A Theoretical Solution of Quasi-3D Compressible Flows in Turbomachines : 2nd Report, Flows on an Assumed S2 Stream Surface

Abstract

Detailed theoretical and numerical methods of a mass-weighted pitch-averaged meridional through flow introduced in our solution in the preceding report are described. The solution for a mean flow may consider secondary flow effects by means of conformal mapping of a twisted S1 surface onto an axisymmetric one and then deal with complicated flows such as those through twisted passages with inlet distortion. Basis relations for the assumed S2 relative surface are reduced to a singular integral equation which fully depends on pseudo-analytic function theories, and solved rigorously. Then itemized numerical method for the solution is shown just in the same way as that for S1 relative surfaces in the report. Owing to the existence and uniqueness of a solution of the equation successive iteration is used. A numerical example is presented. The computation procedure is clear and easy to accomplish.