Mathematical solution of direct and inverse problem for transonic cascade flows

Abstract

The work deals with numerical solution of direct and inverse problem of transonic cascade flows based on potential model. Governing equation of a direct problem is full potential equation, governing equation of an inverse problem is equation for Mach number in hodograph plane (~,~), #-velocity potential, b-stream function. Both equations are partial differential equations of second order, mixed elliptic-hyperbolic type. In the solution of direct problem one can consider discontinuity of the first derivatives along some curves called shock waves, in the inverse problem one must find classical solution. Numerical solution of both problems is based on using finite difference method and Jameson's rotated difference scheme. The system of difference equations is solved iteratively using succesive line relaxation method. The work presents results of numerical solution of transonic flows in cascade of compressor and turbine type and one example of numerical solution of inverse problem.