A criterion for rotational augmentation based on a boundary-layer analysis

Rotational augmentation is a well-known phenomenon of rotating aerofoils on wind turbines and helicopters where the lift or torque is improved compared to that of stationary aerofoils.

We present an analysis which is based on the concept of a developing boundary layer and the Ekman boundary layer using a 3D Finite-Element Analysis of the developing laminar boundary layer over a flat plate in a rotating frame of reference. A parametric analysis addresses the Reynolds number, the Ekman number and the speed ratio in turn.

The results demonstrate that the surface's rotation limits the boundary layer to the thinner of the two boundary layers, and that it induces a span-wise flow in the radial direction which in turn leads to Ekman suction. This Ekman suction provides a mechanism to counteract an adverse pressure gradient and thus prevent stall. The criterion derived from this was successfully applied and tested against observations and full CFD results.