Wind Turbine Performance Predictions Using a Differential Actuator-Lifting Disk Model

Abstract

This paper presents a method based on the imposition of velocity discontinuities to model flow perturbation due to the existence of vortical structures. The proposed method uses actuator-disk and lifting line concepts in order to provide a framework of analysis that respects conservation laws for momentum, energy, and vorticity, which is not always the case for engineering methods used in the wind industry. The flow field is described by the Euler equations. In the proposed mathematical model, the attitude toward flow determination is entirely linked to the vorticity structure of the flow, which is modeled by velocity discontinuities. The numerical method has been applied to four wind turbines: NREL phases II, IV, and VI rotors, as well as to the Tjaereborg rotor, and has shown satisfactory predictions compared to measurements up to peak power. Comparisons have also been undertaken with the results of a previous method, developed by the same authors, where the velocity field is not allowed to be discontinuous and the actuator disk is analyzed as a source of external forces only. In the stall regime of the turbine, the relative differences in power output between the two methods have been evaluated at 5% on the average.