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Stabilizing/destabilizing the large-scale circulation in turbulent Rayleigh–Bénard convection with sidewall temperature control

Published online by Cambridge University Press:  09 March 2021

Shengqi Zhang Open the ORCID record for Shengqi Zhang [Opens in a new window] ,
Xin Chen Open the ORCID record for Xin Chen [Opens in a new window] ,
Zhenhua Xia Open the ORCID record for Zhenhua Xia [Opens in a new window] ,
Heng-Dong Xi Open the ORCID record for Heng-Dong Xi [Opens in a new window] ,
Quan Zhou Open the ORCID record for Quan Zhou [Opens in a new window]  and
Shiyi Chen Open the ORCID record for Shiyi Chen [Opens in a new window]
Shengqi Zhang
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, Peking University, Beijing 100871, PR China
Xin Chen
Affiliation:
Institute of Extreme Mechanics and School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, PR China
Zhenhua Xia*
Affiliation:
Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, PR China
Heng-Dong Xi
Affiliation:
Institute of Extreme Mechanics and School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, 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: xiazh@zju.edu.cn, chensy@sustech.edu.cn
†Email addresses for correspondence: xiazh@zju.edu.cn, chensy@sustech.edu.cn
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Abstract

In this paper, we designed two different configurations with locally isothermal sidewalls, where the temperature is set to be the bulk temperature, to control the large-scale circulation in turbulent Rayleigh–Bénard convection, namely two-point control and four-point control. At fixed Rayleigh number $Ra=10^8$ and Prandtl number $Pr=2$, a series of direct numerical simulations are performed on both two-dimensional (2-D) and quasi-two-dimensional (quasi-2-D) cavities with both types of control, where the width of the control area is fixed at $\delta _c=0.05$ and the vertical distance from the cavity centre $h_c$ varies from 0 to 0.45 with an interval of 0.05. Our results show that the control effect depends on $h_c$, the control configurations as well as the flow dimensions. For 2-D cavities, both two-point control and four-point control suppress the flow reversal when $h_c \geq 0.05$, accompanied by the enhancement of vertical heat transfer and the strength of the large-scale circulation. For quasi-2-D cavities, the suppression of the flow reversals is obvious with two-point control and $h_c\geq 0.05$, while the effect is rather limited with four-point control. Further experiments with $Pr=5.7$ and $Ra$ up to $7.36\times10^8$ show that two-point control with $h_c=0.15$ can effectively suppress the flow reversal, while two-point control with $h_c=0$ can suppress the reversals at low $Ra=1.93\times 10^8$ and activate them at higher $Ra=7.36\times 10^8$, which agrees well with our numerical simulations.

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 915 , 25 May 2021 , A14
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© The Author(s), 2021. Published by Cambridge University Press

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References

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. 2008 a Azimuthal asymmetries of the large-scale circulation in turbulent Rayleigh–Bénard convection. Phys. Fluids 20 (10), 105105.CrossRefGoogle Scholar
Brown, E. & Ahlers, G. 2008 b 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.CrossRefGoogle Scholar
Brown, E., Funfschilling, D. & Ahlers, G. 2007 Anomalous Reynolds-number scaling in turbulent Rayleigh–Bénard convection. J. Stat. Mech.-Theory Exp. 2007 (10), P10005.CrossRefGoogle 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
Castillo-Castellanos, A., Sergent, A., Podvin, B. & Rossi, M. 2019 Cessation and reversals of large-scale structures in square Rayleigh–Bénard cells. J. Fluid Mech. 877, 922–954.CrossRefGoogle Scholar
Chandra, M. & Verma, M.K. 2011 Dynamics and symmetries of flow reversals in turbulent convection. Phys. Rev. E 83, 067303.CrossRefGoogle 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
Chen, X., Wang, D.-P. & Xi, H.-D. 2020 Reduced flow reversals in turbulent convection in the absence of corner vortices. J. Fluid Mech. 891, R5.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
van Doorn, E., Dhruva, B., Sreenivasan, K.R. & Cassella, V. 2000 Statistics of wind direction and its increments. Phys. Fluids 12 (6), 1529–1534.CrossRefGoogle Scholar
Glatzmaiers, G.A. & Roberts, P.H. 1995 A three-dimensional self-consistent computer simulation of a geomagnetic field reversal. Nature 377 (6546), 203–209.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.CrossRefGoogle ScholarPubMed
Hartmann, D.L., Moy, L.A. & Fu, Q. 2001 Tropical convection and the energy balance at the top of the atmosphere. J. Climate 14 (24), 4495–4511.2.0.CO;2>CrossRefGoogle Scholar
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
Huang, S.-D. & Xia, K.-Q. 2016 Effects of geometric confinement in quasi-2-d turbulent Rayleigh–Bénard convection. J. Fluid Mech. 794, 639–654.CrossRefGoogle Scholar
Kooij, G., Botchev, M., Frederix, E., Geurts, B., Horn, S., Lohse, D., van der Poel, E., Shishkina, O., Stevens, R.J. & Verzicco, R. 2018 Comparison of computational codes for direct numerical simulations of turbulent Rayleigh–Bénard convection. Comput. Fluids 166, 1–8.CrossRefGoogle Scholar
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.CrossRefGoogle 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
Qiu, X.-L., Xia, K.-Q. & Tong, P. 2005 Experimental study of velocity boundary layer near a rough conducting surface in turbulent natural convection. J. Turbul. 6, N30.CrossRefGoogle Scholar
Sreenivasan, K., Bershadskii, A. & Niemela, J.J. 2002 Mean wind and its reversal in thermal convection. Phys. Rev. E 65, 056306.CrossRefGoogle ScholarPubMed
Stevens, R.J., Lohse, D. & Verzicco, R. 2014 Sidewall effects in Rayleigh–Bénard convection. J. Fluid Mech. 741, 1–27.CrossRefGoogle Scholar
Sugiyama, K., Ni, R., Stevens, R.J., 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
Tsuji, Y., Mizuno, T., Mashiko, T. & Sano, M. 2005 Mean wind in convective turbulence of mercury. Phys. Rev. Lett. 94, 034501.CrossRefGoogle ScholarPubMed
Van Der Poel, E.P., Ostilla-Mónico, R., Donners, J. & Verzicco, R. 2015 A pencil distributed finite difference code for strongly turbulent wall-bounded flows. Comput. Fluids 116, 10–16.CrossRefGoogle Scholar
Vasil'ev, A. & Frick, P.G. 2011 Reversals of large-scale circulation in turbulent convection in rectangular cavities. J. Expl Theor. Phys. 93, 330–334.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. 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
Wang, B.-F., Zhou, Q. & Sun, C. 2020 Vibration-induced boundary-layer destabilization achieves massive heat-transport enhancement. Sci. Adv. 6, eaaz8239.CrossRefGoogle ScholarPubMed
Xi, H.-D. & Xia, K.-Q. 2007 Cessations and reversals of the large-scale circulation in turbulent thermal convection. Phys. Rev. E 75, 066307.CrossRefGoogle ScholarPubMed
Xi, H.-D. & Xia, K.-Q. 2008 Azimuthal motion, reorientation, cessation, and reversal of the large-scale circulation in turbulent thermal convection: a comparative study in aspect ratio one and one-half geometries. Phys. Rev. E 78, 036326.CrossRefGoogle ScholarPubMed
Xia, S.-N., Wan, 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., 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.CrossRefGoogle Scholar
Zhang, S., Xia, Z., Zhou, Q. & Chen, S. 2020 Controlling flow reversal in two-dimensional Rayleigh–Bénard convection. J. Fluid Mech. 891, R4.CrossRefGoogle Scholar
Zhu, X., Stevens, R.J.A.M., Shishkina, O., Verzicco, R. & Lohse, D. 2019 $Nu\sim Ra^{1/2}$ scaling enabled by multiscale wall roughness in Rayleigh–Bénard turbulence. J. Fluid Mech. 869, R4.CrossRefGoogle Scholar