Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-17T03:24:35.844Z Has data issue: false hasContentIssue false
  • English
  • Français

Controlling flow reversal in two-dimensional Rayleigh–Bénard convection

Published online by Cambridge University Press:  25 March 2020

Shengqi Zhang Open the ORCID record for Shengqi Zhang [Opens in a new window] ,
Zhenhua Xia Open the ORCID record for Zhenhua Xia [Opens in a new window] ,
Quan Zhou Open the ORCID record for Quan Zhou [Opens in a new window]  and
Shiyi Chen
Shengqi Zhang
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, Peking University, Beijing 100871, PR China
Zhenhua Xia*
Affiliation:
Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, PR China
Quan Zhou
Affiliation:
Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, Shanghai University, Shanghai 200072, PR China
Shiyi Chen*
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, Peking University, Beijing 100871, PR China Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, PR China
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper, we report that reversals of large-scale circulation in two-dimensional Rayleigh–Bénard convection could be suppressed or enhanced by imposing local constant-temperature control on sidewalls. When the control area is away from the centre of the sidewalls, the control can successfully eliminate the flow reversal if the size of the control region is large enough. With a proper location, the width can be as small as 1 % of the system size. When the control region is located around the centre, the control may enhance the flow reversal. It may also stimulate the occurrence of a double-roll mode when the control is located in the centre. Explanations are also discussed based on the twofold effects of the control region on the nearby plumes and the concept of symmetry. The present work provides a new way to control the flow reversals in Rayleigh–Bénard convection through modifying sidewall boundary conditions.

JFM classification

Turbulent Flows: Turbulent convection
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 891 , 25 May 2020 , R4
Copyright
© The Author(s), 2020. Published by 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.)

References

Ahlers, G., Grossmann, S. & Lohse, D. 2009 Heat transfer and large scale dynamics in turbulent Rayleigh–Bénard convection. Rev. Mod. Phys. 81 (2), 503–537.CrossRefGoogle Scholar
Araujo, F. F., Grossmann, S. & Lohse, D. 2005 Wind reversals in turbulent Rayleigh–Bénard convection. Phys. Rev. Lett. 95, 084502.CrossRefGoogle ScholarPubMed
Assaf, M., Angheluta, L. & Goldenfeld, N. 2011 Rare fluctuations and large-scale circulation cessations in turbulent convection. Phys. Rev. Lett. 107, 044502.CrossRefGoogle ScholarPubMed
Benzi, R. 2005 Flow reversal in a simple dynamical model of turbulence. Phys. Rev. Lett. 95, 024502.CrossRefGoogle Scholar
Brown, E. & Ahlers, G. 2007 Large-scale circulation model for turbulent Rayleigh–Bénard convection. Phys. Rev. Lett. 98, 134501.CrossRefGoogle ScholarPubMed
Brown, E. & Ahlers, G. 2008a Azimuthal asymmetries of the large-scale circulation in turbulent Rayleigh–Bénard convection. Phys. Fluids 20 (10), 105105.Google Scholar
Brown, E. & Ahlers, G. 2008b A model of diffusion in a potential well for the dynamics of the large-scale circulation in turbulent Rayleigh–Bénard convection. Phys. Fluids 20, 075101.Google Scholar
Brown, E., Nikolaenko, A. & Ahlers, G. 2005 Reorientation of the large-scale circulation in turbulent Rayleigh–Bénard convection. Phys. Rev. Lett. 95, 084503.CrossRefGoogle ScholarPubMed
Chandra, M. & Verma, M. K. 2011 Dynamics and symmetries of flow reversals in turbulent convection. Phys. Rev. E 83, 067303.Google ScholarPubMed
Chandra, M. & Verma, M. K. 2013 Flow reversals in turbulent convection via vortex reconnections. Phys. Rev. Lett. 110, 114503.CrossRefGoogle ScholarPubMed
Chen, X., Huang, S.-D., Xia, K.-Q. & Xi, H.-D. 2019 Emergence of substructures inside the large-scale circulation induces transition in flow reversals in turbulent thermal convection. J. Fluid Mech. 877, R1.CrossRefGoogle Scholar
Chong, K. L., Wagner, S., Kaczorowski, M., Shishkina, O. & Xia, K.-Q. 2018 Effect of Prandtl number on heat transport enhancement in Rayleigh–Bénard convection under geometrical confinement. Phys. Rev. Fluids 3, 013501.CrossRefGoogle 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
Grossmann, S. & Lohse, D. 2000 Scaling in thermal convection: a unifying theory. J. Fluid Mech. 407, 27–56.CrossRefGoogle Scholar
Grossmann, S. & Lohse, D. 2001 Thermal convection for large Prandtl numbers. Phys. Rev. Lett. 86, 3316–3319.CrossRefGoogle ScholarPubMed
Grossmann, S. & Lohse, D. 2002 Prandtl and Rayleigh number dependence of the Reynolds number in turbulent thermal convection. Phys. Rev. E 66, 016305.Google ScholarPubMed
Huang, S.-D., Wang, F., Xi, H.-D. & Xia, K.-Q. 2015 Comparative experimental study of fixed temperature and fixed heat flux boundary conditions in turbulent thermal convection. Phys. Rev. Lett. 115, 154502.CrossRefGoogle ScholarPubMed
Krishnamurti, R. & Howard, L. N. 1981 Large-scale flow generation in turbulent convection. Proc. Natl Acad. Sci. USA 78 (4), 1981–1985.CrossRefGoogle ScholarPubMed
Lohse, D. & Xia, K.-Q. 2010 Small-scale properties of turbulent Rayleigh–Bénard convection. Annu. Rev. Fluid Mech. 42, 335–364.CrossRefGoogle Scholar
Ni, R., Huang, S.-D. & Xia, K.-Q. 2015 Reversals of the large-scale circulation in quasi-2D Rayleigh–Bénard convection. J. Fluid Mech. 778, R5.CrossRefGoogle Scholar
Petschel, K., Wilczek, M., Breuer, M., Friedrich, R. & Hansen, U. 2011 Statistical analysis of global wind dynamics in vigorous Rayleigh–Bénard convection. Phys. Rev. E 84, 026309.Google ScholarPubMed
Podvin, B. & Sergent, A. 2015 A large-scale investigation of wind reversal in a square Rayleigh–Bénard cell. J. Fluid Mech. 766, 172–201.CrossRefGoogle Scholar
van del Poel, E. P., Stevens, R. J. A. M. & Lohse, D. 2013 Comparison between two- and three-dimensional Rayleigh–Bénard convection. J. Fluid Mech. 736, 177–194.CrossRefGoogle Scholar
Ripesi, P., Biferale, L., Sbragaglia, M. & Wirth, A. 2014 Natural convection with mixed insulating and conducting boundary conditions: low-and high-Rayleigh-number regimes. J. Fluid Mech. 742, 636–663.CrossRefGoogle Scholar
Shishkina, O., Stevens, R. J. A. M., Grossmann, S. & Lohse, D. 2010 Boundary layer structure in turbulent thermal convection and its consequences for the required numerical resolution. New J. Phys. 12, 075022.Google Scholar
Sreenivasan, K., Bershadskii, A. & Niemela, J. J. 2002 Mean wind and its reversal in thermal convection. Phys. Rev. E 65, 056306.Google ScholarPubMed
Stevens, R. J. A. M., Lohse, D. & Verzicco, R. 2014 Sidewall effects in Rayleigh–Bénard convection. J. Fluid Mech. 741, 1–27.CrossRefGoogle Scholar
Sugiyama, K., Calzavarini, E., Grossmann, S. & Lohse, D. 2009 Flow organization in two-dimensional non-Oberbeck–Boussinesq Rayleigh–Bénard convection in water. J. Fluid Mech. 637, 105–135.CrossRefGoogle Scholar
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.CrossRefGoogle ScholarPubMed
Sun, C., Xi, H.-D. & Xia, K.-Q. 2005 Azimuthal symmetry, flow dynamics, and heat transport in turbulent thermal convection in a cylinder with an aspect ratio of 0.5. Phys. Rev. Lett. 95, 074502.CrossRefGoogle Scholar
Tangborn, A. 1992 A two-dimensional instability in a mixed convection flow with spatially periodic temperature boundary conditions. Phys. Fluids A 4, 1583–1586.CrossRefGoogle Scholar
Tsuji, Y., Mizuno, T., Mashiko, T. & Sano, M. 2005 Mean wind in convective turbulence of mercury. Phys. Rev. Lett. 94, 034501.CrossRefGoogle ScholarPubMed
Vasil’ev, A. & Frick, P. G. 2011 Reversals of large-scale circulation in turbulent convection in rectangular cavities. JETP Lett. 93, 330–334.CrossRefGoogle Scholar
Verma, M. K., Ambhire, S. C. & Pandey, A. 2015 Flow reversals in turbulent convection with free-slip walls. Phys. Fluids 27, 047102.CrossRefGoogle Scholar
Wagner, S. & Shishkina, O. 2013 Aspect-ratio dependency of Rayleigh–Bénard convection in box-shaped containers. Phys. Fluids 25, 085110.CrossRefGoogle Scholar
Wan, Z. H., Wei, P., Verzicco, R., Lohse, D., Ahlers, G. & Stevens, R. J. A. M. 2019 Effect of sidewall on heat transfer and flow structure in Rayleigh–Bénard convection. J. Fluid Mech. 881, 218–243.CrossRefGoogle Scholar
Wang, Q., Xia, S.-N., Wang, B.-F., Sun, D.-J., Zhou, Q. & Wan, Z.-H. 2018 Flow reversals in two-dimensional thermal convection in tilted cells. J. Fluid Mech. 849, 355–372.CrossRefGoogle Scholar
Wang, Q., Xu, B.-L., Xia, S.-N., Wan, Z.-H. & Sun, D.-J. 2017 Thermal convection in a tilted rectangular cell with aspect ratio 0.5. Chin. Phys. Lett. 34, 104401.CrossRefGoogle Scholar
Xi, H.-D. & Xia, K.-Q. 2007 Cessations and reversals of the large-scale circulation in turbulent thermal convection. Phys. Rev. E 75, 066307.Google ScholarPubMed
Xi, H. D. & Xia, K.-Q. 2008 Flow mode transitions in turbulent thermal convection. Phys. Fluids 20, 055104.CrossRefGoogle Scholar
Xi, H.-D., Zhou, Q. & Xia, K.-Q. 2006 Azimuthal motion of the mean wind in turbulent thermal convection. Phys. Rev. E 73, 056312.Google ScholarPubMed
Xia, S.-N., W., Z.-H., Liu, S., Wang, Q. & Sun, D.-J. 2016 Flow reversals in Rayleigh–Bénard convection with non-Oberbeck–Boussinesq effects. J. Fluid Mech. 798, 628–642.CrossRefGoogle Scholar
Zhang, Y.-Z. & Bao, Y. 2015 Direct solution method of efficient large-scale parallel computation for 3D turbulent Rayleigh–Benard convection. Act. Phys. Sin. 64 (15), 154702.Google Scholar

Zhang et al. supplementary movie 1

Left: Temperature contours and velocity vectors of the whole domain; Right: Contours of temperature and $F^b_x$ in $[0.1,0.5]\times[-0.45,-0.05]$ at $Ra=5\times 10^7, Pr=2$ without sidewall control.
Download Zhang et al. supplementary movie 1(Video)
Video 13.2 MB

Zhang et al. supplementary movie 2

Left: Temperature contours and velocity vectors of the whole domain; Right: Contours of temperature and $F^b_x$ in $[0.1,0.5]\times[-0.45,-0.05]$ at $Ra=5\times 10^7, Pr=2$ with $h_c=0.2$ and $\delta_c=0.02$.
Download Zhang et al. supplementary movie 2(Video)
Video 8.9 MB

Zhang et al. supplementary movie 3

Left: Temperature contours and velocity vectors of the whole domain; Right: Contours of temperature and $F^b_x$ in $[0.1,0.5]\times[-0.45,-0.05]$ at $Ra=5\times 10^7, Pr=2$ with $h_c=0.2$ and $\delta_c=0.06$.
Download Zhang et al. supplementary movie 3(Video)
Video 11 MB

Zhang et al. supplementary movie 4

Left: Temperature contours and velocity vectors of the whole domain; Right: Contours of temperature and $F^b_x$ in $[0.1,0.5]\times[-0.45,-0.05]$ at $Ra=5\times 10^7, Pr=2$ with $h_c=0.4$ and $\delta_c=0.06$.
Download Zhang et al. supplementary movie 4(Video)
Video 11.5 MB

Zhang et al. supplementary movie 5

Left: Temperature contours and velocity vectors of the whole domain; Right: Contours of temperature and $F^b_x$ in $[0.1,0.5]\times[-0.2,0.2]$ at $Ra=5\times 10^7, Pr=6$ with $h_c=0.0$ and $\delta_c=0.06$.
Download Zhang et al. supplementary movie 5(Video)
Video 12.2 MB