The potential of cross-stream aligned sub-arrays to increase tidal turbine efficiency

A theoretical model is proposed for a row of sub-arrays of tidal turbines aligned in a cross-stream fashion across part of a wide channel. This model builds on previous work investigating the behaviour of a single partial row array that split the problem into two flow scales; device and channel. In the present work, three flow scales are proposed: device, sub-array and channel flow, allowing the mass, energy and momentum conservation balance to be assessed separately at each scale. The power potential of a row of sub-arrays with varying blockage ratios at each flow scale is investigated, and it is found that increasing device local blockage has the greatest potential to increase power yield. It is also found that, for such a single row tidal farm with a sufficient number of devices in a very wide channel, splitting the long fence array into multiple smaller co-linear sub-fences can increase the overall energy extraction potential. A new maximum power coefficient is found in infinitely wide flow, increasing from the Lanchester-Betz limit of 0.593 for turbines in unblocked flow, past the partial row array limit of 0.798, to a new limiting value of 0.865 for a row of multiple sub-arrays.