Two-scale blockage correction for an array of tidal turbines
Authors: Dehtyriov Daniel , Vogel Christopher , Willden Richard 
Published: September 2023

It has been shown theoretically that tidal fences consisting of multiple turbines placed side-by-side can makeuse of constructive interference (local blockage) effects to raise the energy extraction efficiency of the fenceabove that of the Betz limit applicable to unblocked flow problems. For the two-scale problem of a longarray of turbines partially spanning the width of a much wider channel (vanishing global blockage) theefficiency of energy extraction, normalised on the undisturbed kinetic energy flux, rises from the Betz limitof 0.593 to the partial fence limit of 0.798 [1]. Experiments on pairs of side-by-side turbines at largelaboratory scale [2] have confirmed the important aspects of the underlying partial fence theory and thatsome of the performance benefits offered by constructive interference effects can be achieved in practice.
Experimental validation in wind tunnels, towing tanks and other laboratory facilities are however prone toglobal blockage effects not seen in full-scale open flows due to the close proximity of flow boundaries to thebody. These global blockage effects modify the thrust and power performance of the turbines, such thatcorrections to experimental curves are necessary to either translate laboratory-scale experimental results tofull-scale conditions, or to calculate the expected loads and power on tidal turbines deployed in blocked-flowconditions [3][4]. The difficulty applying blockage corrections to turbine arrays is the non-linear interactionbetween local and global blockage. These two effects cannot be simply decoupled as for various turbine tip-to-tip spacings (affecting local blockage), changes in the global blockage have a different impact on turbineperformance.
A number of blockage corrections have been developed for single turbines operating in blocked flowconditions. These corrections typically seek to describe an equivalent free-stream velocity which, in theabsence of global blockage, would result in the same thrust and velocity through the turbine as in the blockedcase. Thrust and power curves are then scaled non-linearly with the ratio of the experimental tank velocityand the equivalent free-stream velocity [5]. These single turbine blockage corrections can however onlyaccount for global blockage, and simplifications must currently be made based on the assumption that globaland local blockage effects can be linearly decoupled [2].
This work therefore presents an analytical blockage correction for co-planar arrays of tidal turbines based ontwo-scale momentum theory [1]. This correction is then compared to other models, particularly for turbinearray experimental test data. Finally, RANS computations for a turbine array at various global blockageratios is compared to the analytical model, demonstrating its validity. A particularly useful aspect of thetheoretical model is to allow for experimental quantification of the local-blockage effect for finite lengthfences. For instance, doubling the fence length doubles the global blockage, but increases in fence thrust andpower cannot be attributed only to the change in global blockage due to non-linear coupling. This correctionallows for a decoupling of these two effects, such that the local blockage effect can be isolated andquantified.