Hostname: page-component-848d4c4894-r5zm4 Total loading time: 0 Render date: 2024-07-06T11:58:31.127Z Has data issue: false hasContentIssue false
  • English
  • Français

An analytical blockage correction model for high-solidity turbines

Published online by Cambridge University Press:  20 September 2022

K. Steiros Open the ORCID record for K. Steiros [Opens in a new window] ,
N. Bempedelis Open the ORCID record for N. Bempedelis [Opens in a new window]  and
M.M. Cicolin Open the ORCID record for M.M. Cicolin [Opens in a new window]
K. Steiros*
Affiliation:
Department of Aeronautics, Imperial College London, London SW7 2AZ, UK
N. Bempedelis
Affiliation:
Department of Aeronautics, Imperial College London, London SW7 2AZ, UK
M.M. Cicolin
Affiliation:
Department of Aeronautics, Imperial College London, London SW7 2AZ, UK
*
†Email address for correspondence: k.steiros@imperial.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

A significant challenge in the experimental or computational characterisation of porous bodies and wind turbines is the correction of the obtained flow quantities for wall interference effects. Conventional corrective models are based on the Rankine–Froude theory, which is valid when the body solidity, or turbine induction factor, is sufficiently low. To resolve this issue, this work presents a new corrective model that builds on an extension of the Rankine–Froude theory, valid at arbitrary solidities, coupled with the method of mirror images to account for the existence of channel walls. The predictions of the new model are validated using laboratory and numerical experiments of porous plates and wind turbines. The results show that the new model performs equally as well as conventional ones when the solidity is low, but becomes increasingly more accurate as the latter grows.

JFM classification

Wakes/Jets: Wakes Nonlinear Dynamical Systems: Low-dimensional models
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 948 , 10 October 2022 , A57
Check for updates
Copyright
© The Author(s), 2022. 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

Apelt, C.J. & West, G.S. 1975 The effects of wake splitter plates on bluff-body flow in the range $10^4 < R < 5 \times 10^4$. Part 2. J. Fluid Mech. 71 (1), 145–160.CrossRefGoogle Scholar
Ayati, A.A., Steiros, K., Miller, M.A., Duvvuri, S. & Hultmark, M. 2019 A double-multiple streamtube model for vertical axis wind turbines of arbitrary rotor loading. Wind Energy Sci. 4 (4), 653–662.CrossRefGoogle Scholar
Bahaj, A.S., Molland, A.F., Chaplin, J.R. & Batten, W.M.J. 2007 Power and thrust measurements of marine current turbines under various hydrodynamic flow conditions in a cavitation tunnel and a towing tank. Renew. Energy 32 (3), 407–426.CrossRefGoogle Scholar
Barnsley, M.J. & Wellicome, J.F. 1990 Final report on the 2nd phase of development and testing of a horizontal axis wind turbine test rig for the investigation of stall regulation aerodynamics. ETSU.Google Scholar
Bartholomew, P., Deskos, G., Frantz, R.A.S., Schuch, F.N., Lamballais, E. & Laizet, S. 2020 Xcompact3d: an open-source framework for solving turbulence problems on a Cartesian mesh. SoftwareX 12, 100550.CrossRefGoogle Scholar
Bempedelis, N. & Steiros, K. 2022 Analytical all-induction state model for wind turbine wakes. Phys. Rev. Fluids 7 (3), 034605.CrossRefGoogle Scholar
Castro, I.P. 1971 Wake characteristics of two-dimensional perforated plates normal to an air-stream. J. Fluid Mech. 46 (3), 599–609.CrossRefGoogle Scholar
Chapman, J.C., Masters, I., Togneri, M. & Orme, J.A.C. 2013 The Buhl correction factor applied to high induction conditions for tidal stream turbines. Renew. Energy 60, 472–480.CrossRefGoogle Scholar
Chen, T.Y. & Liou, L.R. 2011 Blockage corrections in wind tunnel tests of small horizontal-axis wind turbines. Exp. Therm. Fluid Sci. 35 (3), 565–569.CrossRefGoogle Scholar
Cicolin, M.M., Buxton, O.R.H., Assi, G.R.S. & Bearman, P.W. 2021 The role of separation on the forces acting on a circular cylinder with a control rod. J. Fluid Mech. 915, A33.CrossRefGoogle Scholar
Dehtyriov, D., Schnabl, A.M., Vogel, C.R., Draper, S., Adcock, T.A.A. & Willden, R.H.J. 2021 Fractal-like actuator disc theory for optimal energy extraction. J. Fluid Mech. 927, A40.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), 779–794.CrossRefGoogle Scholar
Deskos, G., Laizet, S. & Piggott, M.D. 2019 Turbulence-resolving simulations of wind turbine wakes. Renew. Energy 134, 989–1002.CrossRefGoogle Scholar
Draper, S., Nishino, T., Adcock, T.A.A. & Taylor, P.H. 2016 Performance of an ideal turbine in an inviscid shear flow. J. Fluid Mech. 796, 86–112.CrossRefGoogle Scholar
Garrett, C. & Cummins, P. 2007 The efficiency of a turbine in a tidal channel. J. Fluid Mech. 588, 243–251.CrossRefGoogle Scholar
Glauert, H. 1935 Airplane propellers. In Aerodynamic Theory, pp. 169–360. Springer.CrossRefGoogle Scholar
Graham, J.M.R. 1976 Turbulent flow past a porous plate. J. Fluid Mech. 73 (3), 565–591.CrossRefGoogle Scholar
Hansen, M. 2015 Aerodynamics of Wind Turbines. Routledge.CrossRefGoogle Scholar
Houlsby, G.T., Draper, S. & Oldfield, M.L.G. 2008 Application of linear momentum actuator disc theory to open channel flow. Rep. no. OUEL 2296/08. University of Oxford.Google Scholar
Kinsey, T. & Dumas, G. 2017 Impact of channel blockage on the performance of axial and cross-flow hydrokinetic turbines. Renew. Energy 103, 239–254.CrossRefGoogle Scholar
Koo, J.-K. & James, D.F. 1973 Fluid flow around and through a screen. J. Fluid Mech. 60 (3), 513–538.CrossRefGoogle Scholar
Krogstad, P.-Å. & Eriksen, P.E. 2013 ‘Blind test’ calculations of the performance and wake development for a model wind turbine. Renew. Energy 50, 325–333.CrossRefGoogle Scholar
Laizet, S. & Lamballais, E. 2009 High-order compact schemes for incompressible flows: a simple and efficient method with quasi-spectral accuracy. J. Comput. Phys. 228 (16), 5989–6015.CrossRefGoogle Scholar
Laizet, S. & Li, N. 2011 Incompact3d: a powerful tool to tackle turbulence problems with up to ${O}(10^5)$ computational cores. Intl J. Numer. Meth. Fluids 67 (11), 1735–1757.CrossRefGoogle Scholar
Maskell, E.C. 1963 A theory of the blockage effects on bluff bodies and stalled wings in a closed wind tunnel. Aero. Res. Counc. R&M 3400.Google Scholar
McTavish, S., Feszty, D. & Nitzsche, F. 2014 An experimental and computational assessment of blockage effects on wind turbine wake development. Wind Energy 17 (10), 1515–1529.CrossRefGoogle Scholar
Mikkelsen, R. & Sørensen, J.N. 2002 Modelling of wind turbine blockage. In 15th IEA Symposium on the Aerodynamics of Wind Turbines. FOI Swedish Defence Research Agency.Google Scholar
Miller, M.A., Duvvuri, S. & Hultmark, M. 2021 Solidity effects on the performance of vertical-axis wind turbines. Flow 1, E9.CrossRefGoogle Scholar
Nishino, T. & Draper, S. 2015 Local blockage effect for wind turbines. J. Phys.: Conf. Ser. 625, 012010.Google Scholar
Roshko, A. 1954 A new hodograph for free-streamline theory. NACA Tech. Rep. TN 3168.Google Scholar
Ross, H. & Polagye, B. 2020 a An experimental assessment of analytical blockage corrections for turbines. Renew. Energy 152, 1328–1341.CrossRefGoogle Scholar
Ross, H. & Polagye, B. 2020 b An experimental evaluation of blockage effects on the wake of a cross-flow current turbine. J. Ocean Engng Marine Energy 6 (3), 263–275.CrossRefGoogle Scholar
Ryi, J., Rhee, W., Hwang, U.C. & Choi, J.-S. 2015 Blockage effect correction for a scaled wind turbine rotor by using wind tunnel test data. Renew. Energy 79, 227–235.CrossRefGoogle Scholar
Sarlak, H., Nishino, T., Martínez-Tossas, L.A., Meneveau, C. & Sørensen, J.N. 2016 Assessment of blockage effects on the wake characteristics and power of wind turbines. Renew. Energy 93, 340–352.CrossRefGoogle Scholar
Segalini, A. & Inghels, P. 2014 Confinement effects in wind-turbine and propeller measurements. J. Fluid Mech. 756, 110–129.CrossRefGoogle Scholar
Sørensen, J.N., Shen, W.Z. & Mikkelsen, R. 2006 Wall correction model for wind tunnels with open test section. AIAA J. 44 (8), 1890–1894.CrossRefGoogle Scholar
Steiros, K., Bempedelis, N. & Ding, L. 2021 Recirculation regions in wakes with base bleed. Phys. Rev. Fluids 6 (3), 034608.CrossRefGoogle Scholar
Steiros, K. & Hultmark, M. 2018 Drag on flat plates of arbitrary porosity. J. Fluid Mech. 853, R3.CrossRefGoogle Scholar
Steiros, K., Kokmanian, K., Bempedelis, N. & Hultmark, M. 2020 The effect of porosity on the drag of cylinders. J. Fluid Mech. 901, R2.CrossRefGoogle Scholar
Taylor, G.I. 1944 Air resistance of a flat plate of very porous material. Aero. Res. Counc. R&M 2236, 159–162.Google Scholar
Taylor, G.I. & Davies, R.M. 1944 The aerodynamics of porous sheets. Aero. Res. Counc. R&M 2237.Google Scholar
Tennekes, H. & Lumley, J.L. 1972 A First Course in Turbulence. MIT Press.CrossRefGoogle Scholar
Werle, M.J. 2010 Wind turbine wall-blockage performance corrections. J. Propul. Power 26 (6), 1317–1321.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
Yeung, W.W.H. & Parkinson, G.V. 2000 Base pressure prediction in bluff-body potential-flow models. J. Fluid Mech. 423, 381–394.CrossRefGoogle Scholar
Zaghi, S., Muscari, R. & Di Mascio, A. 2016 Assessment of blockage effects in wind tunnel testing of wind turbines. J. Wind Engng Ind. Aerodyn. 154, 1–9.CrossRefGoogle Scholar