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Length of near-wall plumes in turbulent convection

  • Baburaj A. Puthenveettil (a1), G. S. Gunasegarane (a1), Yogesh K. Agrawal (a2), Daniel Schmeling (a3), Johannes Bosbach (a3) and Jaywant H. Arakeri (a4)...
Abstract
Abstract

We present planforms of line plumes formed on horizontal surfaces in turbulent convection, along with the length of line plumes measured from these planforms, in a six decade range of Rayleigh numbers () and at three Prandtl numbers (). Using geometric constraints on the relations for the mean plume spacings, we obtain expressions for the total length of near-wall plumes on horizontal surfaces in turbulent convection. The plume length per unit area (), made dimensionless by the near-wall length scale in turbulent convection (), remains constant for a given fluid. The Nusselt number is shown to be directly proportional to for a given fluid layer of height . The increase in has a weak influence in decreasing . These expressions match the measurements, thereby showing that the assumption of laminar natural convection boundary layers in turbulent convection is consistent with the observed total length of line plumes. We then show that similar relationships are obtained based on the assumption that the line plumes are the outcome of the instability of laminar natural convection boundary layers on the horizontal surfaces.

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Email address for correspondence: apbraj@iitm.ac.in
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1. R. J. Adrian , R. T. D. S. Ferreira & T. Boberg 1986 Turbulent thermal convection in wide horizontal fluid layers. Exp. Fluids 4, 121141.

2. G. Ahlers , S. Grossmann & D. Lohse 2009 Heat transfer and large-scale dynamics in turbulent Rayleigh–Bénard convection. Rev. Mod. Phys. 81, 503.

3. J. D. Baker 1966 A technique for the precise measurement of small fluid velocities. J. Fluid Mech. 26 (3), 573575.

5. T. Fuji 1963 Theory of the steady laminar natural convection above a horizontal line source and a point heat source. Intl J. Heat Mass Transfer 6, 597606.

6. D. Funfschilling & G. Ahlers 2004 Plume motion and large scale circulation in a cylindrical Rayleigh–Bénard cell. Phys. Rev. Lett. 92 (19), 194502.

7. B. Gebhart , L. Pera & A. W. Schorr 1970 Steady laminar natural convection plume above a horizontal line heat source. Intl J. Heat Mass Transfer 13, 161171.

9. W. N. Gill , D. W. Zeh & E. del Casal 1965 Free convection on a horizontal plate. Z. Angew. Math. Phys. 16, 532541.

11. S. Grossman & D. Lohse 2000 Scaling in thermal convection: a unifying theory. J. Fluid Mech. 407, 27.

12. S. Grossman & D. Lohse 2004 Fluctuations in turbulent Rayleigh Bénard convection: the role of plumes. Phys. Fluids 16, 44624472.

14. T. Haramina & A. Tilgner 2004 Coherent structures in boundary layers of Rayleigh–Bénard convection. Phys. Rev. E 69, 056306.

16. R. B. Husar & E. M. Sparrow 1968 Patterns of free convection flow adjacent to horizontal heated surfaces. Intl J. Heat Mass Transfer 11, 12081211.

17. J. J. Niemela , L. Skrbek , K. R. Sreenivasan & R. J. Donnely 2001 The wind in confined thermal convection. J. Fluid Mech. 449, 169178.

18. L. Pera & B. Gebhart 1973 On the stability of natural convection boundary layer flow over horizontal and slightly inclined surfaces. Intl J. Heat Mass Transfer 16, 11471163.

19. B. A. Puthenveettil , G. Ananthakrishna & J. H. Arakeri 2005 Multifractal nature of plume structure in high Rayleigh number convection. J. Fluid Mech. 526, 245256.

20. B. A. Puthenveettil & J. H. Arakeri 2005 Plume structure in high Rayleigh number convection. J. Fluid Mech. 542, 217249.

21. B. A. Puthenveettil & J. H. Arakeri 2008 Convection due to an unstable density difference across a permeable membrane. J. Fluid Mech. 609, 139170.

22. G. V. Ramareddy & B. A. Puthenveettil 2011 The Pe ∼ 1 regime of convection across a horizontal permeable membrane. J. Fluid Mech. 679, 476504.

23. Z. Rotem & L. Classen 1969 Natural convection above unconfined horizontal surfaces. J. Fluid Mech. 39 (part 1), 173192.

24. O. Shishkina & C. Wagner 2007 Local fluxes in turbulent Rayleigh–Bénard convection. Phys. Fluids 19, 085107.

25. O. Shishkina & C. Wagner 2008 Analyis of sheet-like thermal plumes in turbulent Rayleigh–Bénard convection. J. Fluid Mech. 599, 383404.

27. N. Tamai & T. Asaeda 1984 Sheet like plumes near a heated bottom plate at large Rayleigh number. J. Geophys. Res. 89, 727734.

28. S. A. Theerthan & J. H. Arakeri 1998 A model for near wall dynamics in turbulent Rayleigh–Bénard convection. J. Fluid Mech. 373, 221254.

29. S. A. Theerthan & J. H. Arakeri 2000 Plan form structure and heat transfer in turbulent free convection over horizontal surfaces. Phys. Fluids 12, 884894.

30. A. A. Townsend 1959 Temperature fluctuations over a heated horizontal surface. J. Fluid Mech. 5, 209211.

31. K. Q. Xia , S. Lam & S. Q. Zhou 2002 Heat flux measurement in high Prandtl number turbulent Rayleigh–Bénard convection. Phys. Rev. Lett. 88 (6), 064501.

32. Q. Zhou , C. Sun & K. Q. Xia 2007 Morphological evolution of thermal plumes in turbulent Rayleigh–Bénard convection. Phys. Rev. Lett. 98, 074501.

33. Q. Zhou & K. Q. Xia 2010 Physical and geometrical properties of thermal plumes in turbulent Rayleigh Bénard convection. New J. Phys. 12, 075006.

34. G. Zocchi , E. Moses & A. Libchaber 1990 Coherent structures in turbulent convection, an experimental study. Physica A 166, 387407.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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