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A correction to the enhanced bottom drag parameterisation of tidal turbines

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  • Kramer, Stephan C.
  • Piggott, Matthew D.

Abstract

Hydrodynamic modelling is an important tool for the development of tidal stream energy projects. Many hydrodynamic models incorporate the effect of tidal turbines through an enhanced bottom drag. In this paper we show that although for coarse grid resolutions (kilometre scale) the resulting force exerted on the flow agrees well with the theoretical value, the force starts decreasing with decreasing grid sizes when these become smaller than the length scale of the wake recovery. This is because the assumption that the upstream velocity can be approximated by the local model velocity, is no longer valid. Using linear momentum actuator disc theory however, we derive a relationship between these two velocities and formulate a correction to the enhanced bottom drag formulation that consistently applies a force that remains close to the theoretical value, for all grid sizes down to the turbine scale. In addition, a better understanding of the relation between the model, upstream, and actual turbine velocity, as predicted by actuator disc theory, leads to an improved estimate of the usefully extractable energy. We show how the corrections can be applied (demonstrated here for the models MIKE 21 and Fluidity) by a simple modification of the drag coefficient.

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  • Kramer, Stephan C. & Piggott, Matthew D., 2016. "A correction to the enhanced bottom drag parameterisation of tidal turbines," Renewable Energy, Elsevier, vol. 92(C), pages 385-396.
    • Handle: RePEc:eee:renene:v:92:y:2016:i:c:p:385-396
    DOI: 10.1016/j.renene.2016.02.022
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    Cited by:

    1. Ramos, V. & Carballo, R. & Ringwood, John V., 2019. "Application of the actuator disc theory of Delft3D-FLOW to model far-field hydrodynamic impacts of tidal turbines," Renewable Energy, Elsevier, vol. 139(C), pages 1320-1335.
    2. Li, Xiaorong & Li, Ming & Amoudry, Laurent O. & Ramirez-Mendoza, Rafael & Thorne, Peter D. & Song, Qingyang & Zheng, Peng & Simmons, Stephen M. & Jordan, Laura-Beth & McLelland, Stuart J., 2020. "Three-dimensional modelling of suspended sediment transport in the far wake of tidal stream turbines," Renewable Energy, Elsevier, vol. 151(C), pages 956-965.
    3. Guillou, Nicolas & Thiébot, Jérôme, 2016. "The impact of seabed rock roughness on tidal stream power extraction," Energy, Elsevier, vol. 112(C), pages 762-773.
    4. Garcia-Oliva, Miriam & Djordjević, Slobodan & Tabor, Gavin R., 2017. "The influence of channel geometry on tidal energy extraction in estuaries," Renewable Energy, Elsevier, vol. 101(C), pages 514-525.
    5. Marco Piano & Peter E. Robins & Alan G. Davies & Simon P. Neill, 2018. "The Influence of Intra-Array Wake Dynamics on Depth-Averaged Kinetic Tidal Turbine Energy Extraction Simulations," Energies, MDPI, vol. 11(10), pages 1-21, October.
    6. Avdis, Alexandros & Candy, Adam S. & Hill, Jon & Kramer, Stephan C. & Piggott, Matthew D., 2018. "Efficient unstructured mesh generation for marine renewable energy applications," Renewable Energy, Elsevier, vol. 116(PA), pages 842-856.
    7. Vogel, C.R. & Willden, R.H.J. & Houlsby, G.T., 2019. "Tidal stream turbine power capping in a head-driven tidal channel," Renewable Energy, Elsevier, vol. 136(C), pages 491-499.
    8. Philip A. Gillibrand & Roy A. Walters & Jason McIlvenny, 2016. "Numerical Simulations of the Effects of a Tidal Turbine Array on Near-Bed Velocity and Local Bed Shear Stress," Energies, MDPI, vol. 9(10), pages 1-22, October.
    9. Álvarez, M. & Ramos, V. & Carballo, R. & Arean, N. & Torres, M. & Iglesias, G., 2020. "The influence of dredging for locating a tidal stream energy farm," Renewable Energy, Elsevier, vol. 146(C), pages 242-253.
    10. Vogel, C.R. & Willden, R.H.J. & Houlsby, G.T., 2017. "Power available from a depth-averaged simulation of a tidal turbine array," Renewable Energy, Elsevier, vol. 114(PB), pages 513-524.
    11. Goss, Z.L. & Coles, D.S. & Kramer, S.C. & Piggott, M.D., 2021. "Efficient economic optimisation of large-scale tidal stream arrays," Applied Energy, Elsevier, vol. 295(C).
    12. Nasteho Djama Dirieh & Jérôme Thiébot & Sylvain Guillou & Nicolas Guillou, 2022. "Blockage Corrections for Tidal Turbines—Application to an Array of Turbines in the Alderney Race," Energies, MDPI, vol. 15(10), pages 1-18, May.

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