A Theoretical Solution of Three-Dimensional Flows in Subsonic, Transonic and Supersonic Turbomachines: An Exact Solution and its Numerical Method

A theoretical solution of a nonviscous flow through subsonic, transonic and supersonic arbitrary turbomachines is presented. The basic relations given by Wu are finally reduced to complex integral equations and then solved rigorously with pseudo-analytic function theories for boundary value problems and conformal mapping theorems which may simplify given flow fields. As the numerical method of the solution successive iteration is used. In the present paper only a schema of computational procedures of the three-dimensional flow is described. Moreover, detailed consideration on problems associated with Wu’s model is omitted. The numerical method is easy to accomplish in the whole flow regions, because numerical procedures are done mainly along the boundaries. Numerical examples given are limited to those for subsonic and shock free transonic flows.