Gray area mitigation in grid-adaptive simulation for wall-bounded turbulent flows

Wall-bounded turbulence is a pivotal phenomenon in fluid dynamics, especially in aerodynamics and aeronautics. Traditional hybrid Reynolds-averaged Navier–Stokes (RANS) and large eddy simulation (LES) methods often encounter difficulties in accurately predicting wall-bounded turbulent flows due to the gray area issues. In this study, the performance of various hybrid RANS-LES methods (HRLMs) across three quintessential wall-bounded turbulent flow scenarios is rigorously evaluated. The fully developed turbulent channel flow, flow over periodic hills, and flow over a NASA wall-mounted hump are tested. Comparisons are conducted between the recently proposed grid-adaptive simulation (GAS) method and established HRLMs, including scale-adaptive simulation (SAS) and delayed detached eddy simulation (DDES). Compared with SAS and DDES, GAS method reduces the relative error of the reattachment location and the turbulent Reynolds stress in the core recirculation region by over 60 % on identical coarse computational grids. The gray area issues in SAS and DDES are pronounced under low-resolution grids, especially in wall-bounded separation flows due to severe resolved turbulent stress depletion (RSD), and the predictions are even worse than RANS models. Further investigation reveals that both SAS and DDES markedly overestimate turbulent viscosity within the shear layer. Conversely, the turbulent viscosity within the shear layer is adeptly adjusted by the GAS method, leveraging local turbulent and grid length scales. Hence, more accurate predictions for mean flow and turbulence statistics are obtained. For gray area mitigation, the GAS method can adapt to low-resolution grids without additional empirical modifications, which has good potential for engineering applications.