A Study of Unsteady Transonic Flows with Shock Waves in Two Dimensional Channels

摘要

A two dimensional unsteady transonic flow of a perfect gas with constant specific heats is considered, with solutions found in the form of perturbations from a uniform, sonic, isentropic flow. Longitudinal viscous stress terms are included so that shock waves can be considered. The case where the characteristic time of a temporal flow disturbance is large compared to the time taken by a sonic disturbance to cross the transonic regime is considered. A similarity solution involving an arbitrary function of time is found and it is shown that this solution corresponds to unsteady channel flows with shock waves, for the case where the walls are in general not stationary. Solutions are presented for thick (shock fills transonic region) and thin (shock tends to a discontinuity) shock waves in unsteady flows, both for decelerating and accelerating channel flows. For the thin shock case, both numerical and asymptotic solutions are given. (Author)