@article{Dehtyriov_Vogel_Willden_2023, title={A Two-scale blockage correction for an array of tidal turbines}, volume={15}, url={https://submissions.ewtec.org/proc-ewtec/article/view/366}, DOI={10.36688/ewtec-2023-366}, abstractNote={<p>It has been shown theoretically that tidal fences consisting of multiple turbines placed side-by-side can make<br>use of constructive interference (local blockage) effects to raise the energy extraction efficiency of the fence<br>above that of the Betz limit applicable to unblocked flow problems. For the two-scale problem of a long<br>array of turbines partially spanning the width of a much wider channel (vanishing global blockage) the<br>efficiency of energy extraction, normalised on the undisturbed kinetic energy flux, rises from the Betz limit<br>of 0.593 to the partial fence limit of 0.798 [1]. Experiments on pairs of side-by-side turbines at large<br>laboratory scale [2] have confirmed the important aspects of the underlying partial fence theory and that<br>some of the performance benefits offered by constructive interference effects can be achieved in practice.</p> <p><br>Experimental validation in wind tunnels, towing tanks and other laboratory facilities are however prone to<br>global blockage effects not seen in full-scale open flows due to the close proximity of flow boundaries to the<br>body. These global blockage effects modify the thrust and power performance of the turbines, such that<br>corrections to experimental curves are necessary to either translate laboratory-scale experimental results to<br>full-scale conditions, or to calculate the expected loads and power on tidal turbines deployed in blocked-flow<br>conditions [3][4]. The difficulty applying blockage corrections to turbine arrays is the non-linear interaction<br>between local and global blockage. These two effects cannot be simply decoupled as for various turbine tip-<br>to-tip spacings (affecting local blockage), changes in the global blockage have a different impact on turbine<br>performance.</p> <p><br>A number of blockage corrections have been developed for single turbines operating in blocked flow<br>conditions. These corrections typically seek to describe an equivalent free-stream velocity which, in the<br>absence of global blockage, would result in the same thrust and velocity through the turbine as in the blocked<br>case. Thrust and power curves are then scaled non-linearly with the ratio of the experimental tank velocity<br>and the equivalent free-stream velocity [5]. These single turbine blockage corrections can however only<br>account for global blockage, and simplifications must currently be made based on the assumption that global<br>and local blockage effects can be linearly decoupled [2].</p> <p><br>This work therefore presents an analytical blockage correction for co-planar arrays of tidal turbines based on<br>two-scale momentum theory [1]. This correction is then compared to other models, particularly for turbine<br>array experimental test data. Finally, RANS computations for a turbine array at various global blockage<br>ratios is compared to the analytical model, demonstrating its validity. A particularly useful aspect of the<br>theoretical model is to allow for experimental quantification of the local-blockage effect for finite length<br>fences. For instance, doubling the fence length doubles the global blockage, but increases in fence thrust and<br>power cannot be attributed only to the change in global blockage due to non-linear coupling. This correction<br>allows for a decoupling of these two effects, such that the local blockage effect can be isolated and<br>quantified.</p>}, journal={Proceedings of the European Wave and Tidal Energy Conference}, author={Dehtyriov, Daniel and Vogel, Christopher and Willden, Richard}, year={2023}, month={Sep.} }