Study on k−ω−Shear Stress Transport Corrections Applied to Airfoil Leading-Edge Roughness Under RANS Framework

Abstract

A computational fluid dynamics study is carried out to model the effects of distributed roughness at the airfoil leading-edge using the equivalent sand grain approach and Reynolds-averaged Navier–Stokes equations. The turbulence model k−ω−shear stress transport (SST) is selected to emulate a fully turbulent flow. Three k and ω boundary conditions are studied to model roughness effects. One refers to Wilcox's boundary condition and the other two refer to Aupoix's boundary conditions. Besides, Hellsten's correction is used to ensure Wilcox's boundary condition compatibility with the shear stress transport limiter. After validating the implementation of these boundary conditions, they are applied to three different airfoils. One of them is a thick airfoil with industrial relevance. For this airfoil, Wilcox's boundary condition significantly underestimates the roughness impact on aerodynamic coefficients. The pressure gradient simplification in Wilcox's boundary condition formulation is the driving factor behind this effect. The pressure gradient effect on Aupoix's boundary condition is minimal.