Hybrid problems of determining unknown shape of bladings in compressible S2-flow in mixed-flow turbomachinery via variational technique

Using the semi-inverse method proposed by the present author, a family of variational principle for direct problem of S2-flow in mixed-flow turbomachinery is obtained; then, applying the functional variation with variable domain, two families of variational principles are established for the hybrid problems of determining the unknown shape of bladings, where pressure or velocity is over-specified. The present variational models are well posed for redundant data at boundaries. The theory provides both rational ways for best contouring the hub/casing walls to meet various practical design requirements and a theoretical basis for introducing the finite element method into computational aerodynamics of turbomachinery.