On the Scaling of Wind Turbine Rotors

This article formulates laws for scaling wind turbine rotors. Although the analysis is general, the article primarily focuses on subscaling, i.e. on the design of a smaller size model mimicking a full-scale machine. The present study considers both the steady-state and transient response cases, including the effects of aerodynamic, elastic, inertial and gravitational forces. The analysis reveals the changes to physical characteristics induced by a generic change of scale, indicates which characteristics can be matched faithfully by a sub-scaled model, and states the conditions that must be fulfilled for desired matchings to hold. Based on the scaling laws formulated here, two different strategies to design scaled rotors are considered: in the first strategy the scaled model is simply geometrically zoomed from the reference full-scale one, while in the second strategy the scaled rotor is completely redesigned in order to match desired characteristics of the full-scale machine. The two strategies are discussed and compared, highlighting their respective advantages and disadvantages. The comparison considers the scaling of a reference 10-MW wind turbine of about 180?m of diameter down to three different sizes of 54, 27 and 2.8?m. Simulation results indicate that, with the proper choices, several key performance indicators can be accurately matched even by models characterized by significant scaling factors.