Abstract
When an array of turbines occupies a substantial fraction of a tidal or river channel’s cross-sectional area, the flow confinement caused with the channel boundaries increases the mass flux through the turbines relative to unconfined flow conditions. Because this increases turbine power output, exploiting these physics has the potential to reduce the levelized cost of energy. However, this is not a foregone conclusion because confinement also substantially increases the forces on the turbine blades and support structures. Here, we employ a control co-design framework for arrays of cross-flow (“vertical axis”) turbines to demonstrate that confinement does, in fact, reduce overall energy costs.
Non-dimensional torque and force coefficients for counter-rotating turbine pairs are obtained from either laboratory experiments or simulations. To date, we have evaluated the characteristics for over 45 turbine geometries at blockage ratios ranging from 35 to 55%. Dimensional rotor performance is then evaluated for a conceptual array at a reference site (Angoon, AK) employing either “underspeed” or “overspeed” control once the inflow velocity surpasses rated speed (transition point between power-maximizing and constant power control). This dimensional rotor performance is the basis for the design and evaluation of the powertrain, as well as support structures and foundations. When simulation data are used, structural evaluation extends to the blade design. This information is then integrated into an economic framework to identify the rated speed with the lowest associated levelized cost of energy.
Using this co-design framework with simulation data, we predict a 40% reduction in the levelized cost of energy for an array occupying 50% of the channel cross-section, as compared to an unconfined array. This demonstrates that the increased energy production more than compensates for the higher cost of structural and powertrain components. Comparing control strategies, we find overspeed control results in substantially lower costs than underspeed due to more favorable powertrain utilization. Similarly, looking across geometries (Figure 1), we observe significant cost variations with blade count, chord-to-radius ratio, and preset pitch angle for both control strategies, though blade count has more influence when underspeed control is employed. Unexpectedly, we find that advanced control strategies, such as coordinated-phase intracycle control, do not appear to provide benefit at higher confinement, potentially because the oscillatory thrust associated with intracycle control reduces the benefits of flow confinement.
Overall, these results suggest that tidal and river current turbine arrays may be able to benefit economically from confinement, particularly when rotor geometries produce moderately high, steady thrust. Whether these benefits can be realized in practice at larger scale requires balancing them against environmental and multi-use considerations.