Falkner-Skan wall model for laminar boundary layers

Modeling of the laminar and transitional regions of flow remains one of the key challenges in the numerical simulation of wall-bounded flows. As described in NASA’s CFD Vision 2030 Study (Slotnick et al. 2014), this issue is of particular concern for wall-modeled large-eddy simulations, in which it has been shown that the laminar region can require 10-100 times more grid points than the turbulent region to properly capture the amplification of disturbances leading to transition. Under-resolving the laminar region can lead to large errors in the prediction of mean quantities of interest such as lift and drag. A wall model based on the Falkner-Skan similarity solution of laminar wedge flows has been developed for use in the laminar portion of transitional wall-bounded flows, particularly for use near the leading edge of airfoils (Gonzalez, et al., 2020) at coarse resolutions. This wall model has previously been tested on stagnation flow and pressure gradient boundary layer flows where it has been shown to provide an improvement in the prediction of wall-stress compared to other existing models. In this study, we present further results from the model when applied to a NACA0012 airfoil.