on the analytical solutions. Three-dimensional FEA is performed to validate the theoretical solutions. It demonstrates that the crack face closure occurs actually over an area, not on a line, but the theoretical solutions of the stress intensity
NASA Astrophysics Data System (ADS)
Lee, Young J.; Huh, Kang Y.
2012-02-01
Simulation is performed to analyse the characteristics of turbulent spray combustion in conventional low and high speed diesel engine conditions. Turbulence-chemistry interaction is resolved by the Conditional Moment Closure (CMC) model in the spatially integrated form of an Incompletely Stirred Reactor (ISR). After validation against measured pressure traces, characteristic length and time scales and dimensionless numbers are estimated at the locations of sequentially injected fuel groups. Conditional flame structures are calculated for sequentially evaporated fuel groups to consider different available periods for ignition chemistry. Injection overlaps the combustion period in the high rpm engine, while most combustion occurs after injection and evaporation are complete in the low rpm engine. Ignition occurs in rich premixture with the initial peak temperature at the equivalence ratio around 2-4 as observed in Dec [2]. It corresponds to the most reactive mixture fraction of the minimum ignition delay for the given mixture states. Combustion proceeds to lean and rich sides in the mixture fraction space as a diffusion process by turbulence. The mean scalar dissipation rates (SDRs) are lower than the extinction limit to show stability of diffusion flames throughout the combustion period.
Effects of Lewis number on turbulent scalar transport and its modelling in turbulent premixed flames
Chakraborty, Nilanjan; Cant, R.S.
2009-07-15
The behaviour of the turbulent scalar flux in premixed flames has been studied using Direct Numerical Simulation (DNS) with emphasis on the effects of Lewis number in the context of Reynolds-averaged closure modelling. A database was obtained from DNS of three-dimensional freely propagating statistically planar turbulent premixed flames with simplified chemistry and a range of global Lewis numbers from 0.34 to 1.2. Under the same initial conditions of turbulence, flames with low Lewis numbers are found to exhibit counter-gradient transport, whereas flames with higher Lewis numbers tend to exhibit gradient transport. The Reynolds-averaged transport equation for the turbulent scalar flux is analysed in detail and the performance of existing models for the unclosed terms is assessed with respect to corresponding quantities extracted from DNS data. Based on this assessment, existing models which are able to address the effects of non-unity Lewis number on turbulent scalar flux transport are identified, and new or modified models are suggested wherever necessary. In this way, a complete set of closure models for the scalar flux transport equation is prescribed for use in Reynolds-Averaged Navier-Stokes simulations. (author)
Calculation of turbulent free mixing: Status and problems
NASA Technical Reports Server (NTRS)
Bushnell, D. M.
1973-01-01
An overview of turbulence closure methods is presented along with discussions concerning which method works where and which approaches deserve further development. A table is given which lists the various computational techniques together with their prime usage areas. In addition, free mixing phenomena which were not specifically included in the basic data considered for the conference are summarized.
NASA Astrophysics Data System (ADS)
Davidsen, Joern
2010-03-01
How much information do you need to distinguish between different mechanisms for spatiotemporal chaos in three-dimensions? In this talk, I will show that the observation of the dynamics on the surface of a medium can be sufficient. Studying mechanisms for filament turbulence in the context of reaction-diffusion media, we found numerically that two major classes of instabilities leave a very different signature on what can be observed on the surface of a three-dimensional medium. These results are of direct relevance in the context of ventricular fibrillation - a turbulent electrical wave activity that destroys the coherent contraction of the ventricular muscle and its main pumping function leading to sudden cardiac death. While it has been proposed that the three-dimensional structure of the heart plays an important role in this type of filament turbulence, only the surface of the heart is currently accessible to experimental observation preventing the study of the full dynamics. Our results suggest that such observations might be sufficient.
NASA Astrophysics Data System (ADS)
Kühnen, Jakob; Hof, Björn
2015-11-01
We show that a simple modification of the velocity profile in a pipe can lead to a complete collapse of turbulence and the flow fully relaminarises. The annihilation of turbulence is achieved by a steady manipulation of the streamwise velocity component alone, greatly reducing control efforts. Several different control techniques are presented: one with a local modification of the flow profile by means of a stationary obstacle, one employing a nozzle injecting fluid through a small gap at the pipe wall and one with a moving wall, where a part of the pipe is shifted in the streamwise direction. All control techniques act on the flow such that the streamwise velocity profile becomes more flat and turbulence gradually grows faint and disappears. In a smooth straight pipe the flow remains laminar downstream of the control. Hence a reduction in skin friction by a factor of 8 and more can be accomplished. Stereoscopic PIV-measurements and movies of the development of the flow during relaminarisation are presented.
NASA Astrophysics Data System (ADS)
Lewandowski, M. T.; Pozorski, J.
2016-10-01
The present work reports on the assessment of different turbulence-chemistry interaction closures for the modelling of turbulent non-premixed combustion. Two-dimensional axisymmetric simulations have been carried out based on three different laboratory flames. The methane fueled, piloted jet flame Sandia D, the simple jet syngas flame and the so-called Delft Jet-in-Hot Coflow flame are studied. All the flames can be characterised as non-premixed but differ by some features which are taken into account through appropriate modelling approach.
Turbulent Flow Between Rotating Cylinders
NASA Technical Reports Server (NTRS)
Shih-I, Pai
1943-01-01
The turbulent air flow between rotating cylinders was investigated. The distributions of mean speed and of turbulence were measured in the gap between a rotating inner and a stationary outer cylinder. The measurements led to the conclusion that the turbulent flow in the gap cannot be considered two dimensional, but that a particular type of secondary motion takes place. It is shown that the experimentally found velocity distribution can be fully understood under the assumption that this secondary motion consists of three-dimensional ring-shape vortices. The vortices occur only in pairs, and their number and size depend on the speed of the rotating cylinder; the number was found to decrease with increasing speed. The secondary motion has an essential part in the transmission of the moment of momentum. In regions where the secondary motion is negligible, the momentum transfer follows the laws known for homologous turbulence. Ring-shape vortices are known to occur in the laminar flow between rotating cylinders, but it was hitherto unknown that they exist even at speeds that are several hundred times the critical limit.
THOR Turbulence Electron Analyser: TEA
NASA Astrophysics Data System (ADS)
Fazakerley, Andrew; Moore, Tom; Owen, Chris; Pollock, Craig; Wicks, Rob; Samara, Marilia; Rae, Jonny; Hancock, Barry; Kataria, Dhiren; Rust, Duncan
2016-04-01
Turbulence Heating ObserveR (THOR) is the first mission ever flown in space dedicated to plasma turbulence. The Turbulence Electron Analyser (TEA) will measure the plasma electron populations in the mission's Regions of Interest. It will collect a 3D electron velocity distribution with cadences as short as 5 ms. The instrument will be capable of measuring energies up to 30 keV. TEA consists of multiple electrostatic analyser heads arranged so as to measure electrons arriving from look directions covering the full sky, i.e. 4 pi solid angle. The baseline concept is similar to the successful FPI-DES instrument currently operating on the MMS mission. TEA is intended to have a similar angular resolution, but a larger geometric factor. In comparison to earlier missions, TEA improves on the measurement cadence. For example, MMS FPI-DES routinely operates at 30 ms cadence. The objective of measuring distributions at rates as fast as 5 ms is driven by the mission's scientific requirements to resolve electron gyroscale size structures, where plasma heating and fluctuation dissipation is predicted to occur. TEA will therefore be capable of making measurements of the evolution of distribution functions across thin (a few km) current sheets travelling past the spacecraft at up to 600 km/s, of the Power Spectral Density of fluctuations of electron moments and of distributions fast enough to match frequencies with waves expected to be dissipating turbulence (e.g. with 100 Hz whistler waves).
The pdf approach to turbulent flow
NASA Technical Reports Server (NTRS)
Kollmann, W.
1990-01-01
This paper provides a detailed discussion of the theory and application of probability density function (pdf) methods, which provide a complete statistical description of turbulent flow fields at a single point or a finite number of points. The basic laws governing the flow of Newtonian fluids are set up in the Eulerian and the Lagrangian frame, and the exact and linear equations for the characteristic functionals in those frames are discussed. Pdf equations in both frames are derived as Fourier transforms of the equations of the characteristic functions. Possible formulations for the nonclosed terms in the pdf equation are discussed, their properties are assessed, and closure modes for the molecular-transport and the fluctuating pressure-gradient terms are reviewed. The application of pdf methods to turbulent combustion flows, supersonic flows, and the interaction of turbulence with shock waves is discussed.
Spectral Analysis of Cluster Induced Turbulence
NASA Astrophysics Data System (ADS)
Patel, Ravi; Ireland, Peter; Capecelatro, Jesse; Fox, Rodney; Desjardins, Olivier
2015-11-01
Particle laden turbulent flows are an important feature of many industrial processes such as fluidized bed reactors. The study of cluster-induced turbulence (CIT), wherein particles falling under gravity generate turbulence in the carrier gas via fluctuations in particle concentration, may lead to better models for these processes. We present a spectral analysis of a database of statistically stationary CIT simulations. These simulations were previously performed using a two way coupled Eulerian-Lagrangian approach for various mass loadings and particle-scale Reynolds numbers. The Lagrangian particle data is carefully filtered to obtain Eulerian fields for particle phase volume fraction, velocity, and granular temperature. We perform a spectral decomposition of the particle and fluid turbulent kinetic energy budget. We investigate the contributions to the particle and fluid turbulent kinetic energy by pressure strain, viscous dissipation, drag exchange, viscous exchange, and pressure exchange over the range of wavenumbers. Results from this study may help develop closure models for large eddy simulation of particle laden turbulent flows.
Structure of nonlocality of plasma turbulence
NASA Astrophysics Data System (ADS)
Gürcan, Ö. D.; Vermare, L.; Hennequin, P.; Berionni, V.; Diamond, P. H.; Dif-Pradalier, G.; Garbet, X.; Ghendrih, P.; Grandgirard, V.; McDevitt, C. J.; Morel, P.; Sarazin, Y.; Storelli, A.; Bourdelle, C.; the Tore Supra Team
2013-07-01
Various indications on the weakly nonlocal character of turbulent plasma transport both from experimental fluctuation measurements from Tore Supra and observations from the full-f, flux-driven gyrokinetic code GYSELA are reported. A simple Fisher equation model of this weakly nonlocal dynamics can be formulated in terms of an evolution equation for the turbulent entropy density, which contains the basic phenomenon of radial turbulence spreading in addition to avalanche-like dynamics via coupling to profile modulations. A derivation of this model, which contains the so-called beach effect, a diffusive and convective flux components for the flux of turbulence intensity, in addition to linear group propagation is given, starting from the drift-kinetic equation. The proposed model has the form of a transport equation for turbulence intensity, and may be considered as an addition to transport modelling. The kinetic fluxes given, can be computed using model closures, or local gyrokinetics. The model is also used in a particular setup that represents the near edge region as a relatively stable zone between the core and edge region where the energy injection is locally more substantial. It is observed that with constant, physical coefficients, the model gives a convincing qualitative profile of fluctuation intensity when the turbulence is coming from the core region with either a group velocity or a convective flux.
Comparative Study of Advanced Turbulence Models for Turbomachinery
NASA Technical Reports Server (NTRS)
Hadid, Ali H.; Sindir, Munir M.
1996-01-01
A computational study has been undertaken to study the performance of advanced phenomenological turbulence models coded in a modular form to describe incompressible turbulent flow behavior in two dimensional/axisymmetric and three dimensional complex geometry. The models include a variety of two equation models (single and multi-scale k-epsilon models with different near wall treatments) and second moment algebraic and full Reynolds stress closure models. These models were systematically assessed to evaluate their performance in complex flows with rotation, curvature and separation. The models are coded as self contained modules that can be interfaced with a number of flow solvers. These modules are stand alone satellite programs that come with their own formulation, finite-volume discretization scheme, solver and boundary condition implementation. They will take as input (from any generic Navier-Stokes solver) the velocity field, grid (structured H-type grid) and computational domain specification (boundary conditions), and will deliver, depending on the model used, turbulent viscosity, or the components of the Reynolds stress tensor. There are separate 2D/axisymmetric and/or 3D decks for each module considered. The modules are tested using Rocketdyn's proprietary code REACT. The code utilizes an efficient solution procedure to solve Navier-Stokes equations in a non-orthogonal body-fitted coordinate system. The differential equations are discretized over a finite-volume grid using a non-staggered variable arrangement and an efficient solution procedure based on the SIMPLE algorithm for the velocity-pressure coupling is used. The modules developed have been interfaced and tested using finite-volume, pressure-correction CFD solvers which are widely used in the CFD community. Other solvers can also be used to test these modules since they are independently structured with their own discretization scheme and solver methodology. Many of these modules have been
Assessment of dynamic closure for premixed combustion large eddy simulation
NASA Astrophysics Data System (ADS)
Langella, Ivan; Swaminathan, Nedunchezhian; Gao, Yuan; Chakraborty, Nilanjan
2015-09-01
Turbulent piloted Bunsen flames of stoichiometric methane-air mixtures are computed using the large eddy simulation (LES) paradigm involving an algebraic closure for the filtered reaction rate. This closure involves the filtered scalar dissipation rate of a reaction progress variable. The model for this dissipation rate involves a parameter βc representing the flame front curvature effects induced by turbulence, chemical reactions, molecular dissipation, and their interactions at the sub-grid level, suggesting that this parameter may vary with filter width or be a scale-dependent. Thus, it would be ideal to evaluate this parameter dynamically by LES. A procedure for this evaluation is discussed and assessed using direct numerical simulation (DNS) data and LES calculations. The probability density functions of βc obtained from the DNS and LES calculations are very similar when the turbulent Reynolds number is sufficiently large and when the filter width normalised by the laminar flame thermal thickness is larger than unity. Results obtained using a constant (static) value for this parameter are also used for comparative evaluation. Detailed discussion presented in this paper suggests that the dynamic procedure works well and physical insights and reasonings are provided to explain the observed behaviour.
27 CFR 26.231 - Affixing closures.
Code of Federal Regulations, 2012 CFR
2012-04-01
... OF THE TREASURY LIQUORS LIQUORS AND ARTICLES FROM PUERTO RICO AND THE VIRGIN ISLANDS Closures for Distilled Spirits From the Virgin Islands General § 26.231 Affixing closures. Closures or other devices...
27 CFR 26.231 - Affixing closures.
Code of Federal Regulations, 2011 CFR
2011-04-01
... OF THE TREASURY LIQUORS LIQUORS AND ARTICLES FROM PUERTO RICO AND THE VIRGIN ISLANDS Closures for Distilled Spirits From the Virgin Islands General § 26.231 Affixing closures. Closures or other devices...
27 CFR 26.136 - Affixing closures.
Code of Federal Regulations, 2011 CFR
2011-04-01
... OF THE TREASURY LIQUORS LIQUORS AND ARTICLES FROM PUERTO RICO AND THE VIRGIN ISLANDS Closures for Distilled Spirits From Puerto Rico § 26.136 Affixing closures. Closures or other devices shall be securely...
27 CFR 26.136 - Affixing closures.
Code of Federal Regulations, 2012 CFR
2012-04-01
... OF THE TREASURY LIQUORS LIQUORS AND ARTICLES FROM PUERTO RICO AND THE VIRGIN ISLANDS Closures for Distilled Spirits From Puerto Rico § 26.136 Affixing closures. Closures or other devices shall be securely...
27 CFR 26.136 - Affixing closures.
Code of Federal Regulations, 2010 CFR
2010-04-01
... OF THE TREASURY LIQUORS LIQUORS AND ARTICLES FROM PUERTO RICO AND THE VIRGIN ISLANDS Closures for Distilled Spirits From Puerto Rico § 26.136 Affixing closures. Closures or other devices shall be securely...
27 CFR 26.136 - Affixing closures.
Code of Federal Regulations, 2014 CFR
2014-04-01
... OF THE TREASURY ALCOHOL LIQUORS AND ARTICLES FROM PUERTO RICO AND THE VIRGIN ISLANDS Closures for Distilled Spirits From Puerto Rico § 26.136 Affixing closures. Closures or other devices shall be securely...
27 CFR 26.136 - Affixing closures.
Code of Federal Regulations, 2013 CFR
2013-04-01
... OF THE TREASURY ALCOHOL LIQUORS AND ARTICLES FROM PUERTO RICO AND THE VIRGIN ISLANDS Closures for Distilled Spirits From Puerto Rico § 26.136 Affixing closures. Closures or other devices shall be securely...
Moment tensors of ten witwatersrand mine tremors
McGarr, A.
1992-01-01
Ground motions, recorded both underground and on the surface in two of the South African Gold mining districts, were inverted to determine complete moment tensors for 10 mining-induced tremors in the magnitude range 1.9 to 3.3. The resulting moment tensors fall into two separate categories. Seven of the events involve substantial coseismic volumetric reduction-??V together with normal faulting entailing shear deformation ??AD, where the summation is over fault planes of area A and average slip D. For these events the ratio-??V/??AD ranges from 0.58 to 0.92, with an average value of 0.71. For the remaining three events ??V is not significantly different from zero; these events are largely double-couple sources involving normal faulting. Surprisingly, the two types of source mechanism appear to be very distinct in that there is not a continuous distribution of the source mix from ??V=0 to-??V?????AD. Presumably, the coseismic closure indicates substantial interaction between a mine stope and adjacent shear failure in the surrounding rock, under the influence of an ambient stress for which the maximum principal stress is oriented vertically. ?? 1992 Birkha??user Verlag.
Closedure - Mine Closure Technologies Resource
NASA Astrophysics Data System (ADS)
Kauppila, Päivi; Kauppila, Tommi; Pasanen, Antti; Backnäs, Soile; Liisa Räisänen, Marja; Turunen, Kaisa; Karlsson, Teemu; Solismaa, Lauri; Hentinen, Kimmo
2015-04-01
Closure of mining operations is an essential part of the development of eco-efficient mining and the Green Mining concept in Finland to reduce the environmental footprint of mining. Closedure is a 2-year joint research project between Geological Survey of Finland and Technical Research Centre of Finland that aims at developing accessible tools and resources for planning, executing and monitoring mine closure. The main outcome of the Closedure project is an updatable wiki technology-based internet platform (http://mineclosure.gtk.fi) in which comprehensive guidance on the mine closure is provided and main methods and technologies related to mine closure are evaluated. Closedure also provides new data on the key issues of mine closure, such as performance of passive water treatment in Finland, applicability of test methods for evaluating cover structures for mining wastes, prediction of water effluents from mine wastes, and isotopic and geophysical methods to recognize contaminant transport paths in crystalline bedrock.
Modeling variable density turbulence in the wake of an air-entraining transom stern
NASA Astrophysics Data System (ADS)
Hendrickson, Kelli; Yue, Dick
2015-11-01
This work presents a priori testing of closure models for the incompressible highly-variable density turbulent (IHVDT) flows in the near wake region of a transom stern. This three-dimensional flow is comprised of convergent corner waves that originate from the body and collide on the ship center plane forming the ``rooster tail'' that then widens to form the divergent wave train. These violent free-surface flows and breaking waves are characterized by significant turbulent mass flux (TMF) at Atwood number At = (ρ2 -ρ1) / (ρ2 +ρ1) ~ 1 for which there is little guidance in turbulence closure modeling for the momentum and scalar transport along the wake. To whit, this work utilizes high-resolution simulations of the near wake of a canonical three-dimensional transom stern using conservative Volume-of-Fluid (cVOF), implicit Large Eddy Simulation (iLES), and Boundary Data Immersion Method (BDIM) to capture the turbulence and large scale air entrainment. Analysis of the simulation results across and along the wake for the TMF budget and turbulent anisotropy provide the physical basis of the development of multiphase turbulence closure models. Performance of isotropic and anisotropic turbulent mass flux closure models will be presented. Sponsored by the Office of Naval Research.
Large-eddy simulations of mean and turbulence dynamics in unsteady Ekman boundary layers
NASA Astrophysics Data System (ADS)
Momen, Mostafa; Bou-Zeid, Elie
2015-11-01
Unsteady geostrophic forcing in the atmosphere or ocean not only influences the mean wind, but also affects the turbulent statistics. In order to see when turbulence is in quasi-equilibrium with the mean, one needs to understand how the turbulence decays or develops, and how do the turbulent production, transport and dissipation respond to changes in the imposed forcing. This helps us understand the underlying dynamics of the unsteady boundary layers and develop better turbulence closures for weather/climate models and engineering applications. The present study focuses on the unsteady Ekman boundary layer where pressure gradient, Coriolis, and friction forces interact but are not necessarily in equilibrium. Several cases are simulated using LES to examine how the turbulence and resolved TKE budget terms are modulated by the variability of the mean pressure gradient. We also examine the influence of the forcing variability time-scale on the turbulence equilibrium and TKE budget. It is shown that when the forcing time-scale is in the order of the turbulence characteristic time-scale, the turbulence is no longer in quasi-equilibrium due to highly nonlinear mean-turbulence interactions and hence the conventional log-law and turbulence closures are no longer valid. NSF-PDM under AGS-10266362. Simulations performed at NCAR, and Della server at Princeton University. Cooperative Institute for Climate Science, NOAA-Princeton University under NA08OAR4320752.
Plasma sheet turbulence observed by Cluster II
NASA Technical Reports Server (NTRS)
Weygand, James M.; Kivelson, M. G.; Khurana, K. K.; Schwarzl, H. K.; Thompson, S. M.; McPherron, R. L.; Balogh, A.; Kistler, L. M.; Goldstein, M. L.; Borovsky, J.
2005-01-01
Cluster fluxgate magnetometer (FGM) and ion spectrometer (CIS) data are employed to analyze magnetic field fluctuations within the plasma sheet during passages through the magnetotail region in the summers of 2001 and 2002 and, in particular, to look for characteristics of magnetohydrodynamic (MHD) turbulence. Power spectral indices determined from power spectral density functions are on average larger than Kolmogorov's theoretical value for fluid turbulence as well as Kraichnan's theoretical value for MHD plasma turbulence. Probability distribution functions of the magnetic fluctuations show a scaling law over a large range of temporal scales with non-Gaussian distributions at small dissipative scales and inertial scales and more Gaussian distribution at large driving scales. Furthermore, a multifractal analysis of the magnetic field components shows scaling behavior in the inertial range of the fluctuations from about 20 s to 13 min for moments through the fifth order. Both the scaling behavior of the probability distribution functions and the multifractal structure function suggest that intermittent turbulence is present within the plasma sheet. The unique multispacecraft aspect and fortuitous spacecraft spacing allow us to examine the turbulent eddy scale sizes. Dynamic autocorrelation and cross correlation analysis of the magnetic field components allow us to determine that eddy scale sizes fit within the plasma sheet. These results suggest that magnetic field turbulence is occurring within the plasma sheet resulting in turbulent energy dissipation.
Conservational PDF Equations of Turbulence
NASA Technical Reports Server (NTRS)
Shih, Tsan-Hsing; Liu, Nan-Suey
2010-01-01
Recently we have revisited the traditional probability density function (PDF) equations for the velocity and species in turbulent incompressible flows. They are all unclosed due to the appearance of various conditional means which are modeled empirically. However, we have observed that it is possible to establish a closed velocity PDF equation and a closed joint velocity and species PDF equation through conditions derived from the integral form of the Navier-Stokes equations. Although, in theory, the resulted PDF equations are neither general nor unique, they nevertheless lead to the exact transport equations for the first moment as well as all higher order moments. We refer these PDF equations as the conservational PDF equations. This observation is worth further exploration for its validity and CFD application
Alyami, Mohammad S.; Lundberg, Peter W.; Cotte, Eddy G.; Glehen, Olivier J.
2016-01-01
Iatrogenic ileostomies are routinely placed during colorectal surgery for the diversion of intestinal contents to permit healing of the distal anastomosis prior to elective reversal. We present an interesting case of spontaneous closure of a diverting ileostomy without any adverse effects to the patient. A 65-year-old woman, positive for hereditary non-polyposis colorectal cancer type-I, with locally invasive cancer of the distal colon underwent en-bloc total colectomy, hysterectomy, and bilateral salpingoophorectomy with creation of a proximal loop ileostomy. The ostomy temporarily closed without reoperation at 10 weeks, after spontaneously reopening, it definitively closed, again without surgical intervention at 18 weeks following the original surgery. This rare phenomenon has occurred following variable colorectal pathology and is poorly understood, particularly in patients with aggressive disease and adjunct perioperative interventions. PMID:27279518
Noce, T.E.; Holzer, T.L.
2003-01-01
The long-term stability of deep holes 1.75 inches. (4.4 cm) in diameter by 98.4 feet (30 m) created by cone penetration testing (CPT) was monitored at a site in California underlain by Holocene and Pleistocene age alluvial fan deposits. Portions of the holes remained open both below and above the 28.6-foot (8.7 m)-deep water table for approximately three years, when the experiment was terminated. Hole closure appears to be a very slow process that may take decades in the stiff soils studied here. Other experience suggests holes in softer soils may also remain open. Thus, despite their small diameter, CPT holes may remain open for years and provide paths for rapid migration of contaminants. The observations confirm the need to grout holes created by CPT soundings as well as other direct-push techniques in areas where protection of shallow ground water is important.
Revisiting large neutrino magnetic moments
NASA Astrophysics Data System (ADS)
Lindner, Manfred; Radovčić, Branimir; Welter, Johannes
2017-07-01
Current experimental sensitivity on neutrino magnetic moments is many orders of magnitude above the Standard Model prediction. A potential measurement of next-generation experiments would therefore strongly request new physics beyond the Standard Model. However, large neutrino magnetic moments generically tend to induce large corrections to the neutrino masses and lead to fine-tuning. We show that in a model where neutrino masses are proportional to neutrino magnetic moments. We revisit, discuss and propose mechanisms that still provide theoretical consistent explanations for a potential measurement of large neutrino magnetic moments. We find only two viable mechanisms to realize large transition magnetic moments for Majorana neutrinos only.
[Turbulent characteristics in forest canopy under atmospheric neutral condition].
Diao, Yi-Wei; Guan, De-Xin; Jin, Chang-Jie; Wang, An-Zhi; Pei, Tie-Fan
2010-02-01
Based on the micrometeorological data of broad-leaved Korean pine forest in Changbai Mountain in 2003, a second-order closure model was employed to calculate and analyze the turbulent characteristics within and above the canopy of the forest. The calculated mean wind profile was coincident with the measured one. The Reynolds stress within the forest was significantly attenuated. The turbulent strength, velocity flux, and skew were the largest at forest-atmosphere interface, as well the wind shear. With the increase of velocity skew, the turbulent intermittence became more significant, and the downward turbulent eddy within the canopy was limited. Most of the turbulent deeply within the forest canopy was produced by the non-local contributions above the canopy.
Doppler lidar signal and turbulence study
NASA Technical Reports Server (NTRS)
Frost, W.; Huang, K. H.
1983-01-01
Wind fields were measured with the ground-based NASA/MSFC lidar are compared with the in situ NASA RB-57 aircraft measurements. The mean wind fields, the turbulence intensities, and the turbulence spectra determined from measurements by both systems are in very good agreement. Turbulence intensities and spectra were calculated from the fluctuations with time in the radial wind speed component. The second moment or Doppler frequency spectral width of the lidar measurements was also compared with turbulence intensities measured by the aircraft. These second moments could only be resolved at the very low altitudes (in three range bins). Turbulence intensities estimated from the spectral width data were an order of magnitude higher than those measured by the aircraft. An interesting boundary layer evolved during the progress of the experiment. The breakup of a stable boundary layer resulted in winds blowing in one direction above 600 m msl and in the opposite direction below that level. Both the aircraft and the lidar systems clearly identified this unusual boundary layer flow and showed the identical trends.
Wittmann, Marc
2011-01-01
It has been suggested that perception and action can be understood as evolving in temporal epochs or sequential processing units. Successive events are fused into units forming a unitary experience or “psychological present.” Studies have identified several temporal integration levels on different time scales which are fundamental for our understanding of behavior and subjective experience. In recent literature concerning the philosophy and neuroscience of consciousness these separate temporal processing levels are not always precisely distinguished. Therefore, empirical evidence from psychophysics and neuropsychology on these distinct temporal processing levels is presented and discussed within philosophical conceptualizations of time experience. On an elementary level, one can identify a functional moment, a basic temporal building block of perception in the range of milliseconds that defines simultaneity and succession. Below a certain threshold temporal order is not perceived, individual events are processed as co-temporal. On a second level, an experienced moment, which is based on temporal integration of up to a few seconds, has been reported in many qualitatively different experiments in perception and action. It has been suggested that this segmental processing mechanism creates temporal windows that provide a logistical basis for conscious representation and the experience of nowness. On a third level of integration, continuity of experience is enabled by working memory in the range of multiple seconds allowing the maintenance of cognitive operations and emotional feelings, leading to mental presence, a temporal window of an individual’s experienced presence. PMID:22022310
Construction of momentum theorem using cross moments
NASA Astrophysics Data System (ADS)
Hahm, T. S.; Wang, Lu; Diamond, P. H.
2009-11-01
Charney-Drazin theorem has been extended to Hasegawa Wakatani system for zonal flow problem in magnetic fusion [P.H. Diamond, et al., Plasma Phys. Control. Fusion 50, 124018 (2008)]. For this model, the guiding center density is the potential vorticity and zonal flow is influenced by the particle flux. In this work we construct momentum theorems in terms of a hierarchy of cross moments
A Study of Low Cloud Climate Feedbacks Using a Generalized Higher-Order Closure Subgrid Model
NASA Astrophysics Data System (ADS)
Firl, Grant J.
One of the biggest uncertainties in projections of future climate is whether and how low cloudiness will change and whether that change will feed back on the climate system. Much of the uncertainty revolves around the difference in scales between the processes that govern low cloudiness and the processes that can be resolved in climate models, a fact that relegates shallow convection to the parameterization realm with varying levels of success. A new subgrid-scale parameterization, named THOR, has been developed in an effort to improve the representation of low cloudiness via parameterization in climate models. THOR uses the higher-order closure approach to determine the statistics describing subgrid-scale processes. These statistics are used to determine a trivariate double-Gaussian PDF among vertical velocity, ice-liquid water potential temperature, and total water specific humidity. With this information, one can diagnose what portion of the grid cell is cloudy, subgrid-scale cloud water content, and subgrid-scale vertical cloud water flux. In addition, samples are drawn from the trivariate PDF in order to drive the microphysics and radiation schemes. Although schemes similar to THOR have been developed over the past decade, THOR includes several novel concepts, like the generalization of the saturation curve to include condensation over both ice and liquid substrates, the determination of the PDF parameters from the given turbulence statistics, the introduction of a stochastic parcel entrainment process for the turbulence length scale, and a sub-column approach for calculating radiative transfer using the PDF. The new model is validated by simulating five test cases spanning a wide range of boundary layer cloud types, from stratocumulus to cumulus and the transition between the two. The results are compared to an ensemble of LES models running the same cases, with particular attention paid to turbulence statistics and cloud structure. For all cloud types tested
Reynolds stress closure in jet flows using wave models
NASA Technical Reports Server (NTRS)
Morris, P. J.
1988-01-01
Ways of implementing the turbulence closure scheme based on modeling the large scale coherent structures as instability waves were sought. The computational tools necessary to apply this scheme to jets of arbitrary geometry were developed. The model, developed earlier, was extended to the shock structure of supersonic jets of arbitrary geometry and multiple jets. It was found that though the qualititate features of the unsteady flow field could be predicted there were always difficulties with some of the quantitative features. This led to the new formation of the closure scheme. The schemes for computations tools which were developed are efficient and represent the application of the very powerful mathematical tools to the problems of practical significance.
Inverse cascade of magnetic helicity in magnetohydrodynamic turbulence.
Müller, Wolf-Christian; Malapaka, Shiva Kumar; Busse, Angela
2012-01-01
The nonlinear dynamics of magnetic helicity HM, which is responsible for large-scale magnetic structure formation in electrically conducting turbulent media, is investigated in forced and decaying three-dimensional magnetohydrodynamic turbulence. This is done with the help of high-resolution direct numerical simulations and statistical closure theory. The numerically observed spectral scaling of HM is at variance with earlier work using a statistical closure model [Pouquet et al., J. Fluid Mech. 77, 321 (1976)]. By revisiting this theory, a universal dynamical balance relation is found that includes the effects of kinetic helicity as well as kinetic and magnetic energies on the inverse cascade of HM and explains the above-mentioned discrepancy. Consideration of the result in the context of mean-field dynamo theory suggests a nonlinear modification of the α-dynamo effect, which is important in the context of magnetic-field excitation in turbulent plasmas.
On explicit algebraic stress models for complex turbulent flows
NASA Technical Reports Server (NTRS)
Gatski, T. B.; Speziale, C. G.
1992-01-01
Explicit algebraic stress models that are valid for three-dimensional turbulent flows in noninertial frames are systematically derived from a hierarchy of second-order closure models. This represents a generalization of the model derived by Pope who based his analysis on the Launder, Reece, and Rodi model restricted to two-dimensional turbulent flows in an inertial frame. The relationship between the new models and traditional algebraic stress models -- as well as anistropic eddy visosity models -- is theoretically established. The need for regularization is demonstrated in an effort to explain why traditional algebraic stress models have failed in complex flows. It is also shown that these explicit algebraic stress models can shed new light on what second-order closure models predict for the equilibrium states of homogeneous turbulent flows and can serve as a useful alternative in practical computations.
NASA Technical Reports Server (NTRS)
Hsu, Andrew T.
1992-01-01
Turbulent combustion can not be simulated adequately by conventional moment closure turbulent models. The probability density function (PDF) method offers an attractive alternative: in a PDF model, the chemical source terms are closed and do not require additional models. Because the number of computational operations grows only linearly in the Monte Carlo scheme, it is chosen over finite differencing schemes. A grid dependent Monte Carlo scheme following J.Y. Chen and W. Kollmann has been studied in the present work. It was found that in order to conserve the mass fractions absolutely, one needs to add further restrictions to the scheme, namely alpha(sub j) + gamma(sub j) = alpha(sub j - 1) + gamma(sub j + 1). A new algorithm was devised that satisfied this restriction in the case of pure diffusion or uniform flow problems. Using examples, it is shown that absolute conservation can be achieved. Although for non-uniform flows absolute conservation seems impossible, the present scheme has reduced the error considerably.
A Global Turbulence Model for Neutrino-driven Convection in Core-collapse Supernovae
NASA Astrophysics Data System (ADS)
Murphy, Jeremiah W.; Meakin, Casey
2011-12-01
Simulations of core-collapse supernovae (CCSNe) result in successful explosions once the neutrino luminosity exceeds a critical curve, and recent simulations indicate that turbulence further enables explosion by reducing this critical neutrino luminosity. We propose a theoretical framework to derive this result and take the first steps by deriving the governing mean-field equations. Using Reynolds decomposition, we decompose flow variables into background and turbulent flows and derive self-consistent averaged equations for their evolution. As basic requirements for the CCSN problem, these equations naturally incorporate steady-state accretion, neutrino heating and cooling, non-zero entropy gradients, and turbulence terms associated with buoyant driving, redistribution, and dissipation. Furthermore, analysis of two-dimensional (2D) CCSN simulations validate these Reynolds-averaged equations, and we show that the physics of turbulence entirely accounts for the differences between 1D and 2D CCSN simulations. As a prelude to deriving the reduction in the critical luminosity, we identify the turbulent terms that most influence the conditions for explosion. Generically, turbulence equations require closure models, but these closure models depend upon the macroscopic properties of the flow. To derive a closure model that is appropriate for CCSNe, we cull the literature for relevant closure models and compare each with 2D simulations. These models employ local closure approximations and fail to reproduce the global properties of neutrino-driven turbulence. Motivated by the generic failure of these local models, we propose an original model for turbulence which incorporates global properties of the flow. This global model accurately reproduces the turbulence profiles and evolution of 2D CCSN simulations.
1991-10-01
system of codes for missile detection, the SPIRITS system of codes for aircraft/helicopter detection, the HSCT system of codes (MICOM) NSWC, etc) for...Academic Press, N.Y. 1974. Cebeci, T. and Smith, A.M.O., "Analysis of Turbulent Boundary Layers", Series in A01jed Mathematics and MW1WiG Vol. XV ...647-6, (Naval Ordnance Lab Research Rpt. 280), Jan. 1964. Dash, S.M., et. al., "Computer Code for HSCT Exhaust Flowfield Simulation and Observations
Explosive turbulent magnetic reconnection.
Higashimori, K; Yokoi, N; Hoshino, M
2013-06-21
We report simulation results for turbulent magnetic reconnection obtained using a newly developed Reynolds-averaged magnetohydrodynamics model. We find that the initial Harris current sheet develops in three ways, depending on the strength of turbulence: laminar reconnection, turbulent reconnection, and turbulent diffusion. The turbulent reconnection explosively converts the magnetic field energy into both kinetic and thermal energy of plasmas, and generates open fast reconnection jets. This fast turbulent reconnection is achieved by the localization of turbulent diffusion. Additionally, localized structure forms through the interaction of the mean field and turbulence.
Angle closure in younger patients.
Chang, Brian M; Liebmann, Jeffrey M; Ritch, Robert
2002-01-01
PURPOSE: Angle-closure glaucoma is rare in children and young adults. Only scattered cases associated with specific clinical entities have been reported. We evaluated the findings in patients in our database aged 40 or younger with angle closure. METHODS: Our database was searched for patients with angle closure who were 40 years old or younger. Data recorded included age at initial consultation; age at the time of diagnosis; gender; results of slit-lamp examination, gonioscopy, and ultrasound biomicroscopy (from 1993 onward); clinical diagnosis; and therapy. Patients with previous incisional surgery were excluded, as were patients with anterior chamber proliferative mechanisms leading to angle closure. RESULTS: Sixty-seven patients (49 females, 18 males) met entry criteria. Mean age (+/- SD) at the time of consultation was 34.4 +/- 9.4 years (range, 3-68 years). Diagnoses included plateau iris syndrome (35 patients), iridociliary cysts (8 patients), retinopathy of prematurity (7 patients), uveitis (5 patients), isolated nanophthalmos (3 patients), relative pupillary block (2 patients), Weill-Marchesani syndrome (3 patients), and 1 patient each with Marfan syndrome, miotic-induced angle closure, persistent hyperplastic primary vitreous, and idiopathic lens subluxation. CONCLUSION: The etiology of angle closure in young persons is different from that in the older population and is typically associated with structural or developmental ocular anomalies rather than relative pupillary block. Following laser iridotomy, these eyes should be monitored for recurrent angle closure and the need for additional laser or incisional surgical intervention. PMID:12545694
Wang, Liang Germaschewski, K.; Hakim, Ammar H.; Bhattacharjee, A.
2015-01-15
We introduce an extensible multi-fluid moment model in the context of collisionless magnetic reconnection. This model evolves full Maxwell equations and simultaneously moments of the Vlasov-Maxwell equation for each species in the plasma. Effects like electron inertia and pressure gradient are self-consistently embedded in the resulting multi-fluid moment equations, without the need to explicitly solving a generalized Ohm's law. Two limits of the multi-fluid moment model are discussed, namely, the five-moment limit that evolves a scalar pressures for each species and the ten-moment limit that evolves the full anisotropic, non-gyrotropic pressure tensor for each species. We first demonstrate analytically and numerically that the five-moment model reduces to the widely used Hall magnetohydrodynamics (Hall MHD) model under the assumptions of vanishing electron inertia, infinite speed of light, and quasi-neutrality. Then, we compare ten-moment and fully kinetic particle-in-cell (PIC) simulations of a large scale Harris sheet reconnection problem, where the ten-moment equations are closed with a local linear collisionless approximation for the heat flux. The ten-moment simulation gives reasonable agreement with the PIC results regarding the structures and magnitudes of the electron flows, the polarities and magnitudes of elements of the electron pressure tensor, and the decomposition of the generalized Ohm's law. Possible ways to improve the simple local closure towards a nonlocal fully three-dimensional closure are also discussed.
NASA Astrophysics Data System (ADS)
Wang, Liang; Hakim, Ammar H.; Bhattacharjee, A.; Germaschewski, K.
2015-01-01
We introduce an extensible multi-fluid moment model in the context of collisionless magnetic reconnection. This model evolves full Maxwell equations and simultaneously moments of the Vlasov-Maxwell equation for each species in the plasma. Effects like electron inertia and pressure gradient are self-consistently embedded in the resulting multi-fluid moment equations, without the need to explicitly solving a generalized Ohm's law. Two limits of the multi-fluid moment model are discussed, namely, the five-moment limit that evolves a scalar pressures for each species and the ten-moment limit that evolves the full anisotropic, non-gyrotropic pressure tensor for each species. We first demonstrate analytically and numerically that the five-moment model reduces to the widely used Hall magnetohydrodynamics (Hall MHD) model under the assumptions of vanishing electron inertia, infinite speed of light, and quasi-neutrality. Then, we compare ten-moment and fully kinetic particle-in-cell (PIC) simulations of a large scale Harris sheet reconnection problem, where the ten-moment equations are closed with a local linear collisionless approximation for the heat flux. The ten-moment simulation gives reasonable agreement with the PIC results regarding the structures and magnitudes of the electron flows, the polarities and magnitudes of elements of the electron pressure tensor, and the decomposition of the generalized Ohm's law. Possible ways to improve the simple local closure towards a nonlocal fully three-dimensional closure are also discussed.
Simulations of anti-parallel reconnection using a nonlocal heat flux closure
NASA Astrophysics Data System (ADS)
Ng, Jonathan; Hakim, Ammar; Bhattacharjee, A.; Stanier, Adam; Daughton, W.
2017-08-01
The integration of kinetic effects in fluid models is important for global simulations of the Earth's magnetosphere. In particular, it has been shown that ion kinetics play a crucial role in the dynamics of large reconnecting systems, and that higher-order fluid moment models can account for some of these effects. Here, we use a ten-moment model for electrons and ions, which includes the off diagonal elements of the pressure tensor that are important for magnetic reconnection. Kinetic effects are recovered by using a nonlocal heat flux closure, which approximates linear Landau damping in the fluid framework. The closure is tested using the island coalescence problem, which is sensitive to ion dynamics. We demonstrate that the nonlocal closure is able to self-consistently reproduce the structure of the ion diffusion region, pressure tensor, and ion velocity without the need for fine-tuning of relaxation coefficients present in earlier models.
Simulations of anti-parallel reconnection using a nonlocal heat flux closure
Ng, Jonathan; Hakim, Ammar; Bhattacharjee, A.; ...
2017-08-08
The integration of kinetic effects in fluid models is important for global simulations of the Earth's magnetosphere. In particular, it has been shown that ion kinetics play a crucial role in the dynamics of large reconnecting systems, and that higher-order fluid moment models can account for some of these effects. Here, we use a ten-moment model for electrons and ions, which includes the off diagonal elements of the pressure tensor that are important for magnetic reconnection. Kinetic effects are recovered by using a nonlocal heat flux closure, which approximates linear Landau damping in the fluid framework. Moreover, the closure ismore » tested using the island coalescence problem, which is sensitive to ion dynamics. We also demonstrate that the nonlocal closure is able to self-consistently reproduce the structure of the ion diffusion region, pressure tensor, and ion velocity without the need for fine-tuning of relaxation coefficients present in earlier models.« less
40 CFR 265.280 - Closure and post-closure.
Code of Federal Regulations, 2014 CFR
2014-07-01
... contaminants caused by wind erosion; and (4) Compliance with § 265.276 concerning the growth of food-chain... unit as appropriate for its post-closure use; (3) Assure that growth of food chain crops complies with...
40 CFR 265.280 - Closure and post-closure.
Code of Federal Regulations, 2011 CFR
2011-07-01
... contaminants caused by wind erosion; and (4) Compliance with § 265.276 concerning the growth of food-chain... unit as appropriate for its post-closure use; (3) Assure that growth of food chain crops complies with...
40 CFR 265.280 - Closure and post-closure.
Code of Federal Regulations, 2013 CFR
2013-07-01
... contaminants caused by wind erosion; and (4) Compliance with § 265.276 concerning the growth of food-chain... unit as appropriate for its post-closure use; (3) Assure that growth of food chain crops complies with...
40 CFR 265.280 - Closure and post-closure.
Code of Federal Regulations, 2012 CFR
2012-07-01
... contaminants caused by wind erosion; and (4) Compliance with § 265.276 concerning the growth of food-chain... unit as appropriate for its post-closure use; (3) Assure that growth of food chain crops complies with...
Robotic atrial septal defect closure.
Senay, Sahin; Gullu, Ahmet Umit; Kocyigit, Muharrem; Degirmencioglu, Aleks; Karabulut, Hasan; Alhan, Cem
2014-01-01
Atrial septal defect (ASD) is one of the most common congenital cardiac diseases. This pathology can be treated with percutaneous devices. However, some of the ASDs are not suitable for device closure. Also, there may be device-related late complications of transcatheter ASD closure. Currently, robotic surgical techniques allow surgeons to close ASDs in a totally endoscopic fashion with a high success rate and a low complication rate. This study demonstrates the basic concepts and technique of robotic ASD closure. © The Author 2014. Published by Oxford University Press on behalf of the European Association for Cardio-Thoracic Surgery. All rights reserved.
Not Available
1994-01-01
This report has been prepared to satisfy Section 3156(b) of Public Law 101-189 (Reports in Connection with Permanent Closures of Department of Energy Defense Nuclear Facilities), which requires submittal of a Closure Report to Congress by the Secretary of Energy upon the permanent cessation of production operations at a US Department of Energy (DOE) defense nuclear facility (Watkins 1991). This closure report provides: (1) A complete survey of the environmental problems at the facility; (2) Budget quality data indicating the cost of environmental restoration and other remediation and cleanup efforts at the facility; (3) A proposed cleanup schedule.
Near-wall response in turbulent shear flows subjected to imposed unsteadiness
NASA Technical Reports Server (NTRS)
Mankbadi, Reda R.; Liu, Joseph T. C.
1992-01-01
Rapid-distortion theory is adapted to introduce a truly unsteady closure into a simple phenomenological turbulence model in order to describe the unsteady response of a turbulent wall layer exposed to a temporarily oscillating pressure gradient. The closure model is built by taking the ratio of turbulent shear stress to turbulent kinetic energy to be a function of the effective strain. The latter accounts for the history of the flow. The computed unsteady velocity fluctuations and modulated turbulent stresses compare favorably in the 'non-quasi-steady' frequency range, where quasi-steady assumptions would fail. This suggests that the concept of rapid distortion is especially appropriate for unsteady flows. This paper forms the basis for acoustical studies of the problem to be reported elsewhere.
Progress in turbulence modeling for complex flow fields including effects of compressibility
NASA Technical Reports Server (NTRS)
Wilcox, D. C.; Rubesin, M. W.
1980-01-01
Two second-order-closure turbulence models were devised that are suitable for predicting properties of complex turbulent flow fields in both incompressible and compressible fluids. One model is of the "two-equation" variety in which closure is accomplished by introducing an eddy viscosity which depends on both a turbulent mixing energy and a dissipation rate per unit energy, that is, a specific dissipation rate. The other model is a "Reynolds stress equation" (RSE) formulation in which all components of the Reynolds stress tensor and turbulent heat-flux vector are computed directly and are scaled by the specific dissipation rate. Computations based on these models are compared with measurements for the following flow fields: (a) low speed, high Reynolds number channel flows with plane strain or uniform shear; (b) equilibrium turbulent boundary layers with and without pressure gradients or effects of compressibility; and (c) flow over a convex surface with and without a pressure gradient.
New dynamical mean-field dynamo theory and closure approach.
Blackman, Eric G; Field, George B
2002-12-23
We develop a new nonlinear mean field dynamo theory that couples field growth to the time evolution of the magnetic helicity and the turbulent electromotive force, E. We show that the difference between kinetic and current helicities emerges naturally as the growth driver when the time derivative of E is coupled into the theory. The solutions predict significant field growth in a kinematic phase and a saturation rate/strength that is magnetic Reynolds number dependent/independent in agreement with numerical simulations. The amplitude of early time oscillations provides a diagnostic for the closure.
NASA Astrophysics Data System (ADS)
Corsini, A.; Rispoli, F.; Santoriello, A.; Tezduyar, T. E.
2006-09-01
Recent advances in turbulence modeling brought more and more sophisticated turbulence closures (e.g. k-ɛ, k-ɛ - v 2- f, Second Moment Closures), where the governing equations for the model parameters involve advection, diffusion and reaction terms. Numerical instabilities can be generated by the dominant advection or reaction terms. Classical stabilized formulations such as the Streamline Upwind/Petrov Galerkin (SUPG) formulation (Brook and Hughes, comput methods Appl Mech Eng 32:199 255, 1982; Hughes and Tezduyar, comput methods Appl Mech Eng 45: 217 284, 1984) are very well suited for preventing the numerical instabilities generated by the dominant advection terms. A different stabilization however is needed for instabilities due to the dominant reaction terms. An additional stabilization term, called the diffusion for reaction-dominated (DRD) term, was introduced by Tezduyar and Park (comput methods Appl Mech Eng 59:307 325, 1986) for that purpose and improves the SUPG performance. In recent years a new class of variational multi-scale (VMS) stabilization (Hughes, comput methods Appl Mech Eng 127:387 401, 1995) has been introduced, and this approach, in principle, can deal with advection diffusion reaction equations. However, it was pointed out in Hanke (comput methods Appl Mech Eng 191:2925 2947) that this class of methods also need some improvement in the presence of high reaction rates. In this work we show the benefits of using the DRD operator to enhance the core stabilization techniques such as the SUPG and VMS formulations. We also propose a new operator called the DRDJ (DRD with the local variation jump) term, targeting the reduction of numerical oscillations in the presence of both high reaction rates and sharp solution gradients. The methods are evaluated in the context of two stabilized methods: the classical SUPG formulation and a recently-developed VMS formulation called the V-SGS (Corsini et al. comput methods Appl Mech Eng 194:4797 4823, 2005
Aspects of Turbulent / Non-Turbulent Interfaces
NASA Technical Reports Server (NTRS)
Bisset, D. K.; Hunt, J. C. R.; Rogers, M. M.; Koen, Dennis (Technical Monitor)
1999-01-01
A distinct boundary between turbulent and non-turbulent regions in a fluid of otherwise constant properties is found in many laboratory and engineering turbulent flows, including jets, mixing layers, boundary layers and wakes. Generally, the flow has mean shear in at least one direction within t he turbulent zone, but the non-turbulent zones have no shear (adjacent laminar shear is a different case, e.g. transition in a boundary layer). There may be purely passive differences between the turbulent and non-turbulent zones, e.g. small variations in temperature or scalar concentration, for which turbulent mixing is an important issue. The boundary has several major characteristics of interest for the present study. Firstly, the boundary advances into the non-turbulent fluid, or in other words, nonturbulent fluid is entrained. Secondly, the change in turbulence properties across the boundary is remarkably abrupt; strong turbulent motions come close to the nonturbulent fluid, promoting entrainment. Thirdly, the boundary is irregular with a continually changing convoluted shape, which produces statistical intermittency. Its shape is contorted at all scales of the turbulent motion.
Turbulence and turbulent mixing in natural fluids
NASA Astrophysics Data System (ADS)
Gibson, Carl H.
2010-12-01
Turbulence and turbulent mixing in natural fluids begin with big bang turbulence powered by spinning combustible combinations of Planck particles and Planck antiparticles. Particle prograde accretions on a spinning pair release 42% of the particle rest mass energy to produce more fuel for turbulent combustion. Negative viscous stresses and negative turbulence stresses work against gravity, extracting mass-energy and space-time from the vacuum. Turbulence mixes cooling temperatures until strong-force viscous stresses freeze out turbulent mixing patterns as the first fossil turbulence. Cosmic microwave background temperature anisotropies show big bang turbulence fossils along with fossils of weak plasma turbulence triggered as plasma photon-viscous forces permitting gravitational fragmentation on supercluster to galaxy mass scales. Turbulent morphologies and viscous-turbulent lengths appear as linear gas-protogalaxy-clusters in the Hubble ultra-deep field at z~7. Protogalaxies fragment into Jeans mass clumps of primordial-gas planets at decoupling: the dark matter of galaxies. Shortly after the plasma-to-gas transition, planet mergers produce stars that explode on overfeeding to fertilize and distribute the first life.
Lagrangian statistics in laboratory 2D turbulence
NASA Astrophysics Data System (ADS)
Xia, Hua; Francois, Nicolas; Punzmann, Horst; Shats, Michael
2014-05-01
Turbulent mixing in liquids and gases is ubiquitous in nature and industrial flows. Understanding statistical properties of Lagrangian trajectories in turbulence is crucial for a range of problems such as spreading of plankton in the ocean, transport of pollutants, etc. Oceanic data on trajectories of the free-drifting instruments, indicate that the trajectory statistics can often be described by a Lagrangian integral scale. Turbulence however is a state of a flow dominated by a hierarchy of scales, and it is not clear which of these scales mostly affect particle dispersion. Moreover, coherent structures often coexist with turbulence in laboratory experiments [1]. The effect of coherent structures on particle dispersion in turbulent flows is not well understood. Recent progress in scientific imaging and computational power made it possible to tackle this problem experimentally. In this talk, we report the analysis of the higher order Lagrangian statistics in laboratory two-dimensional turbulence. Our results show that fluid particle dispersion is diffusive and it is determined by a single measurable Lagrangian scale related to the forcing scale [2]. Higher order moments of the particle dispersion show strong self-similarity in fully developed turbulence [3]. Here we introduce a new dispersion law that describes single particle dispersion during the turbulence development [4]. These results offer a new way of predicting dispersion in turbulent flows in which one of the low energy scales are persistent. It may help better understanding of drifter Lagrangian statistics in the regions of the ocean where small scale coherent eddies are present [5]. Reference: 1. H. Xia, H. Punzmann, G. Falkovich and M. Shats, Physical Review Letters, 101, 194504 (2008) 2. H. Xia, N. Francois, H. Punzmann, and M. Shats, Nature Communications, 4, 2013 (2013) 3. R. Ferrari, A.J. Manfroi , W.R. Young, Physica D 154 111 (2001) 4. H. Xia, N. Francois, H. Punzmann and M. Shats, submitted (2014
NASA Technical Reports Server (NTRS)
Kim, S.-W.; Chen, C.-P.
1989-01-01
A multiple-time-scale turbulence model of a single point closure and a simplified split-spectrum method is presented. In the model, the effect of the ratio of the production rate to the dissipation rate on eddy viscosity is modeled by use of the multiple-time-scales and a variable partitioning of the turbulent kinetic energy spectrum. The concept of a variable partitioning of the turbulent kinetic energy spectrum and the rest of the model details are based on the previously reported algebraic stress turbulence model. Example problems considered include: a fully developed channel flow, a plane jet exhausting into a moving stream, a wall jet flow, and a weakly coupled wake-boundary layer interaction flow. The computational results compared favorably with those obtained by using the algebraic stress turbulence model as well as experimental data. The present turbulence model, as well as the algebraic stress turbulence model, yielded significantly improved computational results for the complex turbulent boundary layer flows, such as the wall jet flow and the wake boundary layer interaction flow, compared with available computational results obtained by using the standard kappa-epsilon turbulence model.
NASA Technical Reports Server (NTRS)
Kim, S.-W.; Chen, C.-P.
1989-01-01
A multiple-time-scale turbulence model of a single point closure and a simplified split-spectrum method is presented. In the model, the effect of the ratio of the production rate to the dissipation rate on eddy viscosity is modeled by use of the multiple-time-scales and a variable partitioning of the turbulent kinetic energy spectrum. The concept of a variable partitioning of the turbulent kinetic energy spectrum and the rest of the model details are based on the previously reported algebraic stress turbulence model. Example problems considered include: a fully developed channel flow, a plane jet exhausting into a moving stream, a wall jet flow, and a weakly coupled wake-boundary layer interaction flow. The computational results compared favorably with those obtained by using the algebraic stress turbulence model as well as experimental data. The present turbulence model, as well as the algebraic stress turbulence model, yielded significantly improved computational results for the complex turbulent boundary layer flows, such as the wall jet flow and the wake boundary layer interaction flow, compared with available computational results obtained by using the standard kappa-epsilon turbulence model.
MEANS: python package for Moment Expansion Approximation, iNference and Simulation.
Fan, Sisi; Geissmann, Quentin; Lakatos, Eszter; Lukauskas, Saulius; Ale, Angelique; Babtie, Ann C; Kirk, Paul D W; Stumpf, Michael P H
2016-09-15
Many biochemical systems require stochastic descriptions. Unfortunately these can only be solved for the simplest cases and their direct simulation can become prohibitively expensive, precluding thorough analysis. As an alternative, moment closure approximation methods generate equations for the time-evolution of the system's moments and apply a closure ansatz to obtain a closed set of differential equations; that can become the basis for the deterministic analysis of the moments of the outputs of stochastic systems. We present a free, user-friendly tool implementing an efficient moment expansion approximation with parametric closures that integrates well with the IPython interactive environment. Our package enables the analysis of complex stochastic systems without any constraints on the number of species and moments studied and the type of rate laws in the system. In addition to the approximation method our package provides numerous tools to help non-expert users in stochastic analysis. https://github.com/theosysbio/means m.stumpf@imperial.ac.uk or e.lakatos13@imperial.ac.uk Supplementary data are available at Bioinformatics online. © The Author 2016. Published by Oxford University Press.
MEANS: python package for Moment Expansion Approximation, iNference and Simulation
Fan, Sisi; Geissmann, Quentin; Lakatos, Eszter; Lukauskas, Saulius; Ale, Angelique; Babtie, Ann C.; Kirk, Paul D. W.; Stumpf, Michael P. H.
2016-01-01
Motivation: Many biochemical systems require stochastic descriptions. Unfortunately these can only be solved for the simplest cases and their direct simulation can become prohibitively expensive, precluding thorough analysis. As an alternative, moment closure approximation methods generate equations for the time-evolution of the system’s moments and apply a closure ansatz to obtain a closed set of differential equations; that can become the basis for the deterministic analysis of the moments of the outputs of stochastic systems. Results: We present a free, user-friendly tool implementing an efficient moment expansion approximation with parametric closures that integrates well with the IPython interactive environment. Our package enables the analysis of complex stochastic systems without any constraints on the number of species and moments studied and the type of rate laws in the system. In addition to the approximation method our package provides numerous tools to help non-expert users in stochastic analysis. Availability and implementation: https://github.com/theosysbio/means Contacts: m.stumpf@imperial.ac.uk or e.lakatos13@imperial.ac.uk Supplementary information: Supplementary data are available at Bioinformatics online. PMID:27153663
NASA Astrophysics Data System (ADS)
Milam, David; Murray, James E.; Estabrook, Kent G.; Boley, Charles D.; Sell, Walter D.; Nielsen, Norman D.; Kirkwood, R. K.; Zakharenkov, Yuri A.; Afeyan, Bedros B.
1999-07-01
Spatial-filter pinholes and knife-edge samples were irradiated in vacuum by 1053-nm, 5-20 ns pulses at intensities to 500 GW/cm2. The knife-edge samples were fabricated of plastic, carbon, aluminum, stainless steel, molybdenum, tantalum, gold, and an absorbing glass. Time- resolved two-beam interferometry with a 40-ns probe pulse was used to observe phase shifts in the expanding laser- induced plasma. For al of these materials, at any time during square-pulse irradiation, the phase shift fell exponentially with distance from the edge of the sample.. The expansion was characterized by the propagation velocity V2(pi ) of the contour for a 2(pi) phase shift. To within experimental error, V2(pi ) was constant during irradiation at a particular intensity, and it increased linearly with intensity for intensities < 300 GW/cm2. For metal samples V2(pi ) exhibited an approximate M-0.5 dependence where M is the atomic mass. Plasmas of plastic, carbon, and absorbing glass produced larger phase shifts, and expanded more rapidly, than plasmas of heavy metals. The probe beam and interferometer were also used to observe the closing of pinholes. With planar pinholes, accumulation of on-axis plasma was observed along with the advance of plasma away from the edge of the hole. On-axis closure was not observed in square, 4-leaf pinholes.
Neglected ends: clinical ethics consultation and the prospects for closure.
Fiester, Autumn
2015-01-01
Clinical ethics consultations (CECs) are sometimes deemed complete at the moment when the consultants make a recommendation. In CECs that involve actual ethical conflict, this view of a consult's endpoint runs the risk of overemphasizing the conflict's resolution at the expense of the consult's process, which can have deleterious effects on the various parties in the conflict. This overly narrow focus on reaching a decision or recommendation in consults that involve profound moral disagreement can result in two types of adverse, lingering sequelae: moral distress or negative moral emotions. The problem, succinctly named, is that such consults have insufficient "closure" for patients, families, and providers. To promote closure, and avoid the ills of moral distress and the moral emotions, I argue that CECs need to prioritize assisted conversation between the different stakeholders in these conflicts, what is often referred to as "bioethics mediation."
Turbulent Transport in a Three-dimensional Solar Wind
NASA Astrophysics Data System (ADS)
Shiota, D.; Zank, G. P.; Adhikari, L.; Hunana, P.; Telloni, D.; Bruno, R.
2017-03-01
Turbulence in the solar wind can play essential roles in the heating of coronal and solar wind plasma and the acceleration of the solar wind and energetic particles. Turbulence sources are not well understood and thought to be partly enhanced by interaction with the large-scale inhomogeneity of the solar wind and the interplanetary magnetic field and/or transported from the solar corona. To investigate the interaction with background inhomogeneity and the turbulence sources, we have developed a new 3D MHD model that includes the transport and dissipation of turbulence using the theoretical model of Zank et al. We solve for the temporal and spatial evolution of three moments or variables, the energy in the forward and backward fluctuating modes and the residual energy and their three corresponding correlation lengths. The transport model is coupled to our 3D model of the inhomogeneous solar wind. We present results of the coupled solar wind-turbulence model assuming a simple tilted dipole magnetic configuration that mimics solar minimum conditions, together with several comparative intermediate cases. By considering eight possible solar wind and turbulence source configurations, we show that the large-scale solar wind and IMF inhomogeneity and the strength of the turbulence sources significantly affect the distribution of turbulence in the heliosphere within 6 au. We compare the predicted turbulence distribution results from a complete solar minimum model with in situ measurements made by the Helios and Ulysses spacecraft, finding that the synthetic profiles of the turbulence intensities show reasonable agreement with observations.
EDQNM closure: A homogeneous simulation to support it. A quasi-homogeneous simulation to disprove it
NASA Technical Reports Server (NTRS)
Bertoglio, J. P.; Squires, K.; Ferziger, J. H.
1987-01-01
It is known that two-point closures are useful tools for understanding and predicting turbulence. Among the various closures, the Eddy Damped Quasi-Normal Markovian (EDQNM) approach is one of the simplest and, at the same time, most useful. Direct numerical simulations (DNS) can provide information that can be used to test the validity of two-point theories. It is the purpose of the present work to use DNS to validate, or improve upon, EDQNM. A case was selected for which EDQNM is known to give satisfactory results: homogeneous isotropic turbulence. Quantities were then evaluated which may be used to test the assumptions of two-point closure approximations: spectral Lagrangian time scales. The goal was to make a careful and refined study to validate the EDQNM theory. A reference case was built for which EDQNM is likely to give poor results. An attempt to generate a quasi-homogeneous turbulent field containing organized structures, was built by artifically injecting them in the initial conditions. The results of direct simulations using such initial conditions are expected to provide a challenge for EDQNM since this kind of field is simple enough to allow comparisons with two-point theories, but at the same time contains coherent structures which cannot be expected to be accurately accounted for by closures based on expansions about Gaussianity.
Closure and Sealing Design Calculation
T. Lahnalampi; J. Case
2005-08-26
The purpose of the ''Closure and Sealing Design Calculation'' is to illustrate closure and sealing methods for sealing shafts, ramps, and identify boreholes that require sealing in order to limit the potential of water infiltration. In addition, this calculation will provide a description of the magma that can reduce the consequences of an igneous event intersecting the repository. This calculation will also include a listing of the project requirements related to closure and sealing. The scope of this calculation is to: summarize applicable project requirements and codes relating to backfilling nonemplacement openings, removal of uncommitted materials from the subsurface, installation of drip shields, and erecting monuments; compile an inventory of boreholes that are found in the area of the subsurface repository; describe the magma bulkhead feature and location; and include figures for the proposed shaft and ramp seals. The objective of this calculation is to: categorize the boreholes for sealing by depth and proximity to the subsurface repository; develop drawing figures which show the location and geometry for the magma bulkhead; include the shaft seal figures and a proposed construction sequence; and include the ramp seal figure and a proposed construction sequence. The intent of this closure and sealing calculation is to support the License Application by providing a description of the closure and sealing methods for the Safety Analysis Report. The closure and sealing calculation will also provide input for Post Closure Activities by describing the location of the magma bulkhead. This calculation is limited to describing the final configuration of the sealing and backfill systems for the underground area. The methods and procedures used to place the backfill and remove uncommitted materials (such as concrete) from the repository and detailed design of the magma bulkhead will be the subject of separate analyses or calculations. Post-closure monitoring will not
A Multiscale Morphing Continuum Description for Turbulence
NASA Astrophysics Data System (ADS)
Chen, James; Wonnell, Louis
2015-11-01
Turbulence is a flow physics phenomena invlolving multiple length scales. The popular Navier- Stokes equations only possess one length/time scale. Therefore, extremely fine mesh is needed for DNS attempting to resolve the small scale motion, which comes with a burden of excessive computational cost. For practical application with complex geometries, the research society rely on RANS and LES, which requre turbulence model or subgrid scale (SGS) model for closure problems. Different models not only lead to different results but usually are invalidated on solid physical grounds, such as objectivity and entropy principle.The Morphing Continuum Theory (MCT) is a high-order continuum theory formulated under the framework of thermalmechanics for physics phenomena involving microstructure. In this study, a theoretical perspective for the multiscale nature of the Morphing Continuum Theory is connected with the multiscale nature of turbulence physics. The kinematics, balance laws, constitutive equations and a Morphing Continuum description of turbulence are introduced. The equations were numerically implemented for a zero pressure gradient flat plate. The simulations are compate with the laminar, transitional and turbulence cases.
Turbulence dynamics in unsteady atmospheric flows
NASA Astrophysics Data System (ADS)
Momen, Mostafa; Bou-Zeid, Elie
2016-11-01
Unsteady pressure-gradient forcing in geophysical flows challenges the quasi-steady state assumption, and can strongly impact the mean wind and higher-order turbulence statistics. Under such conditions, it is essential to understand when turbulence is in quasi-equilibrium, and what are the implications of unsteadiness on flow characteristics. The present study focuses on the unsteady atmospheric boundary layer (ABL) where pressure gradient, Coriolis, buoyancy, and friction forces interact. We perform a suite of LES with variable pressure-gradient. The results indicate that the dynamics are mainly controlled by the relative magnitudes of three time scales: Tinertial, Tturbulence, and Tforcing. It is shown that when Tf Tt , the turbulence is no longer in a quasi-equilibrium state due to highly complex mean-turbulence interactions; consequently, the log-law and turbulence closures are no longer valid in these conditions. However, for longer and, surprisingly, for shorter forcing times, quasi-equilibrium is maintained. Varying the pressure gradient in the presence of surface buoyancy fluxes primarily influences the buoyant destruction in the stable ABLs, while under unstable conditions it mainly influences the transport terms. NSF-PDM under AGS-10266362. Cooperative Institute for Climate Science, NOAA-Princeton University under NA08OAR4320752. Simulations performed at NCAR, and Della server at Princeton University.
Spectral formulation of turbulent flame speed with consideration of hydrodynamic instability.
Chaudhuri, Swetaprovo; Akkerman, V'yacheslav; Law, Chung K
2011-08-01
Effects of Darrieus-Landau (DL) instability on the structure and propagation of turbulent premixed flame fronts are considered. By first hypothesizing separation of time scales of instability and turbulence, we estimate whether the instability can develop in the presence of turbulence of given flow rms-velocity and integral length scale. As a result, we modify the standard turbulent premixed combustion regime diagram by introducing new boundaries, limiting the domain where the instability influences the global flame shape and speed. Based on this analysis, a "turbulence-induced DL cutoff" as a function of turbulence and instability parameters is introduced, which when combined with a turbulent flame speed without DL instability yields the turbulent flame speed accounting for the instability. The consumption turbulent flame speed for no DL instability is formulated from the spectral closure of the G equation, thus accounting for the scale-dependent "turbulent" nature of the problem. Finally, an analytical form of the turbulent flame speed is derived, which is found to agree well with the corresponding experimentally measured turbulent flame speed from literature over wide ranges of normalized turbulence intensities and length scales.
Understanding the basis of space closure in Orthodontics for a more efficient orthodontic treatment
Ribeiro, Gerson Luiz Ulema; Jacob, Helder B.
2016-01-01
ABSTRACT Introduction: Space closure is one of the most challenging processes in Orthodontics and requires a solid comprehension of biomechanics in order to avoid undesirable side effects. Understanding the biomechanical basis of space closure better enables clinicians to determine anchorage and treatment options. In spite of the variety of appliance designs, space closure can be performed by means of friction or frictionless mechanics, and each technique has its advantages and disadvantages. Friction mechanics or sliding mechanics is attractive because of its simplicity; the space site is closed by means of elastics or coil springs to provide force, and the brackets slide on the orthodontic archwire. On the other hand, frictionless mechanics uses loop bends to generate force to close the space site, allowing differential moments in the active and reactive units, leading to a less or more anchorage control, depending on the situation. Objective: This article will discuss various theoretical aspects and methods of space closure based on biomechanical concepts. PMID:27275623
Disturbance Dynamics in Transitional and Turbulent Flows
NASA Technical Reports Server (NTRS)
Grosch, Chester E.
1999-01-01
In order to expand the predictive capability of single-point turbulence closure models to account for the early-stage transition regime, a methodology for the formulation and calibration of model equations for the ensemble-averaged disturbance kinetic energy and energy dissipation rate is presented. First the decay of laminar disturbances and turbulence in mean shear-free flows is studied. In laminar flows, such disturbances are linear superpositions of modes governed by the Orr-Sommerfeld equation. In turbulent flows, disturbances are described through transport equations for representative mean quantities. The link between a description based on a deterministic evolution equation and a probability based mean transport equation is established. Because an uncertainty in initial conditions exists in the laminar as well as the turbulent regime, a probability distribution must be defined even in the laminar case. Using this probability distribution, it is shown that the exponential decay of the linear modes in the laminar regime can be related to a power law decay of both the (ensemble) mean disturbance kinetic energy and the dissipation rate. The evolution of these mean disturbance quantities is then described by transport equations similar to those for the corresponding turbulent decaying flow. Second, homogeneous shear flow, where disturbances can be described by rapid distortion theory (RDT), is studied. The relationship between RDT and linear stability theory is exploited in order to obtain a closed set of modeled equations. The linear disturbance equations are solved directly so that the numerical simulation yields a database from which the closure coefficients in the ensemble-averaged disturbance equations can be determined.
B.B. Rokhman
2007-09-15
This article considers the Eulerian continuum description of turbulent transfer of momentum and moment of momentum in a solid phase on the basis of the equations of transfer of the second and third moments of pulsations of the linear and angular velocities of particles. The pulsating characteristics of a gas are computed using the two-parameter model of turbulence generalized to the case of gas-dispersed turbulent flows.
NASA Astrophysics Data System (ADS)
Shatskii, I. P.; Makoviichuk, N. V.
2011-05-01
The problem of closure of collinear cracks during bending of a shallow shell is considered within the framework of the Kirchhoff theory. Crack closure is described using the model of contact along a line on one of the shell faces. Strain and moment intensity factors and fracture load are studied as functions of shell curvature and defect location, and the distribution of contact forces along the cracks is investigated.
Turbulence Modeling Effects on the Prediction of Equilibrium States of Buoyant Shear Flows
NASA Technical Reports Server (NTRS)
Zhao, C. Y.; So, R. M. C.; Gatski, T. B.
2001-01-01
The effects of turbulence modeling on the prediction of equilibrium states of turbulent buoyant shear flows were investigated. The velocity field models used include a two-equation closure, a Reynolds-stress closure assuming two different pressure-strain models and three different dissipation rate tensor models. As for the thermal field closure models, two different pressure-scrambling models and nine different temperature variance dissipation rate, Epsilon(0) equations were considered. The emphasis of this paper is focused on the effects of the Epsilon(0)-equation, of the dissipation rate models, of the pressure-strain models and of the pressure-scrambling models on the prediction of the approach to equilibrium turbulence. Equilibrium turbulence is defined by the time rate (if change of the scaled Reynolds stress anisotropic tensor and heat flux vector becoming zero. These conditions lead to the equilibrium state parameters. Calculations show that the Epsilon(0)-equation has a significant effect on the prediction of the approach to equilibrium turbulence. For a particular Epsilon(0)-equation, all velocity closure models considered give an equilibrium state if anisotropic dissipation is accounted for in one form or another in the dissipation rate tensor or in the Epsilon(0)-equation. It is further found that the models considered for the pressure-strain tensor and the pressure-scrambling vector have little or no effect on the prediction of the approach to equilibrium turbulence.
Turbulence modeling for hypersonic flows
NASA Technical Reports Server (NTRS)
Marvin, J. G.; Coakley, T. J.
1989-01-01
Turbulence modeling for high speed compressible flows is described and discussed. Starting with the compressible Navier-Stokes equations, methods of statistical averaging are described by means of which the Reynolds-averaged Navier-Stokes equations are developed. Unknown averages in these equations are approximated using various closure concepts. Zero-, one-, and two-equation eddy viscosity models, algebraic stress models and Reynolds stress transport models are discussed. Computations of supersonic and hypersonic flows obtained using several of the models are discussed and compared with experimental results. Specific examples include attached boundary layer flows, shock wave boundary layer interactions and compressible shear layers. From these examples, conclusions regarding the status of modeling and recommendations for future studies are discussed.
Inquiry-Based Science: Turning Teachable Moments into Learnable Moments
ERIC Educational Resources Information Center
Haug, Berit S.
2014-01-01
This study examines how an inquiry-based approach to teaching and learning creates teachable moments that can foster conceptual understanding in students, and how teachers capitalize upon these moments. Six elementary school teachers were videotaped as they implemented an integrated inquiry-based science and literacy curriculum in their…
Inquiry-Based Science: Turning Teachable Moments into Learnable Moments
ERIC Educational Resources Information Center
Haug, Berit S.
2014-01-01
This study examines how an inquiry-based approach to teaching and learning creates teachable moments that can foster conceptual understanding in students, and how teachers capitalize upon these moments. Six elementary school teachers were videotaped as they implemented an integrated inquiry-based science and literacy curriculum in their…
Turbulence radiation interaction modeling in hydrocarbon pool fire simulations
BURNS,SHAWN P.
1999-12-01
The importance of turbulent fluctuations in temperature and species concentration in thermal radiation transport modeling for combustion applications is well accepted by the radiation transport and combustion communities. A number of experimental and theoretical studies over the last twenty years have shown that fluctuations in the temperature and species concentrations may increase the effective emittance of a turbulent flame by as much as 50% to 300% over the value that would be expected from the mean temperatures and concentrations. With the possibility of such a large effect on the principal mode of heat transfer from a fire, it is extremely important for fire modeling efforts that turbulence radiation interaction be well characterized and possible modeling approaches understood. Toward this end, this report seeks to accomplish three goals. First, the principal turbulence radiation interaction closure terms are defined. Second, an order of magnitude analysis is performed to understand the relative importance of the various closure terms. Finally, the state of the art in turbulence radiation interaction closure modeling is reviewed. Hydrocarbon pool fire applications are of particular interest in this report and this is the perspective from which this review proceeds. Experimental and theoretical analysis suggests that, for this type of heavily sooting flame, the turbulent radiation interaction effect is dominated by the nonlinear dependence of the Planck function on the temperature. Additional effects due to the correlation between turbulent fluctuations in the absorptivity and temperature may be small relative to the Planck function effect for heavily sooting flames. This observation is drawn from a number of experimental and theoretical discussions. Nevertheless, additional analysis and data is needed to validate this observation for heavily sooting buoyancy dominated plumes.
Multigrid acceleration and turbulence models for computations of 3D turbulent jets in crossflow
NASA Technical Reports Server (NTRS)
Demuren, A. O.
1991-01-01
A multigrid method is presented for the calculation of three-dimensional turbulent jets in crossflow. Turbulence closure is achieved with either the standard k-epsilon model or a Reynolds Stress Model (RSM). Multigrid acceleration enables convergence rates which are far superior to that for a single grid method. With the k-epsilon model the rate approaches that for laminar flow, but with RSM it is somewhat slower. The increased stiffness of the system of equations in the latter may be responsible. Computed results with both turbulence models are compared with experimental data for a pair of opposed jets in crossflow. Both models yield reasonable agreement with mean flow velocity but RSM yields better prediction of the Reynolds stresses.
NASA Astrophysics Data System (ADS)
Venaille, Antoine; Nadeau, Louis-Philippe; Vallis, Geoffrey
2014-12-01
We investigate the non-linear equilibration of a two-layer quasi-geostrophic flow in a channel with an initial eastward baroclinically unstable jet in the upper layer, paying particular attention to the role of bottom friction. In the limit of low bottom friction, classical theory of geostrophic turbulence predicts an inverse cascade of kinetic energy in the horizontal with condensation at the domain scale and barotropization in the vertical. By contrast, in the limit of large bottom friction, the flow is dominated by ribbons of high kinetic energy in the upper layer. These ribbons correspond to meandering jets separating regions of homogenized potential vorticity. We interpret these results by taking advantage of the peculiar conservation laws satisfied by this system: the dynamics can be recast in such a way that the initial eastward jet in the upper layer appears as an initial source of potential vorticity levels in the upper layer. The initial baroclinic instability leads to a turbulent flow that stirs this potential vorticity field while conserving the global distribution of potential vorticity levels. Statistical mechanical theory of the 1 1/2 layer quasi-geostrophic model predicts the formation of two regions of homogenized potential vorticity separated by a minimal interface. We explain that cascade phenomenology leads to the same result. We then show that the dynamics of the ribbons results from a competition between a tendency to reach the equilibrium state and baroclinic instability that induces meanders of the interface. These meanders intermittently break and induce potential vorticity mixing, but the interface remains sharp throughout the flow evolution. We show that for some parameter regimes, the ribbons act as a mixing barrier which prevents relaxation toward equilibrium, favouring the emergence of multiple zonal (eastward) jets.
Toward a Turbulence Constitutive Relation for Rotating Flows
NASA Technical Reports Server (NTRS)
Ristorcelli, J. R.
1996-01-01
In rapidly rotating turbulent flows the largest scales of the motion are in approximate geostrophic balance. Single-point turbulence closures, in general, cannot attain a geostrophic balance. This article addresses and resolves the possibility of constitutive relation procedures for single-point second order closures for a specific class of rotating or stratified flows. Physical situations in which the geostrophic balance is attained are described. Closely related issues of frame-indifference, horizontal nondivergence, Taylor-Proudman theorem and two-dimensionality are, in the context of both the instantaneous and averaged equations, discussed. It is shown, in the absence of vortex stretching along the axis of rotation, that turbulence is frame-indifferent. A derivation and discussion of a geostrophic constraint which the prognostic equations for second-order statistics must satisfy for turbulence approaching a frame-indifferent limit is given. These flow situations, which include rotating and nonrotating stratified flows, are slowly evolving flows in which the constitutive relation procedures are useful. A nonlinear non-constant coefficient representation for the rapid-pressure strain covariance appearing in the Reynolds stress and heat flux equations consistent with the geostrophic balance is described. The rapid-pressure strain model coefficients are not constants determined by numerical optimization but are functions of the state of the turbulence as parameterized by the Reynolds stresses and the turbulent heat fluxes. The functions are valid for all states of the turbulence attaining their limiting values only when a limit state is achieved. These issues are relevant to strongly vortical flows as well as flows such as the planetary boundary layers, in which there is a transition from a three-dimensional shear driven turbulence to a geostrophic or horizontal turbulence.
Simulation and modeling of homogeneous, compressed turbulence
Wu, C.T.; Ferziger, J.H.; Chapman, D.R.
1985-05-01
Low Reynolds number homogeneous turbulence undergoing low Mach number isotropic and one-dimensional compression was simulated by numerically solving the Navier-Stokes equations. The numerical simulations were performed on a CYBER 205 computer using a 64 x 64 x 64 mesh. A spectral method was used for spatial differencing and the second-order Runge-Kutta method for time advancement. A variety of statistical information was extracted from the computed flow fields. These include three-dimensional energy and dissipation spectra, two-point velocity correlations, one-dimensional energy spectra, turbulent kinetic energy and its dissipation rate, integral length scales, Taylor microscales, and Kolmogorov length scale. Results from the simulated flow fields were used to test one-point closure, two-equation models. A new one-point-closure, three-equation turbulence model which accounts for the effect of compression is proposed. The new model accurately calculates four types of flows (isotropic decay, isotropic compression, one-dimensional compression, and axisymmetric expansion flows) for a wide range of strain rates.
Simulation and modeling of homogeneous, compressed turbulence
NASA Technical Reports Server (NTRS)
Wu, C. T.; Ferziger, J. H.; Chapman, D. R.
1985-01-01
Low Reynolds number homogeneous turbulence undergoing low Mach number isotropic and one-dimensional compression was simulated by numerically solving the Navier-Stokes equations. The numerical simulations were performed on a CYBER 205 computer using a 64 x 64 x 64 mesh. A spectral method was used for spatial differencing and the second-order Runge-Kutta method for time advancement. A variety of statistical information was extracted from the computed flow fields. These include three-dimensional energy and dissipation spectra, two-point velocity correlations, one-dimensional energy spectra, turbulent kinetic energy and its dissipation rate, integral length scales, Taylor microscales, and Kolmogorov length scale. Results from the simulated flow fields were used to test one-point closure, two-equation models. A new one-point-closure, three-equation turbulence model which accounts for the effect of compression is proposed. The new model accurately calculates four types of flows (isotropic decay, isotropic compression, one-dimensional compression, and axisymmetric expansion flows) for a wide range of strain rates.
Observations of turbulent mixing in a shallow coral reef
NASA Astrophysics Data System (ADS)
Huang, Z. C.
2016-02-01
In situ measurements of waves, currents, and turbulence are presented to study turbulence properties within a depression that is surrounded by multiple coral-reef colonies in a fringing reef in Hobihu, Nan-Wan Bay, southern Taiwan. Turbulence was measured using a dual velocimetry technique, and wave bias contamination in the turbulence is controlled using ogive curve testing of the turbulent shear stress. The observed turbulent dissipation rate is approximately five times greater than simultaneous observations over the nearby sandy bottom site, which indicates stronger mixing within the coral reef than on sandy bottoms. Energetic downward momentum flux exists due to sweeping process; the turbulent kinetic energy is transported downward into the depression through the mechanisms of vertical turbulent transport and advection. The observed turbulent dissipation rate exceeds the shear production rate, which suggests that transport terms or other source terms might be important. The wake flow caused by the resistance force of coral colonies is examined. The form drag coefficient was estimated from the time-averaged alongshore linear momentum between two sites upstream and within the coral reef. The work done due to the form drag, which is termed the wake production, is found to strongly correlate and approximate well to the observed turbulent dissipation rate. The effects of waves and currents on the wake production are discussed. The observed TSS can be described well by classic turbulence closure model when the empirical stability function is adjusted. This study suggests that the complex canopy structure of multiple colonies and the coexistence of the wave-induced and current flows are significant factors for energetic turbulence in the coral reef, which could have positive effects to the health of the coral reefs.
RCRA closure of mixed waste impoundments
Blaha, F.J.; Greengard, T.C.; Arndt, M.B.
1989-11-01
A case study of a RCRA closure action at the Rocky Flats Plant is presented. Closure of the solar evaporation ponds involves removal and immobilization of a mixed hazardous/radioactive sludge, treatment of impounded water, groundwater monitoring, plume delineation, and collection and treatment of contaminated groundwater. The site closure is described within the context of regulatory negotiations, project schedules, risk assessment, clean versus dirty closure, cleanup levels, and approval of closure plans and reports. Lessons learned at Rocky Flats are summarized.
NASA Astrophysics Data System (ADS)
Kaufmann, A.; Moreau, M.; Simonin, O.; Helie, J.
2008-06-01
The purpose of this paper is to evaluate the accuracy of the mesoscopic approach proposed by Février et al. [P. Février, O. Simonin, K.D. Squires, Partitioning of particle velocities in gas-solid turbulent flows into a continuous field and a spatially uncorrelated random distribution: theoretical formalism and numerical study, J. Fluid Mech. 533 (2005) 1-46] by comparison against the Lagrangian approach for the simulation of an ensemble of non-colliding particles suspended in a decaying homogeneous isotropic turbulence given by DNS. The mesoscopic Eulerian approach involves to solve equations for a few particle PDF moments: number density, mesoscopic velocity, and random uncorrelated kinetic energy (RUE), derived from particle flow ensemble averaging conditioned by the turbulent fluid flow realization. In addition, viscosity and diffusivity closure assumptions are used to compute the unknown higher order moments which represent the mesoscopic velocity and RUE transport by the uncorrelated velocity component. A detailed comparison between the two approaches is carried out for two different values of the Stokes number based on the initial fluid Kolmogorov time scale, St=0.17 and 2.2. In order to perform reliable comparisons for the RUE local instantaneous distribution and for the mesoscopic kinetic energy spectrum, the error due to the computation method of mesoscopic quantities from Lagrangian simulation results is evaluated and minimized. A very good agreement is found between the mesoscopic Eulerian and Lagrangian predictions for the small particle Stokes number case corresponding to the smallest particle inertia. For larger particle inertia, a bulk viscous term is included in the mesoscopic velocity governing equation to avoid spurious spatial oscillation that may arise due to the inability of the numerical scheme to resolve sharp number density gradients. As a consequence, for St=2.2, particle number density and RUE spatial distribution predicted by the
Vingerhoets, P.; Avgoulea, M.; Bissell, M. L.; De Rydt, M.; Neyens, G.; Flanagan, K. T.; Billowes, J.; Cheal, B.; Mane, E.; Blaum, K.; Schug, M.; Brown, B. A.; Forest, D. H.; Tungate, G.; Geppert, Ch.; Noertershaeuser, W.; Honma, M.; Kowalska, M.; Kraemer, J.; Krieger, A.
2010-12-15
Measurements of the ground-state nuclear spins and magnetic and quadrupole moments of the copper isotopes from {sup 61}Cu up to {sup 75}Cu are reported. The experiments were performed at the CERN online isotope mass separator (ISOLDE) facility, using the technique of collinear laser spectroscopy. The trend in the magnetic moments between the N=28 and N=50 shell closures is reasonably reproduced by large-scale shell-model calculations starting from a {sup 56}Ni core. The quadrupole moments reveal a strong polarization of the underlying Ni core when the neutron shell is opened, which is, however, strongly reduced at N=40 due to the parity change between the pf and g orbits. No enhanced core polarization is seen beyond N=40. Deviations between measured and calculated moments are attributed to the softness of the {sup 56}Ni core and weakening of the Z=28 and N=28 shell gaps.
A turbulence model for pulsatile arterial flows.
Younis, B A; Berger, S A
2004-10-01
Difficulties in predicting the behavior of some high Reynolds number flows in the circulatory system stem in part from the severe requirements placed on the turbulence model chosen to close the time-averaged equations of fluid motion. In particular, the successful turbulence model is required to (a) correctly capture the "nonequilibrium" effects wrought by the interactions of the organized mean-flow unsteadiness with the random turbulence, (b) correctly reproduce the effects of the laminar-turbulent transitional behavior that occurs at various phases of the cardiac cycle, and (c) yield good predictions of the near-wall flow behavior in conditions where the universal logarithmic law of the wall is known to be not valid. These requirements are not immediately met by standard models of turbulence that have been developed largely with reference to data from steady, fully turbulent flows in approximate local equilibrium. The purpose of this paper is to report on the development of a turbulence model suited for use in arterial flows. The model is of the two-equation eddy-viscosity variety with dependent variables that are zero-valued at a solid wall and vary linearly with distance from it. The effects of transition are introduced by coupling this model to the local value of the intermittency and obtaining the latter from the solution of a modeled transport equation. Comparisons with measurements obtained in oscillatory transitional flows in circular tubes show that the model produces substantial improvements over existing closures. Further pulsatile-flow predictions, driven by a mean-flow wave form obtained in a diseased human carotid artery, indicate that the intermittency-modified model yields much reduced levels of wall shear stress compared to the original, unmodified model. This result, which is attributed to the rapid growth in the thickness of the viscous sublayer arising from the severe acceleration of systole, argues in favor of the use of the model for the
Morphological Moments of Binary Images
NASA Astrophysics Data System (ADS)
Lomov, N.; Sidyakin, S.
2017-05-01
The concept of morphological moments of binary images is introduced. Morphological moments can be used as a shape descriptor combining an integral width description of an object with a description of its spatial distribution. The relationship between the proposed descriptor and the disc cover of the figure is discussed and an exact analytical method for descriptor calculation is proposed within the continuous morphology framework. The approach is based on the approximation of the shape by a polygonal figure and the extraction of its medial representation in the form of the continuous skeleton and the radial function. The proposed method for calculation of morphological moments achieves high accuracy and it is computationally efficient. Experimentations have been conducted. Obtained results indicate that the morphological moments are a more informative and rich shape descriptor than the area of the disc cover. Application of morphological moments to the font recognition task improves the recognition quality.
NASA Astrophysics Data System (ADS)
Bolla, Michele; Farrace, Daniele; Wright, Yuri M.; Boulouchos, Konstantinos; Mastorakos, Epaminondas
2014-03-01
The influence of the turbulence-chemistry interaction (TCI) for n-heptane sprays under diesel engine conditions has been investigated by means of computational fluid dynamics (CFD) simulations. The conditional moment closure approach, which has been previously validated thoroughly for such flows, and the homogeneous reactor (i.e. no turbulent combustion model) approach have been compared, in view of the recent resurgence of the latter approaches for diesel engine CFD. Experimental data available from a constant-volume combustion chamber have been used for model validation purposes for a broad range of conditions including variations in ambient oxygen (8-21% by vol.), ambient temperature (900 and 1000 K) and ambient density (14.8 and 30 kg/m3). The results from both numerical approaches have been compared to the experimental values of ignition delay (ID), flame lift-off length (LOL), and soot volume fraction distributions. TCI was found to have a weak influence on ignition delay for the conditions simulated, attributed to the low values of the scalar dissipation relative to the critical value above which auto-ignition does not occur. In contrast, the flame LOL was considerably affected, in particular at low oxygen concentrations. Quasi-steady soot formation was similar; however, pronounced differences in soot oxidation behaviour are reported. The differences were further emphasised for a case with short injection duration: in such conditions, TCI was found to play a major role concerning the soot oxidation behaviour because of the importance of soot-oxidiser structure in mixture fraction space. Neglecting TCI leads to a strong over-estimation of soot oxidation after the end of injection. The results suggest that for some engines, and for some phenomena, the neglect of turbulent fluctuations may lead to predictions of acceptable engineering accuracy, but that a proper turbulent combustion model is needed for more reliable results.
Linearly exact parallel closures for slab geometry
NASA Astrophysics Data System (ADS)
Ji, Jeong-Young; Held, Eric D.; Jhang, Hogun
2013-08-01
Parallel closures are obtained by solving a linearized kinetic equation with a model collision operator using the Fourier transform method. The closures expressed in wave number space are exact for time-dependent linear problems to within the limits of the model collision operator. In the adiabatic, collisionless limit, an inverse Fourier transform is performed to obtain integral (nonlocal) parallel closures in real space; parallel heat flow and viscosity closures for density, temperature, and flow velocity equations replace Braginskii's parallel closure relations, and parallel flow velocity and heat flow closures for density and temperature equations replace Spitzer's parallel transport relations. It is verified that the closures reproduce the exact linear response function of Hammett and Perkins [Phys. Rev. Lett. 64, 3019 (1990)] for Landau damping given a temperature gradient. In contrast to their approximate closures where the vanishing viscosity coefficient numerically gives an exact response, our closures relate the heat flow and nonvanishing viscosity to temperature and flow velocity (gradients).
Fast-Tracking Colostomy Closures.
Nanavati, Aditya J; Prabhakar, Subramaniam
2015-12-01
There have been very few studies on applying fast-track principles to colostomy closures. We believe that outcome may be significantly improved with multimodal interventions in the peri-operative care of patients undergoing this procedure. A retrospective study was carried out comparing patients who had undergone colostomy closures by the fast-track and traditional care protocols at our centre. We intended to analyse peri-operative period and recovery in colostomy closures to confirm that fast-track surgery principles improved outcomes. Twenty-six patients in the fast-track arm and 24 patients in the traditional care arm had undergone colostomy closures. Both groups were comparable in terms of their baseline parameters. Patients in the fast-track group were ambulatory and accepted oral feeding earlier. There was a significant reduction in the duration of stay (4.73 ± 1.43 days vs. 7.21 ± 1.38 days, p = 0.0000). We did not observe a rise in complications or 30-day re-admissions. Fast-track surgery can safely be applied to colostomy closures. It shows earlier ambulation and reduction in length of hospital stay.
Chaos and Predictability of Homogeneous-Isotropic Turbulence
NASA Astrophysics Data System (ADS)
Boffetta, G.; Musacchio, S.
2017-08-01
We study the chaoticity and the predictability of a turbulent flow on the basis of high-resolution direct numerical simulations at different Reynolds numbers. We find that the Lyapunov exponent of turbulence, which measures the exponential separation of two initially close solutions of the Navier-Stokes equations, grows with the Reynolds number of the flow, with an anomalous scaling exponent, larger than the one obtained on dimensional grounds. For large perturbations, the error is transferred to larger, slower scales, where it grows algebraically generating an "inverse cascade" of perturbations in the inertial range. In this regime, our simulations confirm the classical predictions based on closure models of turbulence. We show how to link chaoticity and predictability of a turbulent flow in terms of a finite size extension of the Lyapunov exponent.
A review of Reynolds stress models for turbulent shear flows
NASA Technical Reports Server (NTRS)
Speziale, Charles G.
1995-01-01
A detailed review of recent developments in Reynolds stress modeling for incompressible turbulent shear flows is provided. The mathematical foundations of both two-equation models and full second-order closures are explored in depth. It is shown how these models can be systematically derived for two-dimensional mean turbulent flows that are close to equilibrium. A variety of examples are provided to demonstrate how well properly calibrated versions of these models perform for such flows. However, substantial problems remain for the description of more complex turbulent flows where there are large departures from equilibrium. Recent efforts to extend Reynolds stress models to nonequilibrium turbulent flows are discussed briefly along with the major modeling issues relevant to practical naval hydrodynamics applications.
Cabled butterfly closure: a novel technique for sternal closure.
Jolly, Shashank; Flom, Beau; Dyke, Cornelius
2012-10-01
Impaired sternal wound healing remains problematic after median sternotomy and can lead to significant morbidity after cardiac surgical procedures. Although metal plating systems exist for closing the sternum, their use is limited by expense and practicality, and simple wire closure remains the most common technique to close the sternum. We describe a cabling technique for sternal closure that is secure, uses standard sternal wire, and may be used on every patient. We have used the technique routinely in 291 patients with no sternal dehiscence or wound healing problems.
THOR Turbulence Electron Analyser: TEA
NASA Astrophysics Data System (ADS)
Fazakerley, Andrew; Samara, Marilia; Hancock, Barry; Wicks, Robert; Moore, Tom; Rust, Duncan; Jones, Jonathan; Saito, Yoshifumi; Pollock, Craig; Owen, Chris; Rae, Jonny
2017-04-01
Turbulence Heating ObserveR (THOR) is the first mission ever flown in space dedicated to plasma turbulence. The Turbulence Electron Analyser (TEA) will measure the plasma electron populations in the mission's Regions of Interest. It will collect a 3D electron velocity distribution with cadences as short as 5 ms. The instrument will be capable of measuring energies up to 30 keV. TEA consists of multiple electrostatic analyser heads arranged so as to measure electrons arriving from look directions covering the full sky, i.e. 4 pi solid angle. The baseline concept is similar to the successful FPI-DES instrument currently operating on the MMS mission. TEA is intended to have a similar angular resolution, but a larger geometric factor. In comparison to earlier missions, TEA improves on the measurement cadence. For example, MMS FPI-DES routinely operates at 30 ms cadence. The objective of measuring distributions at rates as fast as 5 ms is driven by the mission's scientific requirements to resolve electron gyroscale size structures, where plasma heating and fluctuation dissipation is predicted to occur. TEA will therefore be capable of making measurements of the evolution of distribution functions across thin (a few km) current sheets travelling past the spacecraft at up to 600 km/s, of the Power Spectral Density of fluctuations of electron moments and of distributions fast enough to match frequencies with waves expected to be dissipating turbulence (e.g. with 100 Hz whistler waves). A novel capability to time tag individual electron events during short intervals for the purposes of ground analysis of wave-particle interactions is also planned.
Hazak, G; Elbaz, Y; Zalesak, S; Wygoda, N; Schmitt, A J
2010-02-01
The kinetic theory is developed for the mass mixing of two incompressible immiscible fluids due to Rayleigh-Taylor instability (as an example for turbulence in variable-density statistically inhomogeneous incompressible fluids). An expression is derived for the fine grain force in terms of the mass-density and velocity fields. This expression enables the conversion of the Navier-Stokes equation into an exact explicit conservation equation in phase space. The equation is a generalization, to the variable-density case, of the Lundgren equation [T. S. Lundgren, Phys. Fluids 10, 969 (1967)]. The conserved quantity is the fine grain density-velocity distribution (FGDVD). The fine grain mass-density and fluid velocity fields are the two lowest moments of the FGDVD. The joint density-velocity probability density function (DVPDF) is the ensemble average of the FGDVD. Using detailed numerical solutions of the Navier-Stokes equation, it is found that the correlation between the acceleration and the FGDVD is weak. This result identifies a small parameter which enables the derivation, by controlled approximations, of closed equations for the DVPDFs. The lowest order yields the mean-field approximation. It is shown by a numerical solution of the closed kinetic equation in the mean-field approximation that it properly describes the time evolution of the system for periods shorter than the relaxation time. Closure schemes beyond the mean field are discussed.
Closure of Building 624 incinerator
Ridley, M.N.; Hallisey, M.L.; Terusaki, S.; Steverson, M.
1992-06-01
The Building 624 incinerator was a Resource Conservation Recovery Act (RCRA) mixed waste incinerator at Lawrence Livermore National Laboratory (LLNL). This incinerator was in operation from 1978 to 1989. The incinerator was to be closed as a mixed waste incinerator, but was to continue burning classified nonhazardous solid waste. The decision was later made to discontinue all use of the incinerator. Closure activities were performed from June 15 to December 15, 1991, when a clean closure was completed. The main part of the closure was the characterization, which included 393 samples and 30 blanks. From these 393 samples, approximately 13 samples indicated the need for further investigation, such as an isotopic scan; however, none of the samples was concluded to be hazardous or radioactive.