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On the arrangement of tidal turbines in rough and oscillatory channel flow

  • P. A. J. Bonar (a1) (a2), L. Chen (a2), A. M. Schnabl (a2), V. Venugopal (a1), A. G. L. Borthwick (a1) and T. A. A. Adcock (a2)...


Fast tidal streams are a promising source of clean, predictable power, but the task of arranging tidal turbines for maximum power capture is complicated. Actuator disc models, such as the two-scale actuator disc theory, have proven useful in seeking optimal turbine arrangements, yet these models assume flows that are frictionless and steady, and thus quite unlike the channel flow conditions that actual tidal turbines experience. In this paper, we use numerical methods to relax these assumptions and explore how optimal turbine arrangements change as the flow transitions from frictionless and steady to rough and oscillatory. In so doing, we show that, under certain conditions, the assumption of quasi-steady flow in models of tidal turbines may neglect leading-order physics. When the ratio of drag to inertial forces in the unexploited channel is very low, for instance, the optimal turbine arrangements are found to be quite different, and the potential for enhanced power capture is found to be much greater than predicted by two-scale actuator disc theory.


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Adcock, T. A. A., Draper, S. & Nishino, T. 2015 Tidal power generation – a review of hydrodynamic modelling. Proc. IMechE A 229 (7), 755771.10.1177/0957650915570349
Bonar, P. A. J., Adcock, T. A. A., Venugopal, V. & Borthwick, A. G. L. 2018 Performance of non-uniform tidal turbine arrays in uniform flow. J. Ocean Engng Mar. Energy 4 (3), 231241.10.1007/s40722-018-0118-x
Bonar, P. A. J., Venugopal, V., Borthwick, A. G. L. & Adcock, T. A. A. 2016 Numerical modelling of two-scale flow dynamics. In Proceedings of the 5th Oxford Tidal Energy Workshop, Oxford, UK. Tidal Energy Research Group, University of Oxford.
Borthwick, A. G. L. & Barber, R. W. 1992 River and reservoir flow modelling using the transformed shallow water equations. Intl J. Numer. Meth. Fluids 14 (10), 11931217.10.1002/fld.1650141005
Cooke, S. C., Willden, R. H. J., Byrne, B. W., Stallard, T. & Olczak, A. 2015 Experimental investigation of thrust and power on a partial fence array of tidal turbines. In Proceedings of the 11th European Wave and Tidal Energy Conference, Nantes, France. Tidal Energy Research Group, University of Oxford.
Creed, M. J., Draper, S., Nishino, T. & Borthwick, A. G. L. 2017 Flow through a very porous obstacle in a shallow channel. Proc. R. Soc. Lond. A 473 (2200), 20160672.
Cummins, P. F. 2013 The extractable power from a split tidal channel: an equivalent circuit analysis. Renew. Energy 50, 395401.10.1016/j.renene.2012.07.002
Divett, T.2014 Optimising design of large tidal energy arrays in channels: layout and turbine tuning for maximum power capture using large eddy simulations with adaptive mesh. PhD thesis, University of Otago, New Zealand.
Divett, T., Vennell, R. & Stevens, C. 2014 Channel scale optimisation of large tidal turbine arrays in packed rows using large eddy simulations with adaptive mesh. In Proceedings of the 2nd Asian Wave and Tidal Energy Conference, Tokyo, Japan.
Draper, S., Adcock, T. A. A., Borthwick, A. G. L. & Houlsby, G. T. 2014 An electrical analogy for the Pentland Firth tidal stream power resource. Proc. R. Soc. Lond. A 470 (2161), 20130207.
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 (6), 545554.10.1049/iet-rpg.2009.0196
Draper, S. & Nishino, T. 2014a Centred and staggered arrangements of tidal turbines. J. Fluid Mech. 739, 7293.10.1017/jfm.2013.593
Draper, S. & Nishino, T. 2014b Centred and staggered arrangements of tidal turbines – erratum. J. Fluid Mech. 743, 636.
Draper, S., Stallard, T., Stansby, P., Way, S. & Adcock, T. 2013 Laboratory scale experiments and preliminary modelling to investigate basin scale tidal stream energy extraction. In Proceedings of the 10th European Wave and Tidal Energy Conference, Aalborg, Denmark. Tidal Energy Research Group, University of Oxford.
Funke, S. W., Farrell, P. E. & Piggott, M. D. 2014 Tidal turbine array optimisation using the adjoint approach. Renew. Energy 63, 658673.10.1016/j.renene.2013.09.031
Garrett, C. & Cummins, P. 2005 The power potential of tidal currents in channels. Proc. R. Soc. Lond. A 461 (2060), 25632572.
Garrett, C. & Cummins, P. 2007 The efficiency of a turbine in a tidal channel. J. Fluid Mech. 588, 243251.10.1017/S0022112007007781
Garrett, C. & Cummins, P. 2013 Maximum power from a turbine farm in shallow water. J. Fluid Mech. 714, 634643.10.1017/jfm.2012.515
Gupta, V. & Young, A. M. 2017 A one-dimensional model for tidal array design based on three-scale dynamics. J. Fluid Mech. 825, 651676.10.1017/jfm.2017.399
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, Department of Engineering Science, University of Oxford, UK.
Kubatko, E. J., Bunya, S., Dawson, C. & Westerink, J. J. 2009 Dynamic p-adaptive Runge–Kutta discontinuous Galerkin methods for the shallow water equations. Comput. Meth. Appl. Mech. Engng 198 (21–26), 17661774.
Kubatko, E. J., Westerink, J. J. & Dawson, C. 2006 hp discontinuous Galerkin methods for advection dominated problems in shallow water flow. Comput. Meth. Appl. Mech. Engng 196 (1–3), 437451.10.1016/j.cma.2006.05.002
Kuipers, J. & Vreugdenhil, C. B.1973 Calculations of two-dimensional horizontal flow. Res. Rep. S163, Part 1, Delft Hydraulics Laboratory, The Netherlands.
Lloyd, P. M., Stansby, P. K. & Chen, D. 2001 Wake formation around islands in oscillatory laminar shallow-water flows. Part 1. Experimental investigation. J. Fluid Mech. 429, 217238.10.1017/S0022112000002822
Nishino, T. & Willden, R. H. J. 2012a Effects of 3-D channel blockage and turbulent wake mixing on the limit of power extraction by tidal turbines. Intl J. Heat Fluid Flow 37, 123135.10.1016/j.ijheatfluidflow.2012.05.002
Nishino, T. & Willden, R. H. J. 2012b 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, 220244.10.1017/jfm.2013.340
Perez-Campos, E. & Nishino, T. 2015 Numerical validation of the two-scale actuator disc theory for marine turbine arrays. In Proceedings of the 11th European Wave and Tidal Energy Conference, Nantes, France.
Serhadlıoğlu, S.2014 Tidal stream resource assessment of the Anglesey Skerries and the Bristol Channel. DPhil thesis, University of Oxford, UK.
Soulsby, R. 1997 Dynamics of Marine Sands: A Manual for Practical Applications. Thomas Telford Publications.
Vennell, R. 2010 Tuning turbines in a tidal channel. J. Fluid Mech. 663, 253267.10.1017/S0022112010003502
Vennell, R. 2016 An optimal tuning strategy for tidal turbines. Proc. R. Soc. Lond. A 472 (2195), 20160047.10.1098/rspa.2016.0047
Vennell, R. & Adcock, T. A. A. 2014 Energy storage inherent in large tidal turbine farms. Proc. R. Soc. Lond. A 470 (2166), 20130580.
Vennell, R., Funke, S. W., Draper, S., Stevens, C. & Divett, T. 2015 Designing large arrays of tidal turbines: a synthesis and review. Renew. Sust. Energy Rev. 41, 454472.10.1016/j.rser.2014.08.022
Vogel, C. R., Houlsby, G. T. & Willden, R. H. J. 2016 Effect of free surface deformation on the extractable power of a finite width turbine array. Renew. Energy 88, 317324.10.1016/j.renene.2015.11.050
Willden, R. H. J., Nishino, T. & Schluntz, J. 2014 Tidal stream energy: designing for blockage. In Proceedings of the 3rd Oxford Tidal Energy Workshop, Oxford, UK. Tidal Energy Research Group, University of Oxford.
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