Analytical all-induction state model for wind turbine wakes

Abstract

Analytical wind turbine wake models are an integral component of wind farm design and optimization. However, when the turbine induction factor increases, these models are prone to failure, as they do not account for the increasingly important effects of low wake pressure. To resolve this issue, this paper proposes an analytical wake model which incorporates the effect of wake pressure in its predictions. The model is based on inviscid flow theory for the initial wake region [K. Steiros and M. Hultmark. J. Fluid Mech. 853, R3 (2018)0022-112010.1017/jfm.2018.621] and an extension of Morton's [B. R. Morton. J. Fluid Mech. 10, 101 (1961)0022-112010.1017/S0022112061000093] theory for the far wake, both of which include the effects of wake pressure. Comparison with high-fidelity wind turbine simulations shows that the model is comparable to conventional ones at low induction factors, but continues to be accurate at higher induction factors where existing models break down.