Transonic Cascade Flow Solved by the Combined Shock-Capturing and Shock-Fitting Method

Abstract

A method for solving steady transonic flows has been developed that is a combination of the shock-capturing and shock-fitting methods and takes full advantage of each of these two approaches. In the calculation procedure, by use of the artificial compressibility and the approximate factorization scheme for transonic flowfields (AF2), a full-potential equation is used first to calculate the whole blade-to-blade flowfield and smeared shock waves are captured automatically as regions of steep gradients in flow variables. Subsequently, the definite position of shocks is fitted from these regions based on the shock relations. The Kutta and exit boundary conditions are modified to allow for the effect of entropy variation, and the nonisentropic potential formulation is utilized to solve the flow after the shocks. The numerical experiments show that the present method can automatically give clear and sharp shock discontinuities and reasonable distributions of gas variables. The calculation time is only about twice that needed by a standard potential solution. Hence, this method is effective as well as economical