## “CFD Wake Modelling with a BEM Wind Turbine Sub-Model”Authors: Anders Hallanger and Ivar Ø. Sand,
Affiliation: Christian Michelsen Research
Reference: 2013, Vol 34, No 1, pp. 19-33. |

**Keywords:**CFD, Wake, BEM, Wind Turbine

**Abstract:**Modelling of wind farms using computational fluid dynamics (CFD) resolving the flow field around each wind turbine´s blades on a moving computational grid is still too costly and time consuming in terms of computational capacity and effort. One strategy is to use sub-models for the wind turbines, and sub-grid models for turbulence production and dissipation to model the turbulent viscosity accurately enough to handle interaction of wakes in wind farms. A wind turbine sub-model, based on the Blade Momentum Theory, see Hansen (2008), has been implemented in an in-house CFD code, see Hallanger et al. (2002). The tangential and normal reaction forces from the wind turbine blades are distributed on the control volumes (CVs) at the wind turbine rotor location as sources in the conservation equations of momentum. The classical k-epsilon turbulence model of Launder and Spalding (1972) is implemented with sub-grid turbulence (SGT) model, see Sha and Launder (1979) and Sand and Salvesen (1994). Steady state CFD simulations were compared with flow and turbulence measurements in the wake of a model scale wind turbine, see Krogstad and Eriksen (2011). The simulated results compared best with experiments when stalling (boundary layer separation on the wind turbine blades) did not occur. The SGT model did improve turbulence level in the wake but seems to smear the wake flow structure. It should be noted that the simulations are carried out steady state not including flow oscillations caused by vortex shedding from tower and blades as they were in the experiments. Further improvement of the simulated velocity defect and turbulence level seems to rely on better parameter estimation to the SGT model, improvements to the SGT model, and possibly transient- instead of steady state simulations.

PDF (1272 Kb) DOI: 10.4173/mic.2013.1.3

**DOI forward links to this article:**

[1] Per-Åge Krogstad, Lars Sætran and Muyiwa Samuel Adaramola (2014), doi:10.1016/j.jfluidstructs.2014.10.002 | |

[2] Zhengru Ren, Zhiyu Jiang, Roger Skjetne and Zhen Gao (2018), doi:10.1016/j.oceaneng.2018.05.011 | |

[3] F Balduzzi, S Bigalli and A Bianchini (2018), doi:10.1088/1742-6596/1037/7/072029 |

**References:**

[1] Buhl, M.L. (2005). A New Empirical Relation between Trust Coefficients and Induction Factor for the Turbulent Windmill State, Technical Report TP-500-368344, NREL.

[2] Chorin, A. (1968). Numerical Solution of the Navier Stokes Equations, volume22 of Maths of Computation, Pergamon Press, second edition.

[3] Drela, M. Youngren, H. (2001). XFOIL 6,94 User Guide MIT 10 Dec 2001, Technical report, MIT, http://web.mit.edu/drela/Public/web/xfoil.

[4] Favre, A. (1965). Equations des gaz turbulents compressibles, Journal de Mechanique, .3:361--390.

[5] Ferziger, J. Peric, M. (1996). Computational methods for fluid dynamics, Springer-Verlag Berlin Heidelberg doi:10.1007/978-3-642-97651-3

[6] Hallanger, A., Frøysa, K.-E., Lunde, P. (2002). CFD simulation and installation effects for ultrasonic flow meters in pipes with bends, Int. J. of Applied Mechanics and Engineering, .1:33--64.

[7] Hansen, M. O.L. (2008). Aerodynamics of Wind Turbines, Earthscan, London, England, second edition.

[8] Hjertager, B. (1985). Computer Simulation of Turbulent Reactive Gas Dynamics, J. Modeling, Identification and Control, 5:211--236 doi:10.4173/mic.1984.4.3

[9] Hoerner, S. (1965). Fluid-Dynamic Drag, Published by the author.

[10] Karlsen, J.A. (2009). Calculation for a Model Turbine, Master´s thesis, NTNU, Trondheim, Norway.

[11] Krogstad, P.-Å. Eriksen, P. (2011). Blind Test Workshop Calculations for a Model Wind Turbine, Summary report 10 October.

[12] Krogstad, P.-Å. Lund, J. (2012). An experimental and numerical study of the performance of a model turbine, Wind Energy, 1.3:443--457 doi:10.1002/we.482

[13] Launder, B. Spalding, D. (1972). Mathematical Models of Turbulence, Academic Press, London and New York.

[14] Lu, H. Porte-Agel, F. (2011). Large-eddy simulation of a very large wind farm in a stable atmospheric boundary layer, Physics of Fluids, 23.

[15] Moriarty, P. Hansen, A. (2005). AeroDyn Theory Manual, EL-500-36881, NREL, Technical Report.

[16] Patankar, S. (1980). Numerical heat transfer and fluid flow, McGraw-Hill, New York.

[17] Patankar, S. Spalding, D. (1972). A Calculation Procedure for Heat, Mass and Momentum Transfer in Three-Dimensional Parabolic Flows, Int. J. Heat Mass Transfer, 15:1787--1806 doi:10.1016/0017-9310(72)90054-3

[18] Rae, W. Pope, A. (1984). Low-Speed Wind Tunnel Testing, John Wiley and& Sons, New York, second edition.

[19] Sand, I. Salvesen, H.-C. (1994). Subgrid Modelling of Drag, Turbulence Generation and Turbulence Dissipation, CMI-94-F25014, Christian Michelsen Institutt.

[20] Sand, I.Ø. (2011). BEM Wind Turbine Modelling with Extension to Yaw, Wind Energy Capture, NORCOWE-RR-C-11-WP4-002, NORCOWE, 48 pages.

[21] Sandersee, B., Pijl, S., Koren, B. (2011). Review of computational fluid dynamics for wind turbine wake aerodynamics, Wind Energy, 1.7:799--819 doi:10.1002/we.458

[22] Sha, W. Launder, B. (1979). A Model for Turbulent Momentum and Heat Transfer in a Large Rod Bundels, Report ANL-77-73, Argonne National Laboratory.

[23] Spera, D.A., editor. (2009). WIND TURBINE TECHNOLOGY, Fundamental Concepts of Wind Turbine Engineering, ASME Press New York, second edition.

[24] VanLeer, B. (1974). Towards the ultimate conservative differencing scheme ii: Monotonicity and conservation combined in a second-order scheme, J. Comp. Phys., 14:361--370 doi:10.1016/0021-9991(74)90019-9

**BibTeX:**

@article{MIC-2013-1-3,

title={{CFD Wake Modelling with a BEM Wind Turbine Sub-Model}},

author={Hallanger, Anders and Sand, Ivar Ø.},

journal={Modeling, Identification and Control},

volume={34},

number={1},

pages={19--33},

year={2013},

doi={10.4173/mic.2013.1.3},

publisher={Norwegian Society of Automatic Control}

};