The linearized flow field of a relaxing gas through a non-uniform channel and in a jet at supersonic speeds

Abstract

Summary. A study is made of the linearized differential equation for supersonic flow of a gas relaxing in one mode, assuming a linear rate equation, in a two-dimensional non-uniform channel. An exact solution to this equation is found which includes the corner flow problem as a special case. This solution clearly demon- strates the exponential decay of disturbances along the frozen characteristics associated with the relaxation process. The results obtained for the corner flow problem agree with the earlier results of J. F. Clarke and J. J. Der. Approximate solutions are also obtained which are shown to be adequate for most practical values of the ratio of the equilibrium to the frozen speed of sound. Similar exact and approximate solutions are also found for the linearized case of a two dimensional jet expanding into a uniform pressure field.