Law of Incipient Separation over Curved Ramps as Inferred by Reynolds-Averaged Navier–Stokes

Abstract

In this study, numerical simulations of spatially developing incompressible turbulent boundary layers (SDTBLs) with adverse pressure gradient (APG) over two-dimensional smooth curved ramps have been performed by solving the Reynolds-averaged Navier–Stokes (RANS) equations. First, it has been verified that the RANS results converge with respect to domain and grid size, and the effects of different inflow conditions have been assessed. Then, the RANS results have been validated by comparing them with the experiments of Song and Eaton (Experiments in Fluids, Vol. 36, No. 2, 2004, pp. 246–258) for the separated turbulent flow over an arc at a reference Reynolds number based on the momentum thickness of . Furthermore, the effects of the ramp’s slope and curvature on the skin-friction and pressure coefficients for polynomial and half-Gaussian ramps at have been investigated. From this investigation, a numerical criterion has been discovered for the inception of flow separation in SDTBL over smooth curved ramps. The criterion relies only on the geometrical parameters of normalized maximum slope magnitude, , and height-to-length ratio of the ramp, , and on the Reynolds number of the flow based on the ramp length, . Specifically, incipient separation occurs when the magnitude of the normalized maximum slope, , reaches a critical value specified as , where , , and are constants. Accordingly, the flow separates over a smooth curved ramp for which .