A Two-scale blockage correction for an array of tidal turbines

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.