Subgrid-scale Reynolds Stress Research Articles

Assessment of two-parameter mixed models for large eddy simulations of transitional and turbulent flows

In the present study, improved two-parameter mixed models for large eddy simulations are proposed based on previous two-parameter mixed models of Salvetti and Banerjee [1] and Horiuti [2]. The subgrid-scale (SGS) stress in our models is decomposed into the modified Leonard stress, modified cross stress and modified SGS Reynolds stress terms. Although the modified Leonard stress term is explicitly calculated based on the scale-similarity, the modified cross stress term is built using an extension of the filtered Bardina model proposed by Horiuti [3] for better predictions of the interaction between resolved and unresolved scales (i.e., energy exchange). The modified SGS Reynolds stress is modeled by the dynamic Smagorinsky model or by a dynamic global model, leading to two unknown model coefficients for the modified cross stress and the modified SGS Reynolds stress terms. In order to demonstrate the reliability of the proposed SGS models, large eddy simulations of two types of flows (i.e., a fully developed turbulent channel flow and a transitional boundary layer flow) are performed. It is shown that the modified cross stress term makes an important contribution to the accurate predictions of such flows because the emergence of negative SGS dissipation (backward scatter) by the modified cross stress term decreases the excessive positive SGS dissipation (forward scatter). A direct comparison of the turbulent statistics with those from previous SGS models shows that the proposed SGS models result in better prediction performance both in transitional and turbulent flows.

A dynamic global-coefficient mixed subgrid-scale model for large-eddy simulation of turbulent flows

A dynamic global-coefficient mixed subgrid-scale eddy-viscosity model for large-eddy simulation of turbulent flows in complex geometries is developed. In the present model, the subgrid-scale stress is decomposed into the modified Leonard stress, cross stress, and subgrid-scale Reynolds stress. The modified Leonard stress is explicitly computed assuming a scale similarity, while the cross stress and the subgrid-scale Reynolds stress are modeled using the global-coefficient eddy-viscosity model. The model coefficient is determined by a dynamic procedure based on the global-equilibrium between the subgrid-scale dissipation and the viscous dissipation. The new model relieves some of the difficulties associated with an eddy-viscosity closure, such as the nonalignment of the principal axes of the subgrid-scale stress tensor and the strain rate tensor and the anisotropy of turbulent flow fields, while, like other dynamic global-coefficient models, it does not require averaging or clipping of the model coefficient for numerical stabilization. The combination of the global-coefficient eddy-viscosity model and a scale-similarity model is demonstrated to produce improved predictions in a number of turbulent flow simulations.

Effect of Sub-Grid Scales on Large Eddy Simulation of Particle Deposition in a Turbulent Channel Flow

Large-eddy simulations (LES) of particle transport and deposition in turbulent channel flow were presented. Particular attention was given to the effect of subgrid scales on particle dispersion and deposition processes. A computational scheme for simulating the effect of subgrid scales (SGS) turbulence fluctuation on particle motion was developed and tested. Large-eddy simulation of Navier-Stokes equations using a finite volume method was used for finding instantaneous filtered fluid velocity fields of the continuous phase in the channel. Selective structure function model was used to account for the subgrid-scale Reynolds stresses. It was shown that the LES was capable of capturing the turbulence near wall coherent eddy structures. The Lagrangian particle tracking approach was used and the transport and deposition of particles in the channel were analyzed. The drag, lift, Brownian, and gravity forces were included in the particle equation of motion. The Brownian force was simulated using a white noise st...

Multi-scale analysis of subgrid stress and energy dissipation in turbulent channel flow

In present study, the subgrid scale (SGS) stress and dissipation for multiscale formulation of large eddy simulation are analyzed using the data of turbulent channel flow at Re τ = 180 obtained by direct numerical simulation. It is found that the small scale SGS stress is much smaller than the large scale SGS stress for all the stress components. The dominant contributor to large scale SGS stress is the cross stress between small scale and subgrid scale motions, while the cross stress between large scale and subgrid scale motions make major contributions to small scale SGS stress. The energy transfer from resolved large scales to subgrid scales is mainly caused by SGS Reynolds stress, while that between resolved small scales and subgrid scales are mainly due to the cross stress. The multiscale formulation of SGS models are evaluated a priori, and it is found that the small–small model is superior to other variants in terms of SGS dissipation.

A Family of Dynamic Subgrid-Scale Models Consistent with Asymptotic Material Frame Indifference

It is claimed in the subgrid-scale (SGS) modeling of incompressible turbulent flows that none of the (modified) Leonard terms, the (modified) cross terms, or their sums can be neglected, in principle, due to the constraint of material frame indifference in the limit of two-dimensional turbulence [C. G. Speziale: Geophys. Astrophys. Fluid Dyn. 23 (1983) 69], and that the Clark model [R. A. Clark, J. H. Ferziger and W. C. Reynolds: J. Fluid Mech. 91 (1979) 1] is consistent with this constraint. Furthermore, a family of dynamic SGS models consistent with this constraint is found, and specifically, a two-parameter dynamic SGS model is proposed as the most desirable member, whose expression for the SGS Reynolds stress asymptotically disappears in the limit of two-dimensional turbulence.

Investigation for the One-Equation-Type Subgrid Model with Eddy-Viscosity Expression Including the Shear-Damping Effect.

The model expression for the subgrid-scale(SGS)Reynolds stress and the transport equation of the SGS energy are theoretically derived using a two-scale direct-interaction approximation(TSDIA). Applying the model to three-type flows, i.e.a homogeneous decaying turbulence, a mixing layer and a channel flow, the model constants are optimized and the results are compared with those of the Smagorinsky model in detail. Consequently, it is found that this one-equation model has two deficiencies. One is that the model-constants are dependent on flow fields like the Smagorinsky model. The other is that an exact asymptotic-behavior of the SGS energy in the vicinity of the wall is not satisfied by this one-equation model. Therefore, for the purpose of improving the near-wall profiles for the SGS quantities in this model, a new model for the SGS dissipation rate is suggested on the basis of a low-Reynolds-nomber Κ-e model. Moreover, using the model including a high-order term of the SGS Reynolds stress, a new one-equation model which is applicable to several flows with fixed model-constants is proposed.

Investigation for the One-Equation-Type Subgrid Model with Eddy-Viscosity Expression Including the Shear-Damping Effect.

The model expression for the subgrid-scale(SGS)Reynolds stress and the transport equation of the SGS energy are theoretically derived using a two-scale direct-interaction approximation(TSDIA). Applying the model to three-type flows, i.e.a homogeneous decaying turbulence, a mixing layer and a channel flow, the model constants are optimized and the results are compared with those of the Smagorinsky model in detail. Consequently, it is found that this one-equation model has two deficiencies. One is that the model-constants are dependent on flow fields like the Smagorinsky model. The other is that an exact asymptotic-behavior of the SGS energy in the vicinity of the wall is not satisfied by this one-equation model. Therefore, for the purpose of improving the near-wall profiles for the SGS quantities in this model, a new model for the SGS dissipation rate is suggested on the basis of a low-Reynolds-nomber Κ-e model. Moreover, using the model including a high-order term of the SGS Reynolds stress, a new one-equation model which is applicable to several flows with fixed model-constants is proposed.

A new dynamic two-parameter mixed model for large-eddy simulation

A new dynamic subgrid-scale (SGS) mixed model is proposed for large-eddy simulation of turbulent flows. This model is based on the decomposition of the SGS stress terms into the modified Leonard, modified cross and modified SGS Reynolds stress terms. In this model, the modified Leonard term is computed explicitly. The modified cross term and modified SGS Reynolds stress are assumed to be proportional to a new term, the form of which is comparable to the generalized central moment, derived as an extension of the filtered Bardina model proposed by Horiuti [J. Phys. Soc. Jpn. 66, 91 (1997)]. Using a linear combination of this new term with the Smagorinsky model for the modified SGS Reynolds stress, the proposed model contains two model parameters, which are computed dynamically. Two formulations for the test-filtered SGS stress reported by Zang et al. [Phys. Fluids A 5, 3186 (1993)] and Vreman et al. [Phys. Fluids 6, 4057 (1994)] are compared, and the compatibility of the SGS models with the standard dynamic SGS model procedure is discussed. The proposed model is assessed for incompressible channel and mixing layer flows, in comparison with the dynamic Smagorinsky model of Germano et al. [Phys. Fluids A 3, 1760 (1991)], the dynamic mixed model of Zang et al. and the dynamic two-parameter mixed model of Salvetti and Banerjee [Phys. Fluids 7, 2831 (1995)]. In the “a priori” test, the proposed model gave the closest agreement with the modified cross term as well as the modified SGS Reynolds stress term. It is shown that the proposed term represents a more general model of the SGS stress than the modified Leonard term and yields a more accurate approximation. These SGS models are tested further in actual LES of channel and mixing layer flows (“a posteriori” test). The results were consistent with those of the “a priori” tests; the proposed model yielded the most accurate results. In the proposed model, the SGS quantities were predominantly represented using the new term, and the contribution of the Smagorinsky model was minimal. The two parameters contained in the model were determined locally in space on a point-by-point basis.

Modeling of the dynamic subgrid-scale viscosity in large eddy simulation

The dynamic subgrid-scale (SGS) viscosity is reexamined on the basis of the production process of the SGS Reynolds stress. A new model for the SGS viscosity is proposed in place of the Smagorinsky-type model of mixing-length form. The model is applied to a channel flow, and the comparison with other models is made.

A priori tests of a new dynamic subgrid-scale model for finite-difference large-eddy simulations

This work focuses on subgrid-scale (SGS) modeling for finite-difference large-eddy simulations, employing filters in physical space. When a filter in physical space is used, an overlap is allowed between the unresolved and the resolved scales. For such a filter, all the three terms in the classical decomposition of the SGS stress tensor are present: the Leonard and cross-terms, due to the overlap between scales, and the true SGS Reynolds tensor, expressing the pure effect of the small scales. A dynamic subgrid-scale stress model is proposed, for finite-difference large-eddy simulation of incompressible and compressible flows in which the Leonard and cross-parts of the SGS stress tensor are assumed to be proportional to the resolved part (the ‘‘modified Leonard term’’), which is computed explicity. The SGS Reynolds stress is modeled by the eddy-viscosity Smagorinsky model. The two unknown parameters in this model are computed dynamically, as in Germano et al. [Phys. Fluids A 3, 1790 (1991)], but using a least squares technique. The model is tested using direct numerical simulation data for fully developed turbulent incompressible flows in presence of solid boundaries and free surfaces, and for compressible homogeneous turbulence. A ‘‘box filter’’ in physical space is used. Other SGS models are also tested, viz. the dynamic model of Germano et al. (DSM), and its compressible extension by Moin et al. [Phys. Fluids A 3, 2746 (1991)], and the dynamic mixed model in Zang et al. [Phys. Fluids A 5, 3186 (1993)] (DMM) and its compressible version developed here. Results on the behavior of the different models with regard to energy exchanges and correlation with the exact SGS stresses are presented for different filter widths. In particular high correlation is found between the modified Leonard and cross-terms thus justifying the basic assumption made in the model.

Subgrid-scale modeling suggested by a two-scale DIA

Subgrid-scale (SGS) modeling in large eddy simulation is studied using the results of a two-scale DIA about the effects of helicity controlling the energy cascade process. Such effects are closely related to vorticity effects on the SGS Reynolds stress that are lacking in the SGS-viscosity representation. These results are applied to the improvement of the SGS models of the Smagorinsky type. Discussion is also made about the relationship with the present two-equation model with the Smagorinsky model and the one-equation model based on the SGS energy.

Subgrid-scale modeling suggested by a two-scale DIA

Subgrid-scale (SGS) modeling in large eddy simulation is studied using the results of a two-scale DIA about the effects of helicity controlling the energy cascade process. Such effects are closely related to vorticity effects on the SGS Reynolds stress that are lacking in the SGS-viscosity representation. These results are applied to the improvement of the SGS models of the Smagorinsky type. Discussion is also made about the relationship with the present two-equation model with the Smagorinsky model and the one-equation model based on the SGS energy.

A proposal for a redefinition of the turbulent stresses in the filtered Navier–Stokes equations

A redefinition of the Leonard term, the subgrid scale cross term, and the subgrid scale Reynolds stress is proposed, consistent with a general statement concerning turbulent stresses. The main advantage of the new redefined stresses consists of their term by term Galilean invariance.

A Statistically-Derived Subgrid-Scale Kinetic Energy Model for the Large-Eddy Simulation of Turbulent Flows

A subgrid-scale (SGS) kinetic energy model for the large-eddy simulation (LES) of turbulent flows is constructed with the aid of the statistical results obtained from the two-scale direct-interaction approximation. In this model, the SGS Reynolds stress is written in terms of a generalized SGS eddy-viscosity representation which is expressed by using the SGS kinetic energy and the characteristic grid width. A model equation for the SGS kinetic energy is combined with the grid-scale Navier-Stokes and continuity equations to lead to an LES model of one-equation type. The usual Smagorinsky model is derived as its special case, and critical comparison is made between them.

Mathematical Description of Turbulent Flows

The mathematical description of uniform density and thermally stratified flows in terms of space averages is reviewed. The governing equations are presented and the use of alternative space filters is discussed. Different models for Sub-Grid-Scale (SGS) turbulent transport are examined. A simple algebraic model for the SGS Reynolds stresses and turbulent heat flumes in thermally stratified flows is presented. The model is cast in eddy viscosity - eddy diffusivity form. Its derivation is based on making appropriate closure approximations in the differential equations for the Reynolds stresses and the turbulent heat fluxes and introducing simplifying assumptions to reduce these equations to a system of algebraic equations. The solution of this system yields eddy coefficients which are functions of a local SGS turbulence length scale and the local structure of the velocity and the temperature fields. The variation of these coefficients with a local Richardson number is examined. Potential numerical problems which can be caused by improper formulation of the model are discussed.

An Algebraic Model for Subgrid-Scale Turbulence in Stratified Flows

Abstract Some aspects of the large eddy simulation method as applied to stratified flows are discussed and an algebraic model for subgrid-scale (SGS) turbulence is proposed. Differential equations for the SGS Reynolds stresses and turbulent heat fluxes are derived and new terms, which appear as a result of filtering nonlinear terms, are discussed. With the introduction of certain simplifying assumptions, the set of differential equations is reduced to a system of algebraic equations. The behavior of the solution of this system is studied for the special case of a locally two-dimensional structure for the large-scale field. Under certain assumptions the form of the algebraic equations for the SGS quantities is similar to the form of the equations for the corresponding “conventional” turbulent quantities. This allows comparison of the predictions made by the present SGS model to the results from “conventional” models and experimental data. The proposed model predicts that, for highly stratified flows, SGS t...

Evaluation of subgrid-scale models using an accurately simulated turbulent flow

A calculation of periodic homogeneous isotropic turbulence is used to simulate the experimental decay of grid turbulence. The calculation is found to match the experiment in a number of important aspects and the computed flow field is then treated as a realization of a physical turbulent flow. From this flow, a calculation is conducted of the large eddy field and the various averages of the subgrid-scale turbulence that occur in the large eddy simulation equations. These quantities are compared with the predictions of the models that are usually applied in large eddy simulation. The results show that the terms which involve the large-scale field are accurately modeled but the subgrid-scale Reynolds stresses are only moderately well modeled. It is also possible to use the method to predict the constants of the models without reference to experiment. Attempts to find improved models have not met with success.