Families of variational principles for inverse and H A hybrid problems of an S 2 stream sheet in mixed flow turbomachines

Abstract

This paper deals with the semi-inverse, H A, and inverse problems of compressible flow along an S 2 stream sheet in mixed flow turbomachines, for which families of variational principles (VPs) are derived. In the VPs for the semi-inverse problem, the distributed gas injection and/or suction along the hub walls and casing walls are accounted for. VP families for axial and radial flow turbomachines can be obtained directly from this paper as special cases. Great attention is paid to taking full advantage of natural boundary conditions and “artificial interfaces” in order to offer a perfect theoretical basis for the finite element method or other direct variational methods in computational aerodynamics of turbomachinery. This theory also provides broader and versatile ways for blading design.