High Reynolds Number Airfoil: From Wall-Resolved to Wall-Modeled LES

This paper presents an in-depth study, using wall-resolved Large-Eddy Simulation (wrLES), of a high Reynolds number airfoil in a near-stall condition. The flow around the NACA4412 airfoil, a widely used test case for turbulence modeling validation, is computed at Reynolds number Re =þinspace1.64 \texttimes 106 and angle of attack $\alpha$ =þinspace12∘. In the first part of the paper, the results are compared to previous experimental and numerical results, showing close agreement with both. In order to aid wall-model development, the second part of the paper characterizes the effect of the adverse pressure-gradient (APG) on the turbulent boundary layer development, and evaluates different wall-models in an a priori manner. It appears that the simple models, which assume an equilibrium flow, provide a better match to the mean flow velocity than allegedly more advanced models. The study reveals also that the often used simplification of the ``Two-Layer Model''(TLM) that takes the pressure-gradient into account but neglects the convective terms, is not adequate. This simplification applied to the TLM indeed leads to a higher error than the simple equilibrium models. Therefore, it is argued that if the convective terms are neglected, the pressure-gradient term needs to be neglected as well.