Cross-flow turbines show great promise for extracting power from water currents since their rectangular projected area allows them to achieve high blockage. As a turbine’s blockage ratio—the ratio of the rotor projected area to the channel cross-sectional area—increases, its efficiency and structural loading increase since both kinetic and potential energy in the freestream are converted to mechanical power. For an array of turbines deployed in a river or tidal channel, the array blockage ratio will vary due to daily or seasonal fluctuations in the water level, as well as when individual turbines are deactivated for maintenance. Consequently, understanding how the performance characteristics of the array change as confinement is varied is of practical interest.
Here, we characterize the performance of a laboratory-scale two-turbine array at various levels of confinement in a recirculating water channel. The array blockage ratio was varied from 30% to 60%—the upper end of what might be realizable in a natural channel. Two experimental approaches for varying the blockage were considered: 1) altering the channel cross-sectional area via a change in water depth, and 2) altering the array projected area by changing the blade span. Across all tested blockage ratios, the nominal chord-based Reynolds number (4.0 x 104) and nominal depth-based Froude number (0.22) were held constant, and the submergence-based Froude number was minimized to avoid ventilation of the turbine rotors at the upper end of the tested blockages. At each blockage ratio, the turbine performance was evaluated across a range of tip-speed ratios under a counter-rotating, phase-locked control scheme, wherein the turbines rotate at the same, constant speed but in opposite directions, with a constant angular phase offset, Δθ, between them. We focus this work on Δθ = 0°, an operating case in which the lateral forces and reaction torques for a pair of turbines are equal and opposite, which is advantageous for support structure design.
As the array blockage ratio is increased, we observe significant increases in the array performance and thrust coefficients, as well as an increase in the range of tip-speed ratios over which the array produces power. For the highest confinements, peak power coefficients exceed unity and thrust coefficients are substantially higher than in conventional array designs. We observe disparities between the power and thrust coefficients for arrays with the same blockage ratio, but different blade spans. We attribute the higher performance for longer blade spans to differences in the relative magnitude of parasitic support structure losses between the two rotors, as well as free surface effects. Further, we explore the effectiveness of techniques for accounting for these performance differences through the estimation of blade-level performance.
Overall, our results provide a solid foundation for understanding how the performance of cross-flow turbine arrays change as a function of the array blockage ratio, and highlight considerations for the design of cross-flow turbine experiments.