LES approach for high Reynolds number wall-bounded flows with application to turbulent channel flow

We describe a large-eddy simulation approach for turbulent channel flow using the stretched-vortex subgrid-scale model. The inner region of the turbulent boundary layer is not included in the modeling of this attached, wall-bounded flow. Appropriate boundary conditions and closure are derived using a combination of elements from asymptotic expansions, matching, and well-established wall-modeling approaches. The modeling approach for this application combines the stretched-vortex subgrid model with a localized wall-shear-stress treatment that relates the instantaneous wall-parallel velocity to the shear stress via the log-law, as appropriate for this (near-) zero pressure gradient flow. The impermeability boundary condition is built into the method such that only the outer-flow solution is simulated, obviating the need to impose the stiff no-slip condition at the wall. This formulation attempts to minimize numerical and modeling errors introduced by the boundary-condition treatment, while preserving the fundamental elements required to predict low-order statistics of these flows. We present simulation results for turbulent channel flow up to Reynolds number based on the wall-friction velocity of 10^6. These compare favorably with results from large-scale DNS and experimental correlations.

[1]  Javier Jiménez,et al.  Scaling of the velocity fluctuations in turbulent channels up to Reτ=2003 , 2006 .

[2]  Holger Foysi,et al.  Compressibility effects and turbulence scalings in supersonic channel flow , 2004, Journal of Fluid Mechanics.

[3]  J. Deardorff.  A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers , 1970, Journal of Fluid Mechanics.

[4]  D. Pullin,et al.  Hybrid tuned center-difference-WENO method for large eddy simulations in the presence of strong shocks , 2004 .

[5]  P. Moin,et al.  Approximate Wall Boundary Conditions in the Large-Eddy Simulation of High Reynolds Number Flow , 2000 .

[6]  Tobias Voelkl,et al.  A physical-space version of the stretched-vortex subgrid-stress model for large-eddy simulation of incompressible flow , 2000 .

[7]  U. Schumann,et al.  Large‐eddy simulation of a neutrally stratified boundary layer: A comparison of four computer codes , 1994 .

[8]  C. Benocci,et al.  Approximate Wall Boundary Conditions for Large Eddy Simulations , 1995 .

[9]  B. Kosović,et al.  Subgrid-scale modeling for large-eddy simulations of compressible turbulence , 2002 .

[10]  Georgi Kalitzin,et al.  An eddy-viscosity based near-wall treatment for coarse grid large-eddy simulation , 2005 .

[11]  Graham V. Candler,et al.  Multi-Block Large-Eddy Simulations of Turbulent Boundary Layers , 2000 .

[12]  H. Schlichting.  Boundary Layer Theory , 1955 .

[13]  M. Lesieur,et al.  New Trends in Large-Eddy Simulations of Turbulence , 1996 .

[14]  P. Spalart.  Comments on the feasibility of LES for wings, and on a hybrid RANS/LES approach , 1997 .

[15]  Pierre Sagaut,et al.  RANS/LES coupling for unsteady turbulent flow simulation at high Reynolds number on coarse meshes , 2006 .

[16]  D. Thomson,et al.  Stochastic backscatter in large-eddy simulations of boundary layers , 1992, Journal of Fluid Mechanics.

[17]  P. J. Mason,et al.  On the magnitude of the subgrid-scale eddy coefficient in large-eddy simulations of turbulent channel flow , 1986, Journal of Fluid Mechanics.

[18]  Franck Nicoud,et al.  Large eddy simulation wall-modeling based on suboptimal control theory and linear stochastic estimation , 2001 .

[19]  S. Pope.  Ten questions concerning the large-eddy simulation of turbulent flows , 2004 .

[20]  R. Benzi.  Advances in Turbulence V , 1995 .

[21]  F. Porté-Agel,et al.  A scale-dependent dynamic model for large-eddy simulation: application to a neutral atmospheric boundary layer , 2000, Journal of Fluid Mechanics.

[22]  Michele Iovieno,et al.  A new large-eddy simulation near-wall treatment , 2004 .

[23]  F. Durst,et al.  Evaluating the law of the wall in two-dimensional fully developed turbulent channel flows , 2003 .

[24]  T. B. Nickels,et al.  Inner scaling for wall-bounded flows subject to large pressure gradients , 2004, Journal of Fluid Mechanics.

[25]  D. Pullin,et al.  A vortex-based subgrid stress model for large-eddy simulation , 1997 .

[26]  Franck Nicoud,et al.  An approach to wall modeling in large-eddy simulations , 2000 .

[27]  Rodney Cannon Schmidt,et al.  Near-wall LES closure based on one-dimensional turbulence modeling , 2003 .

[28]  P. Mason.  Large‐eddy simulation: A critical review of the technique , 1994 .

[29]  Ralf Deiterding,et al.  A low numerical dissipation patch-based adaptive mesh refinement method for large-eddy simulation of compressible flows , 2007, J. Comput. Phys..

[30]  Joel H. Ferziger,et al.  New approximate boundary conditions for large eddy simulations of wall-bounded flows , 1989 .

[31]  U. Schumann.  Subgrid Scale Model for Finite Difference Simulations of Turbulent Flows in Plane Channels and Annuli , 1975 .

[32]  Branko Kosovic,et al.  Subgrid-scale modelling for the large-eddy simulation of high-Reynolds-number boundary layers , 1997, Journal of Fluid Mechanics.

[33]  M. Abel,et al.  Nonlinear stochastic estimation of wall models for LES , 2006 .

[34]  Elias Balaras,et al.  The inner–outer layer interface in large-eddy simulations with wall-layer models , 2003 .

[35]  Dr. M. G. Worster.  Methods of Mathematical Physics , 1947, Nature.

[36]  C. Moeng.  A Large-Eddy-Simulation Model for the Study of Planetary Boundary-Layer Turbulence , 1984 .

[37]  D. Pullin.  A vortex-based model for the subgrid flux of a passive scalar , 2000 .

[38]  D. Coles.  The law of the wake in the turbulent boundary layer , 1956, Journal of Fluid Mechanics.

[39]  L. Biferale,et al.  Dynamics and statistics of heavy particles in turbulent flows , 2006, nlin/0601027.

[40]  K. Hanjalic,et al.  Compound Wall Treatment for RANS Computation of Complex Turbulent Flows and Heat Transfer , 2007 .

[41]  Pierre Sagaut,et al.  Zonal multi‐domain RANS/LES simulations of turbulent flows , 2002 .

[42]  Elias Balaras,et al.  Finite-difference computations of high reynolds number flows using the dynamic subgrid-scale model , 1995 .

[43]  T. Lundgren,et al.  Strained spiral vortex model for turbulent fine structure , 1982 .

[44]  J. McWilliams,et al.  A subgrid-scale model for large-eddy simulation of planetary boundary-layer flows , 1994 .

[45]  R. B. Dean.  Reynolds Number Dependence of Skin Friction and Other Bulk Flow Variables in Two-Dimensional Rectangular Duct Flow , 1978 .

[46]  Ugo Piomelli,et al.  A dynamic stochastic forcing method as a wall-layer model for large-eddy simulation , 2006 .

[47]  U. Piomelli,et al.  Wall-layer models for large-eddy simulations , 2008 .

[48]  S. Ghosal.  An Analysis of Numerical Errors in Large-Eddy Simulations of Turbulence , 1996 .

[49]  W. George.  Recent Advancements Toward the Understanding of Turbulent Boundary Layers , 2005 .

[50]  J. Szmelter.  Incompressible flow and the finite element method , 2001 .

[51]  J. Fröhlich,et al.  Investigation of wall-function approximations and subgrid-scale models in large eddy simulation of separated flow in a channel with streamwise periodic constrictions , 2003 .

[52]  P. Moin,et al.  Model consistency in large eddy simulation of turbulent channel flows , 1988 .

[53]  U. Piomelli,et al.  Two-layer approximate boundary conditions for large-eddy simulations , 1996 .

[54]  H. N. Lim,et al.  Near-wall function for turbulence closure models , 2002 .