Role of Kutta waves on oscillatory shock motion on an airfoil

Abstract

An investigation of wave propagation in transonic flows is carried out using the nonlinear transonic small disturbance equation. The wave fronts are computed from numerical integration of the characteristic equation. The manner in which downstream disturbances, initiated at an airfoil trailing edge, travel to the shock wave is analyzed. Though a relation between the amplitude of the disturbance and the magnitude of shock displacement has not yet been derived to study the interaction process, the results presented are sufficient to give a better understanding of the feedback mechanism proposed in an earlier investigation of oscillatory shock motion observed in transonic airfoil buffeting. The propagation time for downstream disturbances to reach the shock wave is computed for various airfoil geometries and freestream Mach numbers. The results are compared with those obtained from an empirical formulation given by Tijdeman. The accuracy of Tijdeman's relaxation factor is examined. The interaction of upstream moving waves with a time-dependent flowfield is also studied for an airfoil performing trailing-edge flap oscillations. The variation of the disturbance amplitude along the wave front at various instances of time is given for an impulse source at the trailing edge using the method of asymptotic expansion.