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Turbulent Rayleigh–Bénard convection in an annular cell

  • Xu Zhu (a1), Lin-Feng Jiang (a2), Quan Zhou (a1) and Chao Sun (a2)

Abstract

We report an experimental study of turbulent Rayleigh–Bénard (RB) convection in an annular cell of water (Prandtl number $Pr=4.3$ ) with a radius ratio $\unicode[STIX]{x1D702}\simeq 0.5$ . Global quantities, such as the Nusselt number $Nu$ and the Reynolds number $Re$ , and local temperatures were measured over the Rayleigh range $4.2\times 10^{9}\leqslant Ra\leqslant 4.5\times 10^{10}$ . It is found that the scaling behaviours of $Nu(Ra)$ , $Re(Ra)$ and the temperature fluctuations remain the same as those in the traditional cylindrical cells; both the global and local properties of turbulent RB convection are insensitive to the change of cell geometry. A visualization study, as well as local temperature measurements, shows that in spite of the lack of the cylindrical core, there also exists a large-scale circulation (LSC) in the annular system: thermal plumes organize themselves with the ascending hot plumes on one side and the descending cold plumes on the opposite side. Near the upper and lower plates, the mean flow moves along the two circular branches. Our results further reveal that the dynamics of the LSC in this annular geometry is different from that in the traditional cylindrical cell, i.e. the orientation of the LSC oscillates in a narrow azimuthal angle range, and no cessations, reversals or net rotation were detected.

Copyright

Corresponding author

Email addresses for correspondence: qzhou@shu.edu.cn, chaosun@tsinghua.edu.cn

References

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Ahlers, G., Grossmann, S. & Lohse, D. 2009 Heat transfer and large scale dynamics in turbulent Rayleigh–Bénard convection. Rev. Mod. Phys. 81, 503537.10.1103/RevModPhys.81.503
Araujo, F. F., Grossmann, S. & Lohse, D. 2005 Wind reversals in turbulent Rayleigh–Bénard convection. Phys. Rev. Lett. 95, 084502.
Bao, Y., Chen, J., Liu, B.-F., She, Z.-S., Zhang, J. & Zhou, Q. 2015 Enhanced heat transport in partitioned thermal convection. J. Fluid Mech. 784, R5.
Benzi, R. & Verzicco, R. 2008 Numerical simulations of flow reversal in Rayleigh–Bénard convection. Europhys. Lett. 81, 64008.
Brown, E. & Ahlers, G. 2009 The origin of oscillations of the large-scale circulation of turbulent Rayleigh–Bénard convection. J. Fluid Mech. 638, 383400.10.1017/S0022112009991224
Brown, E., Funfschilling, D. & Ahlers, G. 2007 Anomalous Reynolds-number scaling in turbulent Rayleigh–Bénard convection. J. Stat. Mech. 10, 10005.
Brown, E., Nikolaenko, A. & Ahlers, G. 2005 Reorientation of the large-scale circulation in turbulent Rayleigh–Bénard convection. Phys. Rev. Lett. 95, 084503.
Castaing, B., Gnuaratne, 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 turbulent convection. J. Fluid Mech. 204, 130.10.1017/S0022112089001643
Chandra, M. & Verma, M. K. 2013 Flow reversals in turbulent convection via vortex reconnections. Phys. Rev. Lett. 110, 114503.
Chavanne, X., Chilla, F., Chabaud, B., Castaing, B. & Hebral, B. 2001 Turbulence Rayleigh–Bénard convection in gaseous and liquid He. Phys. Fluids 13, 13001320.
Chillà, F., Rastello, M., Chaumat, S. & Castaing, B. 2004 Long relaxation times and tilt sensitivity in Rayleigh–Bénard turbulence. Eur. Phys. J. B 40, 223227.
Chilla, F. & Schumacher, J. 2012 New perspectives in turbulent Rayleigh–Bénard convection. Eur. Phys. J. E 35, 58.
Daya, Z. A. & Ecke, R. E. 2001 Does turbulent convection feel the shape of the container? Phys. Rev. Lett. 87, 184501.
Du, Y.-B. & Tong, P. 2001 Temperature fluctuations in a convection cell with rough upper and lower surfaces. Phys. Rev. E 63, 046303.
Foroozani, N., Niemela, J. J., Armenio, V. & Sreenivasan, K. R. 2017 Reorientations of the large-scale flow in turbulent convection in a cube. Phys. Rev. E 95, 033107.
Funfschilling, D. & Ahlers, G. 2004 Plume motion and large-scale circulation in a cylindrical Rayleigh–Bénard cell. Phys. Rev. Lett. 92, 194502.
Funfschilling, D., Brown, E., Nikolaenko, A. & Ahlers, G. 2005 Heat transport by turbulent Rayleigh–Bénard convection in cylindrical samples with aspect ratio one and larger. J. Fluid Mech. 536, 145154.
Grossmann, S. & Lohse, D. 2002 Prandtl and Rayleigh number dependence of the Reynolds number in turbulent thermal convection. Phys. Rev. E 66, 016305.
Grossmann, S. & Lohse, D. 2004 Fluctuations in turbulent Rayleigh–Bénard convection: the role of plumes. Phys. Fluids 16, 44624472.
He, X.-Z., Bodenschatz, E. & Ahlers, G. 2016 Azimuthal diffusion of the large-scale-circulation plane, and absence of significant non-Boussinesq effects, in turbulent convection near the ultimate-state transition. J. Fluid Mech. 791, R3.
Huang, S.-D., Kaczorowski, M., Ni, R. & Xia, K.-Q. 2013 Confinement-induced heat-transport enhancement in turbulent thermal convection. Phys. Rev. Lett. 111, 104501.
Huang, Y.-X. & Zhou, Q. 2013 Counter-gradient heat transport in two-dimensional turbulent Rayleigh–Bénard convection. J. Fluid Mech. 737, R3.
Lohse, D. & Xia, K.-Q. 2010 Small-scale properties of turbulent Rayleigh–Bénard convection. Annu. Rev. Fluid Mech. 42, 335364.10.1146/annurev.fluid.010908.165152
Mishra, P. K., De, A. K., Verma, M. K. & Eswaran, V. 2011 Dynamics of reorientaiton and reversal of large-scale-flow in Rayleigh–Bénard convection. J. Fluid Mech. 668, 480499.10.1017/S0022112010004830
Niemela, J. J. & Sreenivasan, K. R. 2003 Rayleigh-number evolution of large-scale coherent motion in turbulent convection. Europhys. Lett. 62, 829833.
Pandey, A., Scheel, J. D. & Schumacher, J. 2018 Turbulent superstructures in Rayleigh–Bénard convection. Nat. Commun. 9, 2118.
van der Poel, E. P., Stevens, J. A. M. & Lohse, D. 2013 Comparison between two- and three-dimensional Rayleigh–Bénard convection. J. Fluid Mech. 736, 177194.
Qiu, X.-L. & Tong, P. 2002 Temperature oscillations in turbulent Rayleigh–Bénard convection. Phys. Rev. E 66, 026308.
Song, H. & Tong, P. 2010 Scaling laws in turbulent Rayleigh–Bénard convection under different geometry. Europhys. Lett. 90, 44001.
Stevens, R. J. A. M., Blass, A., Zhu, X., Verzicco, R. & Lohse, D. 2018 Turbulent thermal superstructures in Rayleigh–Bénard convection. Phys. Rev. Fluid 3, 041501(R).
Stevens, R. J. A. M., Clercx, H. J. H. & Lohse, D. 2011a Effect of plumes on measuring the large scale circulation in turbulent Rayleigh–Bénard convection. Phys. Fluids 23, 095110.10.1063/1.3620999
Stevens, R. J. A. M., Lohse, D. & Verzicco, R. 2011b Prandtl and Rayleigh number dependence of heat transport in high Rayleigh number thermal convection. J. Fluid Mech. 688, 3143.
Stevens, R. J. A. M., van der Poel, E. P., Grossmann, S. & Lohse, D. 2013 The unifying theory of scaling in thermal convection: the updated prefactors. J. Fluid Mech. 730, 295308.
Sugiyama, K., Ni, R., Stevens, R. J. A. M., Chan, T.-S., Zhou, S.-Q., Xi, H.-D., Sun, C., Grossmann, S., Xia, K.-Q. & Lohse, D. 2010 Flow reversals in thermally driven turbulence. Phys. Rev. Lett. 105, 034503.
Sun, C., Ren, L.-Y., Song, H. & Xia, K.-Q. 2005 Heat transport by turbulent Rayleigh–Bénard convection in 1 m diameter cylindrical cells of widely varying aspect ratio. J. Fluid Mech. 542, 165174.
Sun, C. & Xia, K.-Q. 2005 Scaling of the Reynolds number in turbulent thermal convection. Phys. Rev. E 72, 067302.
Sun, C. & Xia, K.-Q. 2007 Multi-point local temperature measurements inside the conducting plates in turbulent thermal convection. J. Fluid Mech. 570, 479489.
Sun, C. & Zhou, Q. 2014 Experimental techniques for turbulent Taylor–Couette flow and Rayleigh–Bénard convection. Nonlinearity 27, R89R121.
Verzicco, R. 2004 Effects of nonperfect thermal sources in turbulent thermal convection. Phys. Fluids 16, 19651979.
Vogt, T., Horn, S., Grannan, A. M. & Aurnou, M. 2018 Jump rope vortex in liquid metal convection. Proc. Natl Acad. Sci. USA 12, 260115.
Wagner, S., Shishkina, O. & Wagner, C. 2012 Boundary layers and wind in cylindrical Rayleigh–Bénard cells. J. Fluid Mech. 697, 336366.
Wang, B.-F., Wan, Z.-H., Ma, D.-J. & Sun, D.-J. 2014 Rayleigh–Bénard convection in a vertical annular container near the convection threshold. Phys. Rev. E 89, 043014.
Wang, Y., Lai, P.-Y., Song, H. & P., Tong 2018 Mechanism of large-scale flow reversals in turbulent thermal convection. Sci. Adv. 4, eaat7480.
Xi, H.-D., Lam, S. & Xia, K.-Q. 2004 From laminar plumes to organized flows: the onset of large-scale circulation in turbulent thermal convection. J. Fluid Mech. 503, 4756.
Xi, H.-D. & Xia, K.-Q. 2007 The cessations and reversals of the large-scale circulation in turbulent thermal convection. Phys. Rev. E 75, 066307.
Xi, H.-D., Zhang, Y.-B., Hao, J.-T. & Xia, K.-Q. 2016 Higher-order flow modes in turbulent Rayleigh–Bénard convection. J. Fluid Mech. 805, 3151.
Xi, H.-D., Zhou, Q. & Xia, K.-Q. 2006 Azimuthal motion of the mean wind in turbulent thermal convection. Phys. Rev. E 73, 056312.
Xi, H.-D., Zhou, S.-Q., Zhou, Q., Chan, T.-S. & Xia, K.-Q. 2009 Origin of the temperature oscillation in turbulent thermal convection. Phys. Rev. Lett. 102, 044503.10.1103/PhysRevLett.102.044503
Xia, K.-Q. & Lui, S.-L. 1997 Turbulent thermal convection with an obstructed sidewall. Phys. Rev. Lett. 79 (25), 50065009.10.1103/PhysRevLett.79.5006
Xie, Y.-C., Ding, G.-Y. & Xia, K.-Q. 2018 Flow topology transition via global bifurcation in thermally driven turbulence. Phys. Rev. Lett. 120, 214501.
Xie, Y.-C., Wei, P. & Xia, K.-Q. 2013 Dynamics of the large-scale circulation in high-Prandtl-number turbulent thermal convection. J. Fluid Mech. 717, 322346.10.1017/jfm.2012.574
Zhang, Y., Zhou, Q. & Sun, C. 2017 Statistics of kinetic and thermal energy dissipation rates in two-dimensional turbulent Rayleigh–Bênard convection. J. Fluid Mech. 814, 165184.
Zhang, Y.-Z., Sun, C., Bao, Y. & Zhou, Q. 2018 How surface roughness reduces heat transport for small roughness heights in turbulent Rayleigh–Bénard convection. J. Fluid Mech. 836, R2.
Zhou, Q., Liu, B.-F., Li, C.-M. & Zhong, B.-C. 2012 Aspect ratio dependence of heat transport by turbulent Rayleigh–Bénard convection in rectangular cells. J. Fluid Mech. 710, 260276.
Zhou, Q., Xi, H.-D., Zhou, S.-Q., Sun, C. & Xia, K.-Q. 2009 Oscillations of the large-scale circulation in turbulent Rayleigh–Bénard convection: the sloshing mode and its relationship with the torsional mode. J. Fluid Mech. 630, 367390.
Zhou, Q. & Xia, K.-Q. 2013 Thermal boundary layer structure in turbulent Rayleigh–Bénard convection in a rectangular cell. J. Fluid Mech. 721, 199224.
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Type Description Title
VIDEO
Movies

Zhu et al. supplementary movie 1
The shadowgraph movie about the ascending plumes on one side of the annulus cell, and a schematic draw showing the large-scale circulation and the spatial distribution of thermal plumes at $Ra=4.5 imes10^{10}$. The purple frame marks the visualization window.

 Video (9.4 MB)
9.4 MB
VIDEO
Movies

Zhu et al. supplementary movie 2
The shadowgraph movie about the cold plumes moving along the circular branches near the upper plate, and a schematic draw showing the large-scale circulation and the spatial distribution of thermal plumes at $Ra=4.5 imes10^{10}$. The purple frame marks the visualization window.

 Video (10.1 MB)
10.1 MB
VIDEO
Movies

Zhu et al. supplementary movie 3
The shadowgraph movie about the descending plumes on the opposite side of the annulus cell, and a schematic draw showing the large-scale circulation and the spatial distribution of thermal plumes at $Ra=4.5 imes10^{10}$. The purple frame marks the visualization window.

 Video (9.4 MB)
9.4 MB
VIDEO
Movies

Zhu et al. supplementary movie 4
The shadowgraph movie about the hot plumes moving along the circular branches near the lower plate, and a schematic draw showing the large-scale circulation and the spatial distribution of thermal plumes at $Ra=4.5 imes10^{10}$. The purple frame marks the visualization window.

 Video (10.2 MB)
10.2 MB

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