Analytical Theory of Three Dimensional Flow in Centrifugal Compressors

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Abstract
Inviscid, compressible flow along a rotating elemental stream-tube is taken as a model for flow through a turbomachine blade passage. For this model an analytic expression for the relative secondary vorticity of the flow is derived which permits the mean stream-surface twist about the tube axis to be evaluated. This twist implies a migration of the fluid particles from one tube corner to the contiguous tube corner, a flow feature suppressed by all existing stream-sheet flow calculations in turbomachine blade rows. The analysis is applied to a centrifugal compressor configuration where the effects on the secondary flow of hub/shroud geometry, blade shape, compressibility, and meridional diffusion are investigated. The stream-surface twist, not being primarily dependent upon the elemental nature of the stream-tube is taken as a measure of stream-surface twist and consequent surface flow migration in finite blade passages. The levels of twist obtained from the analysis are similar to those obtained in three dimensional flow calculations using primitive variables as illustrated by Bosman (1) (2)‡ and show that existing streamsheet and streamsheet stacking methods, all of which suppress the relative passage vortex are an inadequate model of the flow in centrifugal compressors. The analysis clearly shows that contrary to common assumption, centrifugal compressor impellers are capable of generating a passage vortex in the same direction as that of blade rotation.