A single-parameter theory of vortex flow in turbo-machines

Abstract

The paper gives a theory of vortex flow in turbo-machines in which the basic assumption is made that the axial-velocity profiles always belong to a family governed by a single parameter, λ. This parameter is a measure of the radial displacement of the streamlines. The flow equations then reduce to a single linear differential equation for λ and a corresponding simplification of ideas about, the way in which these flows behave is achieved. Comparison with experimental results by Horlock and more-accurate calculations by Wu shows that the theory is sufficiently accurate for design purposes. The theory, is applied to compressors with a large number of identical stages, and it is shown how a rapid solution may be obtained by matrix methods. Examples of flow in a ten-stage compressor are given, and the effects of variation of mass flow and of modifications to the inlet guide vanes are demonstrated.