Performance and stability of a counter-rotating windmill using a planetary gearing: Measurements and Simulation

摘要

A counter-rotating (CR) windmill test rig "Contra-Eole II" with two 0.8 m diameter rotors and independent generators has been developed and characterized in a wind tunnel. Experiments have shown that, compared to the single rotor case, the extracted maximum power is increased by ≈ 9%. The blockage effects in the wind tunnel are investigated using both a CFD model and measurement of drag coefficient c_T. The corrected optimal power coefficient amounts to c_p~(opt, corr) = 0.37. The measurements also allow to predict the dynamics and stability properties for the case of a CR windmill with two rotors coupled by a differential planetary gearing to a single generator. When the generator speed is imposed, the resulting system dynamics can be simplified to a nonlinear first-order ordinary differential equation with the rotor speed Ω_1 as independent variable. The equilibrium operating points and their local stability is investigated. The paper concludes with an investigation of the optimal multiplication ratio n_1/n_2 for the planetary gearing.