Reduced-Order Modeling of Torque on a Vertical-Axis Wind Turbine at Varying Tip Speed Ratios

Vertical-axis wind turbine (VAWT) has received significant attention due to its application in urban environment. Torque produced by VAWT determines its efficiency and power output. In this paper, we develop a reduced-order model of torque VAWT at different tip speed ratios (TSR). We numerically simulate both 2D and 3D flows past a three-bladed Darrieus H-type VAWT and compute overall torque acting on the turbine. We then perform higher-order spectral analysis to identify dominant frequencies and nonlinear couplings. We propose a reduced-order model of torque in the form of modified van der Pol equation with additional quadratic term to allow for even harmonics in addition to odd harmonics present in the system. Using, a perturbation approach of method of multiple scales, we solve the proposed model and compute the coefficients at different TSR. The model not only predicts torque accurately in time domain but also in spectral domain. These reduced-order models provide an accurate and computationally efficient means to predict overall performance and output of the turbine with varying free-stream conditions even in predictive setting.