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Effect of free surface deformation on the extractable power of a finite width turbine array

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  • Vogel, C.R.
  • Houlsby, G.T.
  • Willden, R.H.J.

Abstract

The effect of free surface deformation on the power extracted by a tidal turbine array partially spanning a wide channel is investigated using a theoretical model. Two predominant flow scales are assumed; turbine-scale flow, and array-scale flow, which are analysed as quasi-inviscid open channel flow problems in which conservation of mass, momentum, and energy are considered, and coupled through kinematic and dynamic boundary conditions. Power extraction may be maximised by determining the optimum inter-turbine spacing, which also enhances efficiency (ratio of power generated to power removed from the flow). Power extraction and efficiency increase as Froude number increases, improving open channel array performance. In the infinitely wide channel limit, the extracted power depends only on Froude number and local blockage (ratio of turbine to local flow passage areas). At zero Froude number, the peak power coefficient increases from the Lanchester-Betz limit (0.593) to 0.798, occurring when the local blockage ratio is approximately 0.4. Froude numbers in the range of 0.1–0.2, typical of prospective tidal energy sites, increase the peak power coefficient by an additional 1%–4.5% when the array occupies a negligible fraction of the channel, increasing further as a greater proportion of the channel is occupied.

Suggested Citation

  • 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," Renewable Energy, Elsevier, vol. 88(C), pages 317-324.
    • Handle: RePEc:eee:renene:v:88:y:2016:i:c:p:317-324
    DOI: 10.1016/j.renene.2015.11.050
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    1. Vennell, Ross & Funke, Simon W. & Draper, Scott & Stevens, Craig & Divett, Tim, 2015. "Designing large arrays of tidal turbines: A synthesis and review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 41(C), pages 454-472.
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    Cited by:

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    3. Verbeek, M.C. & Labeur, R.J. & Uijttewaal, W.S.J., 2021. "The performance of a weir-mounted tidal turbine: An experimental investigation," Renewable Energy, Elsevier, vol. 168(C), pages 64-75.
    4. Verbeek, M.C. & Labeur, R.J. & Uijttewaal, W.S.J., 2020. "The performance of a weir-mounted tidal turbine: Field observations and theoretical modelling," Renewable Energy, Elsevier, vol. 153(C), pages 601-614.
    5. Ross, Hannah & Polagye, Brian, 2020. "An experimental assessment of analytical blockage corrections for turbines," Renewable Energy, Elsevier, vol. 152(C), pages 1328-1341.
    6. Yosry, Ahmed Gharib & Álvarez, Eduardo Álvarez & Valdés, Rodolfo Espina & Pandal, Adrián & Marigorta, Eduardo Blanco, 2023. "Experimental and multiphase modeling of small vertical-axis hydrokinetic turbine with free-surface variations," Renewable Energy, Elsevier, vol. 203(C), pages 788-801.
    7. 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.
    8. 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.
    9. Lilia Flores Mateos & Michael Hartnett, 2019. "Incorporation of a Non-Constant Thrust Force Coefficient to Assess Tidal-Stream Energy," Energies, MDPI, vol. 12(21), pages 1-17, October.
    10. Patel, Vimal & Eldho, T.I. & Prabhu, S.V., 2019. "Velocity and performance correction methodology for hydrokinetic turbines experimented with different geometry of the channel," Renewable Energy, Elsevier, vol. 131(C), pages 1300-1317.
    11. Maduka, Maduka & Li, Chi Wai, 2022. "Experimental evaluation of power performance and wake characteristics of twin flanged duct turbines in tandem under bi-directional tidal flows," Renewable Energy, Elsevier, vol. 199(C), pages 1543-1567.

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