Potential flow solutions for energy extracting actuator disc flows

Abstract

AbstractThe actuator disc is the oldest representation of a rotor, screw or propeller. Performance prediction is possible by applying momentum theory, giving integrated values for power and velocity. Computational fluid dynamics has provided much more flow details, but a full potential flow solution zooming in on these flow details was still absent. With the wake boundary discretized by vortex rings, flow states for energy extracting discs have been obtained for thrust coefficients up to 0.998. Boundary conditions are met with an accuracy of a few ‰. Results from momentum theory are confirmed.Most rotor design codes use momentum theory in annulus or differential form, assuming that the axial velocity vx at the disc is uniform. However, the absolute velocity |v| is found to be uniform, and arguments for this are presented. The non‐uniformity of vx is an inherent part of the flow solution caused by, in terms of momentum theory, the pressure acting at the annuli. This makes the annuli not independent from each other as assumed in current design codes. Although this was already known, it is now confirmed up to the highest thrust coefficients.Optimizing a rotor design should be carried out for the non‐uniform distribution of vx. To enable this, an equation for the non‐uniformity as function of thrust and radial position is presented, being a surface‐fit to the calculated data. Qualitatively, the non‐uniform distribution does the same as the Prandtl–Glauert–Shen tip correction applied to a uniform distribution. Copyright © 2015 John Wiley & Sons, Ltd.