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Performance of an ideal turbine in an inviscid shear flow

Published online by Cambridge University Press:  28 April 2016

S. Draper ,
T. Nishino ,
T. A. A. Adcock  and
P. H. Taylor
S. Draper*
Affiliation:
School of Civil, Environmental and Mining Engineering, University of Western Australia, WA 6009, Australia
T. Nishino
Affiliation:
Centre for Offshore Renewable Energy Engineering, Cranfield University, Bedfordshire MK43 0AL, UK
T. A. A. Adcock
Affiliation:
Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK
P. H. Taylor
Affiliation:
Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK
*
†Email address for correspondence: [email protected]
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Abstract

Although wind and tidal turbines operate in turbulent shear flow, most theoretical results concerning turbine performance, such as the well-known Betz limit, assume the upstream velocity profile is uniform. To improve on these existing results we extend the classical actuator disc model in this paper to investigate the performance of an ideal turbine in steady, inviscid shear flow. The model is developed on the assumption that there is negligible lateral interaction in the flow passing through the disc and that the actuator applies a uniform resistance across its area. With these assumptions, solution of the model leads to two key results. First, for laterally unbounded shear flow, it is shown that the normalised power extracted is the same as that for an ideal turbine in uniform flow, if the average of the cube of the upstream velocity of the fluid passing through the turbine is used in the normalisation. Second, for a laterally bounded shear flow, it is shown that the same normalisation can be applied, but allowance must also be made for the fact that non-uniform flow bypassing the turbine alters the background pressure gradient and, in turn, the turbines ‘effective blockage’ (so that it may be greater or less than the geometric blockage, defined as the ratio of turbine disc area to cross-sectional area of the flow). Predictions based on the extended model agree well with numerical simulations approximating the incompressible Euler equations. The model may be used to improve interpretation of model-scale results for wind and tidal turbines in tunnels/flumes, to investigate the variation in force across a turbine and to update existing theoretical models of arrays of tidal turbines.

JFM classification

Geophysical and Geological Flows: Coastal engineering Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Shallow water flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 796 , 10 June 2016 , pp. 86 - 112
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Copyright
© 2016 Cambridge University Press 

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References

Ball, D. J., Stansby, P. K. & Allison, N. 1996 Modelling shallow water flow around pile groups. Proc. Ice-Water Maritime Energy 118 (4), 226–236.CrossRefGoogle Scholar
Burton, T., Sharpe, D., Jenkins, N. & Bossanyi, E. 2001 Wind Energy Handbook. Wiley.CrossRefGoogle Scholar
Chamorro, L. P. & Arndt, R. E. 2013 Non-uniform velocity distribution effect on the Betz–Joukowsky limit. Wind Energy 16 (2), 279–282.CrossRefGoogle Scholar
Draper, S.2011 Tidal stream energy extraction in coastal basins. DPhil thesis, University of Oxford.Google Scholar
Draper, S. & Nishino, T. 2014 Centred and staggered arrangements of tidal turbines. J. Fluid Mech. 739, 72–93.CrossRefGoogle Scholar
Draper, S., Nishino, T. & Adcock, T. A. A. 2014 Turbine blockage in non-uniform flow. In 19th Australasian Fluid Mechanics Conference, Melbourne, Australia.Google Scholar
Fleming, C. F., McIntosh, S. C. & Willden, R. H. J. 2013 Tidal turbine performance in sheared flow. In Proceedings of 10th European Wave and Tidal Energy Conference (EWTEC), Aalborg, Denmark.Google Scholar
Garrett, C. & Cummins, P. 2007 The efficiency of a turbine in a tidal channel. J. Fluid Mech. 588, 243–251.CrossRefGoogle Scholar
Goorjian, P. M. 1972 An invalid equation in the general momentum theory of the actuator disc. AIAA 10, 543–544.CrossRefGoogle Scholar
Houlsby, G. T., Draper, S. & Oldfield, M. G. L.2008 Application of linear momentum actuator disc theory to open channel flow. Tech. Rep. OUEL 2296/08. Department of Engineering Science, University of Oxford.Google Scholar
van Kuik, G. A. M. 2007 The Lanchester–Betz–Joukowsky limit. Wind Energy 10 (3), 289–291.CrossRefGoogle Scholar
Myers, L. E. & Bahaj, A. S. 2012 An experimental investigation simulating flow effects in first generation marine current energy converter arrays. Renew. Energy 37, 28–36.CrossRefGoogle Scholar
Nishino, T. & Willden, R. H. J. 2012a The efficiency of an array of tidal turbines partially blocking a wide channel. J. Fluid Mech. 708, 596–606.CrossRefGoogle Scholar
Nishino, T. & Willden, R. H. J. 2012b Effects of 3-D channel blockage and turbulent wake mixing on the limit of power extraction by tidal turbines. Intl J. Heat Fluid Flow 37, 123–135.CrossRefGoogle Scholar
Nishino, T. & Willden, R. H. J. 2013 Two-scale dynamics of flow past a partial cross-stream array of tidal turbines. J. Fluid Mech. 730, 220–244.CrossRefGoogle Scholar
Sanderse, B., Pijl, V. D. S. & Koren, B. 2011 Review of computational fluid dynamics for wind turbine wake aerodynamics. Wind Energy 14 (7), 799–819.CrossRefGoogle Scholar
Santo, H., Taylor, P. H., Bai, W. & Choo, Y. S. 2014 Blockage effects in wave and current: 2D planar simulations of combined regular oscillations and steady flow through porous blocks. Ocean Engng 88, 174–186.CrossRefGoogle Scholar
Sørensen, J. N. 2011 Aerodynamic aspects of wind energy conversion. Annu. Rev. Fluid Mech. 43, 427–448.CrossRefGoogle Scholar
Taylor, P. H.1991 Current blockage: reduced forces on offshore space-frame structures. In Offshore Technology Conference. Paper OTC 6519.CrossRefGoogle Scholar
Vennell, R. 2010 Tuning turbine in a tidal channel. J. Fluid Mech. 663, 253–267.CrossRefGoogle Scholar
Vermeer, L. J., Sørensen, J. N. & Crespo, A. 2003 Wind turbine wake aerodynamics. Prog. Aerosp. Sci. 39 (6), 467–510.CrossRefGoogle Scholar
Wagner, R. M., Courtney, M., Gottshall, J. & Lindelöw-Marsden, P. 2011 Accounting for the speed shear in wind turbine power performance measurement. Wind Energy 14, 993–1004.CrossRefGoogle Scholar
Whelan, J. I., Graham, J. M. R. & Peiro, J. 2009 A free-surface and blockage correction for tidal turbines. J. Fluid Mech. 624, 281–291.CrossRefGoogle Scholar
Wood, C. J. 1964 The effect of base bleed on a periodic wake. J. R. Aero. Soc. 68 (1964), 477–482.CrossRefGoogle Scholar