A Formulation of the Thrust Coefficient for Representing Finite-Sized Farms of Tidal Energy Converters

Tidal energy converter (TEC) arrays in tidal channels generate complex flow phenomena due to interactions with the local environment and among devices. Models with different resolutions are thus employed to study flows past TEC farms, which consider multiple spatial and temporal scales. Simulations over tidal cycles use mesoscale ocean circulation models, incorporating a thrust coefficient to model the momentum sink that represents the effects of the array. In this work, we propose an expression for a thrust coefficient to represent finite-sized farms of TEC turbines at larger scales, C t F a r m , which depends on the spatial organization of the devices. We use a coherent-structure resolving turbulence model coupled with the actuator disk approach to simulate staggered turbine configurations in more detail, varying the separation among devices and the ratios between the channel depths and hub heights. Based on these simulations, we calculate the resultant force for various subsets of devices within the farm, and their corresponding effective thrust coefficient, C t F a r m . We conclude that the thrust coefficient depends solely on the lateral separation of the devices, S y , for farms with only two rows. For farms with more than two rows, the streamwise distance, S x , must be considered as well. With the proposed expression, it is possible to calculate efficiently the effects of finite-sized TEC farms and incorporate a momentum sink into ocean circulation models, without assuming a constant coefficient derived from an infinite farm approximation.