Influence of the Downstream Blade Sweep on Cross-flow Turbine Performance
Authors: Snortland Abigale , Williams Owen , Polagye Brian 
Published: September 2023

Because cross-flow turbines rotate perpendicular to their inflow, the blades encounter a continually fluctuating angle of attack and relative velocity that can lead to the unsteady, non-linear phenomenon of dynamic stall. Additionally, because of appreciable deceleration of the flow through the turbine rotor (induction), the relative velocity a blade experiences during the upstream portion of its cycle differs appreciably to that of the downstream portion. Both dynamic stall severity and turbine induction depend on the ratio of the blade tangential velocity to the inflow velocity - the dimensionless ”tip-speed ratio”. Consequently, the power generated by a blade varies substantially with tip-speed ratio and angular position. As the tip-speed ratio increases, the angle of attack range experienced by the blade decreases, dynamic stall weakens, and the relative velocity incident on the blade increases. In aggregate, this increases the amplitude of the performance peak in the upstream sweep and shifts the peak later in the cycle. In contrast, as the tip-speed ratio increases, power losses during the downstream sweep becomes increasingly detrimental to time-averaged turbine performance. Recent works, both experimental and computational, have investigated the near-blade hydrodynamics of cross-flow turbines in concert with performance measurements. However, despite the significance of the downstream sweep on performance, most attention has focused on the power generating phases.

Here, we specifically investigate the impact of the downstream blade sweep on cross-flow turbine performance using a 1-bladed turbine (NACA 0018 foil). Because turbine torque is measured at the center shaft in our experiments, a one-bladed turbine allows us to isolate the performance contributions for the upstream and downstream sweeps (i.e., with a multi-bladed turbine, the torque contribution from each blade is ambiguous). Additionally, flow fields are investigated to understand the hydrodynamic mechanisms for the observed degradation in downstream performance at high tip-speed ratios. For this purpose, two-component, phase-locked, planar particle image velocimetry data is obtained inside the turbine swept area for two tip-speed ratios.  We find that the average performance in the upstream sweep continues to increase beyond the optimal tip-speed ratio, with respect to time-averaged performance, of 2.5. In contrast, the average performance in the downstream sweep is net neutral until the optimal tip-speed ratio where it begins to decrease at a faster rate than the upstream performance increases. This indicates that the optimal tip-speed ratio is strongly influenced by the point at which the downstream sweep begins to consume appreciable power. These results highlight the importance of understanding hydrodynamics in the downstream sweep, where induction and upstream disturbances violate simple models to predict angles of attack and relative velocity. An improved understanding may suggest strategies to improve performance in the downstream sweep and increase optimal tip-speed ratios and performance of cross-flow turbines.