Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-28T06:46:14.483Z Has data issue: false hasContentIssue false
  • English
  • Français

Experimental and theoretical study of wind turbine wakes in yawed conditions

Published online by Cambridge University Press:  14 October 2016

Majid Bastankhah  and
Fernando Porté-Agel
Majid Bastankhah
Affiliation:
Wind Engineering and Renewable Energy Laboratory (WIRE), École Polytechnique Fédérale de Lausanne (EPFL), EPFL-ENAC-IIE-WIRE, 1015 Lausanne, Switzerland
Fernando Porté-Agel*
Affiliation:
Wind Engineering and Renewable Energy Laboratory (WIRE), École Polytechnique Fédérale de Lausanne (EPFL), EPFL-ENAC-IIE-WIRE, 1015 Lausanne, Switzerland
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

This work is dedicated to systematically studying and predicting the wake characteristics of a yawed wind turbine immersed in a turbulent boundary layer. To achieve this goal, wind tunnel experiments were performed to characterize the wake of a horizontal-axis wind turbine model. A high-resolution stereoscopic particle image velocimetry system was used to measure the three velocity components in the turbine wake under different yaw angles and tip-speed ratios. Moreover, power and thrust measurements were carried out to analyse the performance of the wind turbine. These detailed wind tunnel measurements were then used to perform a budget study of the continuity and Reynolds-averaged Navier–Stokes equations for the wake of a yawed turbine. This theoretical analysis revealed some notable features of the wakes of yawed turbines, such as the asymmetric distribution of the wake skew angle with respect to the wake centre. Under highly yawed conditions, the formation of a counter-rotating vortex pair in the wake cross-section as well as the vertical displacement of the wake centre were shown and analysed. Finally, this study enabled us to develop general governing equations upon which a simple and computationally inexpensive analytical model was built. The proposed model aims at predicting the wake deflection and the far-wake velocity distribution for yawed turbines. Comparisons of model predictions with the wind tunnel measurements show that this simple model can acceptably predict the velocity distribution in the far wake of a yawed turbine. Apart from the ability of the model to predict wake flows in yawed conditions, it can provide valuable physical insight on the behaviour of turbine wakes in this complex situation.

JFM classification

Turbulent Flows: Turbulent Flows Turbulent Flows: Turbulent boundary layers Wakes/Jets: Wakes/Jets
Type
Papers
Information
Journal of Fluid Mechanics , Volume 806 , 10 November 2016 , pp. 506 - 541
Check for updates
Copyright
© 2016 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

Abkar, M. & Porté-Agel, F. 2013 The effect of free-atmosphere stratification on boundary-layer flow and power output from very large wind farms. Energies 6 (5), 2338–2361.Google Scholar
Abkar, M. & Porté-Agel, F. 2015 Influence of atmospheric stability on wind-turbine wakes: a large-eddy simulation study. Phys. Fluids 27 (3), 035104.CrossRefGoogle Scholar
Abraham, G. 1970 The flow of round buoyant jets issuing vertically into ambient fluid flowing in a horizontal direction. In 5th International Water Pollution Research Conference, July–August, San Francisco. Pergamon.Google Scholar
Amoura, Z., Roig, V., Risso, F. & Billet, A. 2010 Attenuation of the wake of a sphere in an intense incident turbulence with large length scales. Phys. Fluids 22 (5), 055105.Google Scholar
Bagchi, P. & Balachandar, S. 2004 Response of the wake of an isolated particle to an isotropic turbulent flow. J. Fluid Mech. 518, 95–123.Google Scholar
Bastankhah, M. & Porté-Agel, F. 2014 A new analytical model for wind-turbine wakes. Renew. Energy 70, 116–123.Google Scholar
Broadwell, J. E. & Breidenthal, R. E. 1984 Structure and mixing of a transverse jet in incompressible flow. J. Fluid Mech. 148, 405–412.Google Scholar
Burton, T., Sharpe, D., Jenkins, N. & Bossanyi, E. 1995 Wind Energy Handbook, 1st edn. Wiley.Google Scholar
Cal, R. B., Lebrón, J., Castillo, L., Kang, H. S. & Meneveau, C. 2010 Experimental study of the horizontally averaged flow structure in a model wind-turbine array boundary layer. J. Renew. Sustain. Energy 2, 013106.Google Scholar
Calaf, M., Meneveau, C. & Meyers, J. 2010 Large eddy simulation study of fully developed wind-turbine array boundary layers. Phys. Fluids 22 (1), 015110.Google Scholar
Coleman, R. P., Feingold, A. M. & Stempin, C. W.1945 Evaluation of the induced-velocity field of an idealized helicoptor rotor. Tech Rep. DTIC Document.Google Scholar
Cortelezzi, L. & Karagozian, A. R. 2001 On the formation of the counter-rotating vortex pair in transverse jets. J. Fluid Mech. 446, 347–373.Google Scholar
Dahlberg, J. Å. & Medici, D. 2003 Potential improvement of wind turbine array efficiency by active wake control (awc). In Proceedings of the European Wind Energy Conference and Exhibition, pp. 65–84. EWEA.Google Scholar
Dufresne, N. P. & Wosnik, M. 2013 Velocity deficit and swirl in the turbulent wake of a wind turbine. Mar. Technol. Soc. J. 47 (4), 193–205.CrossRefGoogle Scholar
Eames, I., Johnson, P. B., Roig, V. & Risso, F. 2011a Effect of turbulence on the downstream velocity deficit of a rigid sphere. Phys. Fluids 23 (9), 095103.CrossRefGoogle Scholar
Eames, I., Jonsson, C. & Johnson, P. B. 2011b The growth of a cylinder wake in turbulent flow. J. Turbul. 12 (9), 1–16.CrossRefGoogle Scholar
Fan, L. N.1967 Turbulent buoyant jets into stratified or flowing ambient fluids. Tech Rep., W. M. Keck Laboratory of Hydraulics and Water Resources.Google Scholar
Fleming, P. A., Gebraad, P. M. O., Lee, S., van Wingerden, J., Johnson, K., Churchfield, M., Michalakes, J., Spalart, P. & Moriarty, P. 2014 Evaluating techniques for redirecting turbine wakes using SOWFA. Renew. Energy 70, 211–218.Google Scholar
Frandsen, S. T., Barthelmie, R., Pryor, S., Rathmann, O., Larsen, S., Højstrup, J. & Thøgersen, M. 2006 Analytical modelling of wind speed deficit in large offshore wind farms. Wind Energy 9, 39–53.Google Scholar
Gebraad, P. M. O., Teeuwisse, F. W., Wingerden, J. W., Fleming, P. A., Ruben, S. D., Marden, J. R. & Pao, L. Y. 2014 Wind plant power optimization through yaw control using a parametric model for wake effects – a CFD simulation study. Wind Energy 19, 95–114.CrossRefGoogle Scholar
Glauert, H. 1926 A General Theory of the Autogyro. HM Stationery Office.Google Scholar
Grant, I. & Parkin, P. 2000 A DPIV study of the trailing vortex elements from the blades of a horizontal axis wind turbine in yaw. Exp. Fluids 28 (4), 368–376.CrossRefGoogle Scholar
Grant, I., Parkin, P. & Wang, X. 1997 Optical vortex tracking studies of a horizontal axis wind turbine in yaw using laser-sheet, flow visualisation. Exp. Fluids 23 (6), 513–519.CrossRefGoogle Scholar
Haans, W.2011 Wind turbine aerodynamics in yaw: unravelling the measured rotor wake. PhD thesis, TU Delft, Delft University of Technology.Google Scholar
Haans, W., van Kuik, G. & van Bussel, G. J. W. 2007 Experimentally observed effects of yaw misalignment on the inflow in the rotor plane. J. Phys. Conf. Ser. 75, 012012.Google Scholar
Haans, W., Sant, T., Van Kuik, G. & van Bussel, G. 2005 Measurement and modelling of tip vortex paths in the wake of a HAWT under yawed flow conditions. In 43th AIAA Aerospace Sciences Meeting and Exhibit, pp. 136–145.Google Scholar
Howland, M. F., Bossuyt, J., A., Martínez-Tossas L., Meyers, J. & Meneveau, C. 2016 Wake structure in actuator disk models of wind turbines in yaw under uniform inflow conditions. J. Renew. Sustain. Energy 8, 043301.Google Scholar
Jensen, N. O.1983 A note on wind turbine interaction. Tech Rep. Ris-M-2411. Risoe National Laboratory, Roskilde, Denmark.Google Scholar
Jiménez, Á., Crespo, A. & Migoya, E. 2010 Application of a LES technique to characterize the wake deflection of a wind turbine in yaw. Wind Energy 13 (6), 559–572.CrossRefGoogle Scholar
Johansson, P. B. V., George, W. K. & Gourlay, M. J. 2003 Equilibrium similarity, effects of initial conditions and local Reynolds number on the axisymmetric wake. Phys. Fluids 15 (3), 603–617.CrossRefGoogle Scholar
Johnson, P. B., Jonsson, C., Achilleos, S. & Eames, I. 2014 On the spread and decay of wind turbine wakes in ambient turbulence. J. Phys. Conf. Ser. 555, 012055.CrossRefGoogle Scholar
Kelso, R. M., Lim, T. T. & Perry, A. E. 1996 An experimental study of round jets in cross-flow. J. Fluid Mech. 306, 111–144.Google Scholar
Kikkert, G. A.2006 Buoyant jets with two and three-dimensional trajectories. PhD thesis, University of Canterbury.Google Scholar
Krogstad, P. & Adaramola, M. S. 2012 Performance and near wake measurements of a model horizontal axis wind turbine. Wind Energy 15 (5), 743–756.Google Scholar
Lee, J. H. & Chu, V. 2012 Turbulent Jets and Plumes: A Lagrangian Approach. Springer.Google Scholar
Legendre, D., Merle, A. & Magnaudet, J. 2006 Wake of a spherical bubble or a solid sphere set fixed in a turbulent environment. Phys. Fluids 18 (4), 048102.CrossRefGoogle Scholar
Lissaman, P. B. S. 1979 Energy effectiveness of arbitrary arrays of wind turbines. J. Energy 3 (6), 323–328.CrossRefGoogle Scholar
Lu, H. & Porté-Agel, F. 2011 Large-eddy simulation of a very large wind farm in a stable atmospheric boundary layer. Phys. Fluids 23 (6), 065101.Google Scholar
Mahesh, K. 2013 The interaction of jets with crossflow. Annu. Rev. Fluid Mech. 45, 379–407.CrossRefGoogle Scholar
Manwell, J. F., McGowan, J. G. & Rogers, A. L. 2010 Wind Energy Explained: Theory, Design and Application. Wiley.Google Scholar
Marzouk, Y. M. & Ghoniem, A. F. 2007 Vorticity structure and evolution in a transverse jet. J. Fluid Mech. 575, 267–305.Google Scholar
Medici, D. & Alfredsson, P. 2006 Measurement on a wind turbine wake: 3D effects and bluff body vortex shedding. Wind Energy 9, 219–236.CrossRefGoogle Scholar
Micallef, D., Bussel, G., Ferreira, C. S. & Sant, T. 2013 An investigation of radial velocities for a horizontal axis wind turbine in axial and yawed flows. Wind Energy 16 (4), 529–544.Google Scholar
Micallef, D., Ferreira, C. S., Sant, T. & van Bussel, G. 2009 Wake skew angle variation with rotor thrust for wind turbines in yaw based on the mexico experiment. In 5th PhD Seminar on Wind Energy in Europe. EAWE.Google Scholar
Muppidi, S. & Mahesh, K. 2006 Two-dimensional model problem to explain counter-rotating vortex pair formation in a transverse jet. Phys. Fluids 18 (8), 085103.Google Scholar
Okulov, V. L., Naumov, I. V., Mikkelsen, R. F. & Sørensen, J. N. 2015 Wake effect on a uniform flow behind wind-turbine model. J. Phys. Conf. Ser. 625, 012011.CrossRefGoogle Scholar
Ooms, G. 1972 A new method for the calculation of the plume path of gases emitted by a stack. Atmos. Environ. 6 (12), 899–909.Google Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.Google Scholar
Porté-Agel, F., Wu, Y. T. & Chen, C. H. 2013 A numerical study of the effects of wind direction on turbine wakes and power losses in a large wind farm. Energies 6 (10), 5297–5313.Google Scholar
Rajaratnam, N. 1976 Turbulent Jets. Elsevier.Google Scholar
Sant, T.2007 Improving BEM-based aerodynamic models in wind turbine design codes. PhD thesis, Delft University of Technology.Google Scholar
Sørensen, J. N. 2015 General Momentum Theory for Horizontal Axis Wind Turbines. Springer.Google Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT.Google Scholar
Vermeer, L., Sørensen, J. & Crespo, A. 2003 Wind turbine wake aerodynamics. Prog. Aerosp. Sci. 39, 467–510.Google Scholar
Vermeulen, P. E. J. 1980 An experimental analysis of wind turbine wakes. In 3rd International Symposium on Wind Energy Systems, pp. 431–450. Lyngby.Google Scholar
Wang, X. & Kikkert, G. A. 2014 Behaviour of oblique jets released in a moving ambient. J. Hydraul. Res. 52 (4), 490–501.CrossRefGoogle Scholar
White, F. M. 2009 Fluid Mechanics. McGraw-Hill.Google Scholar
Wu, J. S. & Faeth, G. M. 1994 Sphere wakes at moderate Reynolds numbers in a turbulent environment. AIAA J. 32 (3), 535–541.Google Scholar
Xie, S. & Archer, C. 2015 Self-similarity and turbulence characteristics of wind turbine wakes via large-eddy simulation. Wind Energy 18, 1815–1838.Google Scholar