Cfd Turbulence and Combustion
Flow, Turbulence and Combustion 63: 269–291, 1999. © 2000 Kluwer Academic Publishers. Printed in the Netherlands.
269
Approximate Wall Boundary Conditions in the Large-Eddy Simulation of High Reynolds Number Flow
W. CABOT and P. MOIN
Center for Turbulence Research, Stanford University, Bldg. 500, 488 Escondido Mall, Stanford, CA 94305-3030, U.S.A.
Abstract. The near-wall regions of high Reynolds numbers turbulent flows must be modelled to treat many practical engineering and aeronautical applications. In this review we examine results from simulations of both attached and separated flows on coarse grids in which the near-wall regions are not resolved and are instead represented by approximate wall boundary conditions. The simulations use the dynamic Smagorinsky subgrid-scale model and a second-order finite-difference method. Typical results are found to be mixed, with acceptable results found in many cases in the core of the flow far from the walls, provided there is adequate numerical resolution, but with poorer results generally found near the wall. Deficiencies in this approach are caused in part by both inaccuracies in subgrid-scale modelling and numerical errors in the low-order finite-difference method on coarse near-wall grids, which should be taken into account when constructing models and performing largeeddy simulation on coarse grids. A promising new method for developing wall models from optimal control theory is also discussed. Key words: turbulence, large-eddy simulation, wall models, channel flow, separation. Abbreviations: DNS – direct numerical simulation; LES – large-eddy simulation; RANS – Reynolds-averaged Navier–Stokes; SGS – subgrid-scale; TBLE – thin boundary layer equations
Nomenclature
A+ B C Cf Cp h k L L M P Pm Reh = = = = = = = = = = = = = damping function parameter log law intercept dynamic coefficient for the Smagorinsky model 2 friction coefficient, 2τw /U∞ 2 relative wall pressure coefficient, 2(Pw − Po )/U∞ step height
269
Approximate Wall Boundary Conditions in the Large-Eddy Simulation of High Reynolds Number Flow
W. CABOT and P. MOIN
Center for Turbulence Research, Stanford University, Bldg. 500, 488 Escondido Mall, Stanford, CA 94305-3030, U.S.A.
Abstract. The near-wall regions of high Reynolds numbers turbulent flows must be modelled to treat many practical engineering and aeronautical applications. In this review we examine results from simulations of both attached and separated flows on coarse grids in which the near-wall regions are not resolved and are instead represented by approximate wall boundary conditions. The simulations use the dynamic Smagorinsky subgrid-scale model and a second-order finite-difference method. Typical results are found to be mixed, with acceptable results found in many cases in the core of the flow far from the walls, provided there is adequate numerical resolution, but with poorer results generally found near the wall. Deficiencies in this approach are caused in part by both inaccuracies in subgrid-scale modelling and numerical errors in the low-order finite-difference method on coarse near-wall grids, which should be taken into account when constructing models and performing largeeddy simulation on coarse grids. A promising new method for developing wall models from optimal control theory is also discussed. Key words: turbulence, large-eddy simulation, wall models, channel flow, separation. Abbreviations: DNS – direct numerical simulation; LES – large-eddy simulation; RANS – Reynolds-averaged Navier–Stokes; SGS – subgrid-scale; TBLE – thin boundary layer equations
Nomenclature
A+ B C Cf Cp h k L L M P Pm Reh = = = = = = = = = = = = = damping function parameter log law intercept dynamic coefficient for the Smagorinsky model 2 friction coefficient, 2τw /U∞ 2 relative wall pressure coefficient, 2(Pw − Po )/U∞ step height