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Turbulent heat transport regimes in a channel

B. Castaing*

E. Rusaouën, J. Salort, and F. Chillà†

  • Univ. Grenoble Alpes, CNRS, Grenoble INP, LEGI, F-38000 Grenoble, France

  • Univ Lyon, Ens de Lyon, Univ Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France

  • *bernard.castaing627@laposte.net
  • †Francesca.Chilla@ens-lyon.fr
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Phys. Rev. Fluids 2, 062801(R) – Published 14 June, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.062801

Abstract

In this paper we focus on the turbulent transport of a scalar through a channel. The scalar flux and the corresponding scalar concentration gradient along the channel allow us to define a Nusselt number and a Grashof number. While the relation between the large-scale velocity field and the input energy rate show perfect inertial (turbulent) behavior, three different regimes can be distinguished, with different scalings between Nusselt and Grashof numbers.

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References (22)

  1. T. Seon, J. P. Hulin, D. Salin, B. Perrin, and E. J. Hinch, Laser-induced fluorescence measurements of buoyancy driven mixing in tilted tubes, Phys. Fluids 18, 041701 (2006).
  2. J. Znaien, Y. Hallez, F. Moisy, J. Magnaudet, J. P. Hulin, D. Salin, and E. J. Hinch, Experimental and numerical investigations of flow structure and momentum transport in a turbulent buoyancy-driven flow inside a tilted tube, Phys. Fluids 21, 115102 (2009).
  3. J. Znaien, F. Moisy, and J. P. Hulin, Flow structure and momentum transport for buoyancy driven mixing flows in long tubes at different tilt angles, Phys. Fluids 23, 035105 (2011).
  4. R. Delgado-Buscalioni and E. Crespo, Flow and heat transfer regimes in inclined differentially heated cavity, Int. J. Heat Mass Transfer 44, 1947 (2001).
  5. M. Gibert, H. Pabiou, F. Chillà, and B. Castaing, High-Rayleigh-Number Convection in a Vertical Channel, Phys. Rev. Lett. 96, 084501 (2006).
  6. M. Gibert, H. Pabiou, J.-C. Tisserand, B. Gertjerenken, B. Castaing, and F. Chillà, Heat convection in a vertical channel: Plumes versus turbulent diffusion, Phys. Fluids 21, 035109 (2009).
  7. J.-C. Tisserand, M. Creyssels, M. Gibert, B. Castaing, and F. Chillà, Convection in a vertical channel, New J. Phys. 12, 075024 (2010).
  8. X. Riedinger, J.-C. Tisserand, F. Seychelles, B. Castaing, and F. Chillà, Heat transport regimes in an inclined channel, Phys. Fluids 25, 015117 (2013).
  9. E. Calzavarini, D. Lohse, F. Toschi, and R. Tripiccione, Rayleigh and Prandtl number scaling in the bulk of Rayleigh-Bénard turbulence, Phys. Fluids 17, 055107 (2005).
  10. L.-E. Schmidt, E. Calzavarini, D. Lohse, F. Toschi, and R. Verzicco, Axially homogeneous Rayleigh-Bénard convection in a cylindrical cell, J. Fluid Mech. 691, 52 (2012).
  11. M. R. Cholemari and J. H. Arakeri, Axially homogeneous, zero mean flow buoyancy-driven turbulence in a vertical pipe, J. Fluid Mech. 621, 69 (2009).
  12. D. J. Tritton, Physical Fluid Dynamics (Oxford University Press, Oxford, 1988), Chaps. 13 and 14.
  13. S. S. Pawar and J. H. Arakeri, Two regimes of flux scaling in axially homogeneous turbulent convection in vertical tube, Phys. Rev. Fluids 1, 042401(R) (2016).
  14. The term “hard turbulence” (as well as “soft turbulence”) was coined by Heslot [15], in the context of Rayleigh-Bénard convection. The transition from soft to hard was associated with the apparition of a scaling range in temperature spectra, together with a change in the temperature histograms shape, without a clear relation between these two characteristics. In his review, Siggia [16] reproaches this lack of precision. Here the apparition of an inertial range when one enters the hard-turbulence regime justifies this appellation by Riedinger
  15. F. Heslot, B. Castaing, and A. Libchaber, Transitions to turbulence in helium gas, Phys. Rev. A 36, 5870 (1987).
  16. E. D. Siggia, High Rayleigh number convection, Annu. Rev. Fluid Mech. 26, 137 (1994).
  17. One may wonder why we do not consider the possibility of a Bolgiano range where 〈θ2〉r depends on the scale r as r2/5, down to a Bolgiano scale ℓB. Such a range has often been reported in convection flows [18],[19]. However, the corresponding velocity structure function behavior (scaling as r6/5) has never been observed. Moreover, ℓB should be of order ℓ and it is never envisaged that ηθ is larger than ℓB. Thus, the limit of the soft turbulence could simply correspond to ηθ=ℓB rather than ℓ, without any change in the conclusions.
  18. F. Chillà, S. Ciliberto, C. Innocenti, and E. Pampaloni, Spectra of local and averaged scalar fields in turbulence, Europhys. Lett. 22, 23 (1993).
  19. S. S. Pawar and J. H. Arakeri, Kinetic energy and scalar spectra in high Rayleigh number axially homogeneous buoyancy driven turbulence, Phys. Fluids 28, 065103 (2016).
  20. H. Tennekes and J. Lumley, A First Course in Turbulence (MIT Press, Cambridge, 1972).
  21. R. O. Tovar, Ph.D. thesis, Universidad Nacional Autonoma de Mexico (2002).
  22. E. Rusaouën, Échanges turbulents en convection thermique, Ph.D. thesis, ENS de Lyon (2014).

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Phys. Rev. Fluids 2, 062801(R)– Published 14 June, 2017
  • Received 4 November 2016

©2017 American Physical Society

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