Hostname: page-component-5447f9dfdb-97xxw Total loading time: 0 Render date: 2025-07-28T16:38:19.270Z Has data issue: false hasContentIssue false
  • English
  • Français

Flow visualization using momentum and energy transport tubes and applications to turbulent flow in wind farms

Published online by Cambridge University Press:  09 January 2013

Johan Meyers  and
Charles Meneveau
Johan Meyers*
Affiliation:
Department of Mechanical Engineering, KU Leuven, Celestijnenlaan 300A, B3001 Leuven, Belgium
Charles Meneveau
Affiliation:
Department of Mechanical Engineering and Center for Environmental and Applied Fluid Mechanics, Johns Hopkins University, 3400 North Charles Street, Baltimore, MD 21218, USA
*
†Email address for correspondence: johan.meyers@mech.kuleuven.be
Get access Rights & Permissions [Opens in a new window]

Abstract

As a generalization of the mass–flux based classical stream tube, the concept of momentum and energy transport tubes is discussed as a flow visualization tool. These transport tubes have the property that no fluxes of momentum or energy exist over their respective tube mantles. As an example application using data from large eddy simulation, such tubes are visualized for the mean-flow structure of turbulent flow in large wind farms, in fully developed wind-turbine-array boundary layers. The three-dimensional organization of energy transport tubes changes considerably when turbine spacings are varied, enabling the visualization of the path taken by the kinetic energy flux that is ultimately available at any given turbine within the array.

JFM classification

Turbulent Flows: Turbulent Flows

Information

Type
Papers
Information
Journal of Fluid Mechanics , Volume 715 , 25 January 2013 , pp. 335 - 358
Copyright
©2013 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.)

Article purchase

Temporarily unavailable

References

Aref, H. 1984 Stirring by chaotic advection. J. Fluid Mech. 143, 1–21.Google Scholar
Barthelmie, R. J., Pryor, S. C., Frandsen, S. T., Hansen, K. S., Schepers, J. G., Rados, K., Schlez, W., Neubert, A., Jensen, L. E. & Neckelmann, S. 2010 Quantifying the impact of wind turbine wakes on power output at offshore wind farms. J. Atmos. Ocean. Technol. 27, 1302–1317.Google Scholar
Batchelor, G. K. 1967 Fluid Mechanics, 1st edn. Cambridge University Press.Google Scholar
Bou-Zeid, E., Meneveau, C. & Parlange, M. B. 2005 A scale-dependent Lagrangian dynamic model for large eddy simulation of complex turbulent flows. Phys. Fluids 17, 025105.Google Scholar
Burton, T., Sharpe, D., Jenkins, N. & Bossanyi, E. 2001 Wind Energy Handbook. John Wiley & Sons.CrossRefGoogle 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. Renewable Sustainable Energy 2, 013106.CrossRefGoogle Scholar
Calaf, M., Meneveau, C. & Meyers, J. 2010 Large eddy simulation study of fully developed wind-turbine array boundary layers. Phys. Fluids 22, 015110.CrossRefGoogle Scholar
Canuto, C., Hussaini, M. Y., Quarteroni, A. & Zang, T. A. 1988 Spectral Methods in Fluid Dynamics. Springer.Google Scholar
Degond, P. & Mustieles, F. J. 1990 A deterministic approximation of diffusion equations using particles. SIAM J. Sci. Stat. Comput. 11, 293–310.Google Scholar
Emeis, S. & Frandsen, S. 1993 Reduction of horizontal wind speed in a boundary layer with obstacles. Boundary-Layer Meteorol. 64, 297–305.Google Scholar
Favre, A., Kosvaznay, L. S. G., Dumas, R., Gaviglio, J. & Coantic, M. 1976 La turbulence en mécanique des Fluides: bases théoriques et expérimentales, méthodes statistiques. Gauthier-Villars.Google Scholar
Fay, J. A. 1994 Introduction to Fluid Mechanics, 1st edn. MIT.Google Scholar
Frandsen, S., Barthelmie, R., Pryor, S., Rathmann, O., Larsen, S., Hojstrup, J. & Thogersen, M. 2006 Analytical modelling of wind speed deficit in large offshore wind farms. Wind Energy 9, 39–53.CrossRefGoogle Scholar
Frandsen, S. T., Jørgensen, H. E., Barthelmie, R., Rathmann, O., Badger, J., Hansen, K., Ott, S., Rethore, P. E., Larsen, S. E. & Jensen, L. E. 2009 The making of a second-generation wind farm efficiency model complex. Wind Energy 12, 445–458.Google Scholar
Frigo, M. & Johnson, S. G. 2005 The design and implementation of FFTW3. Proc. IEEE 93 (2), 216–231.CrossRefGoogle Scholar
Grant, J. R. & Marshall, J. S. 2005 Diffusion velocity for a three-dimensional vorticity field. Theor. Comput. Fluid Dyn. 19, 377–390.Google Scholar
Hermeline, F. 1989 A deterministic particle method for transport diffusion equations: application to the Fokker–Planck equation. J. Comput. Phys. 82, 122–146.CrossRefGoogle Scholar
Ivanell, S., Sørensen, J. N., Mikkelsen, R. & Henningson, D. 2009 Analysis of numerically generated wake structures. Wind Energy 12, 63–80.CrossRefGoogle Scholar
Jimenez, A., Crespo, A., Migoya, E. & Garcia, J. 2007 Advances in large-eddy simulation of a wind turbine wake. J. Phys. Conf. Ser. 75, 012041.Google Scholar
Jimenez, A., Crespo, A., Migoya, E. & Garcia, J. 2008 Large-eddy simulation of spectral coherence in a wind turbine wake. Environ. Res. Lett. 3, 015004.Google Scholar
Lebron, J., Castillo, L. & Meneveau, C. 2012 Experimental study of the kinetic energy budget in a wind turbine stream-tube. J. Turbul. 13, 43.Google 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, 065101.Google Scholar
Mason, P. J. & Thomson, T. J. 1992 Stochastic backscatter in large-eddy simulations of boundary layers. J. Fluid Mech. 242, 51–78.CrossRefGoogle Scholar
Meyers, J. & Meneveau, C. 2010 Large eddy simulations of large wind-turbine arrays in the atmospheric boundary layer. In 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, AIAA 2010–827.Google Scholar
Meyers, J. & Meneveau, C. 2012 Optimal turbine spacing in fully developed wind-farm boundary layers. Wind Energy 15, 305–317.Google Scholar
Moeng, C. -H. 1984 A large-eddy simulation model for the study of planetary boundary-layer turbulence. J. Atmos. Sci. 41, 2052–2062.Google Scholar
Ottino, J. M. 1994 The kinematics of mixing: stretching, chaos, and transport. Cambridge University Press.Google Scholar
Smagorinsky, J. 1963 General circulation experiments with the primitive equations: I. The basic experiment. Mon. Weath. Rev. 91 (3), 99–165.Google Scholar
Smits, A. J. & Dussauge, J. -P. 2006 Turbulent Shear Layers in Supersonic Flow. Springer.Google Scholar
Sorensen, J. N. & Shen, W. Z. 2002 Numerical modelling of wind turbine wakes. J. Fluids Engng 124, 393–399.Google Scholar
Verstappen, R. W. C. P. & Veldman, A. E. P. 2003 Symmetry-preserving discretization of turbulent flow. J. Comput. Phys. 187, 343–368.Google Scholar
White, F. M. 2006 Viscous Fluid Flow, 3rd edn. McGraw Hill.Google Scholar
Wu, Y.-T. & Porté-Agel, F. 2011 Large-eddy simulation of wind-turbine wakes: evaluation of turbine parametrisations. Boundary-Layer Meteorol. 138, 345–366.CrossRefGoogle Scholar