Limit cases for rotor theories with Betz optimization

Abstract

A complete analytical formulation of the vortex approach for the rotor with an ideal load distribution under Betz optimal condition needs some additional assumption about a correct choice of the helical pitch for vortex sheets in the rotor wake. An examination of the three evident assumptions (the pitch is independent from velocities induced by the wake; the pitch depends on the induced velocities in the far wake; the pitch depends on the induced velocities in the rotor plane) was considered by a comparison with the main restriction of the actuator disk theory-the Betz-Joukowsky limit. In the present investigation an analytical solution for the limit case of an infinite number of blades was used to re-examine the choice of the wake pitch. © Published under licence by IOP Publishing Ltd.