Reynolds-Number-Dependence of Length Scales Governing Turbulent-Flow Separation in Wall-Modeled Large Eddy Simulation

This paper proposes a Reynolds number [Formula: see text] scaling for the number of grid points [Formula: see text] required in wall-modeled Large Eddy Simulation (WMLES) of turbulent boundary layers (TBL) to accurately capture the regions of flow separation. Based on the various time scales in a nonequilibrium TBL, a definition of the near-wall “underequilibrium” scales is proposed (in which “equilibrium” refers to a quasi balance between the viscous and the pressure gradient terms). This length scale is shown to vary with Reynolds number as [Formula: see text]. A-priori analysis demonstrates that the resolution ([Formula: see text]) required to reasonably predict the wall stress in several nonequilibrium flows is at least [Formula: see text], irrespective of the Reynolds number and Clauser parameter. Further, a-posteriori studies (on the Boeing speed bump, Song– Eaton diffuser, Notre-Dame Ramp, and the backward-facing step) show that scaling [Formula: see text] such that [Formula: see text] is independent of Reynolds number results in accurate predictions of separation for the same “nominal” grid across different Reynolds numbers. Finally, we suggest that near separation and reattachment points, [Formula: see text] for WMLES scale as [Formula: see text], which is more restrictive than the previous estimates ([Formula: see text]) by Choi and Moin (Choi, H., and Moin, P., “Grid-Point Requirements for Large Eddy Simulation: Chapman’s Estimates Revisited,” Physics of Fluids, Vol. 24, No. 1, 2012, Paper 011702) and Yang and Griffin (Yang, X. I. A., and Griffin, K. P., “Grid-Point and Time-Step Requirements for Direct Numerical Simulation and Large-Eddy Simulation,” Physics of Fluids, Vol. 33, No. 1, 2021, Paper 015108).