Numerical criterion for incipient separation of turbulent flows as inferred by RANS
Simulations of turbulent flows based on the Reynolds-averaged Navier-Stokes (RANS) equations are widely used for engineering applications and are computationally less expensive than other numerical simulations such as large-eddy or direct numerical simulations. We performed RANS simulations over smooth curved surfaces under adverse pressure gradient using a one-equation turbulence model and without wall-functions (i.e., the grid is fine enough to reach the viscous sublayer). First, by investigating the effect of inflow boundary condition, domain size and grid refinement, we assessed the best practices for RANS simulations. Next, we validated the RANS by comparing the results with published experimental measurements. Further, the sensitivity of turbulent flow to the degree of severity of the adverse pressure gradient is investigated by testing different curved ramp geometries, by varying the ramp slope and curvature distribution. Our results show that the key parameter to determine flow separation is the maximum slope of the ramp normalized by the non-dimensional ramp height over its streamwise length, and the location of the maximum curvature has an effect on the magnitude of skin-friction coefficient near the onset of ramp. Lastly, a numerical criterion for incipient separation as inferred by RANS is proposed. Based on this criterion, a new approach is demonstrated to examine flow separation that depends only on the ramp height-to-length ratio, normalized maximum slope and Reynolds number for the range of $2\times10^5 \leq Re_L \leq 8\times10^5$ simulated via RANS.