Hostname: page-component-68c7f8b79f-fc4h8 Total loading time: 0 Render date: 2025-12-19T00:55:45.246Z Has data issue: false hasContentIssue false
  • English
  • Français

Strong coupling of flow structure and heat transport in liquid metal thermal convection

Published online by Cambridge University Press:  17 November 2023

Xin-Yuan Chen Open the ORCID record for Xin-Yuan Chen [Opens in a new window] ,
Yi-Chao Xie Open the ORCID record for Yi-Chao Xie [Opens in a new window] ,
Juan-Cheng Yang Open the ORCID record for Juan-Cheng Yang [Opens in a new window]  and
Ming-Jiu Ni Open the ORCID record for Ming-Jiu Ni [Opens in a new window]
Xin-Yuan Chen
Affiliation:
State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi'an Jiaotong University, Xi'an 710049, PR China
Yi-Chao Xie
Affiliation:
State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi'an Jiaotong University, Xi'an 710049, PR China
Juan-Cheng Yang*
Affiliation:
State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi'an Jiaotong University, Xi'an 710049, PR China
Ming-Jiu Ni*
Affiliation:
State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi'an Jiaotong University, Xi'an 710049, PR China School of Engineering Science, University of Chinese Academy of Sciences, Beijing 101408, PR China
*
†Email addresses for correspondence: yangjc@xjtu.edu.cn, mjni@ucas.ac.cn
†Email addresses for correspondence: yangjc@xjtu.edu.cn, mjni@ucas.ac.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

A typical feature of thermal convection is the formation of large-scale flow (LSF) structures of the order of system size. How this structure affects global heat transport is an important issue in the study of thermal convection. We present an experimental study of the coupling between the flow structure and heat transport in liquid metal convection with different degrees of spatial confinement, characterized by the aspect ratio $\varGamma$ of the convection cell. Combining measurements in two convection cells with $\varGamma =1.0$ and 0.5, the study shows that a large-scale circulation (LSC) transports ${\sim }35\,\%$ more heat than a twisted LSC. It is further found that when the LSF is in the form of the LSC state, the system is in a fully developed turbulence state with a $Nu\sim Ra^{0.29}$ scaling for the heat transport. However, the twisted LSC state with a heat transport scaling of $Nu\sim Ra^{0.37}$ appears when the system is not in the fully developed turbulence state. Bistability is observed when the system evolves from the twisted-LSC-dominated to the LSC-dominated state.

Information

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 975 , 25 November 2023 , A21
Check for updates
Copyright
© The Author(s), 2023. 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.)

Article purchase

Temporarily unavailable

References

Ahlers, G., Grossmann, S. & Lohse, D. 2009 Heat transfer and large scale dynamics in turbulent Rayleigh-Bénard convection. Rev. Mod. Phys. 81 (2), 503.10.1103/RevModPhys.81.503CrossRefGoogle Scholar
Aurnou, J.M., Bertin, V., Grannan, A.M., Horn, S. & Vogt, T. 2018 Rotating thermal convection in liquid gallium: multi-modal flow, absent steady columns. J. Fluid Mech. 846, 846–876.10.1017/jfm.2018.292CrossRefGoogle Scholar
Aurnou, J.M. & Olson, P.L. 2001 Experiments on Rayleigh–Bénard convection, magnetoconvection and rotating magnetoconvection in liquid gallium. J. Fluid Mech. 430, 283–307.CrossRefGoogle Scholar
Batchelor, G.K., Howells, I.D. & Townsend, A.A. 1959 Small-scale variation of convected quantities like temperature in turbulent fluid part 2. The case of large conductivity. J. Fluid Mech. 5 (1), 134–139.10.1017/S0022112059000106CrossRefGoogle Scholar
Brown, E. & Ahlers, G. 2006 Rotations and cessations of the large-scale circulation in turbulent Rayleigh–Bénard convection. J. Fluid Mech. 568, 351–386.10.1017/S0022112006002540CrossRefGoogle Scholar
Brown, E. & Ahlers, G. 2009 The origin of oscillations of the large-scale circulation of turbulent Rayleigh–Bénard convection. J. Fluid Mech. 638, 383–400.10.1017/S0022112009991224CrossRefGoogle 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, 111–140.10.1017/S0022112096004491CrossRefGoogle Scholar
Cortet, P., Chiffaudel, A., Daviaud, F. & Dubrulle, B. 2010 Experimental evidence of a phase transition in a closed turbulent flow. Phys. Rev. Lett. 105 (21), 214501.10.1103/PhysRevLett.105.214501CrossRefGoogle Scholar
Elsasser, W.M. 1956 Hydromagnetic dynamo theory. Rev. Mod. Phys. 28 (2), 135.10.1103/RevModPhys.28.135CrossRefGoogle Scholar
Faranda, D., Sato, Y., Saint-Michel, B., Wiertel, C., Padilla, V., Dubrulle, B. & Daviaud, F. 2017 Stochastic chaos in a turbulent swirling flow. Phys. Rev. Lett. 119 (1), 014502.CrossRefGoogle Scholar
Glazier, J.A, Segawa, T., Naert, A. & Sano, M. 1999 Evidence against ‘ultrahard’ thermal turbulence at very high Rayleigh numbers. Nature 398 (6725), 307–310.10.1038/18626CrossRefGoogle Scholar
Grooms, I., Julien, K., Weiss, J.B. & Knobloch, E. 2010 Model of convective Taylor columns in rotating Rayleigh-Bénard convection. Phys. Rev. Lett. 104 (22), 224501.10.1103/PhysRevLett.104.224501CrossRefGoogle ScholarPubMed
Grossmann, S. & Lohse, D. 2000 Scaling in thermal convection: a unifying theory. J. Fluid Mech. 407, 27–56.CrossRefGoogle Scholar
Hartmann, R., Chong, K.L., Stevens, R.J.A.M., Verzicco, R. & Lohse, D. 2021 Heat transport enhancement in confined Rayleigh-Bénard convection feels the shape of the container. Europhys. Lett. 135 (2), 24004.CrossRefGoogle Scholar
Huisman, S.G., Van Der Veen, R.C., Sun, C. & Lohse, D. 2014 Multiple states in highly turbulent Taylor–Couette flow. Nat. Commun. 5 (1), 1–5.10.1038/ncomms4820CrossRefGoogle ScholarPubMed
Ji, D. & Brown, E. 2020 Low-dimensional model of the large-scale circulation of turbulent Rayleigh-Bénard convection in a cubic container. Phys. Rev. E 5 (6), 064606.Google Scholar
Khalilov, R., Kolesnichenko, I., Pavlinov, A., Mamykin, A., Shestakov, A. & Frick, P. 2018 Thermal convection of liquid sodium in inclined cylinders. Phys. Rev. Fluids 3 (4), 043503.10.1103/PhysRevFluids.3.043503CrossRefGoogle Scholar
King, E.M. & Aurnou, J.M. 2013 Turbulent convection in liquid metal with and without rotation. Proc. Natl Acad. Sci. 110 (17), 6688–6693.10.1073/pnas.1217553110CrossRefGoogle ScholarPubMed
Lohse, D. & Xia, K.-Q. 2010 Small-scale properties of turbulent Rayleigh-Bénard convection. Annu. Rev. Fluid Mech. 42, 335–364.CrossRefGoogle Scholar
Naert, A., Segawa, T. & Sano, M. 1997 High-Reynolds-number thermal turbulence in mercury. Phys. Rev. E 56 (2), R1302.10.1103/PhysRevE.56.R1302CrossRefGoogle Scholar
Plevachuk, Y., Sklyarchuk, V., Eckert, S., Gerbeth, G. & Novakovic, R. 2014 Thermophysical properties of the liquid Ga–In–Sn eutectic alloy. J. Chem. Engng Data 59 (3), 757–763.10.1021/je400882qCrossRefGoogle Scholar
Ravelet, F., Marié, L., Chiffaudel, A. & Daviaud, F. 2004 Multistability and memory effect in a highly turbulent flow: experimental evidence for a global bifurcation. Phys. Rev. Lett. 93 (16), 164501.CrossRefGoogle Scholar
Ren, L., Tao, X., Zhang, L., Ni, M.-J., Xia, K.-Q. & Xie, Y.-C. 2022 Flow states and heat transport in liquid metal convection. J. Fluid Mech. 951, R1.CrossRefGoogle Scholar
Salavy, J., Boccaccini, L.V., Lässer, R., Meyder, R., Neuberger, H., Poitevin, Y., Rampal, G., Rigal, E., Zmitko, M. & Aiello, A. 2007 Overview of the last progresses for the European test blanket modules projects. Fusion Engng Des. 82 (15-24), 2105–2112.CrossRefGoogle Scholar
Schindler, F., Eckert, S., Zürner, T., Schumacher, J. & Vogt, T. 2022 Collapse of coherent large scale flow in strongly turbulent liquid metal convection. Phys. Rev. Lett. 128 (16), 164501.10.1103/PhysRevLett.128.164501CrossRefGoogle ScholarPubMed
Shang, X.-D., Qiu, X.-L., Tong, P. & Xia, K.-Q. 2004 Measurements of the local convective heat flux in turbulent Rayleigh-Bénard convection. Phys. Rev. E 70 (2), 026308.10.1103/PhysRevE.70.026308CrossRefGoogle ScholarPubMed
She, Z.-S. & Jackson, E. 1993 On the universal form of energy spectra in fully developed turbulence. Phys. Fluids 5 (7), 1526–1528.10.1063/1.858591CrossRefGoogle Scholar
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, 295–308.10.1017/jfm.2013.298CrossRefGoogle Scholar
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 (7), 074502.10.1103/PhysRevLett.95.074502CrossRefGoogle Scholar
de la Torre, A. & Burguete, J. 2007 Slow dynamics in a turbulent von Kármán swirling flow. Phys. Rev. Lett. 99 (5), 054101.CrossRefGoogle Scholar
Verzicco, R. & Camussi, R. 2003 Numerical experiments on strongly turbulent thermal convection in a slender cylindrical cell. J. Fluid Mech. 477, 19–49.10.1017/S0022112002003063CrossRefGoogle Scholar
Wang, Q., Verzicco, R., Lohse, D. & Shishkina, O. 2020 Multiple states in turbulent large-aspect-ratio thermal convection: what determines the number of convection rolls? Phys. Rev. Lett. 125 (7), 074501.10.1103/PhysRevLett.125.074501CrossRefGoogle ScholarPubMed
Weiss, S. & Ahlers, G. 2011 Turbulent Rayleigh–Bénard convection in a cylindrical container with aspect ratio $\gamma = 0.50$ and Prandtl number $Pr= 4.38$. J. Fluid Mech. 676, 5–40.10.1017/S0022112010005963CrossRefGoogle Scholar
de Wit, X.M., van Kan, A. & Alexakis, A. 2022 Bistability of the large-scale dynamics in quasi-two-dimensional turbulence. J. Fluid Mech. 939, R2.CrossRefGoogle Scholar
Xi, H.-D. & Xia, K.-Q. 2008 Flow mode transitions in turbulent thermal convection. Phys. Fluids 20 (5), 055104.10.1063/1.2920444CrossRefGoogle Scholar
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 (4), 044503.10.1103/PhysRevLett.102.044503CrossRefGoogle ScholarPubMed
Xia, K.-Q. 2013 Current trends and future directions in turbulent thermal convection. Theor. Appl. Mech. Lett. 3 (5), 052001.CrossRefGoogle Scholar
Xia, K.-Q., Sun, C. & Zhou, S.-Q. 2003 Particle image velocimetry measurement of the velocity field in turbulent thermal convection. Phys. Rev. E 68 (6), 066303.CrossRefGoogle ScholarPubMed
Xie, Y.-C., Ding, G.-Y. & Xia, K.-Q. 2018 Flow topology transition via global bifurcation in thermally driven turbulence. Phys. Rev. Lett. 120 (21), 214501.10.1103/PhysRevLett.120.214501CrossRefGoogle ScholarPubMed
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, 322–346.10.1017/jfm.2012.574CrossRefGoogle Scholar
Xie, Y.-C. & Xia, K.-Q. 2013 Dynamics and flow coupling in two-layer turbulent thermal convection. J. Fluid Mech. 728, R1.CrossRefGoogle Scholar
Xu, Y., Horn, S. & Aurnou, J.M. 2022 Thermoelectric precession in turbulent magnetoconvection. J. Fluid Mech. 930, A8.CrossRefGoogle Scholar
Yanagisawa, T., Yamagishi, Y., Hamano, Y., Tasaka, Y. & Takeda, Y. 2011 Spontaneous flow reversals in Rayleigh-Bénard convection of a liquid metal. Phys. Rev. E 83 (3), 036307.10.1103/PhysRevE.83.036307CrossRefGoogle ScholarPubMed
Yanagisawa, T., Yamagishi, Y., Hamano, Y., Tasaka, Y., Yoshida, M., Yano, K. & Takeda, Y. 2010 Structure of large-scale flows and their oscillation in the thermal convection of liquid gallium. Phys. Rev. E 82 (1), 016320.10.1103/PhysRevE.82.016320CrossRefGoogle ScholarPubMed
Yang, Y., Chen, W., Verzicco, R. & Lohse, D. 2020 Multiple states and transport properties of double-diffusive convection turbulence. Proc. Natl Acad. Sci. 117 (26), 14676–14681.CrossRefGoogle ScholarPubMed
Yang, J.C., Vogt, T. & Eckert, S. 2021 Transition from steady to oscillating convection rolls in Rayleigh-Bénard convection under the influence of a horizontal magnetic field. Phys. Rev. Fluids 6, 023502.CrossRefGoogle Scholar
Zhou, S.-Q. & Xia, K.-Q. 2001 Scaling properties of the temperature field in convective turbulence. Phys. Rev. Lett. 87 (6), 064501.10.1103/PhysRevLett.87.064501CrossRefGoogle ScholarPubMed
Zimmerman, D.S., Triana, S.A. & Lathrop, D.P. 2011 Bi-stability in turbulent, rotating spherical Couette flow. Phys. Fluids 23 (6), 065104.10.1063/1.3593465CrossRefGoogle Scholar
Zürner, T., Schindler, F., Vogt, T., Eckert, S. & Schumacher, J. 2019 Combined measurement of velocity and temperature in liquid metal convection. J. Fluid Mech. 876, 1108–1128.CrossRefGoogle Scholar
Zwirner, L., Khalilov, R., Kolesnichenko, I., Mamykin, A., Mandrykin, S., Pavlinov, A., Shestakov, A., Teimurazov, A., Frick, P. & Shishkina, O. 2020 a The influence of the cell inclination on the heat transport and large-scale circulation in liquid metal convection. J. Fluid Mech. 884, A18.CrossRefGoogle Scholar
Zwirner, L., Tilgner, A. & Shishkina, O. 2020 b Elliptical instability and multiple-roll flow modes of the large-scale circulation in confined turbulent Rayleigh-Bénard convection. Phys. Rev. Lett. 125 (5), 054502.10.1103/PhysRevLett.125.054502CrossRefGoogle ScholarPubMed