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Scale-similar models for large-eddy simulations

Profile image of Fabrizio SarghiniFabrizio Sarghini

1999, Physics of Fluids

https://doi.org/10.1063/1.870021
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Abstract

Scale-similar models employ multiple filtering operations to identify the smallest resolved scales, which have been shown to be the most active in the interaction with the unresolved subgrid scales. They do not assume that the principal axes of the strain-rate tensor are aligned with those of the subgrid-scale stress (SGS) tensor, and allow the explicit calculation of the SGS energy. They can provide backscatter in a numerically stable and physically realistic manner, and predict SGS stresses in regions that are well correlated with the locations where large Reynolds stress occurs. In this paper, eddy viscosity and mixed models, which include an eddy-viscosity part as well as a scale-similar contribution, are applied to the simulation of two flows, a high Reynolds number plane channel flow, and a three-dimensional, nonequilibrium flow. The results show that simulations without models or with the Smagorinsky model are unable to predict nonequilibrium effects. Dynamic models provide a...

Figures (19)
(where p is the pressure, v the kinematic viscosity, and u,, uy, and u3, or u, uv, and w, are the streamwise, wall-normal and spanwise components of velocity, respectively), which govern the dynamics of the large, energy-carrying scales of motion. The effect of the small scales upon the resolved part of turbulence appears in the subgrid-scale (SGS) stress term, where G is the filter function of characteristic width A, and the integral is extended to the entire domain D. The applica- tion of the filtering operation to the continuity and the Navier-Stokes equations gives the resolved Navier-Stokes equations, which, in incompressible flow, are
(where p is the pressure, v the kinematic viscosity, and u,, uy, and u3, or u, uv, and w, are the streamwise, wall-normal and spanwise components of velocity, respectively), which govern the dynamics of the large, energy-carrying scales of motion. The effect of the small scales upon the resolved part of turbulence appears in the subgrid-scale (SGS) stress term, where G is the filter function of characteristic width A, and the integral is extended to the entire domain D. The applica- tion of the filtering operation to the continuity and the Navier-Stokes equations gives the resolved Navier-Stokes equations, which, in incompressible flow, are
TABLE I. Simulation parameters. Two cases were examined: A two-dimensionai plane channel flow, at Re,= du,/v=180 and 1 050, and a three- dimensional (3D) boundary layer. In all cases, periodic boundary conditions were applied in the streamwise and spanwise directions, while the no-slip conditions were used at the solid walls. The three-dimensional boundary layer is a temporally developing flow obtained by imposing an impul- sive spanwise motion, with magnitude equal to 47% of the initial mean centerline velocity, to the wall of a fully devel- oped plane channel flow; the initial condition was a calcula- tion of fully developed plane channel flow at Reynolds num- ber Re,=180. These parameters matched the DNS calculations of Coleman eg al.?’ The flow was allowed to develop until a collateral state (one in which the direction of the mean velocity is the same at each y) was reached. While in the direct numerical simulation (DNS) of Coleman et al?’ only one wall was set in motion, in the present case both walls were moved in opposite directions to double the statis- tical sample. It was verified that the important statistics were not affected up to a dimensionless time tu, ,/5= 1.2 (where u,, is the value of the friction velocity before the walls are set into motion). The two configurations examined are sketched in Fig. 1. Scale-similar models were introduced by Bardina et al.,'© who assumed that the component of the SGS most active in the energy transfer from large to small scales can be estimated with sufficient accuracy from the smallest resolved
TABLE I. Simulation parameters. Two cases were examined: A two-dimensionai plane channel flow, at Re,= du,/v=180 and 1 050, and a three- dimensional (3D) boundary layer. In all cases, periodic boundary conditions were applied in the streamwise and spanwise directions, while the no-slip conditions were used at the solid walls. The three-dimensional boundary layer is a temporally developing flow obtained by imposing an impul- sive spanwise motion, with magnitude equal to 47% of the initial mean centerline velocity, to the wall of a fully devel- oped plane channel flow; the initial condition was a calcula- tion of fully developed plane channel flow at Reynolds num- ber Re,=180. These parameters matched the DNS calculations of Coleman eg al.?’ The flow was allowed to develop until a collateral state (one in which the direction of the mean velocity is the same at each y) was reached. While in the direct numerical simulation (DNS) of Coleman et al?’ only one wall was set in motion, in the present case both walls were moved in opposite directions to double the statis- tical sample. It was verified that the important statistics were not affected up to a dimensionless time tu, ,/5= 1.2 (where u,, is the value of the friction velocity before the walls are set into motion). The two configurations examined are sketched in Fig. 1. Scale-similar models were introduced by Bardina et al.,'© who assumed that the component of the SGS most active in the energy transfer from large to small scales can be estimated with sufficient accuracy from the smallest resolved
FIG. |. Sketch of the physical configurations: (a) Plane channel; (b) three- dimensional boundary layer.
FIG. |. Sketch of the physical configurations: (a) Plane channel; (b) three- dimensional boundary layer.
TABLE II. Wall shear stress.
TABLE II. Wall shear stress.
FIG. 2. Mean velocity profiles in wall coordinates in the two-dimensional plane channel, Re,=1050. Dynamic eddy-viscosity model (plane- averaged). —~ Fourier cutoff filter; --- top-hat filter, A,/8,= V6; — . — top-hat filter. A./A,=2: — logarithmic law.
FIG. 2. Mean velocity profiles in wall coordinates in the two-dimensional plane channel, Re,=1050. Dynamic eddy-viscosity model (plane- averaged). —~ Fourier cutoff filter; --- top-hat filter, A,/8,= V6; — . — top-hat filter. A./A,=2: — logarithmic law.
FIG. 3. Mean velocity profiles in wall coordinates in the two-dimensional plane channel. (a) Re,= 180, (b) Re,= 1 050.x DNS data; —- dynamic eddy-viscosity model, --- dynamic mixed model; — - — one- coefficient Lagrangian mixed model; ---- two-coefficient Lagrangian mixed model; ——— logarithmic law.
FIG. 3. Mean velocity profiles in wall coordinates in the two-dimensional plane channel. (a) Re,= 180, (b) Re,= 1 050.x DNS data; —- dynamic eddy-viscosity model, --- dynamic mixed model; — - — one- coefficient Lagrangian mixed model; ---- two-coefficient Lagrangian mixed model; ——— logarithmic law.
FIG. 4. Turbulence intensity profiles in wall coordinates in the two- dimensional plane channel. (a) Re,=180, (b) Re,=1 050. —- Dynamic eddy-viscosity model; --- dynamic mixed model; — + — one- coefficient Lagrangian mixed model; ---- two-coefficient Lagrangian mixed model; XDNS data (Ref. 36); A experimental data (Ref. 37).
FIG. 4. Turbulence intensity profiles in wall coordinates in the two- dimensional plane channel. (a) Re,=180, (b) Re,=1 050. —- Dynamic eddy-viscosity model; --- dynamic mixed model; — + — one- coefficient Lagrangian mixed model; ---- two-coefficient Lagrangian mixed model; XDNS data (Ref. 36); A experimental data (Ref. 37).
FIG. 5. Subgrid-scale shear stress in the two-dimensional plane channel. (a) Re,= 180, (b) Re,=1 050. — Dynamic eddy-viscosity model, --- dy- namic mixed model, — + — one-coefficient Lagrangian mixed model, . ..- Lagrangian two-coefficients mixed model. Lines: eddy viscosity com- ponent; lines and symbols: eddy viscosity and scale-similar components.
FIG. 5. Subgrid-scale shear stress in the two-dimensional plane channel. (a) Re,= 180, (b) Re,=1 050. — Dynamic eddy-viscosity model, --- dy- namic mixed model, — + — one-coefficient Lagrangian mixed model, . ..- Lagrangian two-coefficients mixed model. Lines: eddy viscosity com- ponent; lines and symbols: eddy viscosity and scale-similar components.
aC. 6. Subgrid-scale dissipation in the two-dimensional plane channel, =180. (a) Dissipation by the eddy-viscosity part of the SGS stresses, oe (b) dissipation by the scale-similar part of the SGS stresses, e¢2, (C) total SGS dissipation, €,,,. —- Dynamic eddy- viscosity model; --- dy- namic mixed model; — - — one-coefficient Lagrangian mixed model: - two-coefficient Lagrangian mixed model.
aC. 6. Subgrid-scale dissipation in the two-dimensional plane channel, =180. (a) Dissipation by the eddy-viscosity part of the SGS stresses, oe (b) dissipation by the scale-similar part of the SGS stresses, e¢2, (C) total SGS dissipation, €,,,. —- Dynamic eddy- viscosity model; --- dy- namic mixed model; — - — one-coefficient Lagrangian mixed model: - two-coefficient Lagrangian mixed model.
FIG. 7. Subgrid-scale dissipation in the two-dimensional plane channel, Re, = 1 050. (a) Dissipation by the eddy-viscosity part of the SGS sees €sgs5 (D) dissipation by the scale-similar part of the SGS stresses, €55,; (c) total SGS dissipation, €,,,. —- Dynamic eddy- viscosity model; --- dy- namic mixed model, — - — one-coefficient Lagrangian mixed model, - two-coefficient Lagrangian mixed model.
FIG. 7. Subgrid-scale dissipation in the two-dimensional plane channel, Re, = 1 050. (a) Dissipation by the eddy-viscosity part of the SGS sees €sgs5 (D) dissipation by the scale-similar part of the SGS stresses, €55,; (c) total SGS dissipation, €,,,. —- Dynamic eddy- viscosity model; --- dy- namic mixed model, — - — one-coefficient Lagrangian mixed model, - two-coefficient Lagrangian mixed model.
FIG. 8. Eddy-viscosity and scale-similar model coefficients in the two- dimensional plane channel. Two-coefficient Lagrangian mixed model. — Re,=1 050; --- Re,= 180. (a) C,,; (b) Coy.
FIG. 8. Eddy-viscosity and scale-similar model coefficients in the two- dimensional plane channel. Two-coefficient Lagrangian mixed model. — Re,=1 050; --- Re,= 180. (a) C,,; (b) Coy.
FIG. 10. Time history of the wall shear stress and average turbulent kinetic energy in the three-dimensional boundary layer flow. All quantities are ini- tialized by their initial values. (a) +, /7,.,; (0) K/K,. — Coarse DNS; --- Smagorinsky model; — - — dynamic eddy-viscosity model; - - - - dynamic mixed model; - - - - - one-coefficient Lagrangian mixed model; --- two-coefficient Lagrangian mixed model; A DNS (Ref. 27).
FIG. 10. Time history of the wall shear stress and average turbulent kinetic energy in the three-dimensional boundary layer flow. All quantities are ini- tialized by their initial values. (a) +, /7,.,; (0) K/K,. — Coarse DNS; --- Smagorinsky model; — - — dynamic eddy-viscosity model; - - - - dynamic mixed model; - - - - - one-coefficient Lagrangian mixed model; --- two-coefficient Lagrangian mixed model; A DNS (Ref. 27).
FIG. 9, Eddy-viscosity model coefficient in the two-dimensional plane channel, Re,= 1050. —- Dynamic eddy-viscosity model; --- dynamic mixed model; — - — one-coefficient Lagrangian mixed model; - - - - two-coefficient Lagrangian mixed model. (a) average; (b) root-mean-square; {c) maximum.
FIG. 9, Eddy-viscosity model coefficient in the two-dimensional plane channel, Re,= 1050. —- Dynamic eddy-viscosity model; --- dynamic mixed model; — - — one-coefficient Lagrangian mixed model; - - - - two-coefficient Lagrangian mixed model. (a) average; (b) root-mean-square; {c) maximum.
FIG. 11. Total (viscous +SGS) dissipation profiles. — Smagorinsky model, --- dynamic eddy-viscosity model, — - — one-coefficient Lagrangian model. (a) t/u,,,<0; (b) t/u,,,=0.08; (c) t/u,,=0.16.
FIG. 11. Total (viscous +SGS) dissipation profiles. — Smagorinsky model, --- dynamic eddy-viscosity model, — - — one-coefficient Lagrangian model. (a) t/u,,,<0; (b) t/u,,,=0.08; (c) t/u,,=0.16.
FIG. 13. Mean velocity profiles in the three-dimensional boundary layer flow. (a) tu,,, /8=0.075; (b) tu,,,/6=0.3; (c) tu,,,/5=0.6. — Dynamic eddy-viscosity model; --- dynamic mixed model, — - — _ one- coefficient Lagrangian mixed model; -- ++ two-coefficient Lagrangian mixed model; A DNS (Ref. 27).
FIG. 13. Mean velocity profiles in the three-dimensional boundary layer flow. (a) tu,,, /8=0.075; (b) tu,,,/6=0.3; (c) tu,,,/5=0.6. — Dynamic eddy-viscosity model; --- dynamic mixed model, — - — _ one- coefficient Lagrangian mixed model; -- ++ two-coefficient Lagrangian mixed model; A DNS (Ref. 27).
FIG. 12. Time-development of the coefficient C,,, in the three-dimensional boundary layer flow. —- y7=6; --- yf 13; - ++ - yj =57. (a) Dynamic eddy-viscosity model; (b) one-coefficient Lagrangian mixed model.
FIG. 12. Time-development of the coefficient C,,, in the three-dimensional boundary layer flow. —- y7=6; --- yf 13; - ++ - yj =57. (a) Dynamic eddy-viscosity model; (b) one-coefficient Lagrangian mixed model.
FIG. 14. Turbulent kinetic energy profiles in the three-dimensional bound- ary layer flow. (a) tu, ,/0= 0.075; (b) tu,,,/d=0.3; (c) tu,,/5=0.6. — Dynamic eddy-viscosity model, --- dynamic mixed model} — - — one-coefficient Lagrangian mixed model; - - - - two-coefficient Lagrangian mixed model; A DNS (Ref. 27).
FIG. 14. Turbulent kinetic energy profiles in the three-dimensional bound- ary layer flow. (a) tu, ,/0= 0.075; (b) tu,,,/d=0.3; (c) tu,,/5=0.6. — Dynamic eddy-viscosity model, --- dynamic mixed model} — - — one-coefficient Lagrangian mixed model; - - - - two-coefficient Lagrangian mixed model; A DNS (Ref. 27).
TABLE III. CPU time required by various models, normalized by that used by the Smagorinsky model. One important consideration regards the increased re- sources required by more complex LES models. The dy- namic model requires more operations and memory than the Smagorinsky one, since the various terms used in the con- tractions must be computed and stored. Mixed models and the Lagrangian averaging procedure require additional effort. Table III reports the CPU time (normalized by the Smagor- insky model) of each model. The numbers reported show, of course, only qualitative trends, since they are strongly implementation- and machine-dependent. In this particular case, all the computations were run on a Cray C90, and the model coefficient (or coefficients) were evaluated once per step, while both the eddy-viscosity and the scale-similar models were computed at each Runge-Kutta stage. It is quite readily seen that the additional cost of the Lagrangian models is significant.
TABLE III. CPU time required by various models, normalized by that used by the Smagorinsky model. One important consideration regards the increased re- sources required by more complex LES models. The dy- namic model requires more operations and memory than the Smagorinsky one, since the various terms used in the con- tractions must be computed and stored. Mixed models and the Lagrangian averaging procedure require additional effort. Table III reports the CPU time (normalized by the Smagor- insky model) of each model. The numbers reported show, of course, only qualitative trends, since they are strongly implementation- and machine-dependent. In this particular case, all the computations were run on a Cray C90, and the model coefficient (or coefficients) were evaluated once per step, while both the eddy-viscosity and the scale-similar models were computed at each Runge-Kutta stage. It is quite readily seen that the additional cost of the Lagrangian models is significant.
FIG. 15. (u'w’) shear stress profiles in the three-dimensional boundary layer flow. (a) ru,,,/5=0.075; (b) tu,,,/5=0.3; (c) tu,,,/5=0.6. — Dy- namic eddy-viscosity model; ——— Lagrangian eddy-viscosity model, - dynamic mixed model; — - — one-coefficient Lagrangian mixed model; - - - - two-coefficient Lagrangian mixed model; A DNS (Ref. 27).
FIG. 15. (u'w’) shear stress profiles in the three-dimensional boundary layer flow. (a) ru,,,/5=0.075; (b) tu,,,/5=0.3; (c) tu,,,/5=0.6. — Dy- namic eddy-viscosity model; ——— Lagrangian eddy-viscosity model, - dynamic mixed model; — - — one-coefficient Lagrangian mixed model; - - - - two-coefficient Lagrangian mixed model; A DNS (Ref. 27).

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References (32)

  1. R. Van Driest, "On the turbulent flow near a wall," J. Aeronaut.
  2. Sci. 23, 1007 (1956).
  3. Piomelli, T. A. Zang, C. G. Speziale, and M. Y. Hussaini, "On the large-eddy simulation of transitional wall-bounded flows," Phys. Fluids A 2, 257 (1990).
  4. Voke and Z. Yang, "Numerical study of bypass transition," Phys. Fluids 7, 2256 (1995).
  5. Germano, U. Piomelli, P. Moin, and W. H. Cabot, "'A dynamic subgrid-scale eddy viscosity model," Phys. Fluids A 3, 1760 (1991).
  6. SD. K. Lilly, "A proposed modification of the Germano subgrid-scale clo- sure method," Phys. Fluids A 4, 633 (1992).
  7. H. Kraichnan, "Eddy viscosity in two and three dimensions," J. Atmo. Sciences 33, 1521 (1976).
  8. _°U. Piomelli, W. H. Cabot, P. Moin, and S. Lee, "Subgrid-scale backscat- ter in turbulent and transitional flows," Phys. Fluids A 3, 1766 (1991). tLS. Liu, C. Meneveau, and J. Katz, "On the properties of similarity subgrid-scale models as deduced from measurements in a turbulent jet,"
  9. J. Fluid Mech. 275, 83 (1994).
  10. Ghosal, T. S. Lund, P. Moin, and K. Akselvoll, "A dynamic localiza- tion model for large-eddy simulation of turbulent flow," J. Fluid Mech. 286, 229 (1995).
  11. A. Domaradzki, W. Liu, and M. E. Brachet, "An analysis of subgrid- scale interactions in numerically simulated isotropic turbulence," Phys.
  12. Fluids A 5, L747 (1993).
  13. A. Domaradzki, W. Liu, C. H_tel, and L. Kleiser, "Energy transfer in numerically simulated wall-bounded turbulent flows," Phys. Fluids 6, 1583 (1994).
  14. _SU. Piomelli, Y. Yu, and R. J. Adrian, "Subgrid-scale energy transfer and near-wall turbulence structure," Phys. Fluids 8, 215 (1996).
  15. Bardina, J. H. Ferziger, and W. C. Reynolds, "Improved subgrid scale models for large eddy simulation," AIAA Pap. 80-1357 (1980).
  16. Horiuti, "The role of the Bardina model in large eddy simulation of turbulent channel flow," Phys. Fluids A 1,426 (1989).
  17. Zang, R. L. Street, and J. Koseff, "A dynamic mixed subgrid-scale . model and its application to turbulent recirculating flows," Phys. Fluids A 5, 3186 (1993).
  18. Vreman, B. Geurts, and H. Kuerten, "On the formulation of the dy- namic mixed subgrid-scale model," Phys. Fluids 6, 4057 (1994).
  19. 2°X. Wu and K. D. Squires, "Large eddy simulation of an equilibrium three dimensional turbulent boundary layer," AIAA J. 1, 67 (1997).
  20. ZIC. Meneveau, T. S. Lund, and W. H. Cabot, "A Lagrangian dynamic subgrid-scale model of turbulence," J. Fluid Mech. 319, 353 (1996).
  21. Anderson and C. Meneveau, " Effects of the similarity model in finite- difference LES of decaying isotropic turbulence using a Lagrangian dy- namic mixed model,"Flow, Turbulence and Combustion (submitted).
  22. M. Salvetti and S. Banerjee, "A priori tests of a new dynamic subgrid- scale model for finite-difference large-eddy simulations," Phys. Fluids 7, 2831 (1995).
  23. Horiuti, "A new dynamic two-parameter mixed model for large eddy simulation," Phys. Fluids 9, 3443 (1997).
  24. _M. V. Salvetti, Y. Zang, R. L. Street, and S. Banerjee, "Large-eddy simu- lation of free-surface decaying turbulence with dynamic subgrid-scale models," Phys. Fluids 9, 2405 (1997).
  25. Piomelli, G. Coleman, and J. Kim, "On the effects of non-equilibrium on the subgrid-scale stresses," Phys. Fluids 9, 2740 (1997).
  26. K. Coleman, J. Kim, and A.-T. Le, "A numerical study of three- dimensional boundary layers," Int. J. Heat Fluid Flow 17, 333 (1996).
  27. A. Zang and M. Y. Hussaini, "On spectral muttigrid methods for the time-dependent Navier-Stokes equations," Appl. Math. Comput. 19, 359 (1986).
  28. ZgR. B. Dean, "Reynolds Number Dependence of Skin Friction and Other Bulk Flow Variables in Two-Dimensional Rectangular Duct Flow," J. Fluids Eng. 100, 215 (1978).
  29. K. Lilly, "The representation of small-scale turbulence in numerical simulation experiments," in Proc. IBM Scientific Computing Symp. on Environmental Sciences (Yorktown Heights, N.Y., 195, 1967).
  30. G. Speziale, "Galilean invariance of subgrid scale stress models in the large eddy simulation of turbulence," J. Fluid Mech. 156, 55 (1985).
  31. Germano, "Turbulence: the filtering approach," J. Fluid Mech. 238, 325 (1992). 331t is assumed here that the coefficients, Ce,, and later C,_ are smooth on the _ scale, and can, therefore, be extracted from the filtering operation.
  32. _T. S. Lund, "On the use of discrete filters for Large-eddy simulation." in

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The present study sheds light on the subgrid modeling problem encountered in the large eddy simulation ͑LES͒ of practical flows, where the turbulence is both inhomogeneous and anisotropic due to mean flow gradients. The subgrid scale stress ͑SGS͒ tensor, the quantity that is key to the success of LES, is studied here in such flows using both analysis and direct numerical simulation ͑DNS͒. It is shown that the SGS tensor, for the case of inhomogeneous flow, where the filtering operation is necessarily performed in physical space, contains two components: a rapid part that depends explicitly on the mean velocity gradient and a slow part that does not. The characterization, rapid and slow, is adopted by analogy to that used in the modeling of the pressure-strain in the Reynolds-averaged Navier-Stokes equations. In the absence of mean flow gradients, the slow part is the only nonzero component and has been the subject of much theoretical study. However, the rapid part can be important in the inhomogeneous flows that are often encountered in practice. An analytical estimate of the relative magnitude of the rapid and slow components is derived and the distinct role of each component in the energy transfer between the resolved grid scales and the unresolved subgrid scales is identified. Results that quantify this new decomposition are obtained from DNS data of a turbulent mixing layer. The rapid part is shown to play an important role when the turbulence is in a nonequilibrium state with turbulence production much larger than dissipation or when the filter size is not very small compared to the characteristic integral scale of the turbulence, as in the case of practical LES applications. More importantly, the SGS is observed to be highly anisotropic due to the close connection of the rapid part with the mean shear. The Smagorinsky eddy viscosity and the scale-similarity models are tested by performing a priori tests with data from DNS of the mixing layer. It is found that the scale-similarity model correctly represents the anisotropic energy transfer between grid and subgrid scales that is associated with the rapid part, while the eddy viscosity model captures the dissipation associated with the slow part. This may be a physical reason for the recent successes of the mixed model ͑Smagorinsky plus scale similarity͒ reported in the literature.

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A dynamic subgrid-scale eddy viscosity model
parviz moin

Physics of Fluids A: Fluid Dynamics, 1991

One major drawback of the eddy viscosity subgrid-scale stress models used in large-eddy simulations is their inability to represent correctly with a single universal constant different turbulent fields in rotating or sheared flows, near solid walls, or in transitional regimes. In the present work a new eddy viscosity model is presented which alleviates many of these drawbacks. The model coefficient is computed dynamically as the calculation progresses rather than input apriori. The model is based on an algebraic identity between the subgrid-scale stresses at two different filtered levels and the resolved turbulent stresses. The subgrid-scale stresses obtained using the proposed model vanish in laminar flow and at a solid boundary, and have the correct asymptotic behavior in the near-wall region of a turbulent boundary layer. The results of large-eddy simulations of transitional and turbulent channel flow that use the proposed model are in good agreement with the direct simulation data.

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A dynamic regularized gradient model of the subgrid-scale stress tensor for large-eddy simulation
Christophe CORRE

Physics of Fluids, 2016

Large-eddy simulation (LES) solves only the large scales part of turbulent flows by using a scales separation based on a filtering operation. The solution of the filtered Navier-Stokes equations requires then to model the subgrid-scale (SGS) stress tensor to take into account the effect of scales smaller than the filter size. In this work, a new model is proposed for the SGS stress model. The model formulation is based on a regularization procedure of the gradient model to correct its unstable behavior. The model is developed based on a priori tests to improve the accuracy of the modeling for both structural and functional performances, i.e., the model ability to locally approximate the SGS unknown term and to reproduce enough global SGS dissipation, respectively. LES is then performed for a posteriori validation. This work is an extension to the SGS stress tensor of the regularization procedure proposed by Balarac et al. ["A dynamic regularized gradient model of the subgrid-scale scalar flux for large eddy simulations," Phys. Fluids 25(7), 075107 (2013)] to model the SGS scalar flux. A set of dynamic regularized gradient (DRG) models is thus made available for both the momentum and the scalar equations. The second objective of this work is to compare this new set of DRG models with direct numerical simulations (DNS), filtered DNS in the case of classic flows simulated with a pseudo-spectral solver and with the standard set of models based on the dynamic Smagorinsky model. Various flow configurations are considered: decaying homogeneous isotropic turbulence, turbulent plane jet, and turbulent channel flows. These tests demonstrate the stable behavior provided by the regularization procedure, along with substantial improvement for velocity and scalar statistics predictions.

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Physical consistency of subgrid-scale models for large-eddy simulation of incompressible turbulent flows
Roel Verstappen

Physics of Fluids

We study the construction of subgrid-scale models for large-eddy simulation of incompressible turbulent flows. In particular, we aim to consolidate a systematic approach of constructing subgrid-scale models, based on the idea that it is desirable that subgrid-scale models are consistent with the mathematical and physical properties of the Navier-Stokes equations and the turbulent stresses. To that end, we first discuss in detail the symmetries of the Navier-Stokes equations, and the near-wall scaling behavior, realizability and dissipation properties of the turbulent stresses. We furthermore summarize the requirements that subgrid-scale models have to satisfy in order to preserve these important mathematical and physical properties. In this fashion, a framework of model constraints arises that we apply to analyze the behavior of a number of existing subgrid-scale models that are based on the local velocity gradient. We show that these subgrid-scale models do not satisfy all the desired properties, after which we explain that this is partly due to incompatibilities between model constraints and limitations of velocity-gradient-based subgrid-scale models. However, we also reason that the current framework shows that there is room for improvement in the properties and, hence, the behavior of existing subgrid-scale models. We furthermore show how compatible model constraints can be combined to construct new subgrid-scale models that have desirable properties built into them. We provide a few examples of such new models, of which a new model of eddy viscosity type, that is based on the vortex stretching magnitude, is successfully tested in large-eddy simulations of decaying homogeneous isotropic turbulence and turbulent plane-channel flow.

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Related topics

  • Engineering
  • Physics
  • Mechanics
  • Large Eddy Simulation
  • Statistical Physics
  • Channel Flow
  • Physics of Fluids

    • Cited by

    Three-dimensional coarse large-eddy simulations of the flow above two-dimensional sinusoidal waves
    François Beux

    International Journal for Numerical Methods in Fluids, 2001

    Large-eddy simulations (LES) of the flow over two-dimensional sinusoidal waves with a very low grid resolution are presented. A dynamic two-parameter subgrid scale (SGS) model is employed. A configuration characterized by a wave length of 0.6096 m, a maximum slope of 0.497, and a bulk velocity of 10 m s − 1 is initially considered. Comparisons with experimental data, and with the results of a previous LES show that, in spite of the very low grid resolution, the mean flow and both the viscous and the pressure drag forces are well predicted. Some details of the flow, such as the presence of a secondary flow, are also captured. Thus, additional LES are carried out to investigate the effect of the Reynolds number (Re), and of the wave amplitude. In particular, the dependence of viscous and pressure drag on these parameters is studied and compared with the results of similar analyses in the literature.

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    A scale-dependent Lagrangian dynamic model for large eddy simulation of complex turbulent flows
    Elie Bou-Zeid

    Physics of Fluids, 2005

    A scale-dependent dynamic subgrid model based on Lagrangian time averaging is proposed and tested in large eddy simulations ͑LES͒ of high-Reynolds number boundary layer flows over homogeneous and heterogeneous rough surfaces. The model is based on the Lagrangian dynamic Smagorinsky model in which required averages are accumulated in time, following fluid trajectories of the resolved velocity field. The model allows for scale dependence of the coefficient by including a second test-filtering operation to determine how the coefficient changes as a function of scale. The model also uses the empirical observation that when scale dependence occurs ͑such as when the filter scale approaches the limits of the inertial range͒, the classic dynamic model yields the coefficient value appropriate for the test-filter scale. Validation tests in LES of high Reynolds number, rough wall, boundary layer flow are performed at various resolutions. Results are compared with other eddy-viscosity subgrid-scale models. Unlike the Smagorinsky-Lilly model with wall-damping ͑which is overdissipative͒ or the scale-invariant dynamic model ͑which is underdissipative͒, the scale-dependent Lagrangian dynamic model is shown to have good dissipation characteristics. The model is also tested against detailed atmospheric boundary layer data that include measurements of the response of the flow to abrupt transitions in wall roughness. For such flows over variable surfaces, the plane-averaged version of the dynamic model is not appropriate and the Lagrangian averaging is desirable. The simulated wall stress overshoot and relaxation after a jump in surface roughness and the velocity profiles at several downstream distances from the jump are compared to the experimental data. Results show that the dynamic Smagorinsky coefficient close to the wall is very sensitive to the underlying local surface roughness, thus justifying the use of the Lagrangian formulation. In addition, the Lagrangian formulation reproduces experimental data more accurately than the planar-averaged formulation in simulations over heterogeneous rough walls.

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    Vector level identity for dynamic subgrid scale modeling in large eddy simulation
    Oleg Vasilyev

    Physics of Fluids, 2002

    The most commonly used dynamic subgrid scale model is based on the Smagorinsky eddy viscosity model with the model coefficient computed dynamically through the tensor level identity by Germano [et al.] However, the tensor level identity does not explicitly account for the effect of the discretization of the governing equations, and thus the computational results strongly depend on grid resolution, especially in a simulation with poor resolution. In this paper, we propose a new dynamic procedure with the vector level identity, which takes the effect of grid resolution into consideration. The new procedure is tested for the dynamic Smagorinsky eddy viscosity model with the vector level identity. All computational tests were done on turbulent channel flow. The numerical results confirm that the mean velocity profile computed using the new subgrid scale model does not depend on the grid resolution.

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    The multiscale formulation of large eddy simulation: Decay of homogeneous isotropic turbulence
    Alan Wray

    Physics of Fluids, 2001

    The variational multiscale method is applied to the large eddy simulation ͑LES͒ of homogeneous, isotropic flows and compared with the classical Smagorinsky model, the dynamic Smagorinsky model, and direct numerical simulation ͑DNS͒ data. Overall, the multiscale method is in better agreement with the DNS data than both the Smagorinsky model and the dynamic Smagorinsky model. The results are somewhat remarkable when one realizes that the multiscale method is almost identical to the Smagorinsky model ͑the least accurate model!͒ except for removal of the eddy viscosity from a very small percentage of the lowest modes.

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    A new development of the dynamic procedure in large-eddy simulation based on a Finite Volume integral approach. Application to stratified turbulence
    Giuliano De Stefano

    2011

    A Finite Volume-based large-eddy simulation method is proposed along with a suitable extension of the dynamic modelling procedure that takes into account for the integral formulation of the governing filtered equations. Discussion about the misleading interpretation of FV in some literature is addressed. Then, the classical Germano identity is congruently rewritten in such a way that the determination of the modelling parameters does not require any arbitrary averaging procedure and thus retains a fully local character. The numerical modelling of stratified turbulence is the specific problem considered in this study, as an archetypal of simple geophysical flows. The original scaling formulation of the dynamic sub-grid scale model proposed by Wong and Lilly (Phys. Fluids 6(6), 1994) is suitably extended to the present integral formulation. This approach is preferred with respect to traditional ones since the eddy coefficients can be independently computed by avoiding the addition of unjustified buoyancy production terms in the constitutive equations. Simple scaling arguments allow us not to use the equilibrium hypothesis according to which the dissipation rate should equal the sub-grid scale energy production. A careful a priori analysis of the relevance of the test filter shape as well as the filter-to-grid ratio is reported. Large-eddy simulation results are a posteriori compared with a reference pseudo-spectral direct numerical solution that is suitably post-filtered in order to have a meaningful comparison. In particular, the spectral distribution of kinetic and thermal energy as well as the viscosity and diffusivity sub-grid scale profiles are illustrated. The good performances of the proposed method, in terms of both evolutions of global quantities and statistics, are very promising for the future development and application of the method.

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