Verification of the Axial Momentum Theory for Propellers with a Uniform Load Distribution

Abstract

The paper provides an evaluation of the errors embodied in the Axial Momentum Theory (AMT) as applied to a uniformly loaded actuator disk model without wake rotation. Although this model exhibits some unphysical features, such as the tip singularity and the violation of the angular momentum equation, it is still considered a touchstone in the theoretical aerodynamics of propellers. To simplify the model, a purely mathematical assumption is commonly used in the differential form of the axial momentum equation, i.e., the contribution of the pressure forces on the lateral surface of the infinitesimal streamtubes swallowed by the disk is neglected. In this paper, the errors introduced by this simplifying assumption are evaluated by comparing the results of the AMT with those of a nonlinear method modelling the free wake as the superposition of ring vortices distributed along the wake boundary. Firstly, the validity of this method is verified in terms of global performance coefficients. Then, using a CFD approach, it is also verified in terms of local flow quantities. The comparison between the ring-vortices method and the AMT shows that, for a highly loaded propeller, significant errors exist in the axial velocity at the disk, especially near the tip. Moreover, despite the uniform load, the axial velocity at the disk varies in the radial direction. Instead, the velocity magnitude remains almost uniform only for values of the thrust coefficient lower than 1.