Abstract
This paper describes a generic free-wake calculation of wind turbine wakes. The expanding, helical, tip vortices are represented by a sequence of straight segments, the blades are modelled as lines of constant bound vorticity, and the hub vortices lie along the axis of rotation. It is shown that this model is consistent with the one-dimensional analysis that leads to the Lanchester-Betz limit, in that the velocity in the far-wake is uniform with radius. Particular attention is paid to turbines operating above the Lanchester-Betz limit. It is shown that the usual relationship between the velocity through the blades and in the far-wake breaks down when there is significant wake expansion, and an empirical modification to that relation is presented. For highly expanding wakes, the dynamics of the turbine depend sensitively on the behaviour of the tip vortices.