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Centred and staggered arrangements of tidal turbines

  • S. Draper (a1) and T. Nishino (a2)
  • Please note a correction has been issued for this article.


In this paper we extend linear momentum actuator disc theory to consider two rows of tidal turbines placed in a centred or staggered arrangement. The extensions assume a streamwise spacing between rows that is sufficient for pressure equalization, but is not too large for significant mixing of the upstream turbine wake before the second row. We first consider a given number of turbines in a tidal channel; in this case the average power for a staggered arrangement over two rows is found to be higher than that for a centred arrangement, but lower than can be obtained by placing all turbines side-by-side in one row (if all turbines have the same local resistance). Furthermore, staggered arrangements extract power more efficiently than centred arrangements, but less efficiently than a single row with the same number of turbines, and this has implications for ranking different arrangements of tidal turbines. We also use the extended actuator disc models (together with an argument of scale separation) to consider some example arrangements of tidal turbines in laterally unconfined flow. Specifically, it is shown that locally staggering a fixed number of turbines in an array to form a tidal farm generates less power than placing the same number of turbines side-by-side. However, if more than one row of turbines is adopted (perhaps to keep the farm spatially compact) then the optimum turbine spacing within a row increases significantly with addition of a second row. This trend suggests that multi-row tidal turbine farms would require wide turbine spacing within each row to maximize the power per turbine, similarly to existing offshore wind farms.


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Betz, A. 1920 Das Maximum der Theoretisch Möglichen Ausnützung des Windes durch Windmotoren. Z. Gesamte Turbinenwesen 26, 307309.
Draper, S., Borthwick, A. G. L. & Houlsby, G. T. 2013 Energy potential of a tidal fence deployed near a coastal headland. Phil. Trans. R. Soc. Lond. A 371, 20120176.
Draper, S., Houlsby, G. T., Oldfield, M. L. G. & Borthwick, A. G. L. 2010 Modelling tidal energy extraction in a depth-averaged coastal domain. IET Renew. Power Gener. 4, 545554.
Garrett, C. & Cummins, P. 2005 The power potential of tidal currents in channels. Phil. Trans. R. Soc. Lond. A 461, 25632572.
Garrett, C. & Cummins, P. 2007 The efficiency of a turbine in a tidal channel. J. Fluid Mech. 588, 243251.
Garrett, C. & Cummins, P. 2013 Maximum power from a turbine farm in shallow water. J. Fluid Mech. 714, 634643.
Houlsby, G. T., Draper, S. & Oldfield, M. L. G. 2008 Application of linear momentum actuator disc theory to open channel flow. Tech. Rep. OUEL 2296/08. University of Oxford.
Joukowsky, N. E. 1920 Windmill of the NEJ type. Trans. Central Inst. Aero-Hydrodynamics of Moscow.
van Kuik, G. A. M. 2007 The Lanchester-Betz-Joukowsky limit. Wind Energy 10, 289291.
Lanchester, F. W. 1915 A contribution to the theory of propulsion and the screw propeller. Trans. Inst. Naval Archit. 57, 98116.
Loth, J. L. & McCoy, H. 1983 Optimization of Darrieus turbines with an upwind and downwind momentum model. AIAA J. Energy 7, 313318.
Newman, B. G. 1983 Actuator disc theory for vertical-axis wind turbines. J. Wind Engng Ind. Aerodyn. 15, 347355.
Newman, B. G. 1986 Multiple actuator-disc theory for wind turbines. J. Wind Engng Ind. Aerodyn. 24, 215225.
Nishino, T. & Willden, R. H. J. 2012 The efficiency of an array of tidal turbines partially blocking a wide channel. J. Fluid Mech. 708, 596606.
Nishino, T. & Willden, R. H. J. 2013 Two-scale dynamics of flow past a partial cross-stream array of tidal turbines. J. Fluid Mech. 730, 220244.
Vennell, R. 2010 Tuning turbines in a tidal channel. J. Fluid Mech. 663, 253267.
Vennell, R. 2011 Tuning tidal turbines in-concert to maximize farm efficiency. J. Fluid Mech. 671, 587604.
Vennell, R. 2012 The energetics of large tidal turbine arrays. Renewable Energy 48, 210219.
Whelan, J. I., Graham, J. M. R. & Peiró, J. 2009 A free-surface and blockage correction for tidal turbines. J. Fluid Mech. 624, 281291.
Wilson, R. E., Lissaman, P. B. S. & Walker, S. N. 1976 Aerodynamic performance of wind turbines. Tech. Rep. NSF/RA-760228. Oregon State University.
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A correction has been issued for this article: