Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-23T14:19:33.677Z Has data issue: false hasContentIssue false

Wave- and drag-driven subharmonic responses of a floating wind turbine

Published online by Cambridge University Press:  27 October 2021

Jana Orszaghova*
Affiliation:
Oceans Graduate School and Wave Energy Research Centre, University of Western Australia,WA 6009, Australia
Paul H. Taylor
Affiliation:
Oceans Graduate School and Wave Energy Research Centre, University of Western Australia,WA 6009, Australia
Hugh A. Wolgamot
Affiliation:
Oceans Graduate School and Wave Energy Research Centre, University of Western Australia,WA 6009, Australia
Freddy J. Madsen
Affiliation:
Department of Wind Energy, Technical University of Denmark, Kgs. Lyngby, DK-2800, Denmark
Antonio M. Pegalajar-Jurado
Affiliation:
Department of Wind Energy, Technical University of Denmark, Kgs. Lyngby, DK-2800, Denmark
Henrik Bredmose
Affiliation:
Department of Wind Energy, Technical University of Denmark, Kgs. Lyngby, DK-2800, Denmark
*
Email address for correspondence: [email protected]

Abstract

The nonlinear hydrodynamic responses of a novel spar-type soft-moored floating offshore wind turbine are investigated via analysis of motion measurements from a wave-basin campaign. A prototype of the TetraSpar floater, supporting a $1:60$ scale model of the DTU 10 MW reference wind turbine, was subjected to irregular wave forcing (with no wind) and shown to exhibit subharmonic resonant motions, which greatly exceeded the wave-frequency motions. These slow-drift responses are excited nonlinearly, since the rigid-body natural frequencies of the system lie below the incident-wave frequency range. Pitch motion is examined in detail, allowing for identification of different hydrodynamic forcing mechanisms. The resonant response is found to contain odd-harmonic components, in addition to the even harmonics expected a priori and excited by second-order difference-frequency hydrodynamic interactions. Data analysis utilising harmonic separation and signal conditioning suggests that Morison drag excitation or third-order subharmonic potential flow forcing could be at play. In the extreme survival-conditions sea state, the odd resonant responses are identified to be drag-driven. Their importance for the tested floater is appreciable, as their magnitude is comparable to the second-order potential flow effects. Under such severe conditions, the turbine would not be operating, and as such neglecting aerodynamic forcing and motion damping is likely to be reasonable. Additionally, other possible drivers of the resonant pitch response are explored. Both Mathieu-type parametric excitation and wavemaker-driven second-order error waves are found to have negligible influence. However, we note slight contamination of the measurements arising from wave-basin sloshing.

Type
JFM Papers
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Adcock, T.A.A., Feng, X., Tang, T., van den Bremer, T.S., Day, S., Dai, S., Li, Y., Lin, Z., Xu, W. & Taylor, P.H. 2019 Application of phase decomposition to the analysis of random time series from wave basin tests. In International Conference on Offshore Mechanics and Arctic Engineering, vol. 9: Rodney Eatock Taylor Honoring Symposium on Marine and Offshore Hydrodynamics; Takeshi Kinoshita Honoring Symposium on Offshore Technology, OMAE2019-95172. ASME.CrossRefGoogle Scholar
Azcona, J., Bouchotrouch, F. & Vittori, F. 2019 Low-frequency dynamics of a floating wind turbine in wave tank–scaled experiments with SiL hybrid method. Wind Energy 22 (10), 14021413.CrossRefGoogle Scholar
Barthel, V., Mansard, E.P.D., Sand, S.E. & Vis, F.C. 1983 Group bounded long waves in physical models. Ocean Engng 10 (4), 261294.CrossRefGoogle Scholar
Bayati, I., Jonkman, J., Robertson, A. & Platt, A. 2014 The effects of second-order hydrodynamics on a semisubmersible floating offshore wind turbine. J. Phys.: Conf. Ser. 524, 012094.Google Scholar
Bonnefoy, F., Le Touzé, D. & Ferrant, P. 2006 A fully-spectral 3D time-domain model for second-order simulation of wavetank experiments. Part B: validation, calibration versus experiments and sample applications. Appl. Ocean Res. 28 (2), 121132.CrossRefGoogle Scholar
Borg, M., Bredmose, H., Stiesdal, H., Jensen, B., Mikkelsen, R., Mirzaei, M., Pegalajar-Jurado, A., Madsen, F., Nielsen, T. & Lomholt, A. 2018 Physical model testing of the TetraSpar floater in two configurations. In 15th Deep Sea Offshore Wind R&D Conference (EERA DeepWind) (ed. J.O. Tande). Trondheim.Google Scholar
Borg, M., Walkusch Jensen, M., Urquhart, S., Andersen, M.T., Thomsen, J.B. & Stiesdal, H. 2020 Technical definition of the TetraSpar Demonstrator floating wind turbine foundation. Energies 13 (18), 4911.CrossRefGoogle Scholar
Bredmose, H., et al. 2017 The Triple Spar campaign: model tests of a 10MW floating wind turbine with waves, wind and pitch control. Energy Procedia 137, 5876.CrossRefGoogle Scholar
Chen, L.F., Taylor, P.H., Ning, D.Z., Cong, P.W., Wolgamot, H., Draper, S. & Cheng, L. 2021 Extreme runup events around a ship-shaped floating production, storage and offloading vessel in transient wave groups. J. Fluid Mech. 911, A40.CrossRefGoogle Scholar
Chen, L.F., Zang, J., Taylor, P.H., Sun, L., Morgan, G.C.J., Grice, J., Orszaghova, J. & Tello Ruiz, M. 2018 An experimental decomposition of nonlinear forces on a surface-piercing column: Stokes-type expansions of the force harmonics. J. Fluid Mech. 848, 4277.CrossRefGoogle Scholar
Coulling, A.J., Goupee, A.J., Robertson, A.N. & Jonkman, J.M. 2013 Importance of second-order difference-frequency wave-diffraction forces in the validation of a FAST semi-submersible floating wind turbine model. International Conference on Offshore Mechanics and Arctic Engineering, vol. 8: Ocean Renewable Energy, OMAE 10398 1–10. ASME.CrossRefGoogle Scholar
Dean, R.G. & Dalrymple, R.A. 2001 Coastal Processes with Engineering Applications. Cambridge University Press.CrossRefGoogle Scholar
Dean, R.G. & Dalrymple, R.A. 2014 Water Wave Mechanics For Engineers And Scientists, Advanced Series on Ocean Engineering, vol. 2. World Scientific Publishing Company.Google Scholar
van Essen, S., Pauw, W. & van den Berg, J. 2016 How to deal with basin modes when generating irregular waves on shallow water. International Conference on Offshore Mechanics and Arctic Engineering, vol. 7: Ocean Engineering, p. OMAE 54134 1-16.Google Scholar
Faltinsen, O.M. 1993 Sea Loads on Ships and Offshore Structures. Cambridge University Press.Google Scholar
Fitzgerald, C.J., Taylor, P.H., Eatock Taylor, R., Grice, J.R. & Zang, J. 2014 Phase manipulation and the harmonic components of ringing forces on a surface-piercing column. Proc. R. Soc. A 470 (2168), 20130847.CrossRefGoogle Scholar
Goupee, A.J., Koo, B.J., Kimball, R.W., Lambrakos, K.F. & Dagher, H.J. 2014 Experimental comparison of three floating wind turbine concepts. Trans. ASME J. Offshore Mech. Arctic Engng 136 (2), 020906.CrossRefGoogle Scholar
Haslum, H.A. & Faltinsen, O.M. 1999 Alternative shape of spar platforms for use in hostile areas. In Offshore Technology Conference, OTC 10953 1–12. ASME.CrossRefGoogle Scholar
Hughes, S.A. 1993 Physical Models and Laboratory Techniques in Coastal Engineering, Advanced Series on Ocean Engineering, vol. 7. World Scientific.CrossRefGoogle Scholar
IRENA 2019 Future of wind: Deployment, investment, technology, grid integration and socio-economic aspects (A Global Energy Transformation paper). Tech. Rep. International Renewable Energy Agency.pp. 1–88.Google Scholar
Jonathan, P. & Taylor, P.H. 1997 On irregular, nonlinear waves in a spread sea. Trans. ASME J. Offshore Mech. Arctic Engng 119 (1), 3741.CrossRefGoogle Scholar
Judge, F.M., Hunt-Raby, A.C., Orszaghova, J., Taylor, P.H. & Borthwick, A.G.L. 2019 Multi-directional focused wave group interactions with a plane beach. Coast. Engng 152, 103531.CrossRefGoogle Scholar
Kim, M.-H. & Yue, D.K.P. 1990 The complete second-order diffraction solution for an axisymmetric body. Part 2. Bichromatic incident waves and body motions. J. Fluid Mech. 211, 557593.CrossRefGoogle Scholar
Koo, B.J., Kim, M.H. & Randall, R.E. 2004 Mathieu instability of a spar platform with mooring and risers. Ocean Engng 31 (17), 21752208.CrossRefGoogle Scholar
Kristoffersen, J.C., Bredmose, H., Georgakis, C.T., Branger, H. & Luneau, C. 2021 Experimental study of the effect of wind above irregular waves on the wave-induced load statistics. Coast. Engng 168, 103940.CrossRefGoogle Scholar
Larsen, T.J. & Hanson, T.D. 2007 A method to avoid negative damped low frequent tower vibrations for a floating, pitch controlled wind turbine. J. Phys.: Conf. Ser. 75, 012073.Google Scholar
Li, H. & Bachynski, E.E. 2021 Experimental and numerical investigation of nonlinear diffraction wave loads on a semi-submersible wind turbine. Renewable Energy 171, 709727.CrossRefGoogle Scholar
Madsen, F.J., Pegalajar-Jurado, A. & Bredmose, H. 2019 Performance study of the QuLAF pre-design model for a 10MW floating wind turbine. Wind Energy Sci. 4 (3), 527547.CrossRefGoogle Scholar
Madsen, P.A. & Fuhrman, D.R. 2012 Third-order theory for multi-directional irregular waves. J. Fluid Mech. 698, 304334.CrossRefGoogle Scholar
Molin, B. 2001 Numerical and physical wavetanks – making them fit. The twenty-second Georg Weinblum memorial lecture. Ship Technol. Res. 48, 122.Google Scholar
Morison, J.R., Johnson, J.W. & Schaaf, S.A. 1950 The force exerted by surface waves on piles. J. Petrol. Technol. 2 (05), 149154.CrossRefGoogle Scholar
Oh, I.G., Nayfeh, A.H. & Mook, D.T. 2000 A theoretical and experimental investigation of indirectly excited roll motion in ships. Phil. Trans. R. Soc. Lond. A 358 (1771), 18531881.CrossRefGoogle Scholar
Orszaghova, J., Taylor, P.H., Borthwick, A.G.L. & Raby, A.C. 2014 Importance of second-order wave generation for focused wave group run-up and overtopping. Coast. Engng 94, 6379.CrossRefGoogle Scholar
Orszaghova, J., Wolgamot, H., Eatock Taylor, R., Taylor, P.H. & Rafiee, A. 2019 Transverse motion instability of a submerged moored buoy. Proc. R. Soc. A 475, 20180459.CrossRefGoogle Scholar
Pegalajar-Jurado, A., Borg, M. & Bredmose, H. 2018 An efficient frequency-domain model for quick load analysis of floating offshore wind turbines. Wind Energy Sci. 3 (2), 693712.CrossRefGoogle Scholar
Pegalajar-Jurado, A. & Bredmose, H. 2019 Reproduction of slow-drift motions of a floating wind turbine using second-order hydrodynamics and operational modal analysis. Mar. Struct. 66,178196.CrossRefGoogle Scholar
Pegalajar-Jurado, A., Madsen, F.J. & Bredmose, H. 2019 Damping identification of the TetraSpar floater in two configurations with Operational Modal Analysis. In ASME 2019 2nd International Offshore Wind Technical Conference, IOWTC2019-7623. ASME.CrossRefGoogle Scholar
Phillips, O.M. 1960 On the dynamics of unsteady gravity waves of finite amplitude. Part 1. The elementary interactions. J. Fluid Mech. 9 (2), 193217.CrossRefGoogle Scholar
Pierella, F., Bredmose, H. & Dixen, M. 2021 Generation of highly nonlinear irregular waves in a wave flume experiment: spurious harmonics and their effect on the wave spectrum. Coast. Engng 164, 103816.CrossRefGoogle Scholar
Pinkster, J.A. 1980 Low frequency second order wave exciting forces on floating structures. PhD thesis, Technische Hogeschool Delft (Delft University of Technology), The Netherlands.Google Scholar
Roald, L., Jonkman, J., Robertson, A. & Chokani, N. 2013 The effect of second-order hydrodynamics on floating offshore wind turbines. Energy Procedia 35, 253264.CrossRefGoogle Scholar
Robertson, A.N., et al. 2020 OC6 Phase I: investigating the underprediction of low-frequency hydrodynamic loads and responses of a floating wind turbine. J. Phys.: Conf. Ser. 1618, 032033.Google Scholar
Robertson, A.N., et al. 2017 OC5 Project Phase II: validation of global loads of the DeepCwind floating semisubmersible wind turbine. Energy Procedia 137, 3857.CrossRefGoogle Scholar
Roux de Reilhac, P., Bonnefoy, F., Rousset, J.M. & Ferrant, P. 2011 Improved transient water wave technique for the experimental estimation of ship responses. J. Fluids Struct. 27 (3), 456466.CrossRefGoogle Scholar
Schäffer, H.A. 1996 Second-order wavemaker theory for irregular waves. Ocean Engng 23 (1), 4788.CrossRefGoogle Scholar
Shemer, L. & Sergeeva, A. 2009 An experimental study of spatial evolution of statistical parameters in a unidirectional narrow-banded random wavefield. J. Geophys. Res.: Oceans 114 (C1), C01015.Google Scholar
Shin, Y.S., Belenky, V.L., Paulling, J.R., Weems, K.M. & Lin, W.M. 2004 Criteria for parametric roll of large containerships in longitudinal seas. Tech. Rep. Society of Naval Architects and Marine Engineers (SNAME), American Bureau of Shipping (ABS) Technical Papers. pp. 117–138.Google Scholar
Simos, A.N., Ruggeri, F., Watai, R.A., Souto-Iglesias, A. & Lopez-Pavon, C. 2018 Slow-drift of a floating wind turbine: an assessment of frequency-domain methods based on model tests. Renewable Energy 116, 133154.CrossRefGoogle Scholar
Stansberg, C.T. 1997 Linear and nonlinear system identification in model testing. In International Conference on Nonlinear Aspects of Physical Model Tests, pp. 1–28.Google Scholar
Taylor, P.H. & Williams, B.A. 2004 Wave statistics for intermediate depth water–newwaves and symmetry. Trans. ASME J. Offshore Mech. Arctic Engng 126 (1), 5459.CrossRefGoogle Scholar
Walker, D.A.G., Taylor, P.H. & Eatock Taylor, R. 2004 The shape of large surface waves on the open sea and the Draupner New Year wave. Appl. Ocean Res. 26 (3), 7383.CrossRefGoogle Scholar
Whittaker, C.N., Fitzgerald, C.J., Raby, A.C., Taylor, P.H., Orszaghova, J. & Borthwick, A.G.L. 2017 Optimisation of focused wave group runup on a plane beach. Coast. Engng 121, 4455.CrossRefGoogle Scholar
Zhang, J. & Chen, L. 1999 General third-order solutions for irregular waves in deep water. J. Engng Mech. 125 (7), 768779.Google Scholar
Zhao, W., Taylor, P.H., Wolgamot, H. & Eatock Taylor, R. 2018 Identifying linear and nonlinear coupling between fluid sloshing in tanks, roll of a barge and external free-surface waves. J. Fluid Mech. 844, 403434.CrossRefGoogle Scholar
Zhao, W., Wolgamot, H.A., Taylor, P.H. & Eatock Taylor, R. 2017 Gap resonance and higher harmonics driven by focused transient wave groups. J. Fluid Mech. 812, 905939.CrossRefGoogle Scholar
Zheng, Y., Lin, Z., Li, Y., Adcock, T.A.A., Li, Y. & van den Bremer, T.S. 2020 Fully nonlinear simulations of unidirectional extreme waves provoked by strong depth transitions: the effect of slope. Phys. Rev. Fluids 5, 064804.CrossRefGoogle Scholar