Flux-Line Theory: A Novel Analytical Model for Cycloturbines

Abstract

In this paper, a novel low-order blade element momentum model, called flux-line theory, is developed for predicting the performance of cycloturbines (variable-pitch vertical-axis wind turbines). It improves upon prior momentum theories by capturing flow expansion/contraction and bending through the turbine. This is accomplished by performing fluid calculations in a coordinate system fixed to streamlines for which the spatial locations are not predescribed. A transformation determines the Cartesian location of streamlines through the rotor disk, and additional calculations determine the power and forces produced. Validations against three sets of experimental data demonstrate improvement over other existing streamtube models. An extension of the theory removes dependence on a blade element model to better understand how turbine–fluid interaction impacts power production. A numerical optimization and simplified analytical analysis identify that maximum power (for a turbine that exclusively decelerates the flow) is produced when the upstream portion of the rotor does not interact with the flow, whereas the downstream portion of the turbine decelerates the flow by just over one-third of the freestream value. The theoretical power coefficient limit falls in a range below 0.8, depending on the prescription of the submodel describing the angle at which the flow crosses the blade path (0.597 for the best-fit model). A larger effective turbine area explains the higher-than-Betz limit result.