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Flow Scales in Cross-Flow Turbines

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Abstract

This work presents analytical estimates for various flow scales encountered in cross-flow turbines (i.e. Darrieus type or vertical axis) for renewable energy generation (both wind and tidal). These estimates enable the exploration of spatial or temporal interactions between flow phenomena and provide quantitative and qualitative bounds of the three main flow phenomena: the foil scale, the vortex scale and wake scale. Finally using the scale analysis, we show using an illustrative example how high order computational methods prove beneficial when solving the flow physics involved in cross-flow turbines.

Keywords

  • Wind Turbine
  • Discontinuous Galerkin Method
  • Vortex Interaction
  • Velocity Deficit
  • Time Scale Separation

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Fig. 1.1
Fig. 1.2

Notes

  1. 1.

    Airfoil aerodynamics and hydrofoil hydrodynamics are equivalent nomenclatures for foils operating in air or water environments. Since this work encompasses both wind and tidal turbine applications, from this point onwards, “foils” will denote either “airfoils” or “hydrofoils”. In addition, the term “aerodynamic” can always be replaced by “hydrodynamic” in this work.

  2. 2.

    β < 1 for unblocked cases but may exceed 1 if blockage leads to accelerated flow through the turbine.

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Acknowledgements

EF would like to acknowledge the financial support of the John Fell OUP fund and the European Commission (ANADE project under grant contract PITN-GA-289428).

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Correspondence to Esteban Ferrer .

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Ferrer, E., Le Clainche, S. (2015). Flow Scales in Cross-Flow Turbines. In: Ferrer, E., Montlaur, A. (eds) CFD for Wind and Tidal Offshore Turbines. Springer Tracts in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-16202-7_1

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  • DOI: https://doi.org/10.1007/978-3-319-16202-7_1

  • Publisher Name: Springer, Cham

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