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Flow regimes of Rayleigh–Bénard convection in a vertical magnetic field

Published online by Cambridge University Press:  11 May 2020

Till Zürner Open the ORCID record for Till Zürner [Opens in a new window] ,
Felix Schindler Open the ORCID record for Felix Schindler [Opens in a new window] ,
Tobias Vogt Open the ORCID record for Tobias Vogt [Opens in a new window] ,
Sven Eckert Open the ORCID record for Sven Eckert [Opens in a new window]  and
Jörg Schumacher Open the ORCID record for Jörg Schumacher [Opens in a new window]
Till Zürner*
Affiliation:
Institute of Thermodynamics and Fluid Mechanics, Technische Universität Ilmenau, Postfach 100565, D-98684Ilmenau, Germany
Felix Schindler
Affiliation:
Department of Magnetohydrodynamics, Institute of Fluid Dynamics, Helmholtz-Zentrum Dresden – Rossendorf, Bautzner Landstraße 400, D-01328Dresden, Germany
Tobias Vogt
Affiliation:
Department of Magnetohydrodynamics, Institute of Fluid Dynamics, Helmholtz-Zentrum Dresden – Rossendorf, Bautzner Landstraße 400, D-01328Dresden, Germany
Sven Eckert
Affiliation:
Department of Magnetohydrodynamics, Institute of Fluid Dynamics, Helmholtz-Zentrum Dresden – Rossendorf, Bautzner Landstraße 400, D-01328Dresden, Germany
Jörg Schumacher
Affiliation:
Institute of Thermodynamics and Fluid Mechanics, Technische Universität Ilmenau, Postfach 100565, D-98684Ilmenau, Germany
*
†Email address for correspondence: [email protected]
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Abstract

The effects of a vertical static magnetic field on the flow structure and global transport properties of momentum and heat in liquid metal Rayleigh–Bénard convection are investigated. Experiments are conducted in a cylindrical convection cell of unity aspect ratio, filled with the alloy GaInSn at a low Prandtl number of $Pr=0.029$. Changes of the large-scale velocity structure with increasing magnetic field strength are probed systematically using multiple ultrasound Doppler velocimetry sensors and thermocouples for a parameter range that is spanned by Rayleigh numbers of $10^{6}\leqslant Ra\leqslant 6\times 10^{7}$ and Hartmann numbers of $Ha\leqslant 1000$. Our simultaneous multi-probe temperature and velocity measurements demonstrate how the large-scale circulation is affected by an increasing magnetic field strength (or Hartmann number). Lorentz forces induced in the liquid metal first suppress the oscillations of the large-scale circulation at low $Ha$, then transform the one-roll structure into a cellular large-scale pattern consisting of multiple up- and downwellings for intermediate $Ha$, before finally expelling any fluid motion out of the bulk at the highest accessible $Ha$ leaving only a near-wall convective flow that persists even below Chandrasekhar’s linear instability threshold. Our study thus proves experimentally the existence of wall modes in confined magnetoconvection. The magnitude of the transferred heat remains nearly unaffected by the steady decrease of the fluid momentum over a large range of Hartmann numbers. We extend the experimental global transport analysis to momentum transfer and include the dependence of the Reynolds number on the Hartmann number.

JFM classification

MHD and Electrohydrodynamics: Magneto convection
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 894 , 10 July 2020 , A21
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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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
Aujogue, K., Pothérat, A., Bates, I., Debray, F. & Sreenivasan, B. 2016 Little Earth Experiment: an instrument to model planetary cores. Rev. Sci. Instrum. 87 (8), 084502.CrossRefGoogle ScholarPubMed
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
Brown, E. & Ahlers, G. 2006 Rotations and cessations of the large-scale circulation in turbulent Rayleigh–Bénard convection. J. Fluid Mech. 568, 351–386.CrossRefGoogle Scholar
Burr, U. & Müller, U. 2001 Rayleigh–Bénard convection in liquid metal layers under the influence of a vertical magnetic field. Phys. Fluids 13 (11), 3247–3257.CrossRefGoogle Scholar
Busse, F. H. 2008 Asymptotic theory of wall-attached convection in a horizontal fluid layer with a vertical magnetic field. Phys. Fluids 20 (2), 024102.CrossRefGoogle Scholar
Çengel, Y. A. 2008 Introduction to Thermodynamics and Heat Transfer, 2nd edn. McGraw-Hill Primis.Google Scholar
Chakraborty, S. 2008 On scaling laws in turbulent magnetohydrodynamic Rayleigh–Bénard convection. Physica D 237 (24), 3233–3236.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability, 3rd edn. Dover Publications, Inc..Google Scholar
Chillà, F. & Schumacher, J. 2012 New perspectives in turbulent Rayleigh–Bénard convection. Eur. Phys. J. E 35 (7), 58.Google ScholarPubMed
Chong, K. L., Yang, Y., Huang, S.-D., Zhong, J.-Q., Stevens, R. J. A. M., Verzicco, R., Lohse, D. & Xia, K.-Q. 2017 Confined Rayleigh–Bénard, rotating Rayleigh–Bénard, and double diffusive convection: a unifying view on turbulent transport enhancement through coherent structure manipulation. Phys. Rev. Lett. 119 (6), 064501.CrossRefGoogle ScholarPubMed
Cioni, S., Chaumat, S. & Sommeria, J. 2000 Effect of a vertical magnetic field on turbulent Rayleigh–Bénard convection. Phys. Rev. E 62 (4), R4520–R4523.Google ScholarPubMed
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
Davidson, P. A. 2001 An Introduction to Magnetohydrodynamics, 1st edn. Cambridge Texts in Applied Mathematics, vol. 25. Cambridge University Press.CrossRefGoogle Scholar
Funfschilling, D. & Ahlers, G. 2004 Plume motion and large-scale circulation in a cylindrical Rayleigh–Bénard cell. Phys. Rev. Lett. 92 (19), 194502.CrossRefGoogle Scholar
Glazier, J. A., Segawa, T., Naert, A. & Sano, M. 1999 Evidence against ‘ultrahard’ thermal turbulence at very high Rayleigh numbers. Nature 398, 307–310.CrossRefGoogle Scholar
Houchens, B. C., Witkowski, L. M. & Walker, J. S. 2002 Rayleigh–Bénard instability in a vertical cylinder with a vertical magnetic field. J. Fluid Mech. 469, 189–207.CrossRefGoogle Scholar
Ihli, T., Basu, T. K., Giancarli, L. M., Konishi, S., Malang, S., Najmabadi, F., Nishio, S., Raffray, A. R., Rao, C. V. S., Sagara, A. et al. 2008 Review of blanket designs for advanced fusion reactors. Fusion Engng Des. 83 (7), 912–919.CrossRefGoogle 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.CrossRefGoogle Scholar
King, E. M. & Aurnou, J. M. 2013 Turbulent convection in liquid metal with and without rotation. Proc. Natl Acad. Sci. USA 110 (17), 6688–6693.CrossRefGoogle ScholarPubMed
King, E. M. & Aurnou, J. M. 2015 Magnetostrophic balance as the optimal state for turbulent magnetoconvection. Proc. Natl Acad. Sci. USA 112 (4), 990–994.CrossRefGoogle ScholarPubMed
Lim, Z. L., Chong, K. L., Ding, G.-Y. & Xia, K.-Q. 2019 Quasistatic magnetoconvection: Heat transport enhancement and boundary layer crossing. J. Fluid Mech. 870, 519–542.CrossRefGoogle Scholar
Liu, W., Krasnov, D. & Schumacher, J. 2018 Wall modes in magnetoconvection at high Hartmann numbers. J. Fluid Mech. 849, R2.CrossRefGoogle Scholar
Moffatt, H. K. & Dormy, E. 2019 Self-Exciting Fluid Dynamos, Cambridge Texts in Applied Mathematics, vol. 59. Cambridge University Press.CrossRefGoogle Scholar
Nakagawa, Y. 1955 An experiment on the inhibition of thermal convection by a magnetic field. Nature 175, 417–419.CrossRefGoogle Scholar
Pal, J., Cramer, A., Gundrum, T. & Gerbeth, G. 2009 MULTIMAG–A multipurpose magnetic system for physical modelling in magnetohydrodynamics. Flow Meas. Instrum. 20 (6), 241–251.CrossRefGoogle 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.CrossRefGoogle Scholar
Scheel, J. D. & Schumacher, J. 2016 Global and local statistics in turbulent convection at low Prandtl numbers. J. Fluid Mech. 802, 147–173.CrossRefGoogle Scholar
Scheel, J. D. & Schumacher, J. 2017 Predicting transition ranges to fully turbulent viscous boundary layers in low Prandtl number convection flows. Phys. Rev. Fluids 2 (12), 123501.CrossRefGoogle 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.CrossRefGoogle Scholar
Sun, C., Xia, K.-Q. & Tong, P. 2005 Three-dimensional flow structures and dynamics of turbulent thermal convection in a cylindrical cell. Phys. Rev. E 72 (2), 026302.Google Scholar
Takeshita, T., Segawa, T., Glazier, J. A. & Sano, M. 1996 Thermal turbulence in mercury. Phys. Rev. Lett. 76 (9), 1465.CrossRefGoogle ScholarPubMed
Tasaka, Y., Igaki, K., Yanagisawa, T., Vogt, T., Zürner, T. & Eckert, S. 2016 Regular flow reversals in Rayleigh–Bénard convection in a horizontal magnetic field. Phys. Rev. E 93 (4), 043109.Google Scholar
Tsuji, Y., Mizuno, T., Mashiko, T. & Sano, M. 2005 Mean wind in convective turbulence of mercury. Phys. Rev. Lett. 94 (3), 034501.CrossRefGoogle ScholarPubMed
Vogt, T., Horn, S., Grannan, A. M. & Aurnou, J. M. 2018a Jump rope vortex in liquid metal convection. Proc. Natl. Acad. Sci. USA 115 (50), 12674–12679.CrossRefGoogle Scholar
Vogt, T., Ishimi, W., Yanagisawa, T., Tasaka, Y., Sakuraba, A. & Eckert, S. 2018b Transition between quasi-two-dimensional and three-dimensional Rayleigh–Bénard convection in a horizontal magnetic field. Phys. Rev. Fluids 3 (1), 013503.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle Scholar
Yan, M., Calkins, M. A., Maffei, S., Julien, K., Tobias, S. M. & Marti, P. 2019 Heat transfer and flow regimes in quasi-static magnetoconvection with a vertical magnetic field. J. Fluid Mech. 877, 1186–1206.CrossRefGoogle Scholar
Yanagisawa, T., Hamano, Y., Miyagoshi, T., Yamagishi, Y., Tasaka, Y. & Takeda, Y. 2013 Convection patterns in a liquid metal under an imposed horizontal magnetic field. Phys. Rev. E 88 (6), 063020.Google 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.Google ScholarPubMed
Zhong, F., Ecke, R. E. & Steinberg, V. 1991 Asymmetric modes and the transition to vortex structures in rotating Rayleigh–Bénard convection. Phys. Rev. Lett. 67 (18), 2473–2476.CrossRefGoogle ScholarPubMed
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, 367–390.CrossRefGoogle Scholar
Zürner, T., Liu, W., Krasnov, D. & Schumacher, J. 2016 Heat and momentum transfer for magnetoconvection in a vertical external magnetic field. Phys. Rev. E 94 (4), 043108.Google 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
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