Investigation of compressibility effects on dynamic stall of pitching airfoil

In the present work, effects of compressibility on the dynamic stall of NACA 0012 airfoil, pitching sinusoidally from 5.03° to 24.79°, are investigated computationally using implicit large eddy simulations in a finite difference framework. Simulations of two-dimensional (2D), high Reynolds number, compressible flows are carried out without any transition or turbulence model to capture the physics of the dynamic stall process. The problem is formulated in a body-fixed, rotating, non-inertial frame. High accuracy, dispersion relation preserving optimized upwind compact scheme is used to compute convective flux derivatives, and an optimized three-stage Runge-Kutta method is used for time integration. Results are presented for free stream Mach number M∞ = 0.283, 0.4, and 0.5, where the Mach number is varied independent of the Reynolds number. The computations have been quite successful in capturing the essential features of the dynamic stall mechanism. It is observed that dynamic moment and lift stalls occur at smaller angles of attack as the Mach number increases. Reduction in the size of airload hysteresis loops and maximum attainable load coefficients are observed with increasing Mach number. Weak shock waves are observed near the leading edge (LE) at M∞ = 0.4, and lambda-shock is formed near the LE for M∞ = 0.5. It is observed that with increasing Mach number, the impact of dynamic stall on the aerodynamic loads (Cl, Cd, and Cm) becomes less dramatic as the maximum value attained by these aerodynamic loads decreases with an increase in the Mach number. An increase in positive damping area in the hysteresis loop is observed with an increase in the Mach number, inhibiting possible vulnerability to stall flutter.