Performance and flow characteristics of the optimum rotors of Betz, Joukowsky, and Glauert at low tip-speed ratio

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The advent of the Internet of Things technology has led to a renewed interest in the use of low tip-speed ratio micro-scale wind turbines to supply power to battery-less microsystems. At low tip-speed ratio (λ), the blade geometry varies significantly depending on the optimal flow conditions used in the classical design method and the blade element/momentum theory (BEMT), and very few papers have examined this controversy. This experimental study aims to investigate the airflow and power characteristics of three 200-cm wind turbines designed according to the BEMT with three different optimum flow conditions at λ = 1: the Betz model, the Glauert model, and the Joukowsky model. Glauert optimum rotor achieves higher maximum power coefficient (Cp,max=0.34) than the optimum rotors of Betz (Cp,max=0.31) and Joukowsky (Cp,max=0.26). The two latter turbines have lower cut-in wind speed and their torque coefficient decreases linearly with the tip-speed ratio. Betz optimum rotor has a highly stable and persistent wake, whereas large recirculation bubbles and vortex breakdown are observed downstream the runners of Glauert and Joukowsky. The airflow velocity fields and induction factor distributions computed from stereoscopic particle image velocimetry acquisitions show significant differences between each rotor and also between the theoretical developments and the experimental results, especially for the Joukowsky rotor. In addition, even though the optimum flow conditions of Glauert or Betz appear to be the most appropriate models, a method based on flow deflection rather than on airfoil polar plots may be more pertinent for the design of low tip-speed ratio micro-scale wind turbines.