Shock Embedding Discontinuous Solution of Elliptic Equation for Inverse Problem of Transonic S2 Flow

Abstract

In the case of the inverse problem of S2 surface flow in a transonic turbomachine, if the meridional component of the relative velocity is subsonic, the equation governing the flow is elliptic. Through the use of a proper conservative form of the stream-function principal equation and embedding the shock relations into the principal equation, the transonic flow over the whole S2 surface containing the discontinuity of the passage shock can be calculated. A computer code employing this method has been programmed. The algorithm, which is only a little different from the subsonic code, is simple, accurate, and reliable. This program is particularly useful in the solution of the three-dimensional transonic flow in a fan or compressor through iterative computation of transonic S1 and S2 flows, when the former is carried out by the recently developed method of “separate-region calculation with shock fitting.” The new computer code is used to calculate the S2 flow in a typical transonic rotor and the difference between the result obtained by this method and that by the commonly used one, in which the shock discontinuity is not taken into account, can be clearly seen.