The Actuator Disc Concept

Abstract

Actuator disc theory is the simplest rotor theory possible: the rotor is replaced by a permeable disc carrying an axisymmetric force field. It is more than a century old, with a first analytical result obtained by Froude in 1889. In 1918 Joukowsky published the first rotor performance prediction for a helicopter rotor in hover; in 1920 Betz and Joukowsky published the maximum efficiency of wind turbine rotors. In modern rotor design codes, this momentum theory still forms the basis, be it with many adaptations and engineering add-ons. This chapter treats the actuator disc theory in two versions. Best known is the classical theory relating to an actuator disc with thrust acting against the flow but without torque, so without wake swirl. This theory gives the Betz-Joukowsky limit. The results deviate when applied to a flow annulus instead of the entire stream tube, due to the role of the pressure exerted by one annulus to the other. The momentum theory for discs with thrust and torque is relevant for rotors operating with high torque at low rotational speed. For increasing rotational speed, the performance increases from zero to the Betz-Joukowsky limit. In all flow cases, with or without torque, the velocity vector in the meridional plane appears to be constant at the disc. For the performance per annulus and the performance with torque, the deviation from the classical momentum theory is explained by classifying force fields as conservative or non-conservative and investigating their impact on energy and momentum balances.