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Onset of wake meandering for a floating offshore wind turbine under side-to-side motion

Published online by Cambridge University Press:  18 January 2022

Zhaobin Li Open the ORCID record for Zhaobin Li [Opens in a new window] ,
Guodan Dong Open the ORCID record for Guodan Dong [Opens in a new window]  and
Xiaolei Yang Open the ORCID record for Xiaolei Yang [Opens in a new window]
Zhaobin Li
Affiliation:
The State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China School of Engineering Sciences, University of Chinese Academy of Sciences, Beijing 100049, PR China
Guodan Dong
Affiliation:
The State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China School of Engineering Sciences, University of Chinese Academy of Sciences, Beijing 100049, PR China
Xiaolei Yang*
Affiliation:
The State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China School of Engineering Sciences, University of Chinese Academy of Sciences, Beijing 100049, PR China
*
†Email address for correspondence: xyang@imech.ac.cn
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Abstract

Wind turbine wakes, being convectively unstable, may behave as an amplifier of upstream perturbations and make downstream turbines experience strong inflow fluctuations. In this work, we investigate the effects of the side-to-side motion of a floating offshore wind turbine (FOWT) on wake dynamics using large-eddy simulation and linear stability analysis (LSA). When the inflow turbulence intensity is low, simulation results reveal that the turbine motion with certain Strouhal numbers $St = fD/U_\infty \in (0.2,0.6)$ (where $f$ is the motion frequency, $D$ is the rotor diameter, and $U_\infty$ is the incoming wind speed), which overlap with the Strouhal numbers of wake meandering induced by the shear layer instability, can lead to wake meandering with amplitudes being one order of magnitude larger than the FOWT motion for the most unstable frequency. For high inflow turbulence intensity, on the other hand, the onset of wake meandering is dominated by the inflow turbulence. The probability density function of the spanwise instantaneous wake centres is observed being non-Gaussian and closely related to that of the side-to-side motion. This complements the existing wake meandering mechanisms, that the side-to-side motion of an FOWT can be a novel origin for the onset of wake meandering. It is also found that LSA can predict the least stable frequencies and the amplification factor with acceptable accuracy for motion amplitude $0.01D$. Effects of nonlinearity are observed when motion amplitude increases to $0.04D$, for which the most unstable turbine oscillations shift slightly to lower frequencies and the amplification factor decreases.

JFM classification

Wakes/Jets: Wakes Instability: Shear-flow instability

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JFM Papers
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Journal of Fluid Mechanics , Volume 934 , 10 March 2022 , A29
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© The Author(s), 2022. Published by Cambridge University Press

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References

REFERENCES

Barlas, E., Buckingham, S. & van Beeck, J.P.A.J. 2016 Roughness effects on wind-turbine wake dynamics in a boundary-layer wind tunnel. Boundary-Layer Meteorol. 158 (1), 27–42.CrossRefGoogle Scholar
Bastankhah, M. & Porté-Agel, F. 2016 Experimental and theoretical study of wind turbine wakes in yawed conditions. J. Fluid Mech. 806, 506–541.CrossRefGoogle Scholar
Bastankhah, M. & Porté-Agel, F. 2017 Wind tunnel study of the wind turbine interaction with a boundary-layer flow: upwind region, turbine performance, and wake region. Phys. Fluids 29 (6), 065105.CrossRefGoogle Scholar
Batchelor, G.K. & Gill, A.E. 1962 Analysis of the stability of axisymmetric jets. J. Fluid Mech. 14 (4), 529–551.CrossRefGoogle Scholar
Chamorro, L.P. & Porté-Agel, F. 2009 A wind-tunnel investigation of wind-turbine wakes: boundary-layer turbulence effects. Boundary-Layer Meteorol. 132 (1), 129–149.CrossRefGoogle Scholar
Chamorro, L.P. & Porté-Agel, F. 2010 Effects of thermal stability and incoming boundary-layer flow characteristics on wind-turbine wakes: a wind-tunnel study. Boundary-Layer Meteorol. 136 (3), 515–533.CrossRefGoogle Scholar
DNV 2019 Coupled analysis of floating wind turbines. Recommended practice. Det Norske Veritas, Oslo, Norway.Google Scholar
Drazin, P.G. & Reid, W.H. 2004 Hydrodynamic Stability. Cambridge University Press.CrossRefGoogle Scholar
Du, Z. & Selig, M. 1998 A 3-D stall-delay model for horizontal axis wind turbine performance prediction. In 1998 ASME Wind Energy Symposium. AIAA Paper 98-0021.CrossRefGoogle Scholar
Espana, G., Aubrun, S., Loyer, S. & Devinant, P. 2011 Spatial study of the wake meandering using modelled wind turbines in a wind tunnel. Wind Energy 14 (7), 923–937.CrossRefGoogle Scholar
Espana, G., Aubrun, S., Loyer, S. & Devinant, P. 2012 Wind tunnel study of the wake meandering downstream of a modelled wind turbine as an effect of large scale turbulent eddies. J. Wind Engng Ind. Aerodyn. 101, 24–33.CrossRefGoogle Scholar
Farrugia, R., Sant, T. & Micallef, D. 2016 A study on the aerodynamics of a floating wind turbine rotor. Renew. Energy 86, 770–784.CrossRefGoogle Scholar
Feist, C., Sotiropoulos, F. & Guala, M. 2021 A quasi-coupled wind wave experimental framework for testing offshore wind turbine floating systems. Theor. Appl. Mech. Lett. 11, 100294.CrossRefGoogle Scholar
Foti, D., Yang, X., Shen, L. & Sotiropoulos, F. 2019 Effect of wind turbine nacelle on turbine wake dynamics in large wind farms. J. Fluid Mech. 869, 1–26.CrossRefGoogle Scholar
Fu, S.F., Jin, Y.Q., Zheng, Y. & Chamorro, L.P. 2019 Wake and power fluctuations of a model wind turbine subjected to pitch and roll oscillations. Appl. Energy 253, 113605.CrossRefGoogle Scholar
Fu, S., Zhang, B., Zheng, Y. & Chamorro, L.P. 2020 In-phase and out-of-phase pitch and roll oscillations of model wind turbines within uniform arrays. Appl. Energy 269, 114921.CrossRefGoogle Scholar
Gatin, I., Liu, S., Vukčević, V. & Jasak, H. 2020 Finite volume method for general compressible naval hydrodynamics. Ocean Engng 196, 106773.CrossRefGoogle Scholar
Ge, L. & Sotiropoulos, F. 2007 A numerical method for solving the 3D unsteady incompressible Navier–Stokes equations in curvilinear domains with complex immersed boundaries. J. Comput. Phys. 225 (2), 1782–1809.CrossRefGoogle ScholarPubMed
Germano, M., Piomelli, U., Moin, P. & Cabot, W.H. 1991 A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3 (7), 1760–1765.CrossRefGoogle Scholar
Gupta, V. & Wan, M. 2019 Low-order modelling of wake meandering behind turbines. J. Fluid Mech. 877, 534–560.CrossRefGoogle Scholar
Heisel, M., Hong, J. & Guala, M. 2018 The spectral signature of wind turbine wake meandering: a wind tunnel and field-scale study. Wind Energy 21 (9), 715–731.CrossRefGoogle Scholar
Hong, J., Toloui, M., Chamorro, L.P., Guala, M., Howard, K., Riley, S., Tucker, J. & Sotiropoulos, F. 2014 Natural snowfall reveals large-scale flow structures in the wake of a 2.5-MW wind turbine. Nat. Commun. 5, 4216.CrossRefGoogle ScholarPubMed
IEC 2019 Design requirements for fixed offshore wind turbine. Standard. IEC, Geneva, Switzerland.Google Scholar
Iungo, G.V., Viola, F., Camarri, S., Porté-Agel, F. & Gallaire, F. 2013 Linear stability analysis of wind turbine wakes performed on wind tunnel measurements. J. Fluid Mech. 737, 499–526.CrossRefGoogle Scholar
Jonkman, J., Butterfield, S., Musial, W. & Scott, G. 2009 Definition of a 5-MW reference wind turbine for offshore system development. Tech. Rep. NREL/TP-500-38060. National Renewable Energy Lab. (NREL).CrossRefGoogle Scholar
Jonkman, J. & Musial, W. 2010 Offshore code comparison collaboration (OC3) for IEA task 23 offshore wind technology and deployment. Tech. Rep. NREL/TP-5000-48191. National Renewable Energy Lab. (NREL).Google Scholar
Kang, S., Yang, X. & Sotiropoulos, F. 2014 On the onset of wake meandering for an axial flow turbine in a turbulent open channel flow. J. Fluid Mech. 744, 376–403.CrossRefGoogle Scholar
Keck, R.-E., de Maré, M., Churchfield, M.J., Lee, S., Larsen, G. & Aagaard Madsen, H. 2014 On atmospheric stability in the dynamic wake meandering model. Wind Energy 17 (11), 1689– 1710.CrossRefGoogle Scholar
Knisely, C.W. 1990 Strouhal numbers of rectangular cylinders at incidence: a review and new data. J. Fluids Struct. 4 (4), 371–393.CrossRefGoogle Scholar
Knoll, D.A. & Keyes, D.E. 2004 Jacobian-free Newton–Krylov methods: a survey of approaches and applications. J. Comput. Phys. 193 (2), 357–397.CrossRefGoogle Scholar
Larsen, G.C., et al. 2007 Dynamic wake meandering modeling. Risø National Laboratory.Google Scholar
Larsen, G.C., Madsen, H.A., Thomsen, K. & Larsen, T.J. 2008 Wake meandering: a pragmatic approach. Wind Energy 11 (4), 377–395.CrossRefGoogle Scholar
Lee, H. & Lee, D.-J. 2019 Effects of platform motions on aerodynamic performance and unsteady wake evolution of a floating offshore wind turbine. Renew. Energy 143, 9–23.CrossRefGoogle Scholar
Leroy, V., Gilloteaux, J.-C., Lynch, M., Babarit, A. & Ferrant, P. 2019 Impact of aerodynamic modeling on seakeeping performance of a floating horizontal axis wind turbine. Wind Energy 22 (8), 1019–1033.Google Scholar
Li, Z., Bouscasse, B., Ducrozet, G., Gentaz, L., Le Touzé, D. & Ferrant, P. 2021 Spectral wave explicit Navier–Stokes equations for wave-structure interactions using two-phase computational fluid dynamics solvers. Ocean Engng 221, 108513.CrossRefGoogle Scholar
Li, Z., Deng, G., Queutey, P., Bouscasse, B., Ducrozet, G., Gentaz, L., Le Touzé, D. & Ferrant, P. 2019 Comparison of wave modeling methods in CFD solvers for ocean engineering applications. Ocean Engng 188, 106237.CrossRefGoogle Scholar
Li, Z. & Yang, X. 2020 Evaluation of actuator disk model relative to actuator surface model for predicting utility-scale wind turbine wakes. Energies 13 (14), 3574.CrossRefGoogle Scholar
Li, Z. & Yang, X. 2021 Large-eddy simulation on the similarity between wakes of wind turbines with different yaw angles. J. Fluid Mech. 921, A11.CrossRefGoogle Scholar
Liu, Y., Xiao, Q., Incecik, A. & Wan, D.-C. 2016 Investigation of the effects of platform motion on the aerodynamics of a floating offshore wind turbine. J. Hydrodyn. 28 (1), 95–101.CrossRefGoogle Scholar
Lyu, G., Zhang, H. & Li, J. 2019 Effects of incident wind/wave directions on dynamic response of a spar-type floating offshore wind turbine system. Acta Mechanica Sin. 35 (5), 954–963.CrossRefGoogle Scholar
Madsen, H.A., Larsen, G.C., Larsen, T.J., Troldborg, N. & Mikkelsen, R. 2010 Calibration and validation of the dynamic wake meandering model for implementation in an aeroelastic code. J. Sol. Energy Engng 132 (4), 041014.CrossRefGoogle Scholar
Mahfouz, M.Y., Molins, C., Trubat, P., Hernández, S., Vigara, F., Pegalajar-Jurado, A., Bredmose, H. & Salari, M. 2021 Response of the international energy agency (IEA) Wind 15 MW WindCrete and Activefloat floating wind turbines to wind and second-order waves. Wind Energy Sci. 6 (3), 867–883.CrossRefGoogle Scholar
Mann, J. 1998 Wind field simulation. Prob. Engng Mech. 13 (4), 269–282.CrossRefGoogle Scholar
Mao, X. & Sørensen, J.N. 2018 Far-wake meandering induced by atmospheric eddies in flow past a wind turbine. J. Fluid Mech. 846, 190–209.CrossRefGoogle Scholar
Méchali, M., Barthelmie, R., Frandsen, S., Jensen, L. & Réthoré, P.-E. 2006 Wake effects at Horns Rev and their influence on energy production. In European Wind Energy Conference and Exhibition, vol. 1, pp. 10–20. Citeseer.Google Scholar
Medici, D. & Alfredsson, P.H. 2006 Measurements on a wind turbine wake: 3D effects and bluff body vortex shedding. Wind Energy 9 (3), 219–236.CrossRefGoogle Scholar
Meneveau, C. 2019 Big wind power: seven questions for turbulence research. J. Turbul. 20 (1), 2–20.CrossRefGoogle Scholar
Muller, Y.-A., Aubrun, S. & Masson, C. 2015 Determination of real-time predictors of the wind turbine wake meandering. Exp. Fluids 56 (3), 1–11.CrossRefGoogle Scholar
Nejad, A.R., Bachynski, E.E. & Moan, T. 2019 Effect of axial acceleration on drivetrain responses in a spar-type floating wind turbine. J. Offshore Mech. Arctic Engng 141 (3), 031901.CrossRefGoogle Scholar
Porté-Agel, F., Bastankhah, M. & Shamsoddin, S. 2020 Wind-turbine and wind-farm flows: a review. Boundary-Layer Meteorol. 174 (1), 1–59.CrossRefGoogle ScholarPubMed
Robertson, A., et al. 2014 Offshore code comparison collaboration continuation within IEA wind task 30: phase II results regarding a floating semisubmersible wind system. In International Conference on Offshore Mechanics and Arctic Engineering, vol. 45547, p. V09BT09A012. American Society of Mechanical Engineers.Google Scholar
Rockel, S., Camp, E., Schmidt, J., Peinke, J., Cal, R.B. & Hölling, M. 2014 Experimental study on influence of pitch motion on the wake of a floating wind turbine model. Energies 7 (4), 1954–1985.CrossRefGoogle Scholar
Rockel, S., Peinke, J., Hölling, M. & Cal, R.B. 2017 Dynamic wake development of a floating wind turbine in free pitch motion subjected to turbulent inflow generated with an active grid. Renew. Energy 112, 1–16.CrossRefGoogle Scholar
Rukes, L., Paschereit, C.O. & Oberleithner, K. 2016 An assessment of turbulence models for linear hydrodynamic stability analysis of strongly swirling jets. Eur. J. Mech. B/Fluids 59, 205–218.CrossRefGoogle Scholar
Saad, Y. 1993 A flexible inner-outer preconditioned GMRES algorithm. SIAM J. Sci. Comput. 14 (2), 461–469.CrossRefGoogle Scholar
Sarmast, S., Dadfar, R., Mikkelsen, R.F., Schlatter, P., Ivanell, S., Sørensen, J.N. & Henningson, D.S. 2014 Mutual inductance instability of the tip vortices behind a wind turbine. J. Fluid Mech. 755, 705–731.CrossRefGoogle Scholar
Schliffke, B., Aubrun, S. & Conan, B. 2020 Wind tunnel study of a ‘floating’ wind turbine's wake in an atmospheric boundary layer with imposed characteristic surge motion. J. Phys.: Conf. Ser. 1618, 062015.Google Scholar
Schmid, P.J., Henningson, D.S. & Jankowski, D.F. 2002 Stability and Transition in Shear Flows. Springer.Google Scholar
Shen, W.Z., Mikkelsen, R., Sørensen, J.N. & Bak, C. 2005 Tip loss corrections for wind turbine computations. Wind Energy 8 (4), 457–475.CrossRefGoogle Scholar
Smagorinsky, J. 1963 General circulation experiments with the primitive equations: I. The basic experiment. Mon. Weath. Rev. 91 (3), 99–164.2.3.CO;2>CrossRefGoogle Scholar
Smits, A.J., McKeon, B.J. & Marusic, I. 2011 High–Reynolds number wall turbulence. Annu. Rev. Fluid Mech. 43, 353–375.CrossRefGoogle Scholar
Sun, H., Gao, X. & Yang, H. 2020 A review of full-scale wind-field measurements of the wind-turbine wake effect and a measurement of the wake-interaction effect. Renew. Sustain. Energy Rev. 132, 110042.CrossRefGoogle Scholar
Tennekes, H. & Lumley, J.L. 1972 A First Course in Turbulence. MIT Press.CrossRefGoogle Scholar
Toffoli, A. & Bitner-Gregersen, E.M. 2017 Types of ocean surface waves, wave classification. In Encyclopedia of Maritime and Offshore Engineering, pp. 1–8. Wiley.CrossRefGoogle Scholar
Towne, A., Schmidt, O.T. & Colonius, T. 2018 Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis. J. Fluid Mech. 847, 821–867.CrossRefGoogle Scholar
Tran, T.T. & Kim, D.-H. 2016 A CFD study into the influence of unsteady aerodynamic interference on wind turbine surge motion. Renew. Energy 90, 204–228.CrossRefGoogle Scholar
Trujillo, J.-J., Bingöl, F., Larsen, G.C., Mann, J. & Kühn, M. 2011 Light detection and ranging measurements of wake dynamics. Part 2. Two-dimensional scanning. Wind Energy 14 (1), 61–75.CrossRefGoogle Scholar
Türk, M. & Emeis, S. 2010 The dependence of offshore turbulence intensity on wind speed. J. Wind Engng Ind. Aerodyn. 98 (8–9), 466–471.CrossRefGoogle Scholar
Veers, P., Dykes, K., Lantz, E., Barth, S., Bottasso, C.L., Carlson, O., Clifton, A., Green, J., Green, P. & Holttinen, H. 2019 Grand challenges in the science of wind energy. Science 366 (6464), eaau2027.CrossRefGoogle ScholarPubMed
van Wingerden, J.W., et al. 2020 Expert elicitation on wind farm control. J. Phys.: Conf. Ser. 1618, 022025.Google Scholar
Wise, A.S. & Bachynski, E.E. 2020 Wake meandering effects on floating wind turbines. Wind Energy 23 (5), 1266–1285.CrossRefGoogle Scholar
Wu, Y.T. & Porté-Agel, F. 2011 Large-eddy simulation of wind-turbine wakes: evaluation of turbine parametrisations. Boundary-Layer Meteorol. 138 (3), 345–366.CrossRefGoogle Scholar
Xie, S. & Archer, C. 2015 Self-similarity and turbulence characteristics of wind turbine wakes via large-eddy simulation. Wind Energy 18 (10), 1815–1838.CrossRefGoogle Scholar
Yang, X., Hong, J., Barone, M. & Sotiropoulos, F. 2016 Coherent dynamics in the rotor tip shear layer of utility-scale wind turbines. J. Fluid Mech. 804, 90–115.CrossRefGoogle Scholar
Yang, X., Pakula, M. & Sotiropoulos, F. 2018 Large-eddy simulation of a utility-scale wind farm in complex terrain. Appl. Energy 229, 767–777.CrossRefGoogle Scholar
Yang, X. & Sotiropoulos, F. 2018 A new class of actuator surface models for wind turbines. Wind Energy 21 (5), 285–302.CrossRefGoogle Scholar
Yang, X. & Sotiropoulos, F. 2019 Wake characteristics of a utility-scale wind turbine under coherent inflow structures and different operating conditions. Phys. Rev. Fluids 4, 024604.CrossRefGoogle Scholar
Yang, X., Sotiropoulos, F., Conzemius, R.J., Wachtler, J.N. & Strong, M.B. 2015 Large-eddy simulation of turbulent flow past wind turbines/farms: the virtual wind simulator (VWiS). Wind Energy 18 (12), 2025–2045.CrossRefGoogle Scholar
Yang, X., Zhang, X., Li, Z. & He, G.-W. 2009 A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations. J. Comput. Phys. 228 (20), 7821–7836.CrossRefGoogle Scholar
Zhang, X.-L., Michelén-Ströfer, C. & Xiao, H. 2020 Regularized ensemble Kalman methods for inverse problems. J. Comput. Phys. 416, 109517.CrossRefGoogle Scholar
Zhao, Y., Yang, J. & He, Y. 2012 Preliminary design of a multi-column TLP foundation for a 5-MW offshore wind turbine. Energies 5 (10), 3874–3891.CrossRefGoogle Scholar
Zhu, L., Goraya, S.A. & Masud, A. 2019 Interface-capturing method for free-surface plunging and breaking waves. J. Engng Mech. 145 (11), 04019088.Google Scholar
Zhu, L. & Masud, A. 2021 Variationally derived interface stabilization for discrete multiphase flows and relation with the ghost-penalty method. Comput. Meth. Appl. Mech. Engng 373, 113404.CrossRefGoogle Scholar