Wind Turbine and Propeller Aerodynamics—Analysis and Design

Wind turbines and propellers are very similar from the aerodynamics point of view, the former extracting energy from the wind, the latter putting energy into the fluid to create a thrust. The main part of this chapter will be devoted to wind turbine analysis and design, as this is currently a major area of research. But much of the theory and numerics is applicable to propellers. Section 10.9 will discuss some results pertinent to propellers. By convention, the power absorbed by a wind turbine rotor will be negative, whereas, that provided by the power plant of a propeller driven system will be positive.

10.1 Introduction—the Different Types of Wind Turbines

Wind-driven machines can be classified according to the orientation of their axis relative to the wind direction. Cross wind-axis machines have their axis in a plane perpendicular to the incoming wind velocity vector; wind-axis machines have their axis parallel to the incoming air flow. This fundamental difference impacts the study of these two types of machines: under the simplest of assumptions of constant wind speed, constant rotation speed and isolated rotor (neglecting support interference), the flow past a wind-axis machine, considered in a frame rotating with the blades is steady, whereas, for a cross wind-axis machine it is always unsteady. Unsteady flows are more complex and costly to analyze analytically and numerically. For this reason we will focus our attention on wind-axis machines. Sources of unsteadiness for wind-axis machines are yaw, when the wind direction is not aligned with the rotor axis, tower interference, earth boundary layer, wind gusts and, ultimately, blade deflection. This will be considered in Sect. 10.6 on unsteady flow. Prior to that, Sect. 10.2 will discuss the general 1-D conservation theorems, commonly called actuator disk theory. Section 10.3 will introduce the vortex model based on Goldstein “airscrew theory” with the treatment of the vortex sheets and the derivation of the torque and thrust in the spirit of the Prandtl lifting line theory. A discretization of the

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J. J. Chattot and M. M. Hafez, Theoretical and Applied Aerodynamics,

DOI 10.1007/978-94-017-9825-9_10

vortex sheet as a lattice is proposed for the application of the Biot-Savart law. The next section, Sect. 10.4, deals with the design of the optimum rotor, discusses the minimum energy condition of Betz and gives a more general result for the optimum condition. Section 10.5 is devoted to the analysis problem, that is of finding the solution of the flow past a given rotor. A technique for handling high incidences and stalled flow on the blades is detailed and illustrated with an example. In Sect. 10.6 the extension of the method to unsteady flow is presented. The key issues are discussed. The effects of yaw and tower interference are assessed and the limits of the method shown by comparisons with experiments. Section 10.7 discusses the hybrid method of coupling a Navier-Stokes code with the vortex model as a means to achieve high fidelity modeling of viscous effects. This is followed, in Sect. 10.8, by perspectives and further development currently under way.