Direct numerical simulation of transitional flow past an airfoil with partially covered wavy roughness elements

We perform direct numerical simulation of flow past the NACA (National Advisory Committee for Aeronautics) 0012 airfoil with partially covered wavy roughness elements near leading edge. The Reynolds number Re c based on freestream velocity ( U 0 ) and chord length C), angle attack (AoA) is fixed, i.e., [Formula: see text]. edge are characterized by streamwise sinusoidal-wave geometry that uniform in spanwise direction fixed height, whereas varying wave numbers k) from to 12. Based validation smooth baseline case k = 0), effects aerodynamic performance evaluated terms lift drag coefficients. coefficient decreases monotonically k, while variation similar “drag crisis” phenomenon observed cylinder flows. sharp variations coefficients 6 8 indicate a critical case, beyond which massive separation occurs almost covers airfoil's suction side dominates performance. To further reveal underlying mechanism, structures, pressure, skin friction coefficients, shear layer transition onset, boundary quantified investigate effects. strongly modify behavior, they have little effect onset. unsteady interactions convections bubbles downward trailing also change wake evolution. scaling asymmetric profiles, we find defect gently decreasing but increase width much stronger. This analysis gains better insight into momentum deficit rate, confirms mechanism different numbers.