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A comparison of turbulent thermal convection between conditions of constant temperature and constant heat flux

Published online by Cambridge University Press:  08 January 2008

R. VERZICCO  and
K. R. SREENIVASAN
R. VERZICCO
Affiliation:
Politecnico di Bari, DIMeG and CEMeC, Via Re David 200, 70125, Bari, Italia
K. R. SREENIVASAN
Affiliation:
International Centre for Theoretical Physics, Strada Costiera 11, 34014 Trieste, Italy
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Abstract

We numerically investigate turbulent thermal convection driven by a horizontal surface of constant heat flux and compare the results with those of constant temperature. Below Ra ≈ 109, where Ra is the Rayleigh number, when the flow is smooth and regular, the heat transport in the two cases is essentially the same. For Ra > 109 the heat transport for imposed heat flux is smaller than that for constant temperature, and is close to experimental data. We provide a simple dimensional argument to indicate that the unsteady emission of thermal plumes renders typical experimental conditions closer to the constant heat flux case.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 595 , 25 January 2008 , pp. 203 - 219
Copyright
Copyright © Cambridge University Press 2008

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References

REFERENCES

Ahlers, G. 2001 Effect of sidewall conductance on heat-transport measurements for turbulent Rayleigh-Benard convection. Phys. Rev. E 63, 015303.Google ScholarPubMed
Ahlers, G., Araujo, F. F., Funfshilling, D., Grossmann, S. & Lohse, D. 2007 Non-Oberbeck-Boussinesq Effects in Gaseous Rayleigh-Bnard Convection Phys. Rev. Lett. 98, 054501.Google Scholar
Ahlers, G. & Xu, X. 2001 Prandtl number dependence of heat transport in turbulent Rayleigh–Bénard convection Phys. Rev. Lett. 86, 3320–3323.Google Scholar
Amati, G., Koal, K., Massaioli, F., Sreenivasan, K. R. & Verzicco, R. 2005 High-Rayleigh number turbulent thermal convection under strictly Boussinesq approximation. Phys. Fluids 17, 121701.Google Scholar
Ashkenazi, S. & Steinberg, V. 1999 High Rayleigh number turbulent convection in a gas near the gas–liquid critical point. Phys. Rev. Lett. 83, 3641–3644.Google Scholar
Belmonte, A., Tilgner, A. & Libchaber, A. 1994 Temperature and velocity boundary layers in turbulent convection Phys. Rev. E 50, 269–279.Google ScholarPubMed
Brown, E., Nikolaenko, A., Funfschilling, D. & Ahlers, G. 2005 Heat transprt in turbulent Rayleigh-Benard convection: Effect of finite top- and bottom-plate conductivity. Phys. Fluids 17, 075108.CrossRefGoogle Scholar
Busse, F. H. & Riahi, N. 1980 Nonlinear convection in a layer with nearly insulating boundaries. J. Fluid Mech. 96, 243–256.Google Scholar
Castaing, B., Gunaratne, G., Heslot, F., Kadanoff, L., Libchaber, A., Thomae, S., Wu, X. Z., Zaleski, S. & Zanetti, G. 1989 Scaling of hard thermal turbulence in Rayleigh-Bénard convection. J. Fluid Mech. 204, 1–30.Google Scholar
Chaumat, S., Castaing, B. & Chillá, F. 2002 Rayleigh-Bénard cells: influence of the plate properties Advances in Turbulence IX, Proc. 9 th Euro. Turb. Conf. (ed. Castro, I. P. & Hancock, P. E..) CIMNe, Barcelona 2002, id:46,1.Google Scholar
Chavanne, X., Chillá, F., Chabaud, B., Castaing, B. & Hebral, B. 2001 Turbulent Rayleigh-Bénard convection in gaseous and liquid He. Phys. Fluids 13, 1300–1320.CrossRefGoogle Scholar
Chillá, F., Rastello, M., Chaumat, S. & Castaing, B. 2004 Ultimate regime in Rayleigh-Bénard convection: The role of plates. Phys. Fluids 16, 2452–2456.Google Scholar
Cioni, S., Ciliberto, S. & Sommeria, J. 1997 Strongly turbulent Rayleigh-Bénard convection in mercury: comparison with results at moderate Prandtl number. J. Fluid Mech. 335, 111–140.CrossRefGoogle Scholar
Du Puits, R., Resagk, C., Tilgner, A., Busse, F. H. & Thess, A. 2007 Structure of thermal boundary layers in turbulent Rayleigh Bénard convection. J. Fluid Mech. 572, 231–254.CrossRefGoogle Scholar
Fleisher, A. S. & Goldstein, R. J. 2002 High Rayleigh number convection of pressurized gases in a horizontal enclosure. J. Fluid Mech. 469, 1–12.Google Scholar
Grossmann, S. & Lohse, D. 2001 Thermal convection for large Prandtl numbers. Phys. Rev. Lett. 86, 3316–3319.CrossRefGoogle ScholarPubMed
Grossmann, S. & Lohse, D. 2004 Fluctuations in turbulent Rayleigh-Bérnard convection. Phys. Fluids 16, 4462–4472.Google Scholar
Hunt, J. C. R., Vrieling, A. J., Nieuwstadt, F. T. M. & Fernando, H. J. S. 2003 The influence of the thermal diffusivity of the lower boundary on eddy motion in convection. J. Fluid Mech. 491, 183–205.CrossRefGoogle Scholar
Malkus, M. V. R. 1954 Heat transport and spectrum of thermal turbulence. Proc. R. Soc. Lond. A 225, 196.Google Scholar
Niemela, J. J., Skrbek, L., Sreenivasan, K. R. & Donnelly, R. J. 2000 Turbulent convection at very high Rayleigh numbers. Nature 404, 837–840.Google Scholar
Niemela, J. J., Skrbek, L., Sreenivasan, K. R. & Donnelly, R. J. 2001 The wind in confined thermal convection. J. Fluid Mech. 449, 169–178.CrossRefGoogle Scholar
Niemela, J. J. & Sreenivasan, K. R. 2002 Thermal fluctuations and their ordering in turbulent convection. Physica A 315, 203–214.Google Scholar
Niemela, J. J. & Sreenivasan, K. R. 2003 Confined turbulent convection. J. Fluid Mech. 481, 355–384.Google Scholar
Niemela, J. J. & Sreenivasan, K. R. 2006 Turbulent convection at high Rayleigh numbers and aspect ratio 4. J. Fluid Mech. 481, 355–384.Google Scholar
Nikolaenko, A., Brown, E., Funfschilling, D. & Ahlers, G. 2005 Heat transport by turbulent Rayleigh-Benard convection in cylindrical cells with aspect ratio one and less. J. Fluid Mech. 523, 251–260.CrossRefGoogle Scholar
Puthenveettil, B. A. & Arakeri, J. H. 2005 Plume structure in high-Rayleigh-number convection. J. Fluid Mech. 542, 217–249.Google Scholar
Roche, P. E., Castaing, B., Chabaud, B., Hébral, B. & Sommeria, J. 2001 Side wall effects in Rayleigh-Bénard experiments. Euro. Phys. J. B 24, 405–408.CrossRefGoogle Scholar
Roche, P. E., Castaing, B., Chabaud, B. & Hebral, B. 2002 Prandtl and Rayleigh numbers dependences in Rayleigh–Bénard convection. Europhys. Lett. E 58, 693–698.CrossRefGoogle Scholar
Shishkina, O. & Wagner, C. 2006 Analysis of thermal dissipation rates in turbulent Rayleigh-Bénard convection. J. Fluid Mech. 546, 51–60.Google Scholar
Shraiman, B. I. & Siggia, E. D. 1990 Heat transport in high Rayleigh number convection. Phys. Rev. A 42, 3650–3653.CrossRefGoogle ScholarPubMed
Sparrow, E. M., Goldstein, R. J. & Jonsson, V. K. 1964 Thermal instability in a horizontal fluid layer: effect of boundary conditions and non-linear temperature profile. J. Fluid Mech. 20, 35–46.CrossRefGoogle Scholar
Stringano, G. & Verzicco, R. 2006 Mean flow structure in thermal convection in a cylindrical cell of aspect ratio one half. J. Fluid Mech. 548, 1–16.CrossRefGoogle Scholar
Swartzrauber, P. N. 1974 A direct method for the discrete solution of separable elliptic equations. SIAM J. Numer. Anal. 11, 1136–1150.Google Scholar
Theerthan, A. S. & Arakeri, J. H. 1998 A model for near-wall dynamics in turbulent Rayleigh-Bénard convection. J. Fluid Mech. 373, 221–254.Google Scholar
Verzicco, R. 2002 Side wall finite conductivity effects in confined turbulent thermal convection. J. Fluid Mech. 473, 201–210.Google Scholar
Verzicco, R. 2003 Turbulent thermal convection in a closed domain: viscous boundary layer and mean flow effects Euro. Phys. J. B 35, 133–141.Google Scholar
Verzicco, R. 2004 Effect of non-perfect thermal sources in turbulent thermal convection. Phys. Fluids 16, 1965–1979.Google Scholar
Verzicco, R. & Camussi, R. 2003 Numerical experiments on strongly turbulent thermal convection in a slender cylindrical cell. J. Fluid Mech. 477, 19–49.CrossRefGoogle Scholar
Verzicco, R. & Orlandi, P. 1996 A finite-difference scheme for three-dimensional incompressible flow in cylindrical coordinates. J. Comput. Phys. 123, 402–414.Google Scholar
Wu, X.-Z. 1991 Along a road to developed turbulence: free thermal convection in low temperature helium gas. PhD thesis, University of Chicago.Google Scholar
Xia, K. Q., Lam, S. & Zhou, S. Q. 2002 Heat-Flux measurement in high-Prandtl-number turbulent Rayleigh-Bénard convection. Phys. Rev. Lett. 88, 064501-1–4.Google Scholar