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A momentum theory which includes the effects of slipstream rotation for wind turbines is presented. The theory accounts for the axial and radial pressure gradients within the slipstream as well as the wake expansion caused by wake rotation. Because of the limiting approximations of previous methods, the effects of slipstream rotation have not been accurately realized. The method included here, which does not suffer from the unrealistic approximations of previous methods, predicts that the effects of slipstream rotation are manifest entirely through an increase in the turbine thrust coefficient. The method predicts, as previous methods do, that the Lanchester–Betz–Joukowski limit of 16/27 is an upper limit for the maximum efficiency, or power coefficient, of a wind turbine. Unlike the results from classical methods that are traditionally reported in terms of the axial induction factor, results of this work are presented in terms of two independent variables, the tip-speed ratio and the torque coefficient. The results included here allow the dependent variables including the thrust coefficient, power coefficient, axial induction factor, and circumferential induction factor to be evaluated in terms of the tip-speed ratio and torque coefficient. Additionally, relationships for the ideal operating conditions of a wind turbine are presented.

Momentum Theory with Slipstream Rotation Applied to Wind Turbines