Analytical body forces in numerical actuator disc model of wind turbines

An analytical model for representing body forces in numerical actuator disc models of wind turbines is developed and validated. The model is based on the assumption that the rotor disc is subject to a constant circulation modified for tip and root effects. The model comprises expressions for both the axial and the azimuthal force distributions, and is generalized to be utilized for all kinds of inflow, including wind shear, turbulence, and shadow effects in wind farms. The advantage of the model is that it does not depend on any detailed knowledge concerning the wind turbine being analysed, but only requires knowledge regarding the rated wind speed and nameplate capacity. To validate the analytical model, results are compared to numerically generated results using detailed information regarding geometry and airfoil data for the 2 MW Tjaereborg wind turbine and the 10 MW DTU reference turbine. The comparisons show very good agreement between the loadings using the new analytical model and the airfoil data based method for the two tested wind turbines, demonstrating that the analytical model is a simple and reliable way of introducing body forces in actuator disc simulations without any prior knowledge of the wind turbine being analysed.