Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-22T21:55:33.488Z Has data issue: false hasContentIssue false

On the spectral behaviour of the turbulence-driven power fluctuations of horizontal-axis turbines

Published online by Cambridge University Press:  06 October 2020

Georgios Deskos*
Affiliation:
National Wind Technology Center, National Renewable Energy Laboratory, Golden, CO80401-3305, USA
Grégory S. Payne
Affiliation:
Laboratoire de recherche en Hydrodynamique, Energétique et Environnement Atmosphérique, Ecole Centrale Nantes, 1 rue de la Noë, 44300Nantes, France
Benoît Gaurier
Affiliation:
Marine Structures Laboratory, IFREMER, 150, quai Gambetta, BP 699, F-62321Boulogne-Sur-Mer, France
Michael Graham
Affiliation:
Department of Aeronautics, Imperial College London, London, SW7 2AZ, UK
*
Email address for correspondence: [email protected]

Abstract

In this article we consider the spectral behaviour of turbulence-driven power fluctuations for a single horizontal-axis turbine. To this end, a small-scale instrumented axial-flow hydrokinetic turbine model ($\textrm {diameter}=0.724\ \textrm {m}$) is deployed in the long water flume situated in the laboratory facilities of IFREMER in Boulogne-sur-Mer, France, and synchronous measurements of the upstream velocity and the rotor are collected for different tip-speed ratios. The study confirms previous findings suggesting that the power spectra follow the velocity spectra behaviour in the large scales region and a steeper power law slope behaviour ($-11/3$) over the inertial frequency sub-range. However, we show that both the amplitude of the power spectra and low-pass filtering effect over the inertial sub-range also depend on the rotor aero/hydrodynamics (e.g. $\mathrm {d}C_L/\mathrm {d}\alpha$) and the approaching flow deceleration and not solely on the rotational effects. In addition, we present a novel semi-analytical model to predict the dominant blade-passing frequency harmonics in the high-frequency regime using the rotationally sampled spectra technique. For all calculations, the distortion of incoming turbulence is taken into account.

Type
JFM Papers
Copyright
© The Author(s), 2020. 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., Drapper, S. & Nishino, T. 2015 Tidal power generation – a review of hydrodynamic modelling. Proc. IMechE A: J. Power Energy 229 (7), 755771.CrossRefGoogle Scholar
Anvari, M., Lohmann, G., Wächter, M., Milan, P., Lorenz, E., Heinemann, D., Tabar, M., Reza, R. & Peinke, J. 2016 Short term fluctuations of wind and solar power systems. New J. Phys. 18 (6), 063027.CrossRefGoogle Scholar
Apt, J. 2007 The spectrum of power from wind turbines. J. Power Sources 169 (2), 369374.CrossRefGoogle Scholar
Bandi, M. M. 2017 Spectrum of wind power fluctuations. Phys. Rev. Lett. 118, 028301.CrossRefGoogle ScholarPubMed
Batchelor, G. K. 1959 The Theory of Homogeneous Turbulence. Cambridge University Press.Google Scholar
Batchelor, G. K. & Proudman, I. A. N. 1954 The effect of rapid distortion of a fluid in turbulent motion. Q. J. Mech. Appl. Maths 7 (1), 83103.CrossRefGoogle Scholar
Bossuyt, J., Howland, M. F., Meneveau, C. & Meyers, J. 2016 Measurement of unsteady loading and power output variability in a micro wind farm model in a wind tunnel. Exp. Fluids 58 (1), 1.CrossRefGoogle Scholar
Bossuyt, J., Meneveau, C. & Meyers, J. 2017 Wind farm power fluctuations and spatial sampling of turbulent boundary layers. J. Fluid Mech. 823, 329344.CrossRefGoogle Scholar
Burton, T., Sharpe, D., Jenkins, N. & Bossanyi, E. 2001 Wind Energy HandBook. John Wiley & Sons.CrossRefGoogle Scholar
Chamorro, L. P., Hill, C., Morton, S., Ellis, C., Arndt, R. E. A. & Sotiropoulos, F. 2013 On the interaction between a turbulent open channel flow and an axial-flow turbine. J. Fluid Mech. 716, 658670.CrossRefGoogle Scholar
Chamorro, L. P., Lee, S.-J., Olsen, D., Milliren, C., Marr, J., Arndt, R. E. A. & Sotiropoulos, F. 2015 Turbulence effects on a full-scale 2.5-mw horizontal-axis wind turbine under neutrally stratified conditions. Wind Energy 18 (2), 339349.CrossRefGoogle Scholar
Churchfield, M. J., Lee, S., Michalakes, J. & Moriarty, P. J. 2012 A numerical study of the effects of atmospheric and wake turbulence on wind turbine dynamics. J. Turbul. 13, N14.CrossRefGoogle Scholar
Connell, J. R. 1982 The spectrum of wind speed fluctuations encountered by a rotating blade of a wind energy conversion system. Solar Energy 29 (5), 363375.CrossRefGoogle Scholar
Conway, J. T. 1995 Analytical solutions for the actuator disk with variable radial distribution of load. J. Fluid Mech. 297, 327355.CrossRefGoogle Scholar
Deskos, G., Laizet, S. & Palacios, R. 2020 WInc3D: a novel framework for turbulence-resolving simulations of wind farm wake interactions. Wind Energy 23 (3), 779794.CrossRefGoogle Scholar
Drela, M. 1989 XFOIL: An Analysis and Design System for Low Reynolds Number Airfoils. Springer, pp. 112.Google Scholar
Gaurier, B., Carlier, C., Germain, G., Pinon, G. & Rivoalen, E. 2020 Three tidal turbines in interaction: an experimental study of turbulence intensity effects on wakes and turbine performance. J. Renew. Energy 148, 11501164.CrossRefGoogle Scholar
Gaurier, B., Germain, G. & Facq, J. V. 2017 Experimental study of the Marine Current Turbine behaviour submitted to macro-particle impacts. In Proceedings of the 12th European Wave and Tidal Energy Conference, Cork, Ireland.Google Scholar
Gaurier, B., Germain, G. & Pinon, G. 2018 How to correctly measure turbulent upstream flow for marine current turbine performances evaluation? In 3rd International Conference on Renewable Energies Offshore (RENEW 2018), Lisbon, Portugal. Taylor & Francis.Google Scholar
Germain, G. 2008 Marine current energy converter tank testing practices. In 2nd International Conference on Ocean Energy (ICOE 2008), Brest, France.Google Scholar
Graham, J. M. R. 2017 Rapid distortion of turbulence into an open turbine rotor. J. Fluid Mech. 825, 764794.CrossRefGoogle Scholar
Grant, H. L., Stewart, R. W. & Moilliet, A. 1962 Turbulence spectra from a tidal channel. J. Fluid Mech. 12, 241268.CrossRefGoogle Scholar
Hansen, K. S., Barthelmie, R. J., Jensen, L. E. & Sommer, A. 2012 The impact of turbulence intensity and atmospheric stability on power deficits due to wind turbine wakes at horns rev wind farm. Wind Energy 15 (1), 183196.CrossRefGoogle Scholar
Heathershaw, A. D. 1979 The turbulent structure of the bottom boundary layer in a tidal current. Geophys. J. Intl 58 (2), 395430.CrossRefGoogle Scholar
Jin, Y., Ji, S. & Chamorro, L. P. 2016 Spectral energy cascade of body rotations and oscillations under turbulence. Phys. Rev. E 94, 063105.CrossRefGoogle ScholarPubMed
von Kármán, T. 1948 Progress in the statistical theory of turbulence. Proc. Natl Acad. Sci. USA 11 (34), 530539.CrossRefGoogle Scholar
Katzenstein, W., Fertig, E. & Apt, J. 2010 The variability of interconnected wind plants. Energy Policy 38 (8), 44004410.CrossRefGoogle Scholar
Kolmogorov, A. N. 1941 The local structure of turbulence in incompressible viscous fluid for very large reynolds numbers. Proc. Acad. Sci. URSS 30, 301305.Google Scholar
Kraichnan, R. H. 1964 Kolmogorov's hypotheses and eulerian turbulence theory. Phys. Fluids 7 (11), 17231734.CrossRefGoogle Scholar
van Kuik, G. A. M., Peinke, J., Nijssen, R., Lekou, D., Mann, J., Sørensen, J. N., Ferreira, C., van Wingerden, J. W., Schlipf, D., Gebraad, P., et al. 2016 Long-term research challenges in wind energy – a research agenda by the European academy of wind energy. Wind Energy Sci. 1 (1), 139.CrossRefGoogle Scholar
Liu, H., Jin, Y., Tobin, N. & Chamorro, L. P. 2017 Towards uncovering the structure of power fluctuations of wind farms. Phys. Rev. E 96, 063117.CrossRefGoogle ScholarPubMed
Mann, J., Peña, A., Troldborg, N. & Andersen, S. J. 2018 How does turbulence change approaching a rotor? Wind Energy Sci. 3 (1), 293300.CrossRefGoogle Scholar
Milan, P., Wächter, M. & Peinke, J. 2013 Turbulent character of wind energy. Phys. Rev. Lett. 110, 138701.CrossRefGoogle ScholarPubMed
Milne, I. A. & Graham, J. M. R. 2019 Turbulence velocity spectra and intensities in the inflow of a turbine rotor. J. Fluid Mech. 870, R3.CrossRefGoogle Scholar
Osalusi, E., Side, J. & Harris, R. 2009 a Reynolds stress and turbulence estimates in bottom boundary layer of fall of warness. Intl Commun. Heat Mass Transfer 36 (5), 412421.CrossRefGoogle Scholar
Osalusi, E., Side, J. & Harris, R. 2009 b Structure of turbulent flow in EMEC's tidal energy test site. Intl Commun. Heat Mass Transfer 36 (5), 422431.CrossRefGoogle Scholar
Payne, G. S., Stallard, T., Martinez, R. & Bruce, T. 2018 Variation of loads on a three-bladed horizontal axis tidal turbine with frequency and blade position. J. Fluids Struct. 83, 156170.CrossRefGoogle Scholar
Stevens, R. J. A. M., Gayme, D. F. & Meneveau, C. 2016 Effects of turbine spacing on the power output of extended wind-farms. Wind Energy 19 (2), 359370.CrossRefGoogle Scholar
Stevens, R. J. A. M. & Meneveau, C. 2014 Temporal structure of aggregate power fluctuations in large-eddy simulations of extended wind-farms. J. Renew. Sustain. Energy 6 (4), 043102.CrossRefGoogle Scholar
Tennekes, H. 1975 Eulerian and lagrangian time microscales in isotropic turbulence. J. Fluid Mech. 67 (3), 561567.CrossRefGoogle Scholar
Tobin, N. & Chamorro, L. P. 2018 Turbulence coherence and its impact on wind-farm power fluctuations. J. Fluid Mech. 855, 11161129.CrossRefGoogle Scholar
Tobin, N., Lavely, A., Schmitz, S. & Chamorro, L. P. 2019 Spatiotemporal correlations in the power output of wind farms: on the impact of atmospheric stability. Energies 12 (8), 1486.CrossRefGoogle Scholar
Tobin, N., Zhu, H. & Chamorro, L. P. 2015 Spectral behaviour of the turbulence-driven power fluctuations of wind turbines. J. Turbul. 16 (9), 832846.CrossRefGoogle Scholar
Veers, P., Dykes, K., Lantz, E., Barth, S., Bottasso, C. L., Carlson, O., Clifton, A., Green, J., Green, P., Holttinen, H., et al. 2019 Grand challenges in the science of wind energy. Science 366 (eaau6464), 2027.CrossRefGoogle ScholarPubMed
Vigueras-Rodríguez, A., Sørensen, P., Cutululis, N. A., Viedma, A. & Donovan, M. H. 2010 Wind model for low frequency power fluctuations in offshore wind farms. Wind Energy 13 (5), 471482.CrossRefGoogle Scholar
Wilczek, M., Stevens, R. J. A. M. & Meneveau, C. 2015 a Spatio-temporal spectra in the logarithmic layer of wall turbulence: large-eddy simulations and simple models. J. Fluid Mech. 769, R1R12.CrossRefGoogle Scholar
Wilczek, M., Stevens, R. J. A. M. & Meneveau, C. 2015 b Height-dependence of spatio-temporal spectra of wall-bounded turbulence – LES results and model predictions. J. Turbul. 16 (10), 937949.CrossRefGoogle Scholar