Energy-based iteration scheme of the double-multiple streamtube model in vertical-axis wind turbines

Due to their simplicity, blade element momentum models, such as the double-multiple streamtube (DMS) model, are among the most common models to predict the performance of Darrieus vertical-axis wind turbines (VAWTs). A two-dimensional energy-based iteration scheme of the DMS model (EB-DMSM) is shown in the present work. Its purpose is to improve predictions of power performance and flow expansion. This new approach is compared with a momentum-based iteration scheme (MB-DMSM) and the results of a two-dimensional computational simulation of a 12-kW straight-bladed VAWT. The mathematical representation of streamlines used for modeling the flow expansion is in good agreement with the simulations. Convergence of both schemes is achieved for tip-speed ratios (TSRs) up to 4. Failure of the models to convergence at higher TSRs is attributed to their inability to adequately represent the aerodynamic forces acting on the blades, due to the simplicity of their formulation. Relative to computational simulations, the maximum differences in the peak power coefficient predictions are 16 and 32 % and in the flow expansion predictions are 53 and 5 % for the MB-DMSM and EB-DMSM, respectively. Corrections are required to improve predictions of power performance and flow expansion of turbines with different geometric and operational parameters.