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Application of Computational Fluid Mechanics

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Abstract

As we have seen in the previous chapters, due the nonlinear behavior it is very difficult—if not impossible—to get simple analytical solutions of the basic fluid dynamic equations in a systematic way. Therefore, it has become normal to use (massive) numerical methods for solving them. In an ideal situation this would mean that only the Eqs. (3.37) from Chap. 3 are used (of course adapted to a suitable form for computers) together with a geometrical description of the problem (a wind turbine wing, for example) and a surrounding control volume for setting the boundary conditions for the unknown fields (pressure and velocity).

You can’t calculate what you haven’t understood. (Originally thought to be from P. W. Anderson.)

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Notes

  1. 1.

    Quadratic correlations may be replaced by diffusions term because of the Fluctuation–Dissipation Theorem from linear and equilibrium statistical mechanics ([54] in Chap. 3). It states that the variance of equilibrium fluctuations determines the strength of losses by small disturbances as well.

  2. 2.

    From now on in this book the term CFD is assumed to be a RANS simulation where only the full 3D geometry of the wind turbine (or its blades) is used.

References

  1. Anderson TJD Jr (1995) Computational fluid dynamics. McGraw-Hill, New York

    Google Scholar 

  2. Boorsma, K, Schepers JG, Gomez-Iradi S, Herraez I, Lutz T, Weihing P, Oggiano L, Pirrung G, Madsen HA, Shen WZ, Rahimi H, Schaffarczyk AP (2018) Final report of IEA Wind Taks 29 Mexnext (phase 3), ECN-E–18-003, Petten, The Netherlands

    Google Scholar 

  3. Boorsma K, Greco L, Bedon G (2018) Rotor wake engineering models for aeroelastic applications. In: Proceeding of TORQUE2018. IOP Conf Ser: J Phys: Conf Ser: 1037:062013

    Google Scholar 

  4. Boorsma K, Schepers G (2014) New Mexico experiment, ECN-E–14-048, Petten, The Netherlands

    Google Scholar 

  5. Branlard E (2013) Wind turbine tip-loss correction. Master’s Thesis (public version). Risø DTU, Copenhagen, Denmark

    Google Scholar 

  6. Carrion M (2013) Understanding wind turbine wake breakdown using CFD, 3rd. IEA wind MexNext II Meeting, Pamplona, Spain

    Google Scholar 

  7. Dose B (2013) CFD simulations of a 2.5 MW wind turbine using ANSYS CFX and OpenFOAM. MSc Thesis, UAS Kiel and FhG IWES, Germany

    Google Scholar 

  8. Ferziger JH, Perić M (2002) Computational methods for fluid dynamics, 3rd edn. Springer, Berlin

    Book  Google Scholar 

  9. Fletcher CAJ (2005) Computational techniques for fluid dynamics, 2 volumes. Springer, Berlin

    Google Scholar 

  10. Hansen MOL (1998) Private communication

    Google Scholar 

  11. Hansen MOL et al (1997) A global Navier-Stokes rotor prediction model. AIAA 97–0970, Reno

    Google Scholar 

  12. Ishihara T, Gotoh T, Kaneda Y (2009) Study of high-reynolds number isotropic turbulence by direct numerical simulation. Annu Rev Fluid Mech 41:165–180

    Article  MathSciNet  Google Scholar 

  13. Jeromin A, Bentamy A, Schaffarcyzk AP (2013) Actuator disk modeling of the Mexico rotor with openFOAM. In: 1st Symposium on openFOAM in wind energy, Oldenburg, Germany

    Google Scholar 

  14. Jeromin A, Schaffarcyzk AP (2012) First steps in simulating laminar-turbulent transition on the Mexico blades, 2nd. IEAwind MexNext II Meeting, NREL, Golden, CO, USA

    Google Scholar 

  15. Kolmogorov AN (1942) Equations of turbulent motion of an incompressible fluid. Izv Akad Nauk SSSR, Ser Fiz VI(1-2):56–58

    Google Scholar 

  16. La Yi et al (2008) A public turbulence database cluster and applications to study Lagrangian evolution of velocity increments in turbulence. J Turb 9(31):1–20

    Google Scholar 

  17. Langtry RB (2006) A correlation-based transition model using local variables for unstructured parallelized CFD codes. Dissertation, Universität Stuttgart

    Google Scholar 

  18. Laursen J, Enevoldsen P, Hjort S (2007) 3D CFD quantification of the performance of a multi-megawatt wind turbine. In: Proceedings of 2nd conference of the science of making torque from wind, Copenhagen, Denmark

    Google Scholar 

  19. Lobo BA, Boorsma K, Schaffarczyk AP (2018) Investigation into boundary layer transition on the Mexico blade. Proceeding of TORQUE2018. IOP Conf Ser: J Phys: Conf Ser: 1037:052020

    Google Scholar 

  20. Mahmoodi E, Schaffarczyk AP (2012) Actuator disc modeling of the Mexico rotor experiment. In: Proceeding of Euromech Coll. 528, Wind energy and the impact of turbulence on the conversion process, Oldenburg, Germany

    Google Scholar 

  21. Martinez-Tossa LA, Meneveau C (2019) Filtered lifting line theory and application to the actuator line method. J Fluid Mech 863:269–292

    Google Scholar 

  22. Menter F (1992) Improved two-equation k-\(\omega \) turbulence models for aerodynamical flows. NASA Technical Memorandum 103975. Moffett Field, CA, USA

    Google Scholar 

  23. Menter F (1994) Two-equation eddy-viscosity turbulence models for engineering applications. AIAA - J 32(8):1598–1605

    Article  Google Scholar 

  24. Menter F, Langtry R (2006) Transitionsmodellierungen technischer Strömungen (Modeling of transitions in engineering flow). ANSYS Germany, Otterfing, Germany

    Google Scholar 

  25. Michelassi V, Rodi W, Zhu J (1993) Testing a low Reynolds number k-\(\epsilon \) model based on direct simulation data. AIAA - J 31(9):1720–1723

    Google Scholar 

  26. Mohammandi B, Pirronneau O (1994) Analysis of the k-epsilon turbulence model. Wiley, Chichester

    Google Scholar 

  27. NN (2009) Transition module (V8.76) user guide (V1.0 beta). Unpublished report, Braunschweig, Germany (in German)

    Google Scholar 

  28. OpenFOAM Foundation (2013) User guide: openFOAM, the open source CFD toolbox

    Google Scholar 

  29. Prandtl L (1925) Bericht über Untersuchungen zur ausgebildeten Turbulenz. Z angew Math und Mech 5

    Google Scholar 

  30. Prandtl L (1945) Über ein neues Formelsystem für die ausgebildete Turbulenz. Nachr. d. Akad. d. Wiss. in Göttingen, Math.-nat. Klasse, S. 6–20

    Google Scholar 

  31. Reichstein T, Schaffarczyk AP, Dollinger C, Balaresque N, Schülein E, Jauch C, Fischer A (2019) Investigation of laminar-turbulent transition on a rotating wind-turbine blade of multimegawatt class with thermography and microphone array. Energies 12(11):2102

    Google Scholar 

  32. Sanders B, van der Pijl SP, Koren B (2011) Review of computational fluid dynamics for wind turbine wake aerodynamics. Wind Energy 14:799–819

    Article  Google Scholar 

  33. Schaffarczyk AP, Boisard R, Boorsma K, Dose B, Lienard C, Lutz T, Madsen HA, Rahimi H, Reichstein T, Schepers G, Sørensen N, Stoevesand B, Weihig P (2018) Comparison of 3d transitional CFD simulations for rotating wind turbine wings with measurements. In: Proceeding of TORQUE2018. IOP Conf Ser: J Phys: Conf Ser: 1027:022012

    Google Scholar 

  34. Schaffarczyk AP (1997) Numerical and theoretical investigation for wind turbines. IEAwind, Annex XI meeting, ECN, Petten, The Netherlands

    Google Scholar 

  35. Schaffarczyk AP, Schwab D, Breuer M (2016) Experimental detection of laminar-turbulent transition on a rotating wind turbine blade in the free atmosphere. Wind Energy 20(2)

    Google Scholar 

  36. Schepers JG, Boorsma K, Gomez-Iradi S, Schaffarczyk AP, Madsen HA, Sørensen NN, Shen WZ, Lutz T, Schulz C, Herraez I, Schreck S (2014) Final report of IEA Wind Taks 29 Mexnext (phase 2), ECN-E–14-060, Petten, The Netherlands

    Google Scholar 

  37. Schlatter P (2005) Large-eddy simulation of transitional turbulence in wall-bounded shear flow. PhD thesis ETH, No. 16000, Zürich, Switzerland

    Google Scholar 

  38. Schmidt Paulsen U (1995) Konceptundersøgelse Nordtanks 500/41 Strukturelle laster, Risø-I-936(DA), Roskilde, Denmark

    Google Scholar 

  39. Schreck S (2008) IEA wind annex XX: Hawt aerodynamics and models from wind tunnel measurements. NREL/TP-500-43508. Golden, CO, USA

    Google Scholar 

  40. Schubert M, Schumacher K (1996) Entwurf einer neuen Aktiv-Stall Rotorblattfamilie (Design of a new family of active stall blades). In: Proceeding of DEWEK ’96, Wilhelmshaven, Germany (in German)

    Google Scholar 

  41. Shen WZ, Zhu WJ, Sørensen JN (2012) Actuator line/Navier-Stokes computations for the Mexico rotor: comparison with detailed measurements. Wind Energy 15(5):811–825

    Google Scholar 

  42. Smith LM, Reynolds WC (1992) On the Yakhot-Orzag renormalization group method for deriving turbulence statistics and models. Phys Fluids A 4:364

    Google Scholar 

  43. Smith LM, Reynolds WC (1998) Renormalization group analysis of turbulence. Ann Rev Fluid Mech 30:275–310

    Google Scholar 

  44. Sørensen JN, Shen WZ (2002) Numerical modelling of wind turbine wakes. J Fluids Eng 124(2):393–399

    Google Scholar 

  45. Sørensen NN, Hansen MOL (1998) Rotor performance prediction using a Navier-Stokes method. AIAA-98-0025. Reno, NV, USA

    Google Scholar 

  46. Sørensen NN, Michelsen JA, Schreck S (2002) Navier-Stokes prediction of the NREL phase VI rotor in the NASA Ames 80 ft x 120 ft wind tunnel. Wind Energy 5:151–168

    Google Scholar 

  47. Sørensen NN (2009) CFD modeling of laminar-turbulent transition for airfoils and rotors using the \(\gamma - \tilde{Re}_{\theta }\) model. Wind Energy 12(8):715–733

    Google Scholar 

  48. Sørensen NN 1998) HypGrid2D a 2-D mesh generator, Risø-R-1035(EN)

    Google Scholar 

  49. Spalart P (1988) Direct simulation of a turbulent boundary layer up to \(R_{\theta } = 1410\). J Fluids Eng 187:61–98

    MATH  Google Scholar 

  50. Spalart P (2000) Strategies for turbzulence modelling and simulations. Int J Heat Fluid Flow 21:225–263

    Article  Google Scholar 

  51. Spalart P (2009) Detached-eddy simulation. Annu Rev Fluid Mech 41:181–202

    Article  Google Scholar 

  52. Spalding B (1991) Kolmogorov’s two-equation model of turbulence. Proc R Soc 434:211–216

    MathSciNet  MATH  Google Scholar 

  53. Trede R (2003) Entwicklung eines Netzgenerators. Diplomarbeit, FH Westküste, Heide (in German)

    Google Scholar 

  54. Tu J, Yeoh GH, Liu C (2008) Computational fluid dynamics. Butterworth-Heinemann, Elsevier, Amsterdam

    Google Scholar 

  55. von Neumann J (1949) Recent theories of turbulence. Unpublished report to the Naval office, in collected work (S. Ulam, Ed.) VI:437–472

    Google Scholar 

  56. Wilcox DC (1993/94) Turbulence modeling for CFD. DCW Industries Inc

    Google Scholar 

  57. Winkler H, Schaffarczyk AP (2003) Numerische Simulation des Reynoldszahlverhaltens von dicken aerodynamischen Profilen für Off-shore Anwendungen. Bericht des Labors für numerische Mechanik, 33, Kiel (in German)

    Google Scholar 

  58. Wu YT, Port-Agel F (2013) Modeling turbine wakes and power losses within a wind farm using LES: an application to the Horns-Rev offshore wind farm. In: Proceeding of ICOWES 2013, Copenhagen, Denmark

    Google Scholar 

  59. Yakhot V, Orszag SA (1986) Renormalization group analysis of turbulence. I. Basic theory. J Sci Comput 1(1)

    Google Scholar 

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Schaffarczyk, A.P. (2020). Application of Computational Fluid Mechanics. In: Introduction to Wind Turbine Aerodynamics. Green Energy and Technology. Springer, Cham. https://doi.org/10.1007/978-3-030-41028-5_7

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  • DOI: https://doi.org/10.1007/978-3-030-41028-5_7

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