Hostname: page-component-5cf477f64f-xc2pj Total loading time: 0 Render date: 2025-04-06T14:55:26.015Z Has data issue: false hasContentIssue false
  • English
  • Français

Rapid distortion of turbulence into an open turbine rotor

Published online by Cambridge University Press:  24 July 2017

J. M. R. Graham Open the ORCID record for J. M. R. Graham [Opens in a new window]
J. M. R. Graham*
Affiliation:
Department of Aeronautics, Imperial College, London SW7 2AZ, UK
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Rapid distortion of turbulence (RDT) theory is applied to homogeneous, isotropic turbulence incident on a horizontal axis turbine rotor such as a wind turbine or tidal-stream turbine. The mean flow field of the rotor which distorts the turbulence is represented by the commonly used axisymmetric actuator disc model due to Betz and Joukowski. The fluctuating streamwise component of the turbulence distorted by this field is calculated at the actuator disc plane. Turbulence velocity intensities and spectra are evaluated for general ratios of turbulence integral length scale to the rotor diameter, including the small-scale limit for which the original homogeneous strain analysis of Batchelor and Proudman may be applied. The distortion of the mean velocity profile of an incident rotor wake which may be considered a zero frequency disturbance relevant to wind and tidal turbine operation in large arrays is also analysed by the same method, treating it as a deterministic disturbance in the incident flow.

JFM classification

Turbulent Flows: Homogeneous turbulence Turbulent Flows: Isotropic turbulence Turbulent Flows: Turbulence theory
Type
Papers
Information
Journal of Fluid Mechanics , Volume 825 , 25 August 2017 , pp. 764 - 794
Check for updates
Copyright
© 2017 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

Argyle, P. & Watson, S. J. 2015 On the effects of directional bin size when simulating large offshore wind farms with cfd. Wind Engng 39 (6), 565–650.Google Scholar
Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.Google Scholar
Batchelor, G. K. & Proudman, I. 1954 The effect of rapid distortion of a fluid in turbulent motion. Q. J. Mech. Appl. Maths 7, 83–103.Google Scholar
Betz, A. 1920 Das maximum der theoretisch moglichen ausnutzung des windes durch windmotoren. Z. das Ges. Turbinenwesen 26, 307–309.Google Scholar
Branlard, E., Gaunaa, M., Mercier, P. & Voutsinas, S. 2016 Impact of a wind turbine on turbulence: unfreezing turbulence by means of a simple vortex particle approach. J. Wind Engng Ind. Aerodyn. 151, 34–47.Google Scholar
Branlard, E., Papadakis, G., Gaunaa, M., Winckelmans, G. & Larsen, T. J. 2015 Aeroelastic large eddy simulations using vortex methods: unfrozen turbulent and sheared inflow. J. Phys. Conf. Ser. 625 (1), 012019.Google Scholar
Conway, J. T. 1995 Analytical solutions for the actuator disc with variable radial distribution of load. J. Fluid Mech. 297, 327–355.Google Scholar
Deaves, D. M. & Harris, R. I.1978 A mathematical model of the structure of strong winds. Construction Industry Research and Information Association: CIRIA Report No. 76.Google Scholar
Durbin, P. A.1978 Rapid distortion theory of turbulent flows. PhD thesis, Cambridge University, UK.Google Scholar
Durbin, P. A. 1981 Distorted turbulence in axisymmetric flow. Q. J. Mech. Appl. Maths 34, 489–500.CrossRefGoogle Scholar
Farr, T. D. & Hancock, P. E. 2012 Torque fluctuations caused by upstream mean flow and turbulence. In The Science of Making Torque From Wind, EAWE Conference, Journal of Physics Conference Series, vol. 555, 2014. IOP.Google Scholar
Froude, R. E. 1911 The acceleration in front of a propeller. Trans. Inst. Naval Architects 53, 39–82.Google Scholar
Glauert, H. 1935 Airplane Propellers, vol. IV. Springer.Google Scholar
Goldstein, M. E. 1978 Unsteady vortical and entropic distortions of potential flows round arbitrary obstacles. J. Fluid Mech. 89, 433–468.CrossRefGoogle Scholar
Goldstein, M. E. & Durbin, P. A. 1980 The effect of finite turbulence spatial scale on the amplification of turbulence by a contracting stream. J. Fluid Mech. 98, 473–508.CrossRefGoogle Scholar
Gradshteyn, I. S. & Ryzhik, I. M. 1980 Tables of Integrals, Series and Products. Academic.Google Scholar
Graham, J. M. R. 1976 Turbulent flow past a porous plate. J. Fluid Mech. 73, 565–591.Google Scholar
Hanazaki, H. & Hunt, J. C. R. 2004 Structure of unsteady stably stratified turbulence with mean shear. J. Fluid Mech. 507, 1–42.Google Scholar
Hancock, P. E. & Pascheke, F. 2014 Wind tunnel simulation of the wake of a large wind turbine in a stable boundary-layer. pt i and ii. Boundary-Layer Meteorol. 151, 3–37.CrossRefGoogle Scholar
Hankin, D. & Graham, J. M. R. 2012 An unsteady vortex lattice model of a hawt operating in an upstream rotor wake. In EAWE Conference Proceedings, Science of Making Torque from Wind, 012049. IOP.Google Scholar
Hough, G. R. & Ordway, D. E. 1965 The generalised actuator disc. In Developments in Theoretical and Applied Mechanics, vol. II, pp. 317–336. Pergamon.Google Scholar
Hunt, J. C. R. 1973 A theory of turbulent flow round two-dimensional bluff bodies. J. Fluid Mech. 61 (4), 625–706.Google Scholar
Hunt, J. C. R. 1978 A review of the theory of rapidly distorted turbulent flows and its applications. Fluid Dynamics Transactions 9, 121–152.Google Scholar
Hunt, J. C. R. & Graham, J. M. R. 1978 Free stream turbulence near plane boundaries. J. Fluid Mech. 84, 209–235.Google Scholar
Irwin, H. P. A. H. 1977 Wind tunnel and analytical investigations of the response of lions’ gate bridge to a turbulent wind. National Research Council of Canada, Report LTR-LA-210.Google Scholar
Joukowsky, J. N. 1920 Windmills of the nej type (article 3). Transactions of the Central Institute for Aero-Hydrodynamics of Moscow, pp. 405–430.Google Scholar
Kaimal, J. C., Izumi, Y., Wyngaard, J. C. & Cote, O. R. 1972 Spectral characteristics of surface layer turbulence. Q. J. R. Meteorol. Soc. 98, 563–589.Google Scholar
Majumdar, S. J. & Peake, N. 1998 Noise generation by the interaction between ingested turbulence and a rotoating fan. J. Fluid Mech. 359, 181–216.Google Scholar
Mann, J. 1994 The spatial structure of neutral atmospheric surface-layer turbulence. J. Fluid Mech. 273, 141–168.Google Scholar
Milne, I. A., Day, A. H., Sharma, R. N. & Flay, R. G. J. 2016 The characterisation of the hydrodynamic loads on tidal turbines due to turbulence. Renew. Sustainable Energy Rev. 56, 851–864.Google Scholar
Prandtl, L.1933 Attaining a steady airstream in wind-tunnels. NACA, Tech. Memo, TM 726.Google Scholar
Simonich, J. C., Amiet, R. K., Schlinker, R. H. & Greitzer, E. M. 1990 Rotor noise due to atmospheric turbulence ingestion – pt.i: Fluid mechanics. J. Aircraft 27, 7–14.Google Scholar
Taylor, G. I. 1944 Air resistance of a flat plate of very porous material. Aero. Research Council, Rep. and Memo. 2236.Google Scholar
Teunissen, H. W. 1970 Characteristics of the mean wind and turbulence in the planetary boundary-layer. In University of Toronto, Institute for Aerospace Studies, UTIAS Review No, 32.Google Scholar
Zahle, F. & Sorensen, N. 2008 Rotor aerodynamics in atmospheric shear flow. In European Wind Energy Conference Proceedings, pp. 1593–1616. EWEA.Google Scholar