A numerical wake alignment method for horizontal axis wind turbines with the lifting line theory

A method to analyze the flow around horizontal axis wind turbines based on the lifting line theory is presented. A non-linear vortex wake alignment scheme is proposed. The wake is discretized in straight line vortices. The velocity induced by the vortex system is computed in multiple sections downstream of the rotor plane. The effect of the radial velocity component is neglected and, therefore, the orientation of each straight line vortex is only given by the axial and tangential velocity components. The convergence of the numerical integration with increasing wake discretization is studied and results are compared with the analytical solution. The effect of increasing number of alignment sections is also analyzed. The results are compared to the ones computed with the constant pitch wake, aligned at the lifting lines. An increase of the blades circulation and power coefficient is obtained. Far downstream the wake geometry does not significantly vary along the axial direction. The numerical results are compared to experimental data available from the literature.