Greenberg's Force Prediction for Vertical-Axis Wind Turbine Blades

We present a method to adapt Greenberg's potential flow model for coupled pitching and surging flow such that it can be applied to predict the loads on a vertical-axis wind turbine blade. The model is extended to compute loads on a blade undergoing multi-harmonic oscillations in effective angle of attack and incoming flow velocity by formulating the blade kinematics as a sum of simple harmonic motions. Each of these functions is a multiple of the main turbine rotational frequency, associated with an individual amplitude, as suggested by Greenberg. The results of the adapted model are compared with experimental data from a scaled-down model of a single-bladed H-type Darrieus wind turbine. The comparison between the predictions by the Greenberg model and experimentally obtained phase-averaged radial force evolutions show that the inviscid Greenberg model predicts well the loads at the start of the upwind portion and the maximum loads during upwind, but fails during the downwind portion when flow separation occurs. The proposed application of Greenberg's model to vertical-axis wind turbine kinematics shows a great potential to diagnose regions of separated flow and for quantifying the relative influences of dynamic stall and intrinsic turbine kinematics on the blade loading. Future research can readily extend this method to any airfoil undergoing an arbitrary combination of pitching, surging, and heaving, following a kinematic profile that can be approximated by a Fourier series.