Comparison of actuator disc and Joukowsky rotor flows, to explore the need for a tip correction

Abstract

In van Kuik & Lignarolo (2015, Wind Energy accepted with modifications) potential flow solutions have been obtained for classical actuator discs (axisymmetric, uniform load) presenting a model for the non-uniformity of the axial velocity at the disc. Current rotor design models proceed from a disc with a uniform axial velocity, modified by a tip correction like the one of Prandtl-Glauert-Shen. A comparison shows that this correction leads to a similar distribution as obtained from the potential flow solutions. A next comparison is made with the velocity distribution at the blade position of a Joukowsky rotor with constant bound circulation, calculated by an Actuator Line and a Lifting Line model. The resulting distributions correspond reasonably well to the potential flow disc distribution, in magnitude as well as shape. This implies that this non-uniform distribution is relevant for a rotor with a finite number of blades, and could be the basis for rotor design instead of the uniform but tip-corrected distribution.