This paper proposes a Reynolds number scaling for the number of grid points 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 . A-priori analysis demonstrates that the resolution () required to reasonably predict the wall stress in several nonequilibrium flows is at least , 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 such that 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, for WMLES scale as , which is more restrictive than the previous estimates () 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).
Reynolds-Number-Dependence of Length Scales Governing Turbulent-Flow Separation in Wall-Modeled Large Eddy Simulation
AIAA Journal ; 62 , 10 ; 3686-3699
2024-10-01
Article (Journal)
Electronic Resource
English