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Numerical Study of 2D Vertical Axis Wind and Tidal Turbines with a Degree-Adaptive Hybridizable Discontinuous Galerkin Method

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Part of the Springer Tracts in Mechanical Engineering book series (STME)

Abstract

This work presents a 2D study of vertical axis turbines with application to wind or tidal energy production. On the one hand, a degree-adaptive Hybridizable Discontinuous Galerkin (HDG) method is used to solve this incompressible Navier–Stokes problem. The HDG method allows to drastically reduce the coupled degrees of freedom (DOF) of the computation, seeking for an approximation of the solution that is defined only on the edges of the mesh. The discontinuous character of the solution provides an optimal framework for a degree-adaptive technique. Degree-adaptivity further reduces the number of DOF in the HDG computation by means of degree-refining only where more precision is needed. On the other hand, the finite volume method of ANSYS® is used to validate and compare the obtained results.

Keywords

  • Wind Turbine
  • Offshore Wind
  • Offshore Wind Turbine
  • Hybridizable Discontinuous Galerkin
  • Move Reference Frame

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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  • DOI: 10.1007/978-3-319-16202-7_2
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References

  1. ANSYS 15.0 Product Documentation (2013)

    Google Scholar 

  2. Cochard S, Letchford CW, Earl TA, Montlaur A (2012) Formation of tip-vortices on triangular prismatic-shaped cliffs. Part 1: A wind tunnel study. J Wind Eng Ind Aerodyn 109:9–20

    CrossRef  Google Scholar 

  3. Cockburn B, Nguyen NC, Peraire J (2010) A comparison of HDG methods for Stokes flow. J Sci Comput 45(1–3):215–237

    MATH  MathSciNet  CrossRef  Google Scholar 

  4. Donea J, Huerta A (2003) Finite element methods for flow problems. Wiley, Chichester

    CrossRef  Google Scholar 

  5. European Wind Energy Association (2014) Wind in power: 2013 European Statistics

    Google Scholar 

  6. Ferrer E, Willden R (2012) A high order discontinuous Galerkin-Fourier incompressible 3D Navier-Stokes solver with rotating sliding meshes. J Comput Phys 231(21):7037–7056

    MATH  MathSciNet  CrossRef  Google Scholar 

  7. Giorgiani G, Fernández-Méndez S, Huerta A (2014) Hybridizable discontinuous Galerkin with degree adaptivity for the incompressible Navier-Stokes equations. Comput Fluids 98:196–208

    MathSciNet  CrossRef  Google Scholar 

  8. Giorgiani G, Fernández-Méndez S, Huerta A (2013) Hybridizable discontinuous Galerkin p-adaptivity for wave propagation problems. Int J Numer Methods Fluids 72(12):1244–1262

    CrossRef  Google Scholar 

  9. Giorgiani G, Fernández-Méndez S, Huerta A (2013) High-order continuous and discontinuous Galerkin methods for wave. Int J Numer Methods Fluids 73(10):883–903

    Google Scholar 

  10. Li L, Sherwin SJ, Bearman PW (2002) A moving frame of reference algorithm for fluid/structure interaction of rotating and translating bodies. Int J Numer Methods Fluids 38(2):187–206

    MATH  CrossRef  Google Scholar 

  11. MODEC (2013) Floating wind and current hybrid power generation—Savonius Keel and wind turbine Darrieus. http://www.modec.com/fps/skwid/pdf/skwid.pdf. Accessed 02 Dec 2014

  12. Montlaur A, Fernandez-Mendez S, Huerta A (2008) Discontinuous Galerkin methods for the Stokes equations using divergence-free approximations. Int J Numer Methods Fluids 57(9):1071–1092

    MATH  MathSciNet  CrossRef  Google Scholar 

  13. Montlaur A, Cochard S, Fletcher DF (2012) Formation of tip-vortices on triangular prismatic-shaped cliffs. Part 2: A computational fluid dynamics study. J Wind Eng Ind Aerodyn 109:21–30

    CrossRef  Google Scholar 

  14. Montlaur A, Fernandez-Mendez S, Huerta A (2012) High-order implicit time integration for unsteady incompressible flows. Int J Numer Methods Fluids 70(5):603–626

    MathSciNet  CrossRef  Google Scholar 

  15. Nguyen NC, Peraire J, Cockburn B (2011) An implicit high-order hybridizable discontinuous Galerkin method for the incompressible Navier-Stokes equations. J Comput Phys 230(4):1147–1170

    MATH  MathSciNet  CrossRef  Google Scholar 

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Correspondence to Adeline Montlaur .

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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. Springer Tracts in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-16202-7_2

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  • DOI: https://doi.org/10.1007/978-3-319-16202-7_2

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-16201-0

  • Online ISBN: 978-3-319-16202-7

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