Abstract
It has been shown theoretically that tidal fences consisting of multiple turbines placed side-by-side can make use of constructive interference (local blockage) effects to raise the energy extraction efficiency of the fence above that of the Betz limit applicable to unblocked flow problems. For the two-scale problem of a long array of turbines partially spanning the width of a much wider channel (vanishing global blockage) the efficiency of energy extraction, normalised on the undisturbed kinetic energy flux, rises from the Betz limit of 0.593 to the partial fence limit of 0.798 [1]. Experiments on pairs of side-by-side turbines at large laboratory scale [2] have confirmed the important aspects of the underlying partial fence theory and that some 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 to global blockage effects not seen in full-scale open flows due to the close proximity of flow boundaries to the body. These global blockage effects modify the thrust and power performance of the turbines, such that corrections to experimental curves are necessary to either translate laboratory-scale experimental results to full-scale conditions, or to calculate the expected loads and power on tidal turbines deployed in blocked-flow conditions [3][4]. The difficulty applying blockage corrections to turbine arrays is the non-linear interaction between 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 turbine performance.
A number of blockage corrections have been developed for single turbines operating in blocked flow conditions. These corrections typically seek to describe an equivalent free-stream velocity which, in the absence of global blockage, would result in the same thrust and velocity through the turbine as in the blocked case. Thrust and power curves are then scaled non-linearly with the ratio of the experimental tank velocity and the equivalent free-stream velocity [5]. These single turbine blockage corrections can however only account for global blockage, and simplifications must currently be made based on the assumption that global and local blockage effects can be linearly decoupled [2].
This work therefore presents an analytical blockage correction for co-planar arrays of tidal turbines based on two-scale momentum theory [1]. This correction is then compared to other models, particularly for turbine array experimental test data. Finally, RANS computations for a turbine array at various global blockage ratios is compared to the analytical model, demonstrating its validity. A particularly useful aspect of the theoretical model is to allow for experimental quantification of the local-blockage effect for finite length fences. For instance, doubling the fence length doubles the global blockage, but increases in fence thrust and power cannot be attributed only to the change in global blockage due to non-linear coupling. This correction allows for a decoupling of these two effects, such that the local blockage effect can be isolated and quantified.