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.
NASA Astrophysics Data System (ADS)
Shin, Jong-Keun; Seo, Jeong-Sik; Choi, Young-Don
2009-06-01
This study describes the amendment of an algebraic anisotropic dissipation rate model (ADRM) and its application to various turbulent flows to test the model's performance. Modeling anisotropies for the turbulence dissipation rate is considered by an analysis of the exact transport equation for the dissipation rate tensor. The second-moment closure, which is based on the explicit amended ADRM, is proposed and it is closely linked to the elliptic-blending model that is used for the prediction of Reynolds stresses. To develop and calibrate the present elliptic-blending second-moment closure that uses the amended ADRM, firstly, the distributions of both the mean velocity and Reynolds stress are solved for flows in a fully developed non-rotating channel and a straight square duct. And then, the fully developed turbulent flows in a rotating channel and a rotating straight square duct are predicted to test the ability of the explicit amended ADRM that is combined with the rotation effect. The prediction results are directly compared with the DNS and the large-eddy simulation (LES) to assess the performance of the new model predictions and to show their reasonable agreement with the DNS and LES data for all the flow fields that are analyzed for the present study. This paper is a modified version of the original article from the Proceedings of the 5th International Symposium on Turbulence and Shear Flow Phenomena held in Munich, Germany on 27-29 August 2007.
Shima, N. . College of Engineering)
1993-03-01
The purpose of this two-part paper is to assess the performance of a second-moment closure applicable up to a wall. In the present part, the turbulence model is applied to the boundary layers with periodic pressure gradient, with wall transpiration and with free-stream turbulence. The predictions are shown to be in good agreement with experiments and a direct simulation. In particular, a tendency towards relaminarization and a subsequent retransition in the oscillating boundary layer are faithfully reproduced, and the effect of the length scale of free-stream turbulence is correctly captured.
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.
Second-moment closures and length scales for weakly stratified turbulent shear flows
NASA Astrophysics Data System (ADS)
Baumert, Helmut; Peters, Hartmut
2000-03-01
For the special hydrodynamic situation of unbounded homogeneous shear layers, turbulence closure models of Mellor-Yamada type (MY) and k-ɛ type are put into a single canonical form. For this situation we show that conventional versions of MY and various k-ɛ versions lack a proper steady state, and are unable to simulate the most basic properties of stratified shear flows exemplified in, for example, the Rohr et al. [1988] experiments: exponential growth at sufficiently low gradient Richardson number (Rg), exponential decay at sufficiently large Rg, and a steady state in between. Proper choice of one special model parameter readily solves the problems. In the fairly general case of structural equilibrium (state of exponential evolution) in weakly to moderately stratified turbulence (Rg ≲ 0.25), the ratio between the Thorpe scale (or Ellison scale) and the Ozmidov scale varies like the gradient Richardson number (Rg) to the power 3/4, and the ratio of the Thorpe scale to the buoyancy scale varies like Rg1/2. Length scales predicted by our current model are consistent with laboratory measurements of Rohr et al. [1988], with large-eddy numerical simulations of Schumann and Gerz [1995], and with microstructure measurements from the 1987 Tropic Heat Experiment in the equatorial Pacific by Peters et al. [1995].
Autonomic closure for turbulence simulations
NASA Astrophysics Data System (ADS)
King, Ryan N.; Hamlington, Peter E.; Dahm, Werner J. A.
2016-03-01
A new approach to turbulence closure is presented that eliminates the need to specify a predefined turbulence model and instead provides for fully adaptive, self-optimizing, autonomic closures. The closure is autonomic in the sense that the simulation itself determines the optimal local, instantaneous relation between any unclosed term and resolved quantities through the solution of a nonlinear, nonparametric system identification problem. This nonparametric approach allows the autonomic closure to freely adapt to varying nonlinear, nonlocal, nonequilibrium, and other turbulence characteristics in the flow. Even a simple implementation of the autonomic closure for large eddy simulations provides remarkably more accurate results in a priori tests than do dynamic versions of traditional prescribed closures.
Autonomic closure for turbulence simulations.
King, Ryan N; Hamlington, Peter E; Dahm, Werner J A
2016-03-01
A new approach to turbulence closure is presented that eliminates the need to specify a predefined turbulence model and instead provides for fully adaptive, self-optimizing, autonomic closures. The closure is autonomic in the sense that the simulation itself determines the optimal local, instantaneous relation between any unclosed term and resolved quantities through the solution of a nonlinear, nonparametric system identification problem. This nonparametric approach allows the autonomic closure to freely adapt to varying nonlinear, nonlocal, nonequilibrium, and other turbulence characteristics in the flow. Even a simple implementation of the autonomic closure for large eddy simulations provides remarkably more accurate results in a priori tests than do dynamic versions of traditional prescribed closures. PMID:27078285
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.
Moment closure and the stochastic logistic model.
Nåsell, Ingemar
2003-03-01
The quasi-stationary distribution of the stochastic logistic model is studied in the parameter region where its body is approximately normal. Improved asymptotic approximations of its first three cumulants are derived. It is shown that the same results can be derived with the aid of the moment closure method. This indicates that the moment closure method leads to expressions for the cumulants that are asymptotic approximations of the cumulants of the quasi-stationary distribution. PMID:12615498
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.
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.
Closure models for turbulent reacting flows
Dutta, A.; Tarbell, J.M. . Dept. of Chemical Engineering)
1989-12-01
In this paper, a simple procedure based on fast and slow reaction asymptotics has been employed to drive first-order closure models for the nonlinear reaction terms in turbulent mass balances from mechanistic models of turbulent mixing and reaction. The coalescence-redispersion (CRD) model, the interaction by exchange with the mean (IEM) model, the three-environment (3E) model, and the four-environment (4E) model have been used to develop closure equations. The closure models have been tested extensively against experimental data for both single and multiple reactions. The closures based on slow asymptotics for the CRD, 3E and 4E models provide very good predictions of all of the experimental data, while other models available either in the literature or derived here are not adequate. The simple new closure equations developed in this paper may be useful in modeling systems involving turbulent mixing and complex chemical reactions.
Moment Closures on Two-Dimensional Cartesian Grids
Energy Science and Technology Software Center (ESTSC)
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.
Mapping Closure Approximation to Conditional Dissipation Rate for Turbulent Scalar Mixing
NASA Technical Reports Server (NTRS)
He, Gouwei; Rubinstein, R.
2000-01-01
A novel mapping closure approximation (MCA) technique is developed to construct a model for the conditional dissipation rate (CDR) of a scalar in homogeneous turbulence. It is shown that the CDR model from amplitude mapping closure is incorrect in asymptotic behavior for unsymmetric binary mixing. The correct asymptotic behavior can be described by the CDR model formulated by the MCA technique. The MCA approach is outlined for constructing successive approximation to probability density function (PDF) and conditional moment.
Quantum hydrodynamic model by moment closure of Wigner equation
NASA Astrophysics Data System (ADS)
Cai, Zhenning; Fan, Yuwei; Li, Ruo; Lu, Tiao; Wang, Yanli
2012-10-01
In this paper, we derive the quantum hydrodynamics models based on the moment closure of the Wigner equation. The moment expansion adopted is of the Grad type first proposed by Grad ["On the kinetic theory of rarefied gases," Commun. Pure Appl. Math. 2(4), 331-407 (1949), 10.1002/cpa.3160020403]. The Grad's moment method was originally developed for the Boltzmann equation. Recently, a regularization method for the Grad's moment system of the Boltzmann equation was proposed by Cai et al. [Commun. Pure Appl. Math. "Globally hyperbolic regularization of Grad's moment system" (in press)] to achieve the global hyperbolicity so that the local well-posedness of the moment system is attained. With the moment expansion of the Wigner function, the drift term in the Wigner equation has exactly the same moment representation as in the Boltzmann equation, thus the regularization applies. The moment expansion of the nonlocal Wigner potential term in the Wigner equation turns out to be a linear source term, which can only induce very mild growth of the solution. As a result, the local well-posedness of the regularized moment system for the Wigner equation remains as for the Boltzmann equation.
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.
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
2015-09-01
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. PMID:26342359
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.
Myong, R. S.; Nagdewe, S. P.
2011-05-20
The Grad's closure for the high-order moment equation is revisited and, by extending his theory, a physically motivated closure is developed for the one-dimensional velocity shear gas flow. The closure is based on the physical argument of the relative importance of various terms appearing in the moment equation. Also, the closure is derived such that the resulting theory may be inclusive of the well established linear theory (Navier-Stokes-Fourier) as limiting case near local thermal equilibrium.
Entropy production moment closures and effective transport coefficients
NASA Astrophysics Data System (ADS)
Christen, Thomas; Kassubek, Frank
2014-09-01
If transport of a given (classical, fermionic, or bosonic) particle species in media is described by a Boltzmann transport equation (BTE), it is often expedient to solve this BTE in the framework of a moment expansion of the particle distribution function, while an exact solution or simulation of the problem with real material properties and complex geometries is unpractical or even unfeasible. Whereas for local thermal equilibrium (LTE) the well-known hydrodynamic equations for the densities of the conserved quantities are derived from the BTE, for non-LTE it is not obvious how to define moments and to close the truncated hierarchy of partial differential equations for these moments. This paper reviews a closure based on entropy production rate minimization, which is applicable to incoherent transport of independent particles in non-LTE interacting with an LTE-medium. The BTE is then linear, includes emission-absorption and elastic scattering processes, and is equivalent to radiative transfer equations. In a large range from diffusive (opaque media) to ballistic (transparent media) transport behaviour, the closure provides useful mean transport coefficients that are exact in the LTE limit, in contrast to the often used maximum entropy moment closure. After an introduction into the underlying theory for massive and wave-like particles, two illustrative examples are discussed. First, the two-moment approximation of radiative heat transfer is reviewed and effective absorption coefficients and the Eddington factor are calculated for a real absorption spectrum. Secondly, the approach is applied to semi-classical electric transport in mesoscopic systems and is shown to provide the correct conductance of a quasi-one-dimensional ballistic conductor with elastic scattering.
Second-order closure models for supersonic turbulent flows
NASA Technical Reports Server (NTRS)
Speziale, Charles G.; Sarkar, Sutanu
1991-01-01
Recent work on the development of a second-order closure model for high-speed compressible flows is reviewed. This turbulent closure is based on the solution of modeled transport equations for the Favre-averaged Reynolds stress tensor and the solenoidal part of the turbulent dissipation rate. A new model for the compressible dissipation is used along with traditional gradient transport models for the Reynolds heat flux and mass flux terms. Consistent with simple asymptotic analyses, the deviatoric part of the remaining higher-order correlations in the Reynolds stress transport equations are modeled by a variable density extension of the newest incompressible models. The resulting second-order closure model is tested in a variety of compressible turbulent flows which include the decay of isotropic turbulence, homogeneous shear flow, the supersonic mixing layer, and the supersonic flat-plate turbulent boundary layer. Comparisons between the model predictions and the results of physical and numerical experiments are quite encouraging.
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.
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.
Contribution to the second-moment modeling of sublayer turbulent transport
NASA Astrophysics Data System (ADS)
Launder, B. E.; Tselepidakis, D. P.
The paper examines the question of developing a full second-moment closure within the viscosity affected sublayer near a wall. The effects of different processes are considered in turn. For the influential pressure-strain process, new forms are adopted that have emerged from research at UMIST on free shear flows. Results indicate the importance of the strongly nonisotropic nature of the dissipation process and the role of pressure-driven transport of both Reynolds stress and the turbulence energy dissipation rate. The question of whether the turbulence Reynolds number must be retained as a parameter in the pressure-containing correlations remains unresolved though, if it does, its influence will be less important than in earlier closure proposals.
Validating a turbulence closure against estuarine microstructure measurements
NASA Astrophysics Data System (ADS)
Peters, Hartmut; Baumert, Helmut Z.
A simple k- ɛ turbulence closure is introduced which has no stability functions but instead a Richardson number-dependent turbulent Prandtl number. Its free parameters are determined in a comparison with microstructure observations from a stratified and sheared tidal estuary and laboratory measurements. The closure is able to simulate observed turbulent dissipation rates ( ɛ) and turbulent length scales ( lth) in regions of strong mean shear and small gradient Richardson number ( Rg) to within factors of 2-3. It fails in regions of small shear and large Rg, presumably because of the dominance of internal wave-driven mixing. Additional simulations with a k- ɛ closure with stability functions taken from Canuto et al. [Canuto, V.M., Howard, A., Cheng, Y., Dubovikov, M.S., 2001. Ocean turbulence I: one-point closure model. Momentum and heat vertical diffusivities. J. Phys. Oceanogr. 31, 1413-1426] and with the closure of Baumert and Peters [Baumert, H., Peters, H., 2004. Turbulence closure, steady state, and collapse into waves. J. Phys. Oceanogr. 34, 505-512] show poor performance. Establishing a valid 1:1 comparison of simulated and observed ɛ and lth requires nudging the model velocity and density toward observed values because free model integrations quickly diverge from the observations. Steady state gradient Richardson numbers are constrained to a range of 0.18-0.25, while flux Richardson numbers are constrained to the range of 0.1-0.22. The closure output is rather insensitive to such parameter variations. The simulations are sensitive, however, to the treatment of the observed velocity and density used to nudge the model. Good closure performance requires averaging the measured tidal flow over about an hour, a time scale for which conventional numerical models of estuarine circulations should be able to match observed shears. In the closure simulations the TKE balance stays close to a production-dissipation balance. The time rate of change and vertical
Fairweather, M.; Woolley, R.M.
2007-07-15
Presented are results obtained from the application of a first- and higher-order conditional moment closure (CMC) approach to the modeling of three methane diffusion flames at differing levels of local extinction. In addition to the analysis of higher-order chemistry applications, the results obtained from an elliptic formulation of the CMC equation are considered next to parabolic results presented in previous work. All predictions are based upon second-moment turbulence and scalar-flux closures, and the chemistry applied to represent mean production rates of species is a 16-step reduced mechanism. A second-order chemistry is implemented on the basis of a two-step kinetic representation of methane combustion, used to correct first-order rates. In general, predictions obtained using the second-order model improve significantly upon first-order results for both major and minor species under fuel-rich conditions. The simplified chemistry employed does not however fully capture the effects of local extinction, and suggestions are made regarding the further developments required to permit the accurate prediction of highly strained flames using CMC methods. (author)
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.
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.
Moment Closure Approximations of the Boltzmann Equation Based on \\varphi -Divergences
NASA Astrophysics Data System (ADS)
Abdelmalik, M. R. A.; van Brummelen, E. H.
2016-07-01
This paper is concerned with approximations of the Boltzmann equation based on the method of moments. We propose a generalization of the setting of the moment-closure problem from relative entropy to \\varphi -divergences and a corresponding closure procedure based on minimization of \\varphi -divergences. The proposed description encapsulates as special cases Grad's classical closure based on expansion in Hermite polynomials and Levermore's entropy-based closure. We establish that the generalization to divergence-based closures enables the construction of extended thermodynamic theories that avoid essential limitations of the standard moment-closure formulations such as inadmissibility of the approximate phase-space distribution, potential loss of hyperbolicity and singularity of flux functions at local equilibrium. The divergence-based closure leads to a hierarchy of tractable symmetric hyperbolic systems that retain the fundamental structural properties of the Boltzmann equation.
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.
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.
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.
Inertial-particle accelerations in turbulence: a Lagrangian closure
NASA Astrophysics Data System (ADS)
Vajedi, S.; Gustavsson, K.; Mehlig, B.; Biferale, L.
2016-07-01
The distribution of particle accelerations in turbulence is intermittent, with non-Gaussian tails that are quite different for light and heavy particles. In this article we analyse a closure scheme for the acceleration fluctuations of light and heavy inertial particles in turbulence, formulated in terms of Lagrangian correlation functions of fluid tracers. We compute the variance and the flatness of inertial particle accelerations and we discuss their dependency on the Stokes number. The closure incorporates effects induced by the Lagrangian correlations along the trajectories of fluid tracers, and its predictions agree well with results of direct numerical simulations of inertial particles in turbulence, provided that the effects induced by the inertial preferential sampling of heavy/light particles outside/inside vortices are negligible. In particular, the scheme predicts the correct functional behaviour of the acceleration variance, as a function of Stokes, as well as the presence of a minimum/maximum for the flatness of the acceleration of heavy/light particles, in good qualitative agreement with numerical data. We also show that the closure works well when applied to the Lagrangian evolution of particles using a stochastic surrogate for the underlying Eulerian velocity field. Our results support the conclusion that there exist important contributions to the statistics of the acceleration of inertial particles independent of the preferential sampling. For heavy particles we observe deviations between the predictions of the closure scheme and direct numerical simulations, at Stokes numbers of order unity. For light particles the deviation occurs for larger Stokes numbers.
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)
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.
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
Moment closures based on minimizing the residual of the PN angular expansion in radiation transport
NASA Astrophysics Data System (ADS)
Zheng, Weixiong; McClarren, Ryan G.
2016-06-01
In this work we present two new closures for the spherical harmonics (PN) method in slab geometry transport problems. Our approach begins with an analysis of the squared-residual of the transport equation where we show that the standard truncation and diffusive closures do not minimize the residual of the PN expansion. Based on this analysis we derive two models, a moment-limited diffusive (ML DN) closure and a transient PN (TPN) closure that attempt to address shortcomings of common closures. The form of these closures is similar to flux-limiters for diffusion with the addition of a time-derivative in the definition of the closure. Numerical results on a pulsed plane source problem, the Gordian knot of slab-geometry transport problems, indicate that our new closure outperforms existing linear closures. Additionally, on a deep penetration problem we demonstrate that the TPN closure does not suffer from the artificial shocks that can arise in the MN entropy-based closure. Finally, results for Reed's problem demonstrate that the TPN solution is as accurate as the PN+3 solution. We further extend the TPN closure to 2D Cartesian geometry. The line source test problem demonstrates the model effectively damps oscillations and negative densities.
Vector Third Moment of Turbulent MHD Fluctuations: Theory and Interpretation
NASA Astrophysics Data System (ADS)
Forman, M. A.; MacBride, B. T.; Smith, C. W.
2006-12-01
We call attention to the fact that a certain vector third moment of turbulent MHD fluctuations, even if they are anisotropic, obeys an exact scaling relation in the inertial range. Politano and Pouquet (1998, PP) proved it from the MHD equations specifically. It is a direct analog of the long-known von Karman-Howarth-Monin (KHM) vector relation in anisotropic hydrodynamic turbulence, which follows from the Navier-Stokes equations (see Frisch, 1995). The relevant quantities in MHD are the plus and minus Elsasser vectors and their fluctuations over vector spatial differences. These are used in the mixed vector third moment S+/-(r). The mixed moment is essential, because in the MHD equations for the Elsasser variables, the z + and z- are mixed in the non-linear term. The PP relation is div (S+/-(r))= -4*(epsilon +/-) where (epsilon +/-) is the turbulent energy dissipation rate in the +/- cascade, in Joules/(kg-sec). Of the many possible vector and tensor third moments of MHD vector fluctuations, S+/-(r) is the only one known to have an exact (although vector differential) scaling valid in anisotropic MHD in the inertial range. The PP scaling of a distinctly non-zero third moment indicates that an inertial range cascade is present. The PP scaling does NOT simply result from a dimensional argument, but is derived directly from the MHD equations. A power-law power spectrum alone does not necessarily imply an inertial cascade is present. Furthermore, only the scaling of S+/-(r) gives the epsilon +/- directly. Earlier methods of determining epsilon +/-, based on the amplitude of the power spectrum, make assumptions about isotropy, Alfvenicity and scaling that are not exact. Thus, the observation of a finite S+/-(r) and its scaling with vector r, are fundamental to MHD turbulence in the solar wind, or in any magnetized plasma. We are engaged in evaluating S+/-(r )and its anisotropic scaling in the solar wind, beginning with ACE field and plasma data. For this, we are using
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.
Exact and approximate moment closures for non-Markovian network epidemics.
Pellis, Lorenzo; House, Thomas; Keeling, Matt J
2015-10-01
Moment-closure techniques are commonly used to generate low-dimensional deterministic models to approximate the average dynamics of stochastic systems on networks. The quality of such closures is usually difficult to asses and furthermore the relationship between model assumptions and closure accuracy are often difficult, if not impossible, to quantify. Here we carefully examine some commonly used moment closures, in particular a new one based on the concept of maximum entropy, for approximating the spread of epidemics on networks by reconstructing the probability distributions over triplets based on those over pairs. We consider various models (SI, SIR, SEIR and Reed-Frost-type) under Markovian and non-Markovian assumption characterising the latent and infectious periods. We initially study with care two special networks, namely the open triplet and closed triangle, for which we can obtain analytical results. We then explore numerically the exactness of moment closures for a wide range of larger motifs, thus gaining understanding of the factors that introduce errors in the approximations, in particular the presence of a random duration of the infectious period and the presence of overlapping triangles in a network. We also derive a simpler and more intuitive proof than previously available concerning the known result that pair-based moment closure is exact for the Markovian SIR model on tree-like networks under pure initial conditions. We also extend such a result to all infectious models, Markovian and non-Markovian, in which susceptibles escape infection independently from each infected neighbour and for which infectives cannot regain susceptible status, provided the network is tree-like and initial conditions are pure. This works represent a valuable step in enriching intuition and deepening understanding of the assumptions behind moment closure approximations and for putting them on a more rigorous mathematical footing. PMID:25975999
A 3-D multiband closure for radiation and neutron transfer moment models
Ripoll, J.-F. Wray, A.A.
2008-02-01
We derive a 3D multi-band moment model and its associated closure for radiation and neutron transfer. The new closure is analytical and nonlinear but very simple. Its derivation is based on the maximum entropy closure and assumes a Wien shape for the intensity when used in the Eddington tensor. In the multi-band approach, the opacity is re-arranged (binned) according to the opacity value. The multi-band model propagates identically all photons/neutrons having the same opacity. This has been found to be a good approximation on average since the transport is mostly determined by the opacities and less by the frequencies. This same concept is used to derive the closure. We prove on two complex test atmospheres (the solar atmosphere and an artificial atmosphere) that the closure we have derived has good accuracy. All approximations made in deriving the model have been carefully numerically checked and quantified.
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. PMID:25829147
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. PMID:26567686
Comparison of different moment-closure approximations for stochastic chemical kinetics
NASA Astrophysics Data System (ADS)
Schnoerr, David; Sanguinetti, Guido; Grima, Ramon
2015-11-01
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.
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.
A k-{\\varepsilon} turbulence closure model of an isothermal dry granular dense matter
NASA Astrophysics Data System (ADS)
Fang, Chung
2015-07-01
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 Technical Reports Server (NTRS)
Shih, Tsan-Hsing; Lumley, John L.
1991-01-01
Recently, several second order closure models have been proposed for closing the second moment equations, in which the velocity-pressure gradient (and scalar-pressure gradient) tensor and the dissipation rate tensor are two of the most important terms. In the literature, these correlation tensors are usually decomposed into a so called rapid term and a return-to-isotropy term. Models of these terms have been used in global flow calculations together with other modeled terms. However, their individual behavior in different flows have not been fully examined because they are un-measurable in the laboratory. Recently, the development of direct numerical simulation (DNS) of turbulence has given us the opportunity to do this kind of study. With the direct numerical simulation, we may use the solution to exactly calculate the values of these correlation terms and then directly compare them with the values from their modeled formulations (models). Here, we make direct comparisons of five representative rapid models and eight return-to-isotropy models using the DNS data of forty five homogeneous flows which were done by Rogers et al. (1986) and Lee et al. (1985). The purpose of these direct comparisons is to explore the performance of these models in different flows and identify the ones which give the best performance. The modeling procedure, model constraints, and the various evaluated models are described. The detailed results of the direct comparisons are discussed, and a few concluding remarks on turbulence models are given.
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.
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.
NASA Astrophysics Data System (ADS)
Podesta, J. J.
It is known that Kolmogorov's four-fifths law for statistically homogeneous and isotropic turbulence can be generalized to anisotropic turbulence. This fundamental result for homogeneous anisotropic turbulence says that in the inertial range the divergence of the vector third-order moment |v(r) is constant and is equal to -4, where is the dissipation rate of the turbulence. This law can be extended to incompressible magnetohydrodyamic (MHD) turbulence where statistical isotropy is often not valid due, for example, to the presence of a large-scale magnetic field. Laws for anisotropic incompressible MHD turbulence were first derived by Politano and Pouquet. In this paper, the laws for vector third-order moments in homogeneous non-isotropic incompressible MHD turbulence are derived by a technique due to Frisch that clarifies the relationship between the energy flux in Fourier space and the vector third-order moments in physical space. This derivation is different from the original derivation of Politano and Pouquet which is based on the Kn-Howarth equation, and provides some new physical insights. Separate laws are derived for the cascades of energy, cross-helicity and magnetic-helicity, the three ideal invariants of incompressible MHD for flows in three dimensions. These laws are of fundamental importance in the theory of MHD turbulence where non-isotropic turbulence is much more prevalent than isotropic turbulence.
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.
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.
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.
A numerical study of a separating and reattaching flow by using Reynolds-stress turbulence closure
NASA Technical Reports Server (NTRS)
Amano, R. S.; Goel, P.
1984-01-01
The numerical study of the Reynolds-stress turbulence closure for separating, reattaching, recirculating and redeveloping flow is summarized. The calculations were made for two different closure models of pressure-strain correlation. The results were compared with the experimental data. Furthermore, these results were compared with the computations made by using the one layer and three layer treatment of k-epsilon turbulence model which were developed. Generally the computations by the Reynolds-stress model show better results than those by the k-epsilon model, in particular, some improvement was noticed in the redeveloping region of the separating and reattaching flow in a pipe with sudden expansion.
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.
A second-order closure prediction of premixed turbulent combustion in jets
NASA Astrophysics Data System (ADS)
Davé, N.; Kollmann, W.
1987-02-01
In this paper, a numerical prediction is reported involving second-order closure of a turbulent flow of a vertically burning, lean mixture of premixed combustible gases discharging from a pipe and developing into a turbulent combusting roundjet. Classical closures are used where available. Expressions for the chemical reaction rate term and other unclosed terms related to variable density flow in the Favre-averaged turbulent transport equations are based on the Bray-Moss-Libby aerothermochemistry for premixed turbulent combustion, extended to variable enthalpy systems. Mixing of hot burned and cool ambient gases and the attendant buoyancy effects are found to be significant physical phenomena in the behavior of such lean premixed combusting jets. Results of the simulation are compared with experimental data of Yoshida [Proceedings of the Eighteenth International Symposium on Combustion (The Combustion Institute, Pittsburgh, 1981), p. 931] with which reasonable numerical agreement is obtained. Reasons for discrepancies and possible lines for future research are discussed.
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.
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.
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.
Triantafyllidis, A.; Mastorakos, E.; Eggels, R.L.G.M.
2009-12-15
Large Eddy Simulations (LES) of forced ignition of a bluff-body stabilised non-premixed methane flame using the Conditional Moment Closure (CMC) turbulent combustion model have been performed. The aim is to investigate the feasibility of the use of CMC/LES for ignition problems and to examine which, if any, of the characteristics already observed in related experiments could be predicted. A three-dimensional formulation of the CMC equation was used with simple and detailed chemical mechanisms, and sparks with different parameters (location, size) were used. It was found that the correct pattern of flame expansion and overall flame appearance were predicted with reasonable accuracy with both mechanisms, but the detailed mechanism resulted in expansion rates closer to the experiment. Moreover, the distribution of OH was predicted qualitatively accurately, with patches of high and low concentration in the recirculation zone during the ignition transient, consistent with experimental data. The location of the spark relative to the recirculation zone was found to determine the pattern of the flame propagation and the total time for the flame stabilisation. The size was also an important parameter, since it was found that the flame extinguishes when the spark is very small, in agreement with expectations from experiment. The stabilisation mechanism of the flame was dominated by the convection and sub-grid scale diffusion of hot combustion products from the recirculation zone to the cold gases that enter the burner, as revealed by analysis of the CMC equation. (author)
NASA Astrophysics Data System (ADS)
Cheng, A.; Xu, K.
2013-12-01
This presentation describes the implementation and testing of an advanced third-order turbulence closure, an intermediately-prognostic higher-order turbulence closure (IPHOC), into the Community Atmosphere Model 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 the subgrid scale variations including 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 diagnostic 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-IP) represents a more unified treatment of boundary layer and shallow convective processes. Results from global climate simulations are presented and suggest that CAM5-IP can provide a better treatment of boundary layer clouds and processes when compared to CAM5. The global annual mean low cloud fraction and precipitation are compared among CAM5, CAM5-IP, and a multi-scale modeling framework model with IPHOC (MMF-IP). The low cloud amounts near the west coast of the subtropical continents are well produced in CAM5-IP and are more abundant than in other two models. The global mean liquid water path is the closest to the SSM/I observation. The cloud structures from CAM5-IP, represented by the cloud fraction and cloud water content at 15°S transect, compare well with the CloudSat/CALIPSO observations. The shallow cumulus
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.
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.
Technology Transfer Automated Retrieval System (TEKTRAN)
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.
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
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.
Analytical methods for the development of Reynolds-stress closures in turbulence
NASA Technical Reports Server (NTRS)
Speziale, Charles G.
1991-01-01
The derivation of Reynolds-stress models for viscous incompressible turbulent flow on the basis of the Navier-Stokes and continuity equations is explored in an analytical review. The formulation of the basic equations is outlined, and particular attention is given to zero-equation and one-equation models based on eddy viscosity, two-equation (k-l, k-epsilon, and k-omega) models, and second-order closure models. The superior performance of the second-order models is demonstrated by numerical results for (1) the return to isotropy from anisotropic homogeneous turbulence, (2) homogeneous turbulent shear flow in a rotating frame, (3) and fully developed inhomogeneous turbulent channel flow in a rotating frame. The inherent limitations of the Reynolds-stress approach and areas for further improvement are discussed.
Computation of turbulent flows using an extended k-epsilon turbulence closure model
NASA Technical Reports Server (NTRS)
Chen, Y.-S.; Kim, S.-W.
1987-01-01
An extended kappa-epsilon turbulence model is proposed and tested with successful results. An improved transport equation for the rate of dissipation of the turbulent kinetic energy, epsilon, is proposed. The proposed model gives more effective response to the energy production rate than does the standard kappa-epsilon turbulence model. An extra time scale of the production range is included in the dissipation rate equation. This enables the present model to perform equally well for several turbulent flows with different characteristics, e.g., plane and axisymmetric jets, turbulent boundary layer flow, turbulent flow over a backward-facing step, and a confined turbulent swirling flow. A second-order accurate finite difference boundary layer code and a nearly second-order accurate finite difference elliptic flow solver are used for the present numerical computations.
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.
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.
Quadrature Moments Method for the Simulation of Turbulent Reactive Flows
NASA Technical Reports Server (NTRS)
Raman, Venkatramanan; Pitsch, Heinz; Fox, Rodney O.
2003-01-01
A sub-filter model for reactive flows, namely the DQMOM model, was formulated for Large Eddy Simulation (LES) using the filtered mass density function. Transport equations required to determine the location and size of the delta-peaks were then formulated for a 2-peak decomposition of the FDF. The DQMOM scheme was implemented in an existing structured-grid LES solver. Simulations of scalar shear layer using an experimental configuration showed that the first and second moments of both reactive and inert scalars are in good agreement with a conventional Lagrangian scheme that evolves the same FDF. Comparisons with LES simulations performed using laminar chemistry assumption for the reactive scalar show that the new method provides vast improvements at minimal computational cost. Currently, the DQMOM model is being implemented for use with the progress variable/mixture fraction model of Pierce. Comparisons with experimental results and LES simulations using a single-environment for the progress-variable are planned. Future studies will aim at understanding the effect of increase in environments on predictions.
NASA Astrophysics Data System (ADS)
Jamaly, Seyed Mohammad; Hasan Saidi, Mohammad; Ghafourian, Akbar
2007-11-01
In this study, due to the weaknesses of the models with Lagrangian approaches, an attempt has been made to model the spray flow with Eulerian approach. In this regard, the quadrature-based moment closure model for the spray equation, the so-called DQMOM, is applied. This method overcomes the shortcoming of other Eulerian methods while it is in good agreement with the Lagrangian methods. After that, the model has been developed to be able to deal with the evaporating droplets. Moreover, the feasibility of applying non-linear external forces, such as drag forces, and evaporation laws for the droplets are considered and implemented. The required order for the equations in this method has been studied thoroughly as well. Finally, the solution procedure for accurate computations of multi dimension problems is presented. In general, the proposed modified DQMOM method can consider and solve all kinds of spray flows with any desirable dimension for the problem. Here, assuming one-way coupling situation with the gas-phase in an axial engine, the spray phase equations are solved by the proposed method to account for evaporating droplets. Results are compared with the methods with Lagrangian approach and the computational costs and accuracies of the methods are compared as well.
NASA Astrophysics Data System (ADS)
Ochrymiuk, Tomasz
2016-06-01
Numerical simulations were performed to predict the film cooling effectiveness on the fiat plate with a three- dimensional discrete-hole film cooling arrangement. The effects of basic geometrical characteristics of the holes, i.e. diameter D, length L and pitch S/D were studied. Different turbulent heat transfer models based on constant and variable turbulent Prandtl number approaches were considered. The variability of the turbulent Prandtl number Pr t in the energy equation was assumed using an algebraic relation proposed by Kays and Crawford, or employing the Abe, Kondoh and Nagano eddy heat diffusivity closure with two differential transport equations for the temperature variance k θ and its destruction rate ɛ θ . The obtained numerical results were directly compared with the data that came from an experiment based on Transient Liquid Crystal methodology. All implemented models for turbulent heat transfer performed sufficiently well for the considered case. It was confirmed, however, that the two- equation closure can give a detailed look into film cooling problems without using any time-consuming and inherently unsteady models.
Wang, Minghuai; Larson, Vincent E.; Ghan, Steven J.; Ovchinnikov, Mikhail; Schanen, D.; Xiao, Heng; Liu, Xiaohong; Rasch, Philip J.; 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 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 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 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). Improved low cloud simulations in MMF make it an even more attractive tool for studying aerosol-cloud-precipitation interactions.
a Second-Order Closure Prediction of Premixed Turbulent Combustion in Jets
NASA Astrophysics Data System (ADS)
Dave, Nikhil
1985-12-01
This thesis is a report on work carried out and results obtained in the prediction of a turbulent flow of premixed combustible gases discharging from a pipe and developing into a turbulent, combusting roundjet. The expressions for the chemical reaction rate term and other unclosed terms in the Favre averaged turbulent transport equations at the level of second-order closure are based on the Bray-Moss-Libby aerothermochemistry for premixed turbulent combustion, extended to variable enthalpy systems as in Bray, Champion, Dave, Libby (referenced herein). The numerical technique used is a parabolic solver developed by Kollmann from the GENMIX program due to Patankar and Spalding. Various test cases such as constant density and variable density jets are calculated using the program and the results are compared herein with experimentally observed values. Results for premixed turbulent combusting jets are compared with experimental data of Yoshida and of Shepherd and Moss. Buoyancy is found to play an important role in the behavior of these primixed combusting jets. Reasonable numerical agreement is obtained with the results of Yoshida, and good qualitative agreement is obtained with the data of Shepherd and Moss. Reasons for the discrepancies and limitations of the numerical simulation are discussed.
Inhomogeneous closure and statistical mechanics for Rossby wave turbulence over topography
NASA Astrophysics Data System (ADS)
Frederiksen, Jorgen S.; O'Kane, Terence J.
2005-09-01
The quasi-diagonal direct interaction approximation (QDIA) closure theory is formulated for the interaction of mean fields, Rossby waves and inhomogeneous turbulence over topography on a generalized beta-plane. An additional small term, corresponding to the solid-body rotation vorticity on the sphere, is included in the barotropic equation and it is shown that this results in a one-to-one correspondence between the dynamical equations, Rossby wave dispersion relations, nonlinear stability criteria and canonical equilibrium theory on the generalized beta-plane and on the sphere. The dynamics, kinetic energy spectra, mean field structures and mean streamfunction tendencies contributed by transient eddies are compared with the ensemble-averaged results from direct numerical simulations (DNS) at moderate resolution. A series of numerical experiments is performed to examine the generation of Rossby waves when eastward large-scale flows impinge on a conical mountain in the presence of moderate to strong two-dimensional turbulence. The ensemble predictability of northern hemisphere flows in 10-day forecasts is also examined on a generalized beta-plane. In all cases, the QDIA closure is found to be in very good agreement with the statistics of DNS except in situations of strong turbulence and weak mean fields where ensemble-averaged DNS fails to predict mean field amplitudes correctly owing to sampling problems even with as many as 1800 ensemble members.
Development of an enstrophy-based two-equation turbulence closure model
NASA Astrophysics Data System (ADS)
Robinson, David Franklin
The development of a new two-equation turbulence closure model based on the exact turbulent kinetic energy, k and the variance of vorticity, or enstrophy, zeta is presented. The primary motivation was to develop a model, applicable to complex three-dimensional flowfields, that employs one set of model constants and does not use damping functions or geometrical factors. Development begins by considering a number of two-dimensional and axisymmetric flowfields in order to determine the appropriate closure coefficients. First, similarity solutions of a variety of both planar and axisymmetric free shear flows are considered. Next, a variety of wall bounded flows are examined beginning with a boundary layer solution of a flat plate and proceeding to the Navier-Stokes solutions for a variety of two-dimensional airfoils. The airfoils considered range from a low speed stalled airfoil to a transonic airfoil with shock induced separation. Final model validation was performed by considering a supersonic three-dimensional Cylinder-Offset flare. In general, good agreement with experiment is indicated. Moreover, the k-zeta model performed, in most cases, as well as or better than the other models. The above objective has been achieved. The current model is shown to accurately predict growth rates as well as similarity profiles of velocity, turbulent kinetic energy, and shear stress for a variety of both planar and axisymmetric free shear flows. Moreover, the model predicts skin-friction, pressure distribution, and shock position with good accuracy for a variety of wall bounded flows, including flows with large adverse pressure gradients and shock induced separation. Also, the current model solves both the free shear and wall bounded flows using only one set of closure coefficients and boundary conditions. Furthermore, the current model is free of wall damping functions and geometrical factors in both the governing equations and in the definition of eddy viscosity. This makes the
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.
Power and Nonpower Laws of Passive Scalar Moments Convected by Isotropic Turbulence
NASA Astrophysics Data System (ADS)
Gotoh, Toshiyuki; Watanabe, Takeshi
2015-09-01
The scaling behavior of the moments of two passive scalars that are excited by two different methods and simultaneously convected by the same isotropic steady turbulence at Rλ=805 and Sc=0.72 is studied by using direct numerical simulation with N =40963 grid points. The passive scalar θ is excited by a random source that is Gaussian and white in time, and the passive scalar q is excited by the mean uniform scalar gradient. In the inertial convective range, the n th-order moments of the scalar increment δ θ (r ) do not obey a simple power law, but have the local scaling exponents ξnθ+βnlog (r /r*) with βn>0 . In contrast, the local scaling exponents of q have well-developed plateaus and saturate with increasing order. The power law of passive scalar moments is not trivial. The universality of passive scalars is found not in the moments, but in the normalized moments.
Power and nonpower laws of passive scalar moments convected by isotropic turbulence.
Gotoh, Toshiyuki; Watanabe, Takeshi
2015-09-11
The scaling behavior of the moments of two passive scalars that are excited by two different methods and simultaneously convected by the same isotropic steady turbulence at R_{λ}=805 and Sc=0.72 is studied by using direct numerical simulation with N=4096^{3} grid points. The passive scalar θ is excited by a random source that is Gaussian and white in time, and the passive scalar q is excited by the mean uniform scalar gradient. In the inertial convective range, the nth-order moments of the scalar increment δθ(r) do not obey a simple power law, but have the local scaling exponents ξ_{n}^{θ}+β_{n}log(r/r_{*}) with β_{n}>0. In contrast, the local scaling exponents of q have well-developed plateaus and saturate with increasing order. The power law of passive scalar moments is not trivial. The universality of passive scalars is found not in the moments, but in the normalized moments. PMID:26406833
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. PMID:12241287
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
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.
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
NASA Astrophysics Data System (ADS)
Łobocki, Lech
2014-03-01
Derivation of surface-layer flux-gradient relationships from a local-equilibrium, turbulence-closure model for a forced flow over inclined terrain is presented. Results are shown as a generalization of Monin-Obukhov universal functions respesenting non-dimensional wind and temperature gradients.
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.
NASA Astrophysics Data System (ADS)
Grete, Philipp; Vlaykov, Dimitar G.; Schmidt, Wolfram; Schleicher, Dominik R. G.
2016-06-01
Even though compressible plasma turbulence is encountered in many astrophysical phenomena, its effect is often not well understood. Furthermore, direct numerical simulations are typically not able to reach the extreme parameters of these processes. For this reason, large-eddy simulations (LES), which only simulate large and intermediate scales directly, are employed. The smallest, unresolved scales and the interactions between small and large scales are introduced by means of a subgrid-scale (SGS) model. We propose and verify a new set of nonlinear SGS closures for future application as an SGS model in LES of compressible magnetohydrodynamics. We use 15 simulations (without explicit SGS model) of forced, isotropic, homogeneous turbulence with varying sonic Mach number Ms=0.2 -20 as reference data for the most extensive a priori tests performed so far in literature. In these tests, we explicitly filter the reference data and compare the performance of the new closures against the most widely tested closures. These include eddy-viscosity and scale-similarity type closures with different normalizations. Performance indicators are correlations with the turbulent energy and cross-helicity flux, the average SGS dissipation, the topological structure and the ability to reproduce the correct magnitude and the direction of the SGS vectors. We find that only the new nonlinear closures exhibit consistently high correlations (median value > 0.8) with the data over the entire parameter space and outperform the other closures in all tests. Moreover, we show that these results are independent of resolution and chosen filter scale. Additionally, the new closures are effectively coefficient-free with a deviation of less than 20%.
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.
Quadrature Method of Moments for the Simulation of Turbulent Reacting Flows
NASA Astrophysics Data System (ADS)
Raman, Venkatramanan; Pitsch, Heinz; Fox, Rodney
2003-11-01
Computational schemes for turbulent reacting flow systems typically solve the species transport equations using a grid-based Eulerian technique. Such schemes inherently do not contain information about the sub-grid scalar PDF required for the computation of the non-linear reaction source terms and sub-grid scalar dissipation. Though a transport equation for the scalar PDF can be formulated, the high-dimensional equation has to be solved using a computationally expensive particle-based Lagrangian scheme. To overcome this difficulty, the Direct Quadrature Method of Moments (DQMOM) is used to approximate the joint composition PDF by a set of delta functions. The delta-functions are characterized by their location and size, both of which are obtained by solving Eulerian transport equations. Using a N-peak description, N species-moments can be forced to be accurate. The Direct QMOM model is extended to LES schemes and comparisons are made with transported-PDF simulations for both reacting and non-reacting mixing layer setup. Re-formulation of the DQMOM equation leads to conditional multi-environment method that can be used for describing combustion systems that exhibit extinction.
NASA Astrophysics Data System (ADS)
Soulard, Olivier; Griffond, Jérôme; Gréa, Benoît-Joseph
2016-06-01
The purpose of this paper is to highlight the existence of simple algebraic expressions linking the second order moments of velocity and concentration in Rayleigh-Taylor turbulence, in the Boussinesq limit. Focusing on the concentration variance, these relations allow to underline the influence of mixing on the remaining second order correlations, as well as on the growth rate of the mixing zone.
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
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.
NASA Astrophysics Data System (ADS)
Thayer-Calder, K.; Larson, V. E.; Gettelman, A.; Craig, C.; Goldhaber, S.; Schanen, D.
2013-12-01
Global climate models (GCMs) have long had trouble representing climate variability that is highly dependent on convective variability. Convective clouds operate on scales far too small to actually simulate on a large GCM grid. To rectify these issues, GCM development is moving in several directions simultaneously. While much work is focusing on improved convective parameterizations, some modelers are increasing resolution to the point where deep convective clouds can be resolved on the grid scale. Others are using a super-parameterized approach, where small-scale models are embedded within the large-scale grid. Our study utilizes a new approach to modeling convective variability that attempts to model coupled convective and microphysics processes more explicitly than traditional parameterizations. Using the new Community Atmosphere Model (CAM) subcolumn framework, we create several instances of local cloudy or clear air profiles within the large-scale GCM grid. Each sub-column is instantiated through Latin-Hypercube sampling of double-gaussian PDFs predicted by a higher-order closure cloud parameterization known as CLUBB (Cloud Layers Unified By Binormals). The CAM microphysics code then runs with each instance, and the resulting heat and moisture tendencies are averaged and returned to the GCM in the same way as traditional parameterizations. Here, we present results from single-column simulations of CAM using this sub-column approach to coupling the moist turbulence parameterization to the microphysics scheme.
NASA Astrophysics Data System (ADS)
Ilıcak, Mehmet; Özgökmen, Tamay M.; Peters, Hartmut; Baumert, Helmut Z.; Iskandarani, Mohamed
Mixing of overflows released from polar and marginal seas is a key process shaping the structure of the meridional overturning circulation. Ocean general circulation models have difficulty in resolving the overflows, and therefore they must rely on parameterizations. In this study, the performance of a set of turbulence closures in reproducing mixing of an overflow is quantified. We simulate the Red Sea overflow by employing standard k- ɛ, k- ω and Mellor-Yamada schemes with various stability functions, as well as a modified k- ɛ model that relies on the prescription of the turbulent Prandtl number rather than on stability functions. The simpler KPP mixing scheme and experiments without turbulent fluxes serve as useful references. To our knowledge, this is the first time that the performance of two-equation turbulence models has been examined so closely using data from an overflow. It is found that without turbulence closures, the hydrodynamic model has difficulty in reproducing the correct three-dimensional pathway of the Red Sea overflow, consisting of a distinct bifurcation into two diverging channels. All turbulence models capture the vertical structure of this overflow consisting of an interfacial layer, characterized by the density gradient, and a well-mixed bottom layer. Mean eddy diffusivity values from most closures are comparable those from observations. But we find that KPP leads to eddy diffusivity values that are too small while those from Mellor-Yamada with Galperin [Galperin, B., Kantha, L.H., Hassid, S., Rosati, A., 1988. A quasi-equilibrium turbulent energy model for geophysical flows. J. Atmos. Sci. 45, 55-62] stability functions are too large. Such high diffusivities lead to excessive mixing in the bottom layer of the overflow, ultimately resulting in a salinity deficit of approximately 1 psu in the product water mass. Salinity deviations between the models and observations are quantified using both data taken along the channels and two
Frasca, Mattia; Sharkey, Kieran J
2016-06-21
Understanding the dynamics of spread of infectious diseases between individuals is essential for forecasting the evolution of an epidemic outbreak or for defining intervention policies. The problem is addressed by many approaches including stochastic and deterministic models formulated at diverse scales (individuals, populations) and different levels of detail. Here we consider discrete-time SIR (susceptible-infectious-removed) dynamics propagated on contact networks. We derive a novel set of 'discrete-time moment equations' for the probability of the system states at the level of individual nodes and pairs of nodes. These equations form a set which we close by introducing appropriate approximations of the joint probabilities appearing in them. For the example case of SIR processes, we formulate two types of model, one assuming statistical independence at the level of individuals and one at the level of pairs. From the pair-based model we then derive a model at the level of the population which captures the behavior of epidemics on homogeneous random networks. With respect to their continuous-time counterparts, the models include a larger number of possible transitions from one state to another and joint probabilities with a larger number of individuals. The approach is validated through numerical simulation over different network topologies. PMID:27038669
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 Technical Reports Server (NTRS)
Helfand, H. M.; Labraga, J. C.
1988-01-01
The suitability of applying the Mellor and Yamada (1974, 1982) Level 2.5 second-order turbulence closure model to general circulation models is investigated by examining not only the scheme's simulation of fully (or nearly fully) developed turbulence, but also its simulation of rapidly growing or strongly decaying turbulence. The behavior of the model is presented over its entire domain of definition, with special consideration given to the pathologies of the model. The model is then 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 performance of the modified Level 2.5 model is compared to the performance of various other modified versions through the numerical simulation for a growing convective PBL. The results show that the modified Level 2.5 model is a viable candidate for the prediction of turbulence and the simulation of the PBL in general circulation models.
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.
Closure theories with non-Gaussian restarts for truncated two-dimensional turbulence
NASA Astrophysics Data System (ADS)
Frederiksen, J. S.; Davies, A. G.; Bell, R. C.
1994-09-01
NonMarkovian closure theories, with and without non-Gaussian restarts, are compared with ensemble averaged direct numerical simulations (DNS) for severely truncated two-dimensional Navier-Stokes flows. Both the closures and DNS are formulated for discrete spectra relevant to flows on the doubly periodic domain allowing unambiguous comparisons between the closure and DNS results. We examine the performance of the direct interaction approximation (DIA), self-consistent field theory (SCFT) and local energy-transfer theory (LET) closures and are particularly interested in the reliability of cumulant update versions of these closures (CUDIA, CUSCFT, and CULET). In the latter, the potentially long time-history integrals are periodically truncated and the closures are restarted using a three-point cumulant as the new non-Gaussian initial conditions, thus yielding computationally much more efficient closures. In 80-day integrations, the DIA replicates the DNS results most faithfully in inviscid, viscous decay and forced dissipative experiments. With an update time of T=10 days, the CUDIA is particularly promising performing nearly as well but with some extra oscillations at intermediate times. The SCFT and particularly LET, have spurious oscillations in inviscid and viscous decay experiments; this is also the case, but to a greater degree, for the CUSCFT and CULET closures.
Workshop on Engineering Turbulence Modeling
Povinelli, L.A.; Liou, W.W.; Shabbir, A.; Shih, T.H.
1992-03-01
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.
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.
NASA Astrophysics Data System (ADS)
Lazeroms, W. M.; Bazile, E.; Brethouwer, G.; Wallin, S.; Johansson, A. V.; Svensson, G.
2014-12-01
Turbulent flows with buoyancy effects occur in many situations, both in industry and in the atmosphere. It is challenging to correctly model such flows, especially in the case of stably stratified turbulence, where vertical motions are damped by buoyancy forces. For this purpose, we have derived a so-called explicit algebraic model for the Reynolds stresses and turbulent heat flux that gives accurate predictions in flows with buoyancy effects. Although inspired by turbulence models from engineering, the main aim of our work is to improve the parametrization of turbulence in the atmospheric boundary layer (ABL). Explicit algebraic turbulence models are a class of parametrizations that, on the one hand, are more advanced than standard eddy-diffusivity relations. On the other hand, they are signficantly easier to handle numerically than models that require the solution of the full flux-budget equations. To derive the algebraic model, we apply the assumption that transport terms of dimensionless fluxes can be neglected. Careful considerations of the algebra lead to a consistent formulation of the Reynolds stresses and turbulent heat flux, which is more general and robust than previous models of a similar kind. The model is shown to give good results compared to direct numerical simulations of engineering test cases, such as turbulent channel flow. Recent work has been aimed at testing the model in an atmospheric context. The first of these tests makes use of the GABLS1 case, in which a stable atmospheric boundary layer develops through a constant surface cooling rate. The model is able to give good predictions of this case compared to LES (see attached figure). Interestingly, the results are very close to the outcome of the recently developed Energy-Flux-Budget (EFB) closure by Zilitinkevich et al. (2013). A detailed discussion of the similarities and differences between these models will be given, which can give insight in the more general gap between engineering and
Applications of direct numerical simulation of turbulence in second order closures
NASA Technical Reports Server (NTRS)
Shih, Tsan-Hsing; Lumley, John L.
1995-01-01
This paper discusses two methods of developing models for the rapid pressure-strain correlation term in the Reynolds stress transport equation using direct numerical simulation (DNS) data. One is a perturbation about isotropic turbulence, the other is a perturbation about two-component turbulence -- an extremely anisotropic turbulence. A model based on the latter method is proposed and is found to be very promising when compared with DNS data and other models.
NASA Technical Reports Server (NTRS)
Bennett, Floyd V.; Yntema, Robert T.
1959-01-01
Several approximate procedures for calculating the bending-moment response of flexible airplanes to continuous isotropic turbulence are presented and evaluated. The modal methods (the mode-displacement and force-summation methods) and a matrix method (segmented-wing method) are considered. These approximate procedures are applied to a simplified airplane for which an exact solution to the equation of motion can be obtained. The simplified airplane consists of a uniform beam with a concentrated fuselage mass at the center. Airplane motions are limited to vertical rigid-body translation and symmetrical wing bending deflections. Output power spectra of wing bending moments based on the exact transfer-function solutions are used as a basis for the evaluation of the approximate methods. It is shown that the force-summation and the matrix methods give satisfactory accuracy and that the mode-displacement method gives unsatisfactory accuracy.
NASA Astrophysics Data System (ADS)
Alldredge, Graham; Schneider, Florian
2015-08-01
We implement a high-order numerical scheme for the entropy-based moment closure, the so-called MN model, for linear kinetic equations in slab geometry. A discontinuous Galerkin (DG) scheme in space along with a strong-stability preserving Runge-Kutta time integrator is a natural choice to achieve a third-order scheme, but so far, the challenge for such a scheme in this context is the implementation of a linear scaling limiter when the numerical solution leaves the set of realizable moments (that is, those moments associated with a positive underlying distribution). The difficulty for such a limiter lies in the computation of the intersection of a ray with the set of realizable moments. We avoid this computation by using quadrature to generate a convex polytope which approximates this set. The half-space representation of this polytope is used to compute an approximation of the required intersection straightforwardly, and with this limiter in hand, the rest of the DG scheme is constructed using standard techniques. We consider the resulting numerical scheme on a new manufactured solution and standard benchmark problems for both traditional MN models and the so-called mixed-moment models. The manufactured solution allows us to observe the expected convergence rates and explore the effects of the regularization in the optimization.
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.
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. PMID:22107393
Boschung, Jonas
2015-10-01
Following an approach by Siggia, we present coefficients C(n) relating the moments of the dissipation of kinetic energy 〈ɛ〉 and the longitudinal velocity gradient 〈∂u(1)/∂x(1)〉 under the assumption of isotropy and continuity. Particularly, we find that the moment 〈ɛ(n)〉 of order n is completely determined by 〈(∂u(1)/∂x(1))(2n)〉 and an order- (and viscosity-) dependent coefficient for all n under the assumption of (local) isotropy. This implies that all theories which specify 〈ɛ(n)〉 also implicitly determine 〈(∂u(1)/∂x(1))(2n)〉 and vice versa. As a corollary to the direct connection between the moments of the dissipation and the longitudinal velocity gradient, the even standardized moments of order 2n of ∂u(1)/∂x(1) (flatness, hyperflatness, and so on) are directly related to the ratio of the moments 〈ɛ(n)〉/〈ɛ〉(n). We compare the theoretical values of the coefficients C(n) up to n=6 with homogeneous isotropic DNS data ranging from Re(λ)=88 to Re(λ)=529. PMID:26565338
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.
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.
NASA Technical Reports Server (NTRS)
Amano, R. S.
1985-01-01
The hybrid model of the Reynolds-stress turbulence closure is tested for the computation of the flows over a step and disk. Here it is attempted to improve the redistributive action of the turbulence energy among the Reynolds stresses. By evaluating the existing models for the pressure-strain correlation, better coefficients are obtained for the prediction of separating shear flows. Furthermore, the diffusion rate of the Reynolds stresses is reevaluated adopting several algebraic correlations for the triple-velocity products. The models of Cormack et al., Daly-Harlow, Hanjalic-Launder, and Shir were tested for the reattaching shear flows. It was generally observed that all these algebraic models give considerably low values of the triple-velocity products. This is attributed to the fact that none of the algebraic models can take the convective effect of the triple-velocity products into account in the separating shear flows, thus resulting in much lower diffusion rate than Reynolds stresses. In order to improve the evaluation of these quantities correction factors are introduced based on the comparison with some experimental data.
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
2015-05-13
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
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.
NASA Astrophysics Data System (ADS)
Artemov, V. I.; Sinkevich, O. A.
1986-02-01
A semiempirical turbulence model describing the interaction between an electric arc and a turbulent gas flow is proposed which is based on the closure of the balance equations of second-order moments. The model accounts for the effect of gas density and electrodynamic parameter fluctuations. Based on the model proposed here, an algorithm is developed for calculating turbulent plasma flows in channels with complex boundary conditions, such as injection and suction. The efficiency of the model is verified experimentally.
Forced Alfvén-wave turbulence and subgrid-scale closure
NASA Astrophysics Data System (ADS)
Zhou, Ye; Vahala, George
1989-02-01
The renormalization-group method is applied to the problem of forced turbulence in the simplified Alfvén model of Chen and Mahajan. The effects of small unresolvable subgrid modes on the large-scale turbulence leads to a renormalized response function ɛ. In certain limits, the resulting recursion relation for the response function can be converted into a differential equation that can be solved analytically. For Gaussian forcing terms satisfying a power-law wavenumber correlation k-y but white-noise frequency spectrum, it is found that the response function exhibits second-harmonic generation of waves at frequency ω = 2ΛvA for all exponents y ≥ 0, where Λ is the wavenumber separating the subgrid and supergrid modes.
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).
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.
Renormalization Group Theory Technique and Subgrid Scale Closure for Fluid and Plasma Turbulence.
NASA Astrophysics Data System (ADS)
Zhou, Ye.
Renormalization group theory is applied to incompressible three-dimension Navier-Stokes turbulence so as to eliminate unresolvable small scales. The renormalized Navier-Stokes equation includes a triple nonlinearity with the eddy viscosity exhibiting a mild cusp behavior, in qualitative agreement with the test-field model results of Kraichnan. For the cusp behavior to arise, not only is the triple nonlinearity necessary but the effects of pressure must be incorporated in the triple term. Renormalization group theory is also applied to a model Alfven wave turbulence equation. In particular, the effect of small unresolvable subgrid scales on the large scales is computed. It is found that the removal of the subgrid scales leads to a renormalized response function. (i) This response function can be calculated analytically via the difference renormalization group technique. Strong absorption can occur around the Alfven frequency for sharply peaked subgrid frequency spectra. (ii) With the epsilon - expansion renormalization group approach, the Lorenzian wavenumber spectrum of Chen and Mahajan can be recovered for finite epsilon , but the nonlinear coupling constant still remains small, fully justifying the neglect of higher order nonlinearities introduced by the renormalization group procedure.
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)
1977-01-01
Basic differential equations governing compressible turbulent boundary layer flow are reviewed, including conservation of mass and energy, momentum equations derived from Navier-Stokes equations, and equations of state. Closure procedures were broken down into: (1) simple or zeroth-order methods, (2) first-order or mean field closure methods, and (3) second-order or mean turbulence field methods.
Closure Models for Turbulent Particle-laden Flows from Particle-resolved Direct Numerical Simulation
NASA Astrophysics Data System (ADS)
Subramaniam, Shankar; Tenneti, Sudheer; Mehrabadi, Mohammad; Garg, Rahul
2012-11-01
Gas-phase velocity fluctuations in fixed particle beds and freely evolving suspensions are quantified using a particle-resolved direct numerical simulation (PR-DNS). The flow regime corresponds to gas-solid systems typically encountered in fluidized bed risers, with high solid to gas density ratio and particle diameter being greater than the dissipative length scales. The kinetic energy associated with gas-phase velocity fluctuations in homogeneous monodisperse fixed beds is characterized as a function of solid volume fraction φ and the Reynolds number based on the mean slip velocity Re. A simple scaling analysis is used to explain the dependence of k on ɛ and Re. The steady value of k results from the balance between the source of k due to interphase transfer of kinetic energy, and the dissipation rate (ɛ) of k in the gas-phase. It is found that the dissipation rate of k in gas-solid flows can be modeled using a length scale that is analogous to the Taylor microscale used in single-phase turbulence. Using the PR-DNS data for k and ɛ we also infer an eddy viscosity for gas-solid flow. For the parameter values considered here, the level of gas-phase velocity fluctuations in freely evolving suspensions differs by only 10% from the value for the corresponding fixed beds. Funded in part by the US Department of Energy's National Energy Technology Laboratory Grant DE-FC26-07NT43098 (Advanced Research) and the National Science Foundation's grant CBET 1134500.
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)
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.
Domingo, Pascale; Vervisch, Luc; Payet, Sandra; Hauguel, Raphaeel
2005-12-01
Two complementary simulations of premixed turbulent flames are discussed. Low Reynolds number two-dimensional direct numerical simulation of a premixed turbulent V flame is first performed, to further analyze the behavior of various flame quantities and to study key ingredients of premixed turbulent combustion modeling. Flame surface density, subgrid-scale variance of progress variables, and unresolved turbulent fluxes are analyzed. These simulations include fully detailed chemistry from a flame-generated tabulation (FPI) and the analysis focuses on the dynamics of the thin flame front. Then, a novel subgrid scale closure for large eddy simulation of premixed turbulent combustion (FSD-PDF) is proposed. It combines the flame surface density (FSD) approach with a presumed probability density function (PDF) of the progress variable that is used in FPI chemistry tabulation. The FSD is useful for introducing in the presumed PDF the influence of the spatially filtered thin reaction zone evolving within the subgrid. This is achieved via the exact relation between the PDF and the FSD. This relation involves the conditional filtered average of the magnitude of the gradient of the progress variable. In the modeling, this conditional filtered mean is approximated from the filtered gradient of the progress variable of the FPI laminar flame. Balance equations providing mean and variance of the progress variable together with the measure of the filtered gradient are used to presume the PDF. A three-dimensional larger Reynolds number flow configuration (ORACLES experiment) is then computed with FSD-PDF and the results are compared with measurements.
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.
NASA Technical Reports Server (NTRS)
Demuren, A. O.; Sarkar, S.
1993-01-01
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.
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.
Advancements in engineering turbulence modeling
NASA Technical Reports Server (NTRS)
Shih, T.-H.
1991-01-01
Some new developments in two-equation models and second order closure models are presented. Two-equation models (k-epsilon models) have been widely used in computational fluid dynamics (CFD) for engineering problems. Most of low-Reynolds number two-equation models contain some wall-distance damping functions to account for the effect of wall on turbulence. However, this often causes the confusion and difficulties in computing flows with complex geometry and also needs an ad hoc treatment near the separation and reattachment points. A set of modified two-equation models is proposed to remove the aforementioned shortcomings. The calculations using various two-equation models are compared with direct numerical simulations of channel flow and flat boundary layers. Development of a second order closure model is also discussed with emphasis on the modeling of pressure related correlation terms and dissipation rates in the second moment equations. All the existing models poorly predict the normal stresses near the wall and fail to predict the 3-D effect of mean flow on the turbulence (e.g. decrease in the shear stress caused by the cross flow in the boundary layer). The newly developed second order near-wall turbulence model is described and is capable of capturing the near-wall behavior of turbulence as well as the effect of 3-D mean flow on the turbulence.
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
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.
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
Deriving statistical closure from dynamical optimization
NASA Astrophysics Data System (ADS)
Turkington, Bruce
2015-11-01
Turbulence theorists have traditionally deduced statistical models by generating a hierarchy of moment equations and invoking some closure rules to truncate the hierarchy. In this talk a conceptually different approach to model reduction and statistical closure will be presented, and its implications for coarse-graining fluid turbulence will be indicated. The author has developed this method in the context of nonequilibrium statistical descriptions of Hamiltonian systems with many degrees of freedom. With respect to a chosen parametric statistical model, the lack-of-fit of model paths to the full dynamics is minimized in a time-integrated, mean-squared sense. This optimal closure method is applied to coarse-grain spectrally-truncated inviscid dynamics, including the Burgers-Hopf equation and incompressible two-dimensional flow, using the means and/or variances of low modes as resolved variables. The derived reduced dynamics for these test cases contain (1) scale-dependent dissipation which is not a local eddy viscosity, (2) modified nonlinear interactions between resolved modes, and (3) coupling between the mean and variance of each resolved mode. These predictions are validated against direct numerical simulations of ensembles for the fully resolved dynamics.
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.
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
Problems in simulating the stratocumulus-topped boundary layer with a third-order closure model
NASA Technical Reports Server (NTRS)
Moeng, C.-H.; Randall, D. A.
1984-01-01
The Andre et al. (1976, 1978) third-order closure model, in which the time rate of change terms, the relaxation and rapid effects for pressure-related terms, and the clipping approximation are used along with the quasi-normal closure, is invoked in the study of turbulence in a cloudy layer that is radiatively cooled from above. A spurious oscillation whose greatest amplitude lies near the inversion is shown by analysis to arise from the mean gradient and buoyancy terms of the triple-moment equations. An attempt is made to damp the oscillation through the introduction of diffusion terms into the triple-moment equations. The results obtained are noted to be sensitive to the ad hoc eddy coefficient applied in the third-moment equations.
The URAPS closure for the normalized Reynolds stress
NASA Astrophysics Data System (ADS)
Koppula, Karuna S.; Muthu, Satish; Bénard, André; Petty, Charles A.
2013-07-01
The Reynolds-averaged Navier-Stokes (RANS)-equation for constant property Newtonian fluids is an exact, albeit unclosed, first-order moment equation for the mean velocity field. The RANS-equation and the Reynolds-averaged continuity equation together with a model for the Reynolds stress provide a set of closed equations that govern the behavior of the mean velocity and mean pressure fields. In this turbulent mixing and beyond (TMB) paper, the key ideas related to a recently developed universal closure for the normalized Reynolds (NR)-stress are reviewed. The new approach relates the NR-stress to four characteristic time scales: a turbulent time scale, a viscous time scale, a time scale related to the mean field velocity gradient and a time scale associated with a rigid body frame-of-reference. The theory stems from an analysis of the Navier-Stokes equation and is formulated as a universal non-negative mapping of the NR-stress into itself. Consequently, all solutions of the NR-stress equation are non-negative dyadic-valued linear operators regardless of the class of benchmark flows used to determine closure parameters. The new closure model predicts that the Coriolis acceleration causes an anisotropic re-distribution of turbulent kinetic energy among the three components of the fluctuating velocity in rotating homogeneous decay.
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.
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.
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.
Modelling of the pressure-velocity correlation in turbulence diffusion
NASA Astrophysics Data System (ADS)
Fu, Song
1993-05-01
In the context of second-moment closure, the mechanism of turbulence diffusion consists of mainly two parts: a triple velocity correlation and a pressure-velocity correlation. The first correlation is measurable and can be analyzed theoretically through its transport equation. The second correlation cannot, however, be obtained directly from experiments and knowledge about it is comparatively limited. Most current computations of turbulent flows adopt diffusion models which neglect the effect of the pressure-velocity correlation in the diffusion process. The importance of this correlation effect is elucidated; the neglect of this effect constitutes some of the major defects in the application of the second-moment closures. Through the relation between the two correlations, established by Lumley (1978), we propose a new type of turbulence diffusion model which takes into account the pressure effect. Application of this new model in the computation of the turbulence shearless mixing layer and plane- and round-jet flows shows that the spreading rates of these flows can be captured satisfactorily.
Philosophies and fallacies in turbulence modeling
NASA Astrophysics Data System (ADS)
Spalart, Philippe R.
2015-04-01
We present a set of positions, likely to be controversial, on turbulence modeling for the Reynolds-Averaged Navier Stokes (RANS) equations. The paper has three themes. First is what we call the "fundamental paradox" of turbulence modeling, between the local character of the Partial Differential Equations strongly favored by CFD methods and the nonlocal physical nature of turbulence. Second, we oppose two philosophies. The "Systematic" philosophy attempts to model the exact transport equations for the Reynolds stresses or possibly higher moments term by term, gradually relegating the Closure Problem to higher moments and invoking the "Principle of Receding Influence" (although rarely formulating it). In contrast, the "Openly Empirical" philosophy produces models which satisfy strict constraints such as Galilean invariance, but lack an explicit connection with terms in the exact turbulence equations. The prime example is the eddy-viscosity assumption. Third, we explain a series of what we perceive as fallacies, many of them widely held and by senior observers, in turbulence knowledge, leading to turbulence models. We divide them into "hard" fallacies for which a short mathematical argument demonstrates that a particular statement is wrong or meaningless, and "soft" fallacies for which approximate physical arguments can be opposed, but we contend that a clear debate is overdue and wishful thinking has been involved. Some fallacies appear to be "intermediate." An example in the hard class is the supposed isotropy of the diagonal Reynolds stresses. Examples in the soft class are the need to match the decay rate of isotropic turbulence, and the value of realizability in a model. Our hope is to help the direct effort in this field away from simplistic and hopeless lines of work, and to foster debates.
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.
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.
Turbulent Convection: Old and New Models
NASA Astrophysics Data System (ADS)
Canuto, V. M.
1996-08-01
This paper contains (1) a physical argument to show that the one-eddy MLT model underestimates the convective flux Fc in the high-efficiency regime, while it overestimates Fc in the low-efficiency regime, and (2) a new derivation of the Fc(MLT) using a turbulence model in the one-eddy approximation. (3) We forsake the one-eddy approximation and adopt the Kolmogorov spectrum to represent the turbulent energy spectrum. The resulting Fc > Fc(MLT) in the high-efficiency regime, and Fc
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).
Turbulent flow computation in a circular U-Bend
NASA Astrophysics Data System (ADS)
Miloud, Abdelkrim; Aounallah, Mohammed; Belkadi, Mustapha; Adjlout, Lahouari; Imine, Omar; Imine, Bachir
2014-03-01
Turbulent flows through a circular 180° curved bend with a curvature ratio of 3.375, defined as the the bend mean radius to pipe diameter is investigated numerically for a Reynolds number of 4.45×104. The computation is performed for a U-Bend with full long pipes at the entrance and at the exit. The commercial ANSYS FLUENT is used to solve the steady Reynolds-Averaged Navier-Stokes (RANS) equations. The performances of standard k-ɛ and the second moment closure RSM models are evaluated by comparing their numerical results against experimental data and testing their capabilities to capture the formation and extend this turbulence driven vortex. It is found that the secondary flows occur in the cross-stream half-plane of such configurations and primarily induced by high anisotropy of the cross-stream turbulent normal stresses near the outer bend.
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.
NASA Astrophysics Data System (ADS)
Bihlo, Alexander; Dos Santos Cardoso-Bihlo, Elsa Maria; Nave, Jean-Christophe; Popovych, Roman
2012-11-01
Various subgrid-scale closure models break the invariance of the Euler or Navier-Stokes equations and thus violate the geometric structure of these equations. A method is shown which allows one to systematically derive invariant turbulence models starting from non-invariant turbulence models and thus to correct artificial symmetry-breaking. The method is illustrated by finding invariant hyperdiffusion schemes to be applied in the two-dimensional turbulence problem.
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.
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…
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.
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.
Inhomogeneous turbulence in magnetic reconnection
NASA Astrophysics Data System (ADS)
Yokoi, Nobumitsu
2016-07-01
Turbulence is expected to play an essential role in enhancing magnetic reconnection. Turbulence associated with magnetic reconnection is highly inhomogeneous: it is generated by inhomogeneities of the field configuration such as the velocity shear, temperature gradient, density stratification, magnetic shear, etc. This self-generated turbulence affects the reconnection through the turbulent transport. In this reconnection--turbulence interaction, localization of turbulent transport due to dynamic balance between several turbulence effects plays an essential role. For investigating inhomogeneous turbulence in a strongly nonlinear regime, closure or turbulence modeling approaches provide a powerful tool. A turbulence modeling approach for the magnetic reconnection is introduced. In the model, the mean-field equations with turbulence effects incorporated are solved simultaneously with the equations of turbulent statistical quantities that represent spatiotemporal properties of turbulence under the effect of large-scale field inhomogeneities. Numerical simulations of this Reynolds-averaged turbulence model showed that self-generated turbulence enhances magnetic reconnection. It was pointed out that reconnection states may be divided into three category depending on the turbulence level: (i) laminar reconnection; (ii) turbulent reconnection, and (iii) turbulent diffusion. Recent developments in this direction are also briefly introduced, which includes the magnetic Prandtl number dependence, spectral evolution, and guide-field effects. Also relationship of this fully nonlinear turbulence approach with other important approaches such as plasmoid instability reconnection will be discussed.
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.
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.
On the prediction of turbulent secondary flows
NASA Technical Reports Server (NTRS)
Speziale, C. G.; So, R. M. C.; Younis, B. A.
1992-01-01
The prediction of turbulent secondary flows, with Reynolds stress models, in circular pipes and non-circular ducts is reviewed. Turbulence-driven secondary flows in straight non-circular ducts are considered along with turbulent secondary flows in pipes and ducts that arise from curvature or a system rotation. The physical mechanisms that generate these different kinds of secondary flows are outlined and the level of turbulence closure required to properly compute each type is discussed in detail. Illustrative computations of a variety of different secondary flows obtained from two-equation turbulence models and second-order closures are provided to amplify these points.
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.
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…
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.
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.
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.
Nonlocal Closures for Plasma Fluid Simulations
NASA Astrophysics Data System (ADS)
Held, Eric
2003-10-01
Theoretical tools applied to lab and astrophysical plasmas tend toward two extremes: kinetic models rife with physics but operating for short times and fluid models employing simplified closure relations but operating for long times. Until computers are fast enough to calculate kinetic physics over resistive times, efforts to extend plasma fluid models to handle a wider range of physics are critical. In this work, we generalize the program of fluid closure to capture kinetic effects in nonlocal, integral forms for higher-order fluid moments. These closures embody collisional, particle-trapping and Landau physics by integrating the fluid drives and closure moments along characteristics of the distribution function, F. The inversion of an operator that includes these physical effects begins with an expansion in eigenfunctions of the collision operator. Next, the characteristics of F are identified by diagonalizing the resultant system of hyperbolic equations. Integrating and taking the closure moments of F results in coupled Volterra equations involving the fluid drives and closures. It is shown that the collisional and nearly collisionless limits of these integral equations match onto previous expressions. In addition to significantly advancing the realism of previous fluid closures, integration along comparatively few ( ˜ 100)characteristics represents a significant reduction in work compared to kinetic treatments that follow millions of particles. These characteristics uncover the essential velocity-space dependence of F and hence render this closure scheme suitable for simulation of long time scale behavior. As a specific example, we conclude this talk by discussing the incorporation of these closures in plasma fluid simulations of neoclassical tearing modes in ITER-relevant discharges.
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.
Electron parallel closures for arbitrary collisionality
Ji, Jeong-Young Held, Eric D.
2014-12-15
Electron parallel closures for heat flow, viscosity, and friction force are expressed as kernel-weighted integrals of thermodynamic drives, the temperature gradient, relative electron-ion flow velocity, and flow-velocity gradient. Simple, fitted kernel functions are obtained for arbitrary collisionality from the 6400 moment solution and the asymptotic behavior in the collisionless limit. The fitted kernels circumvent having to solve higher order moment equations in order to close the electron fluid equations. For this reason, the electron parallel closures provide a useful and general tool for theoretical and computational models of astrophysical and laboratory plasmas.
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.
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.
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
Advances in turbulence studies. [Magnetohydrodynamic flows
Branover, H.; Unger, Y.
1993-01-01
Important contemporary trends in both experimental and theoretical turbulence research are reported. Particular attention is given to vortex reconnection, cascade, and mixing in turbulent flows; intermittent turbulence from closures; tearing instabilities in 2D MHD turbulence; axisymmetric hydromagnetic dynamo; bifurcations in MHD flow generated by electric current discharge; renormalization group analysis of MHD turbulence with low magnetic Reynolds number; Solution for turbulent primary azimuthal velocity in liquid-metal flows in sliding electric contacts; analogies between geophysical and hydromagnetic flows; turbulent electrically-induced vortical flows; dissipation length scale dynamics; two-phase grid turbulence; abridged octave wavenumber ring models for 2D turbulence; rag theory of magnetic fluctuations in turbulent flow; and instabilities of the nonuniform flows of a low-temperature plasma in MHD channels.
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.
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.
Near-wall turbine closure for curved flows
NASA Technical Reports Server (NTRS)
So, R. M. C.; Lai, Y. G.; Hwang, B. C.
1991-01-01
At present, turbulence closures for curved flows only account for curvature effects in the fully turbulent region where the Reynolds number is large. The justification is that, near a wall, viscous effects dominate and curvature effects are only of secondary importance. Recent direct simulation data show that this assumption is not valid, even for simple two-dimensional fully developed turbulent curved channel flows. This paper presents an approach to develop a near-wall turbulence closure for wall-bounded curved flows. The curved channel direct simulation data is used as a guide to held develop such a closure. The proposed closure has the unique property of approaching conventional high-Reynolds-number Reynolds-stress closures far away from the wall. Hence, curvature effects in both the near-wall and the fully turbulent parts of the flow are accounted for properly. Validations of the closure are carried out with a set of low-Reynolds-number simulation data and with experimental measurements at high Reynolds number. Good agreement is obtained in both cases; in particular, the anisotropic behavior of the normal stresses and the shear stress behavior near the convex and concave walls.
NASA Astrophysics Data System (ADS)
Sundaram, Brruntha; Klimenko, Alexander Yuri; Cleary, Matthew John; Ge, Yipeng
2016-07-01
This work presents a direct and transparent interpretation of two concepts for modelling turbulent combustion: generalised Multiple Mapping Conditioning (MMC) and sparse-Lagrangian Large Eddy Simulation (LES). The MMC approach is presented as a hybrid between the Probability Density Function (PDF) method and approaches based on conditioning (e.g. Conditional Moment Closure, flamelet, etc.). The sparse-Lagrangian approach, which allows for a dramatic reduction of computational cost, is viewed as an alternative interpretation of the Filtered Density Function (FDF) methods. This work presents simulations of several turbulent diffusion flame cases and discusses the universality of the localness parameter between these cases and the universality of sparse-Lagrangian FDF methods with MMC.
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.
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.
TURBULENCE MODELING APPLIED TO BUOYANT PLUMES
A viable computer model was developed that is based on second-order closure of the turbulent correlation equations for predicting the fate of nonchemically reacting contaminants released in the atmospheric boundary layer. The invariant turbulence model discussed in previous repor...
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.
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).
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.
Merci, Bart; Roekaerts, Dirk; Naud, Bertrand; Pope, Stephen B.
2006-07-15
Numerical simulation results are presented for turbulent jet diffusion flames with various levels of turbulence-chemistry interaction, stabilized behind a bluff body (Sydney Flames HM1-3). Interaction between turbulence and combustion is modeled with the transported joint-scalar PDF approach. The mass density function transport equation is solved in a Lagrangian manner. A second-moment-closure turbulence model is applied to obtain accurate mean flow and turbulent mixing fields. The behavior of two micromixing models is discussed: the Euclidean minimum spanning tree model and the modified Curl coalescence dispersion model. The impact of the micromixing model choice on the results in physical space is small, although some influence becomes visible as the amount of local extinction increases. Scatter plots and profiles of conditional means and variances of thermochemical quantities, conditioned on the mixture fraction, are discussed both within and downstream of the recirculation region. A distinction is made between local extinction and incomplete combustion, based on the CO species mass fraction. The differences in qualitative behavior between the micromixing models are explained and quantitative comparison to experimental data is made. (author)
NASA Astrophysics Data System (ADS)
Tse, K. L.; Mahalov, A.; Nicolaenko, B.; Joseph, B.
2004-09-01
Shear-convective turbulence is studied using a high resolution 3D direct numerical simulation (DNS). Flow configuration consisting of a modeled jet capping a thermally unstable layer is simulated and the results are compared with the reference situation where only the convective layer is present. Quasi-equilibrium turbulent datasets, in which the turbulent energy budgets are nearly balanced, are obtained. A ‘mechanical’ barrier is identified near the jet centerline in the shear-convective case. Intense and elongated vorticity regions are created in a narrow layer above the barrier in a way similar to the shear-sheltering effect. Vertical profiles of turbulence statistics and budgets are presented. We have unambiguously identified layers of counter-gradient momentum and heat fluxes which occur near regions of penetrative convection. Using quasi-equilibrium DNS datasets, we evaluate the performance of some popular second-order closure models of turbulence. The models satisfactorily predict the triple moments and dissipation, except in the counter-gradient region. The models, however, fail to predict the pressure correlation terms.
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.
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.
Boltzmann kinetic equation for filtered fluid turbulence.
Girimaji, Sharath S
2007-07-20
We develop a kinetic Boltzmann equation for describing filtered fluid turbulence applicable for continuum and noncontinuum effects. The effect of unresolved turbulent motion on the resolved distribution function is elucidated and closure modeling issues of kinetic Boltzmann and Navier-Stokes descriptions are reconciled. This could pave the way for unifying turbulence modeling at kinetic and continuum levels and the development of numerical methods that are valid over a wide range of flow physics. PMID:17678288
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.
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.
40 CFR 264.113 - Closure; time allowed for closure.
Code of Federal Regulations, 2011 CFR
2011-07-01
... 40 Protection of Environment 26 2011-07-01 2011-07-01 false Closure; time allowed for closure. 264... (CONTINUED) STANDARDS FOR OWNERS AND OPERATORS OF HAZARDOUS WASTE TREATMENT, STORAGE, AND DISPOSAL FACILITIES Closure and Post-Closure § 264.113 Closure; time allowed for closure. (a) Within 90 days after...
40 CFR 265.113 - Closure; time allowed for closure.
Code of Federal Regulations, 2011 CFR
2011-07-01
... 40 Protection of Environment 26 2011-07-01 2011-07-01 false Closure; time allowed for closure. 265... (CONTINUED) INTERIM STATUS STANDARDS FOR OWNERS AND OPERATORS OF HAZARDOUS WASTE TREATMENT, STORAGE, AND DISPOSAL FACILITIES Closure and Post-Closure § 265.113 Closure; time allowed for closure. (a) Within...
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
Mechanics of fatigue crack closure
NASA Technical Reports Server (NTRS)
Newman, J. C., Jr. (Editor); Elber, Wolf (Editor)
1988-01-01
Papers are presented on plasticity induced crack closure, crack closure in fatigue crack growth, the dependence of crack closure on fatigue loading variables, and a procedure for standardizing crack closure levels. Also considered are a statistical approach to crack closure determination, the crack closure behavior of surface cracks under pure bending, closure measurements on short fatigue cracks, and crack closure under plane strain conditions. Other topics include fatigue crack closure behavior at high stress ratios, the use of acoustic waves for the characterization of closed fatigue cracks, and the influence of fatigue crack wake length and state of stress on crack closure.
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
Computation of turbulent channel flow using Large-Eddy Interaction Model
NASA Technical Reports Server (NTRS)
Hong, S. K.; Payne, F. R.
1987-01-01
The objective of the paper is to investigate the nature and values of closure parameters appearing in the proposed Large-Eddy Interaction Model for prediction of turbulent flow field. Effects of two closure parameters on predicted Reynolds stresses and other turbulence structural quantities are examined for channel flows at two Reynolds numbers.
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),…
Optimal thermalization in a shell model of homogeneous turbulence
NASA Astrophysics Data System (ADS)
Thalabard, Simon; Turkington, Bruce
2016-04-01
We investigate the turbulence-induced dissipation of the large scales in a statistically homogeneous flow using an ‘optimal closure,’ which one of us (BT) has recently exposed in the context of Hamiltonian dynamics. This statistical closure employs a Gaussian model for the turbulent scales, with corresponding vanishing third cumulant, and yet it captures an intrinsic damping. The key to this apparent paradox lies in a clear distinction between true ensemble averages and their proxies, most easily grasped when one works directly with the Liouville equation rather than the cumulant hierarchy. We focus on a simple problem for which the optimal closure can be fully and exactly worked out: the relaxation arbitrarily far-from-equilibrium of a single energy shell towards Gibbs equilibrium in an inviscid shell model of 3D turbulence. The predictions of the optimal closure are validated against DNS and contrasted with those derived from EDQNM closure.
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.
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.
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.
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.
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.
Turbulence transport with nonlocal interactions
Linn, R.R.; Clark, T.T.; Harlow, F.H.; Turner, L.
1998-03-01
This preliminary report describes a variety of issues in turbulence transport analysis with particular emphasis on closure procedures that are nonlocal in wave-number and/or physical space. Anomalous behavior of the transport equations for large scale parts of the turbulence spectrum are resolved by including the physical space nonlocal interactions. Direct and reverse cascade processes in wave-number space are given a much richer potential for realistic description by the nonlocal formulations. The discussion also describes issues, many still not resolved, regarding new classes of self-similar form functions.
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.
Transcatheter closure of ruptured sinus of valsalva to left ventricle
Manuel, Devi A; Lahiri, Anandaroop; George, Oommen K
2016-01-01
We report a rare case of ruptured right sinus of valsalva into the left ventricle (LV). Transthoracic echocardiography showed a marked turbulent flow from the right aortic sinus to the LV. We describe a novel technique of closure of this defect with duct occluder, involving the formation of an arterio-arterial loop, without resorting to the usual arteriovenous loop. PMID:27011698
Transcatheter closure of ruptured sinus of valsalva to left ventricle.
Manuel, Devi A; Lahiri, Anandaroop; George, Oommen K
2016-01-01
We report a rare case of ruptured right sinus of valsalva into the left ventricle (LV). Transthoracic echocardiography showed a marked turbulent flow from the right aortic sinus to the LV. We describe a novel technique of closure of this defect with duct occluder, involving the formation of an arterio-arterial loop, without resorting to the usual arteriovenous loop. PMID:27011698
Solvents level dipole moments.
Liang, Wenkel; Li, Xiaosong; Dalton, Larry R; Robinson, Bruce H; Eichinger, Bruce E
2011-11-01
The dipole moments of highly polar molecules measured in solution are usually smaller than the molecular dipole moments that are calculated with reaction field methods, whereas vacuum values are routinely calculated in good agreement with available vapor phase data. Whether from Onsager's theory (or variations thereof) or from quantum mechanical methods, the calculated molecular dipoles in solution are found to be larger than those measured. The reason, of course, is that experiments measure the net dipole moment of solute together with the polarized (perturbed) solvent "cloud" surrounding it. Here we show that the reaction field charges that are generated in the quantum mechanical self-consistent reaction field (SCRF) method give a good estimate of the net dipole moment of the solute molecule together with the moment arising from the reaction field charges. This net dipole is a better description of experimental data than the vacuum dipole moment and certainly better than the bare dipole moment of the polarized solute molecule. PMID:21923185
Probability density function of a passive scalar in turbulent shear flows
Kollmann, W.; Janicka, J.
1982-10-01
The transport equation for the probability density function of a scalar in turbulent shear flow is analyzed and the closure based on the gradient flux model for the turbulent flux and an integral model for the scalar dissipation term is put forward. The probability density function equation is complemented by a two-equation turbulence model. Application to several shear flows proves the capability of the closure model to determine the probability density function of passive scalars.
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
Course 4: Statistical Turbulence Modelling for the Computation of Physically Complex Flows
NASA Astrophysics Data System (ADS)
Leschziner, M. A.
Contents 1 Approaches to characterising turbulence 2 Some basic statistical properties of turbulence and associated implications 3 Review of "simple" modelling approaches 3.1 The eddy-viscosity concept 3.2 Model categories 3.3 Model applicability 4 Second-moment equations and implied stress-strain interactions 4.1 Near-wall shear 4.2 Streamline curvature 4.3 Separation and recirculating flow 4.4 Rotation 4.5 Irrotational strain 4.6 Heat transfer and stratification 5 Second moment closure 6 Non-linear eddy-viscosity models 7 Application examples 7.1 Overview 7.2 Asymmetric diffuser 7.3 Aerospatiale aerofoil 7.4 Cascade blade 7.5 Axisymmetric impinging jet 7.6 Prolate spheroid 7.7 Round-to-rectangular transition duct 7.8 Wing/flat-plate junction 7.9 Fin-plate junction 7.10 Jet-afterbody combination 8 Concluding remarks
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.
Realizable Closure Model for the Reynolds Stress in Rotating Frames
NASA Astrophysics Data System (ADS)
Petty, Charles; Benard, Andre
2015-11-01
The Reynolds-averaged Navier-Stokes equation for constant property Newtonian fluids is unclosed due to the explicit appearance of the normalized Reynolds stress and the turbulent kinetic energy. A non-negative algebraic mapping of the normalized Reynolds stress into itself provides a practical closure for a wide class of flows. Unlike eddy viscosity closure models, the theory predict the redistribution of the turbulent kinetic energy among the three components of the fluctuating velocity field for statistically stationary spanwise rotating channel flows as well as the Coriolis re-distribution of turbulent kinetic energy among the three components of the fluctuating velocity field in rotating homogeneous decay. The results partially support the conjecture that the index-of-refraction of the troposphere is anisotropic at all scales.