Abstract: Introducing two stream functions,the mixed direct-inverse problem of the transonic now in the plane cascade is extended to the case of 3- D flow in turbomachinery;a generalized von Mises coordinate system is proposed to overcome the difflcalty of the undeterinined solution region boundaries inherent in the inverse problem.In this coordinate system,a rotating finite dif-ference scheme for the streamline governing equations is constructed.The present method incor-porates calculating the flow field,designing and modifying the blade contour into a unified algorithm.And the superiority of the inverse problem formulation is that one can consider not only the aerodynamic properties of the turbomachinery blade,but also the demands on the strength,cooling,manufacturing,etc.Numerical results show that the present mathematical model is reasonable,and the numerical solution method has the advantages of high accuracy and very rapid convergence.

Key words: transonic flow, turbomachine blades, three dimensional flow, design