Supersonic Flow Through Cascades, with Application to Diffusers

Citation

Buhler, Rolf Dietrich (1948) Supersonic Flow Through Cascades, with Application to Diffusers. Engineer's thesis, California Institute of Technology. doi:10.7907/FJEG-RM29. https://resolver.caltech.edu/CaltechETD:etd-12102008-131330

Abstract

Supersonic flow through a two-dimensional cascade of airfoils is discussed from the point of view of one-dimensional gas dynamics. Two generalizations to compressible flow of the usual velocity vector diagrams are discussed, namely the Mach vector and the reduced velocity vector diagram. A relative mass flow parameter is found which represents the isentropic continuity equation on the two vector diagrams, so that for a set of given cascade inlet conditions all possible outlet velocities and directions appear on the diagrams. The largest possible tangential velocity component and the largest possible change in tangential momentum in a cascade are obtained as functions of the mass flow parameter. From these the largest obtainable stagnation pressure ratio and power of any arrangement of moving and stationary cascades may easily be obtained. Equations are given for the ratios of relative stagnation temperatures, mass flows and Mach numbers in two systems of reference moving with respect to each other. Methods for tracing graphically on the vector diagrams the flow through a stage are presented. The possibility of using cascades instead of shock waves for the transition from supersonic to subsonic flow in diffusers is pointed out. As an example a proposed single cascade supersonic diffuser is briefly analyzed by means of the reduced velocity vector diagram.

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