Wall-modeled large-eddy simulations of the flow over a Gaussian-shaped bump with a relaminarization sensor*

Wall-modelled large-eddy simulations are conducted with a relaminarization sensor to investigate a turbulent boundary layer flow with a freestream Mach number M=0.2 over a Gaussian-shaped bump geometry at two different Reynolds numbers, Re_L=10⁶ and 2x10⁶, based on the bump length. 

The flow exhibits favorable and adverse pressure gradients driven by the bump curvature, leading to a region of relaminarization around the apex, for the Re_L=10⁶, and flow separation downstream of the bump apex, for both Reynolds numbers. This flow configuration serves as a challenging test case for wall-modeling approaches that typically assume the boundary layer to be fully turbulent, overestimating the friction and momentum losses in quasi-laminar regions.

A relaminarization sensor is developed to control the local application of the wall model and no-slip boundary conditions, adjusted by a blending function derived from flow quantities. We assess the performance of the proposed relaminarization sensor by comparing spanwise periodic simulation results with Direct Numerical Simulations by Uzun & Malik (2020, 2022) at both Reynolds numbers. The a posteriori analysis suggests that the sensor correctly distinguishes the relaminarization region in the low Re_L case and improves flow predictions.