Analytical and Numerical Modeling of Performance Characteristics of Cross-Flow Axis Hydrokinetic Turbines

Abstract

A model for cross-flow axis hydrokinetic turbines based on blade element theory (BET) was developed. The model combines an extensive experimental and numerical high Reynolds number data set for symmetric airfoils with governing equations to predict performance characteristics of the turbines. The model allows for any number of turbine blades and for variable hydrofoil sweep angles; both straight blade (H-Darrieus) and helical blade (Gorlov) cross-flow axis turbines are modeled. In this model the free stream velocity and the turbine’s rate of rotation are not coupled hydrodynamically, and experimental calibration of the model for a specific turbine design is necessary. The calibrated model is then used with real inflow data from an actual tidal energy site to predict instantaneous power and energy yield over a period of time. Investigation of tip speed ratios allows for predictions of unsteady loadings, optimal performance and power outputs. The model provides the versatility to predict characteristics of many different shapes and sizes of cross-flow axis turbines. Through investigation of turbine stall characteristics predicted by the model, two, turbine-specific tip speed ratios of interest were determined: the critical and optimal tip speed ratios. The “critical tip speed ratio” is defined as the tip speed ratio above which there are no longer regions of negative torque during the turbine rotation. The “optimal tip speed ratio” is defined as the tip speed ratio for which the coefficient of torque, averaged over one rotation, is maximized. It is hypothesized that these tip speed ratios correspond to specific turbine operating points: A turbine operating under no load conditions will spin near the optimal tip speed ratio, and a turbine operating at peak power conditions will spin near the critical tip speed ratio.