Journal of Fluid Mechanics

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The efficiency of a turbine in a tidal channel

CHRIS GARRETTa1 and PATRICK CUMMINSa2

a1 Department of Physics and Astronomy, University of Victoria, Victoria, BC V8W 3P6, Canada

a2 Institute of Ocean Sciences, Fisheries and Oceans Canada, Sidney, BC V8L 4B2, Canada

Abstract

There is an upper bound to the amount of power that can be generated by turbines in tidal channels as too many turbines merely block the flow. One condition for achievement of the upper bound is that the turbines are deployed uniformly across the channel, with all the flow through them, but this may interfere with other uses of the channel. An isolated turbine is more effective in a channel than in an unbounded flow, but the current downstream is non-uniform between the wake of the turbines and the free stream. Hence some energy is lost when these streams merge, as may occur in a long channel. We show here, for ideal turbine models, that the fractional power loss increases from 1/3 to 2/3 as the fraction of the channel cross-section spanned by the turbines increases from 0 to close to 1. In another scenario, possibly appropriate for a short channel, the speed of the free stream outside the turbine wake is controlled by separation at the channel exit. In this case, the maximum power obtainable is slightly less than proportional to the fraction of the channel cross-section occupied by turbines.

(Received March 23 2007)

(Revised July 16 2007)

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