A wall model for external laminar boundary layer flows applied to the Wall-Modeled LES framework

Wall-Modeled Large Eddy Simulation (WMLES) is a prominent technique for obtaining high-fidelity solutions of turbulent, high Reynolds number flows, with reasonably acceptable computational costs. However, for external flows, the very thin laminar boundary layer developing near the body leading edge imposes quite restrictive mesh resolution requirements, leading to prohibitively high computational costs for practical Reynolds numbers. We propose a wall-modeling approach for the laminar portion of the boundary layer in order to alleviate these costs by reducing the aforementioned mesh resolution requirements. The wall model is based on local self-similar solutions of the boundary layer, and is implemented in the same context of wall-stress models in the WMLES approach. A thorough assessment of the proposed wall model is performed in terms of the distribution of both pressure and skin friction coefficients along the surface, for a fully laminar flow around a NACA 0012 airfoil geometry, with a chord Reynolds number of Rec=5×103 and Mach number of M∞=0.5. Simulations are carried out to evaluate the effects of the wall model height on the solution. The influence of mesh refinement and mesh element distributions along the surface are also analyzed and discussed. The results obtained in the simulations using the proposed wall model are in good agreement with the reference solution, demonstrating the suitability of the model for external laminar flows. •Paper is concerned with wall-modeled large eddy simulations (WMLES).•Enhance existing WMLES capability for solving the complete external boundary layer.•Development of a novel wall model to treat the laminar portion of the boundary layer.•New wall model is algebraic and it only uses local information.