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Simple Models for Cross Flow Turbines

  • Esteban FerrerEmail author
  • Soledad Le Clainche
Chapter
Part of the Springer Tracts in Mechanical Engineering book series (STME)

Abstract

Using a high order discontinuous Galerkin numerical method with sliding meshes, we simulate one, two and three bladed cross-flow turbines to extract statistics of the generated wakes (time averaged velocities and Reynolds stresses). Subsequently, we compare the wakes resulting from simple models (a circular cylinder and an actuator disc) to the time averaged cross-flow turbine wakes. Additionally, we provide results for a reduced order model based on dynamic mode decomposition (Le Clainche and Ferrer, Energies, 11(3), 2018, [1]). Whilst simplified models find difficulties in capturing wake asymmetries characteristic of cross-flow turbines, our proposed reduced order model captures mean values and Reynolds stresses with good accuracy, showing the potential of the last technique to speed up the simulation of cross-flow turbine statistics.

Keywords

Cross-flow turbine High order discontinuous Galerkin High order dynamic mode decomposition Reduced order model 

References

  1. 1.
    Le Clainche S, Ferrer E (2018) A reduced order model to predict transient flows around straight bladed vertical axis wind turbines. Energies 11(3)Google Scholar
  2. 2.
    Gretton GI, Bruce T (2005) Preliminary results from analytical and numerical models of a variable-pitch vertical-axis tidal current turbine. In: 6th European wave and tidal energy conference, Glasgow, UK, September 2005Google Scholar
  3. 3.
    Gretton GI, Bruce T (2006) Hydrodynamic modelling of a vertical-axis tidal current turbine using a Navier–Stokes solver. In: Proceedings of the 9th world renewable energy congress, Florence, Italy, 2006Google Scholar
  4. 4.
    Ferrer E, Willden RHJ (2015) Blade-wake interactions in cross-flow turbines. Int J Mar Energy 11:71–83CrossRefGoogle Scholar
  5. 5.
    Montlaur A, Giorgiani G (2015) Numerical study of 2D vertical axis wind and tidal turbines with a degree-adaptive hybridizable discontinuous Galerkin Method. In: Ferrer E, Montlaur A (eds) CFD for wind and tidal offshore turbines, Chap 2. Springer Tracts in Mechanical Engineering. Springer, Cham pp 13–26Google Scholar
  6. 6.
    Somoano M, Huera-Huarte FJ (2017) Flow dynamics inside the rotor of a three straight bladed cross-flow turbine. Appl Ocean Res 69:138–147CrossRefGoogle Scholar
  7. 7.
    Bachant P, Wosnik M (2015) Characterising the near-wake of a cross-flow turbine. J Turbul 16(4):392–410CrossRefGoogle Scholar
  8. 8.
    Islam M, Ting DSK, Fartaj A (2008) Aerodynamic models for Darrieus-type straight-bladed vertical axis wind turbines. Renew Sustain Energy Rev 12(4):1087–1109CrossRefGoogle Scholar
  9. 9.
    Newman BG (1983) Actuator-disc theory for vertical-axis wind turbines. J Wind Eng Ind Aerodyn 15(1–3):347–355CrossRefGoogle Scholar
  10. 10.
    Araya DB, Colonius T, Dabiri JO (2017) Transition to bluff-body dynamics in the wake of vertical-axis wind turbines. J Fluid Mech 813:346–381MathSciNetCrossRefGoogle Scholar
  11. 11.
    Ferrer E (2012) A high order Discontinuous Galerkin - Fourier incompressible 3D Navier–Stokes solver with rotating sliding meshes for simulating cross-flow turbines. PhD thesis, University of Oxford, 2012Google Scholar
  12. 12.
    Ferrer E, Willden RHJ (2011) A high order discontinuous Galerkin finite element solver for the incompressible Navier–Stokes equations. Comput Fluids 46(1):224–230MathSciNetCrossRefGoogle Scholar
  13. 13.
    Ferrer E, Willden RHJ (2012) A high order discontinuous Galerkin - Fourier incompressible 3D Navier–Stokes solver with rotating sliding meshes. J Comput Phys 231(21):7037–7056MathSciNetCrossRefGoogle Scholar
  14. 14.
    Ferrer E, Moxey D, Willden RHJ, Sherwin S (2014) Stability of projection methods for incompressible flows using high order pressure-velocity pairs of same degree: continuous and discontinuous Galerkin formulations. Commun Comput Phys 16(3):817–840CrossRefGoogle Scholar
  15. 15.
    Ferrer E (2017) An interior penalty stabilised incompressible discontinuous Galerkin - Fourier solver for implicit large eddy simulations. J Comput Phys 348:754–775MathSciNetCrossRefGoogle Scholar
  16. 16.
    Wang ZJ, Fidkowski K, Abgrall R, Bassi F, Caraeni D, Cary A, Deconinck H, Hartmann R, Hillewaert K, Huynh HT, Kroll N, May G, Persson PO, van Leer B, Visbal M (2013) High-order CFD methods: current status and perspective. Int J Numer Methods Fluids 72(8):811–845MathSciNetCrossRefGoogle Scholar
  17. 17.
    Ferrer E, de Vicente J, Valero E (2014) Low cost 3D global instability analysis and flow sensitivity based on dynamic mode decomposition and high-order numerical tools. Int J Numer Methods Fluids 76(3):169–184MathSciNetCrossRefGoogle Scholar
  18. 18.
    Gonzalez LM, Ferrer E, Diaz-Ojeda HR (2017) Onset of three-dimensional flow instabilities in lid-driven circular cavities. Phys Fluids 29(6):064102CrossRefGoogle Scholar
  19. 19.
    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, Chap1. Springer tracts in mechanical engineering. Springer, Cham, pp 1–11Google Scholar
  20. 20.
    Oler JW, Strickland JH, Im BJ, Graham GH (1983) Dynamic stall regulation of the Darrieus turbine. Technical report, Sandia Report SAND83-7029 UC-261Google Scholar
  21. 21.
    Ouro P, Runge S, Luo Q, Stoesser T (2018) Three-dimensionality of the wake recovery behind a vertical axis turbine. Renew EnergyGoogle Scholar
  22. 22.
    Kou J, Le Clainche S, Zhang W (2018) A reduced-order model for compressible flows with buffeting condition using higher order dynamic mode decomposition with a mode selection criterion. Phys Fluids 30(1):016103CrossRefGoogle Scholar
  23. 23.
    Le Clainche S, Vega J (2017) Higher order dynamic mode decomposition. SIAM J Appl Dyn Syst 16(2):882–925MathSciNetCrossRefGoogle Scholar
  24. 24.
    Le Clainche S, Vega J (2017) Higher order dynamic mode decomposition to identify and extrapolate flow patterns. Phys Fluids 29(8):084102CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.ETSIAE-UPM - School of AeronauticsUniversidad Politécnica de MadridMadridSpain

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