Actuator Disk Theory for Incompressible Highly Rotating Flows

Abstract

A solution has been obtained for a stator-rotor pair operating in an annulus with constant hub and tip radii. The stator and rotor are represented as actuator discs, and perfect fluid flow is assumed. The solutions are exact within these limitations, no linearization being required. The forms of blade loadings considered allow the introduction of large vorticity by either the rotor or stator. As a result, the rotor may be a “nonconstant-work” row. The solutions obtained are of summational form, but many of the summations are obtained in closed form, the resultant formulas allowing rapid calculation of desired examples. An example numerical result is included.