How does the presence of a body affect the performance of an actuator disk ?

Abstract

The article seeks to unify the treatment of conservative force interactions between axi-symmetric bodies and actuators in inviscid flow. Applications include the study of hub interference, diffuser augmented wind turbines and boundary layer ingestion propeller configurations. The conservation equations are integrated over infinitesimal streamtubes to obtain an exact momentum model contemplating the interaction between an actuator and a nearby body. No assumptions on the shape or topology of the body are made besides (axi)symmetry. Laws are derived for the thrust coefficient, power coefficient and propulsive efficiency. The proposed methodology is articulated with previous efforts and validated against the numerical predictions of a planar vorticity equation solver. Very good agreement is obtained between the analytical and numerical methods.