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Wind turbine aerodynamics using ALE–VMS: validation and the role of weakly enforced boundary conditions

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Abstract

In this article we present a validation study involving the full-scale NREL Phase VI two-bladed wind turbine rotor. The ALE–VMS formulation of aerodynamics, based on the Navier–Stokes equations of incompressible flows, is employed in conjunction with weakly enforced essential boundary conditions. We find that the ALE–VMS formulation using linear tetrahedral finite elements is able to reproduce experimental data for the aerodynamic (low-speed shaft) torque and cross-section pressure distribution of the NREL Phase VI rotor. We also find that weak enforcement of essential boundary conditions is critical for obtaining accurate aerodynamics results on relatively coarse boundary layer meshes. The proposed numerical formulation is also successfully applied to the aerodynamics simulation of the NREL 5MW offshore baseline wind turbine rotor.

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References

  1. Jonkman JM, Buhl ML Jr (2005) FAST user’s guide. Technical Report NREL/EL-500-38230. National Renewable Energy Laboratory, Golden

  2. Jonkman J, Butterfield S, Musial W, Scott G (2009) Definition of a 5-MW reference wind turbine for offshore system development. Technical Report NREL/TP-500-38060. National Renewable Energy Laboratory, Golden

  3. Sørensen NN, Michelsen JA, Schreck S (2002) Navier–Stokes predictions of the NREL Phase VI rotor in the NASA Ames 80 ft × 120 ft wind tunnel. Wind Energy 5: 151–169

    Article  Google Scholar 

  4. Duque EPN, Burklund MD, Johnson W (2003) Navier–Stokes and comprehensive analysis performance predictions of the NREL Phase VI experiment. J Sol Energy Eng 125: 457–467

    Article  Google Scholar 

  5. Le Pape A, Lecanu J (2004) 3D Navier–Stokes computations of a stall-regulated wind turbine. Wind Energy 7: 309–324

    Article  Google Scholar 

  6. Sezer-Uzol N, Long LN (2006) 3-D time-accurate CFD simulations of wind turbine rotor flow fields. AIAA Paper 2006-0394

  7. Zahle F, Sørensen NN (2008) Overset grid flow simulation on a modern wind turbine. AIAA Paper 2008-6727

  8. Zahle F, Sørensen NN, Johansen J (2009) Wind turbine rotor-tower interaction using an incompressible overset grid method. Wind Energy 12: 594–619

    Article  Google Scholar 

  9. Bazilevs Y, Hsu M-C, Akkerman I, Wright S, Takizawa K, Henicke B, Spielman T, Tezduyar TE (2011) 3D simulation of wind turbine rotors at full scale. Part I: geometry modeling and aerodynamics. Int J Numer Methods Fluids 65: 207–235

    Article  MATH  Google Scholar 

  10. Takizawa K, Henicke B, Tezduyar TE, Hsu M-C, Bazilevs Y (2011) Stabilized space-time computation of wind-turbine rotor aerodynamics. Comput Mech 48: 333–344

    Article  MATH  Google Scholar 

  11. Li Y, Paik K-J, Xing T, Carrica PM (2012) Dynamic overset CFD simulations of wind turbine aerodynamics. Renew Energy 37: 285–298

    Article  Google Scholar 

  12. Guttierez E, Primi S, Taucer F, Caperan P, Tirelli D, Mieres J, Calvo I, Rodriguez J, Vallano F, Galiotis G, Mouzakis D (2003) A wind turbine tower design based on fibre-reinforced composites. Technical report, Joint Research Centre-Ispra, European Laboratory for Structural Assessment (ELSA), Institute For Protection and Security of the Citizen (IPSC), European Commission

  13. Kong C, Bang J, Sugiyama Y (2005) Structural investigation of composite wind turbine blade considering various load cases and fatigue life. Energy 30: 2101–2114

    Article  Google Scholar 

  14. Hansen MOL, Sørensen JN, Voutsinas S, Sørensen N, Madsen HAa (2006) State of the art in wind turbine aerodynamics and aeroelasticity. Prog Aerosp Sci 42: 285–330

    Article  Google Scholar 

  15. Jensen FM, Falzon BG, Ankersen J, Stang H (2006) Structural testing and numerical simulation of a 34 m composite wind turbine blade. Compos Struct 76: 52–61

    Article  Google Scholar 

  16. Kiendl J, Bazilevs Y, Hsu M-C, Wüchner R, Bletzinger K-U (2010) The bending strip method for isogeometric analysis of Kirchhoff–Love shell structures comprised of multiple patches. Comput Methods Appl Mech Eng 199: 2403–2416

    Article  MATH  Google Scholar 

  17. Bazilevs Y, Hsu M-C, Kiendl J, Benson DJ (2012) A computational procedure for pre-bending of wind turbine blades. Int J Numer Methods Eng 89: 323–336

    Article  MATH  Google Scholar 

  18. Bazilevs Y, Hsu M-C, Kiendl J, Wüchner R, Bletzinger K-U (2011) 3D simulation of wind turbine rotors at full scale. Part II: fluid-structure interaction modeling with composite blades. Int J Numer Methods Fluids 65: 236–253

    Article  MATH  Google Scholar 

  19. Hsu M-C, Akkerman I, Bazilevs Y (2011) High-performance computing of wind turbine aerodynamics using isogeometric analysis. Comput Fluids 49: 93–100

    Article  Google Scholar 

  20. Takizawa K, Henicke B, Montes D, Tezduyar TE, Hsu M-C, Bazilevs Y (2011) Numerical-performance studies for the stabilized space-time computation of wind-turbine rotor aerodynamics. Comput Mech 48: 647–657

    Article  MATH  Google Scholar 

  21. Hand MM, Simms DA, Fingersh LJ, Jager DW, Cotrell JR, Schreck S, Larwood SM (2001) Unsteady aerodynamics experiment phase VI: Wind tunnel test configurations and available data campaigns. Technical Report NREL/TP-500-29955. National Renewable Energy Laboratory, Golden

  22. Simms D, Schreck S, Hand M, Fingersh LJ (2001) NREL unsteady aerodynamics experiment in the NASA–Ames wind tunnel: a comparison of predictions to measurements. Technical Report NREL/TP-500-29494, National Renewable Energy Laboratory, Golden, CO

  23. NREL 10 mWind Turbine Testing in NASA Ames 80’ × 120’ Wind Tunnel. http://wind.nrel.gov/amestest/. Accessed 6 Oct 2011

  24. Bazilevs Y, Calo VM, Cottrel JA, Hughes TJR, Reali A, Scovazzi G (2007) Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows. Comput Methods Appl Mech Eng 197: 173–201

    Article  MATH  Google Scholar 

  25. Hughes TJR, Cottrell JA, Bazilevs Y (2005) Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput Methods Appl Mech Eng 194: 4135–4195

    Article  MathSciNet  MATH  Google Scholar 

  26. Cottrell JA, Hughes TJR, Bazilevs Y (2009) Isogeometric analysis: toward integration of CAD and FEA. Wiley, Chichester

    Google Scholar 

  27. Bazilevs Y, Hughes TJR (2007) Weak imposition of Dirichlet boundary conditions in fluid mechanics. Comput Fluids 36: 12–26

    Article  MathSciNet  MATH  Google Scholar 

  28. Bazilevs Y, Michler C, Calo VM, Hughes TJR (2007) Weak Dirichlet boundary conditions for wall-bounded turbulent flows. Comput Methods Appl Mech Eng 196: 4853–4862

    Article  MathSciNet  MATH  Google Scholar 

  29. Bazilevs Y, Michler C, Calo VM, Hughes TJR (2010) Isogeometric variational multiscale modeling of wall-bounded turbulent flows with weakly enforced boundary conditions on unstretched meshes. Comput Methods Appl Mech Eng 199: 780–790

    Article  MathSciNet  MATH  Google Scholar 

  30. Bazilevs Y, Akkerman I (2010) Large eddy simulation of turbulent Taylor–Couette flow using isogeometric analysis and the residual-based variational multiscale method. J Comput Phys 229: 3402–3414

    Article  MathSciNet  MATH  Google Scholar 

  31. Nitsche J (1971) Über ein variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. Abh Math Univ Hamburg 36: 9–15

    Article  MathSciNet  MATH  Google Scholar 

  32. Arnold DN, Brezzi F, Cockburn B, Marini LD (2002) Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J Numer Anal 39: 1749–1779

    Article  MathSciNet  MATH  Google Scholar 

  33. Bazilevs Y, Calo VM, Hughes TJR, Zhang Y (2008) Isogeometric fluid-structure interaction: theory, algorithms, and computations. Comput Mech 43: 3–37

    Article  MathSciNet  MATH  Google Scholar 

  34. Johnson C (1987) Numerical solution of partial differential equations by the finite element method. Cambridge University Press, Sweden

    MATH  Google Scholar 

  35. Brenner SC, Scott LR (2002) The mathematical theory of finite element methods, 2nd ed. Springer, New York

    MATH  Google Scholar 

  36. Ern A, Guermond J-L (2004) Theory and practice of finite elements. Springer, Secaucus

    MATH  Google Scholar 

  37. Brooks AN, Hughes TJR (1982) Streamline upwind/Petrov–Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier–Stokes equations. Comput Methods Appl Mech Eng 32: 199–259

    Article  MathSciNet  MATH  Google Scholar 

  38. Hughes TJR, Tezduyar TE (1984) Finite element methods for first-order hyperbolic systems with particular emphasis on the compressible Euler equations. Comput Methods Appl Mech Eng 45: 217–284

    Article  MathSciNet  MATH  Google Scholar 

  39. Tezduyar TE, Park YJ (1986) Discontinuity capturing finite element formulations for nonlinear convection–diffusion–reaction equations. Comput Methods Appl Mech Eng 59: 307–325

    Article  MATH  Google Scholar 

  40. Hughes TJR, Franca LP, Balestra M (1986) A new finite element formulation for computational fluid dynamics: V. Circumventing the Babuška–Brezzi condition: a stable Petrov–Galerkin formulation of the Stokes problem accommodating equal-order interpolations. Comput Methods Appl Mech Eng 59: 85–99

    Article  MathSciNet  MATH  Google Scholar 

  41. Tezduyar TE, Osawa Y (2000) Finite element stabilization parameters computed from element matrices and vectors. Comput Methods Appl Mech Eng 190: 411–430

    Article  MATH  Google Scholar 

  42. Tezduyar TE (2003) Computation of moving boundaries and interfaces and stabilization parameters. Int J Numer Methods Fluids 43: 555–575

    Article  MathSciNet  MATH  Google Scholar 

  43. Hughes TJR, Scovazzi G, Franca LP (2004) Multiscale and stabilized methods. In: Stein E, Borst R, Hughes TJR (eds) Encyclopedia of computational mechanics, vol. 3, Fluids, chap. 2. Wiley, Chichester

    Google Scholar 

  44. Takizawa K, Tezduyar TE (2011) Multiscale space–time fluid-structure interaction techniques. Comput Mech 48: 247–267

    Article  MathSciNet  MATH  Google Scholar 

  45. Hughes TJR (1995) Multiscale phenomena: Green’s functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles, and the origins of stabilized methods. Comput Methods Appl Mech Eng 127: 387–401

    Article  MATH  Google Scholar 

  46. Hughes TJR, Feijóo GR, Mazzei L, Quincy J-B (1998) The variational multiscale method—a paradigm for computational mechanics. Comput Methods Appl Mech Eng 166: 3–24

    Article  MATH  Google Scholar 

  47. Hughes TJR, Sangalli G (2007) Variational multiscale analysis: the fine-scale Green’s function, projection, optimization, localization, and stabilized methods. SIAM J Numer Anal 45: 539–557

    Article  MathSciNet  MATH  Google Scholar 

  48. Launder BE, Spalding DB (1974) The numerical computation of turbulent flows. Comput Methods Appl Mech Eng 3: 269–289

    Article  MATH  Google Scholar 

  49. Wilcox DC (1998) Turbulence modeling for CFD. DCW Industries, La Canada

    Google Scholar 

  50. Chao DD, van Dam CP (2008) CFD analysis of rotating two-bladed flatback wind turbine rotor. Sandia Report SAND2008-1688, Sandia National Laboratories, Albuquerque

  51. Jonkman JM (2003) Modeling of the UAE wind turbine for refinement of FAST _AD. Technical Report NREL/TP-500-34755. National Renewable Energy Laboratory, Golden

  52. Johansen J, Sørensen NN, Michelsen JA, Schreck S (2002) Detached-eddy simulation of flow around the NREL Phase VI blade. Wind Energy 5: 185–197

    Article  Google Scholar 

  53. Laino DJ, Hansen AC, Minnema JE (2002) Validation of the aerodyn subroutines using NREL unsteady aerodynamics experiment data. Wind Energy 5: 227–244

    Article  Google Scholar 

  54. Tongchitpakdee C, Benjanirat S, Sankar LN (2005) Numerical simulation of the aerodynamics of horizontal axis wind turbines under yawed flow conditions. J Sol Energy Eng 127: 464–474

    Article  Google Scholar 

  55. Schmitz S, Chattot J-J (2006) Characterization of three-dimensional effects for the rotating and parked NREL Phase VI wind turbine. J Sol Energy Eng 128: 445–454

    Article  Google Scholar 

  56. Potsdam MA, Mavriplis DJ (2009) Unstructured mesh CFD aerodynamic analysis of the NREL Phase VI rotor. AIAA Paper 2009–1221

  57. Gómez-Iradi S, Steijl R, Barakos GN (2009) Development and validation of a CFD technique for the aerodynamic analysis of HAWT. J Sol Ener Eng 131: 031009-1-13

    Google Scholar 

  58. Huang J-C, Lin H, Hsieh T-J, Hsieh T-Y (2011) Parallel preconditioned WENO scheme for three-dimensional flow simulation of NREL Phase VI rotor. Comput Fluids 45: 276–282

    Article  MATH  Google Scholar 

  59. Texas advanced computing center (TACC). http://www.tacc.utexas.edu. Accessed 6 Oct 2011

  60. Longhorn user guide. http://www.tacc.utexas.edu/user-services/user-guides/longhorn-user-guide. Accessed 6 Oct 2011

  61. Karypis G, Kumar V (1999) A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM J Sci Comput 20: 359–392

    Article  MathSciNet  MATH  Google Scholar 

  62. Chung J, Hulbert GM (1993) A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-α method. J Appl Mech 60: 371–375

    Article  MathSciNet  MATH  Google Scholar 

  63. Jansen KE, Whiting CH, Hulbert GM (2000) A generalized-α method for integrating the filtered Navier–Stokes equations with a stabilized finite element method. Comput Methods Appl Mech Eng 190: 305–319

    Article  MathSciNet  MATH  Google Scholar 

  64. Saad Y, Schultz MH (1986) GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J Sci Stat Comput 7: 856–869

    Article  MathSciNet  MATH  Google Scholar 

  65. Shakib F, Hughes TJR, Johan Z (1989) A multi-element group preconditioned GMRES algorithm for nonsymmetric systems arising in finite element analysis. Comput Methods Appl Mech Eng 75: 415–456

    Article  MathSciNet  MATH  Google Scholar 

  66. Takizawa K, Moorman C, Wright S, Spielman T, Tezduyar TE (2010) Fluid-structure interaction modeling and performance analysis of the Orion spacecraft parachutes. Int J Numer Methods Fluids 65: 271–285

    Article  Google Scholar 

  67. Takizawa K, Wright S, Moorman C, Tezduyar TE (2010) Fluid-structure interaction modeling of parachute clusters. Int J Numer Methods Fluids 65: 286–307

    Article  Google Scholar 

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  1. Department of Structural Engineering, University of California, San Diego, 9500 Gilman Drive, Mail Code 0085, La Jolla, CA, 92093, USA

    Ming-Chen Hsu, Ido Akkerman & Yuri Bazilevs

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  1. Ming-Chen Hsu
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  2. Ido Akkerman
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  3. Yuri Bazilevs
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Correspondence to Yuri Bazilevs.

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Hsu, MC., Akkerman, I. & Bazilevs, Y. Wind turbine aerodynamics using ALE–VMS: validation and the role of weakly enforced boundary conditions. Comput Mech 50, 499–511 (2012). https://doi.org/10.1007/s00466-012-0686-x

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  • DOI: https://doi.org/10.1007/s00466-012-0686-x

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