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Turbulence velocity spectra and intensities in the inflow of a turbine rotor

Published online by Cambridge University Press:  15 May 2019

I. A. Milne Open the ORCID record for I. A. Milne [Opens in a new window]  and
J. M. R. Graham Open the ORCID record for J. M. R. Graham [Opens in a new window]
I. A. Milne*
Affiliation:
Oceans Graduate School, The University of Western Australia, Crawley, 6009, Australia
J. M. R. Graham
Affiliation:
Department of Aeronautics, Imperial College London, London SW7 2AZ, UK
*
†Email address for correspondence: ian.milne@uwa.edu.au
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Abstract

The changes in spectra and intensities of the streamwise component of turbulent velocity are calculated in the inflow of a turbine rotor. The flow is initially calculated in the limit when the turbulence is of small scale compared with the rotor diameter. Rapid distortion theory (RDT), Batchelor & Proudman (Q. J. Mech. Appl. Maths, vol. 7 (1), 1954, pp. 83–103) (BP), for small-scale turbulence is combined with the effect of the fluctuating potential flow field on the turbulence caused by the direct interaction of the incident turbulence with the rotor as a sheet of resistance. A second computation is then carried out for turbulence of larger length scale. The results of the calculations are compared with velocity measurements in the inflow of both a commercial wind turbine and a tidal turbine rotor.

JFM classification

Turbulent Flows: Turbulence theory
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 870 , 10 July 2019 , R3
Copyright
© 2019 Cambridge University Press 

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References

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 (1), 83–103.Google Scholar
Betz, A. 1920 Das Maximum der theoretisch möglichen Ausnützung des Windes durch Windmotoren. Z. das gesamte Turbinenwesen 26, 307–309; (in German).Google Scholar
Coles, D., Greenwood, C., Vogler, A., Walsh, T. & Taaff, D. 2018 Assessment of the turbulent flow upstream of the Meygen phase 1A tidal stream turbines. In Proceedings of the 4th Asian Wave and Tidal Energy Conference (AWTEC), Taipei, Taiwan.Google Scholar
Conway, J. T. 1995 Analytical solutions for the actuator disk with variable radial distribution of load. J. Fluid Mech. 297, 327–355.Google Scholar
Durbin, P. A. 1981 Distorted turbulence in axisymmetric flow. Q. J. Mech. Appl. Maths 34, 489–500.Google Scholar
Graham, J. M. R. 2017 Rapid distortion of turbulence into an open rotor. J. Fluid Mech. 825, 764–794.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
Mann, J. 1994 The spatial structure of neutral atmospheric surface-layer turbulence. J. Fluid Mech. 273, 141–168.Google Scholar
Mann, J., Peña, A., Troldborg, N. & Andersen, S. J. 2018 How does turbulence change approaching a rotor? Wind Energ. Sci. 3, 293–300.Google Scholar
Milne, I. A., Sharma, R. N., Flay, R. G. J. & Bickerton, S. 2013 Characteristics of the turbulence in the flow at a tidal stream power site. Phil. Trans. R. Soc. Lond. A 371, 20120196.Google Scholar
Peña, A., Mann, J. & Dimitrov, N. 2017 Turbulence characterization from a forward-looking nacelle lidar. Wind Energ. Sci. 2, 133–152.Google Scholar
Taylor, G. I., Batchelor, G. K., Dryden, H. L. & Schubauer, G. B. 1949 The effect of wire gauze on small disturbances in a uniform stream. Q. J. Mech. Appl. Maths 2, 1–29.Google Scholar