A revision of blade element/momentum theory for wind turbines in their high-thrust region

Abstract

Modern horizontal-axis wind turbines produce maximum power at an optimal tip speed ratio, λopt, of around 7. This is also the approximate start of the high-thrust region, which extends to runaway at λR ≈ 2λopt where no power is produced and the thrust is maximized. The runaway thrust coefficient often exceeds unity. It is well known that the conventional axial momentum equation must be modified whenever the thrust coefficient approaches unity, but most past modifications have no sound physical basis. Our main revision is to include the “wake vorticity” term in the axial momentum balance. This term is related to blade element drag and acts to decouple the thrust from the induced axial velocity when it becomes large near the edge of the rotor as the runaway is approached. The wake vorticity term dominates the axial momentum equation in these conditions and leads to estimates of power and thrust that are consistent with the limited amount of high-quality experimental data in the high-thrust region.