On the influence of radial components of blade forces in axial turbomachines

Abstract

The flow of an incompressible inviscid fluid through a turbomachine with infinite number of blades is investigated in this paper in order to determine the effects of radial forces resulting from the twist of the blades on the flow through the machine. Prandtl's method of replacing blade rows by distributed vorticity is used and the mathematical problem is treated from that point of view. The flow through the annulus between hub and outer casing of the machine is treated as two-dimensional flow between two parallel flat plates. By assuming a reasonable vorticity distribution throughout the blade row, equations are given which may be applied to calculate the flow induced by radial forces through stationary blade rows. Examples are presented for flow through free vortex and solid body prerotation vanes with radial leading edges. These examples show the effect of the radial force resulting from twist is of negligible magnitude. The effect of leaning the blades in a plane perpendicular to the axis of rotation is investigated. Examples shown indicate that this may be of considerable importance since by leaning the blades it is possible to reduce the axial velocity at the first stage rotor tip and thereby the relative Mach number on the rotor tip.