Cross-flow turbines show great promise for extracting power from river and tidal currents due to their ability to achieve high blockage in confined flows. As a turbine occupies more of the channel cross-sectional area, its efficiency and structural loading increase since both kinetic and potential energy in the freestream are converted to mechanical power. Because of their rectangular swept area, an array of cross-flow turbines can occupy a significant portion of such a channel more effectively than conventional axial-flow turbines with a circular swept area. However, the performance and control characteristics of these high-blockage cross-flow turbine arrays are largely unexplored.
Here, we present a characterization of the performance of a laboratory-scale two-turbine array operating at high confinement in a recirculating water channel. The array blockage ratio was varied between 30% and 60%—which falls at the upper end of what might be realizable in a natural channel—by varying the channel depth and turbine blade span. Across all blockages, the nominal 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 higher end of the tested blockages. We operated the turbines under counter-rotating coordinated constant speed control, wherein the turbines rotate at the same speed but in opposite directions with some prescribed angular phase offset, Δθ, between their cycles. We focus this work on Δθ = 0°, an operating case which would provide a structural advantage for a full-scale two-turbine array due to the equal and opposite lateral loading experienced by the synchronized counter-rotating turbines.
Under coordinated constant speed control, we measured turbine performance at each blockage over a range of tip-speed ratios. In agreement with prior research, we observe that array-average efficiency (CP), the tip-speed ratio corresponding to maximum efficiency (λopt), and the array-average thrust coefficient (CT) all increase as the confinement is increased. When the blockage ratio is increased from 30% to 60%, the peak array CP increases from 0.5 to 1.4—exceeding the Betz limit for unconfined flow at blockage ratios of 33% and above—, and array CT at peak performance increases from 1.7 to 3.5. λopt increases from 2.4 to 3.8 across the range of tested blockages, and the peak of the CP-λ curve becomes broader as confinement increases, allowing the array to maintain near-peak efficiency across a wider range of tip-speed ratios. Overall, the rates at which CP, λopt, and CT increase with confinement appear themselves to increase with confinement; for example, the performance change associated with an increase in the blockage ratio from 50% to 55% is more significant than that associated with an increase in the blockage ratio from 30% to 35%.
Our initial results provide a solid foundation for understanding how the performance of a cross-flow turbine array changes as a function of the array blockage ratio. We plan to build on this work by exploring how confinement informs the design of both control strategies that enhance efficiency (e.g., intracycle controllers that vary the control torque as a function of angular position) as well as economics-driven power-management strategies for a field-scale deployment (e.g., overspeed or underspeed control). We also plan to further analyze the hydrodynamic interactions between the turbines and the channel—for example, free-surface deformation around the turbines—and how they affect performance.