On the Generalized Formulation for the Optimization of Chord and Twist Angle of Wind Blade
Abstract
The classical Stewart’s (1976) model is widely used in the wind blades design because that model presents low computational cost and easy implementation, especially for the case of small wind rotors (Vaz et al, 2009). However, in the structure of Stewart’s (1976) model the axial induction factor in the wake is twice the inducing factor in the rotor plane, ignoring the generally form established in the work of Wilson and Lissaman (1974) for the influence of vortex wake when the machine operates at low tip-speed-ratios. For values of tip-speed-ratio smaller than 2, a wind rotor tends to operate at low speed even for significant wind speeds. This regime of operation occurs in multiple blade turbines, where the rotation is generally slow, but with high torques, and is widely used for water pumping (Vaz et al. 2011; Mesquita and Alves, 2000). Thus, this work proposes a new mathematical model of aerodynamic optimization based on the relationship between the axial induction factors in the rotor and in the wake, at lower tip-speed ratio. This general relationship was presented by Wilson and Lissaman (1974), where the vortex wake is considered in the calculation of the local power coefficient of the wind blade. Thus, it’s possible to promote an improvement in aerodynamics of the wind turbine with the maximization of the local power coefficient.