A STUDY OF THE TRANSIENT BEHAVIOR OF SHOCK WAVES IN TRANSONIC CHANNEL FLOWS

The accuracy of the result obtained in a fundamental paper by Kantrowitz (NACA TN 1225) that a small short-time lowering of the back pressure in steady, shock-free, transonic diffuser flow causes a sta-tionary or trapped shock to form near the critical sonic channel throat is investigated by considering the contribution of a higher-order term in the short-time calculations which was neglected in Kantrowitz's paper. In this more accurate approximation to the short-time effects, the shock is no longer stationary or trapped unless it Is supported by a negative steady-flow back pressure. The inclusion of the higher-order term in the short-time calculations avoids the use of approximate quasi-steady-flow considerations for the complete diffuser flow to increase the accuracy of the shock motion, as was required in Kantrowitz's paper. In a broad sense, the present paper offers a firmer basis for the short-time approach originated in Kantrowitz's paper. The present results transform into those previously reported in NACA TN 1878 for amplitudes that are small compared to the difference between local and critical sonic velocities of the channel flow