Wall-modeled large-eddy simulations of flow over a Gaussian-shaped bump with a novel sensor-based blended approach

A novel sensor-based blended wall-modelling approach is proposed to investigate the flow over a Gaussian-shaped bump geometry at three different Reynolds numbers: Re_L = 10⁶, 2·10⁶, and 4·10⁶, with a freestream Mach number of M = 0.2. This flow configuration poses challenges for traditional wall-modeling approaches that assume the boundary layer to be fully turbulent, overestimating friction and momentum losses in quasi-laminar flow regions. To address this limitation, we propose several sensors capable of identifying relaminarization regions, taking into account a hysteresis time scale along fluid pathlines, and a blending strategy that combines an equilibrium wall model and a no-slip boundary condition based on the local sensor value. To evaluate the performance, we compare spanwise periodic simulation results with experimental data from Williams et al. (2020, 2021) and Gray et al. (2022), as well as DNS results from Uzun & Malik (2020-2022). Previously developed laminar-to-turbulent transition sensors by Bodart & Larsson (2012) and Mettu & Subbareddy (2018) are also assessed. The predictive capabilities and robustness of the newly proposed approach are evaluated for all three Reynolds numbers. A posteriori analyses suggest that the sensor correctly identifies relaminarization present in the Re_L = 10⁶ case, improving flow predictions.