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The efficiency of a turbine in a tidal channel

Published online by Cambridge University Press:  24 September 2007

CHRIS GARRETT  and
PATRICK CUMMINS
CHRIS GARRETT
Affiliation:
Department of Physics and Astronomy, University of Victoria, Victoria, BC V8W 3P6, Canada
PATRICK CUMMINS
Affiliation:
Institute of Ocean Sciences, Fisheries and Oceans Canada, Sidney, BC V8L 4B2, Canada
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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.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 588 , 10 October 2007 , pp. 243 - 251
Copyright
Copyright © Cambridge University Press 2007

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References

REFERENCES

Bahaj, A. S., Molland, A. F., Chaplin, J. R. & Batten, W. M. J. 2007 Power and thrust measurements of marine current turbines under various hydrodynamic flow conditions in a cavitation tunnel and a towing tank. Renewable Energy 32, 407–426.CrossRefGoogle Scholar
Bergey, K. H. 1980 The Lanchester–Betz limit. J. Energy 3, 382–384.CrossRefGoogle Scholar
Betz, A. 1920 Das maximum der theoretisch möglichen ausnutzüng des windes durch windmotoren. Z. Gesamte Turbinenwesen, Heft 26.Google Scholar
Betz, A. 1926 Wind-Energie und ihre Ausnutzung durch Windmühlen. Vandenhoek and Ruprecht, Göttingen, 64 pp.Google Scholar
Corten, G. P. 2001 Heat generation by a wind turbine. 14th IEA Symposium on the Aerodynamics of Wind Turbines, 2000. ECN Rep. ECN-RX–01-001, 7pp.Google Scholar
Garrett, C. & Cummins, P. 2004 Generating tidal power from currents. J. Waterway, Port, Coastal, Ocean Engng 130, 114–118.CrossRefGoogle Scholar
Garrett, C. & Cummins, P. 2005 The power potential of tidal currents in channels. Proc. R. Soc. Lond. A 461, 2563–2572.Google Scholar
Lanchester, F. W. 1915 A contribution to the theory of propulsion and the screw propeller. Trans. Inst. Naval Archit. LVII. 98–116.Google Scholar
Sutherland, G., Foreman, M. & Garrett, C. 2007 Tidal current energy assessment for Johnstone Strait, Vancouver Island. J. Power Energy 221, 147–157.CrossRefGoogle Scholar