A ring-vortex actuator disk method for wind turbines including hub effects

Due to its robustness and simplicity, the simple actuator disk is still the most used and popular method for performance analysis of horizontal axis wind turbines. However, the hub blockage effect is generally disregarded in this approach, thus worsening the accuracy of its results. This is particularly true for small-sized wind turbines whose ratio between the hub and rotor radii can be as large as 25–30%. In order to obtain some insights onto the impact of the hub blockage-effect on the performance prediction, this paper presents a free-wake ring-vortex actuator disk method accounting for an axisymmetric hub of general shape. The fundamental concept of a uniformly loaded disk without wake rotation is adopted. In the proposed method, the flows induced by the disk and the hub are both modelled by ring sheet-vortices which are discretised through a classical panel method. An iterative solution procedure is developed to evaluate the density strength distribution of the sheets and the wake shape. To this aim, the homogeneous Dirichlet boundary condition is used for the velocity just beneath the hub sheet, while the free force condition is imposed all along the wake boundary. The latter is also required to be aligned with the overall flow field. The method is verified comparing its results with those of a Computational-Fluid-Dynamics-based approach, and of the classical axial momentum theory showing a very good agreement in both cases. Finally, some insights on the hub blockage effect are presented showing that, for a small-sized wind turbine, this effect significantly affect the flow distribution all along the blade span. In the analysed cases, the increment in the axial velocity at the disk, due to the hub blockage, goes from 20% in the hub proximity to 2% at the tip. The above values suggest that the hub blockage effect should never be disregarded in the analysis of small-sized wind turbines.