A nonlinear model for aerodynamic configuration of wake behind horizontal-axis wind turbine

Determination of the aerodynamic configuration of wake is the key to analysis and evaluation of the rotor aerodynamic characteristics of a horizontal-axis wind turbine. According to the aerodynamic configuration, the real magnitude and direction of the on-flow velocity at the rotor blade can be determined, and subsequently, the aerodynamic force on the rotor can be determined. The commonly employed wake aerodynamic models are of the cylindrical form instead of the actual expanding one. This is because the influence of the radial component of the induced velocity on the wake configuration proper is neglected. Therefore, this model should be called a "linear model". Using this model means that the induced velocities at the rotor blades and aerodynamic loads on them would be inexact. An approximately accurate approach is proposed in this paper to determine the so-called "nonlinear" wake aerodynamic configuration by means of the potential theory, where the influence of all three coordinate components of the induced velocity on wake aerodynamic configuration is taken into account to obtain a kind of expanding wake that approximately looks like an actual one. First, the rotor aerodynamic model composed of axial (central), bound, and trailing vortexes is established with the help of the finite aspect wing theory. Then, the Biot-Savart formula for the potential flow theory is used to derive a set of integral equations to evaluate the three components of the induced velocity at any point within the wake. The numerical solution to the integral equations is found, and the loci of all elementary trailing vortex filaments behind the rotor are determined thereafter. Finally, to formulate an actual wind turbine rotor, using the nonlinear wake model, the induced velocity everywhere in the wake, especially that at the rotor blade, is obtained in the case of various tip speed ratios and compared with the wake boundary in a neutral atmospheric boundary layer. Hereby, some useful and referential conclusions are offered for the aerodynamic computation and design of the rotor of the horizontal-axis wind turbine