ROLE OF KUTTA WAVES ON OSCILLATORY SHOCK MOTION ON AN AIRFOIL

An investigation of wave propagation in transonic flows is carried out using the nonlinear transonic small disturbance equation. The wave fr onts are computed from numerical integration of the characteristic equ ation. The manner in which downstream disturbances, initiated at an ai rfoil trailing edge, travel to the shock wave is analyzed. Though a re lation between the amplitude of the disturbance and the magnitude of s hock displacement has not yet been derived to study the interaction pr ocess, the results presented are sufficient to give a better understan ding 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 formu lation given by Tijdeman. The accuracy of Tijdeman's relaxation factor is examined. The interaction of upstream moving waves with a time-dep endent flowfield is also studied for an airfoil performing trailing-ed ge flap oscillations. The variation of the disturbance amplitude along the wave front at various instances of time is given for an impulse s ource at the trailing edge using the method of asymptotic expansion.