This paper proposes a Reynolds number R e scaling for the number of grid points N cv 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 l p R e 2 / 3 . A-priori analysis demonstrates that the resolution ( Δ ) required to reasonably predict the wall stress in several nonequilibrium flows is at least O ( 10 ) l p , 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 Δ such that Δ / l p 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, N cv for WMLES scale as R e 4 / 3 , which is more restrictive than the previous estimates ( R e 1 ) 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).


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    Title :

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


    Contributors:

    Published in:

    AIAA Journal ; 62 , 10 ; 3686-3699


    Publication date :

    2024-10-01




    Type of media :

    Article (Journal)


    Type of material :

    Electronic Resource


    Language :

    English