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

We perform DNS of flow past the NACA (National Advisory Committee for Aeronautics) 0012 airfoil with partially covered wavy roughness elements near the leading edge. The Reynolds number and the angle of attack are fixed, i.e., Rec=5×104, AoA=10◦. The leading edge roughness elements are characterized by streamwise sinusoidal-wave geometry that is uniform in the spanwise-direction with fixed height whereas varying wave-numbers ( k) from 0 to 12. Based on validation of the smooth baseline case ( k=0), the roughness effects on the aerodynamic performance are evaluated in terms of the lift and drag coefficients. The drag coefficient decreases monotonically with k, while the variation of the lift coefficient with k is similar to the "drag crisis" phenomenon observed in cylinder flows. The sharp variations of coefficients from k = 6 to 8 indicate that k = 8 is a critical case, beyond which massive separation occurs and almost covers the airfoil's suction side and dominates the airfoil aerodynamic performance. To further reveal the underlying mechanism, the flow structures, pressure, skin friction coefficients, shear layer transition onset, and boundary layer separation are quantified to investigate the roughness effects. The roughness elements strongly modify the separation behavior, whereas they have little effect on the transition onset. The unsteady interactions and convections of separation bubbles downward the trailing edge also change the wake evolution. We find that the wake defect is gently decreasing with k, but the increase of the wake width is much stronger, which confirms the drag mechanism with different roughness wave numbers.