液态金属热对流典型流动结构实验研究

doi:10.7523/j.ucas.2021.0033

摘要/Abstract

摘要： 通过搭建长宽高比为1：1：2的实验方腔，系统性地研究低普朗特数（0.03）的镓铟锡合金在有/无磁场作用下所产生的热对流结构。实验中上下铜板的温差由2个恒温水浴来实现，通过在铜板上布置测温探头测量温度，在方腔侧壁布置超声波探头实现对液态金属内部速度分布的测量。实验获得了3种典型的流动结构，无磁场环境下液态金属的流动在空间上呈现大尺度环流，靠近冷热端液态金属的温度无序波动，且速度分布符合热湍流的基本特性，为流动结构Ⅰ。当施加水平磁场，磁场极大地抑制对流运动，出现稳定的单涡胞运动结构，即流动结构Ⅱ和振荡的双涡胞运动结构，即流动结构Ⅲ。随后通过对3个不同测量位置的速度分布进行详细分析，深入解析水平磁场存在下的这2种流动结构的典型特征。

关键词: 热对流, 液态金属, 磁流体力学, 单涡胞运动, 振荡双涡胞运动

Abstract: In the present paper, we built a rectangle cell with an aspect ratio of 1:1:2, where the height of the cell is two times the width of the cell. The thermal convection of liquid Galinstan with a low Prandtl number, 0.03, is systematically investigated with/without the influence of the magnetic field. During the experiments, two thermostatic water baths are adopted to keep the upper copper plate and lower copper plate with constant temperature difference where the temperature of the upper copper plate is always lower than that of the lower copper plate. Thermoprobes are inserted in copper plates to record the temperature signal in the copper and liquid metal, while the ultrasonic sensors are inserted through the sidewall of the cell to measure the velocity distribution of liquid metal. From the velocity distribution in the cell, we observe three typical flow structures. Without the influence of the magnetic field, time-dependent large-scale convection is observed in the liquid metal thermal convection, with large velocity fluctuations near the cold and hot copper plates. The characteristics of velocity are similar to the thermal turbulence obtained from the normal liquid which is called as flow structure I. Under the influence of the horizontal magnetic field, the thermal convection is strongly suppressed by the magnetic field, the stable single roll convection, namely the flow structure II, and the double oscillation roll convection, namely the flow structure III are observed. Furthermore, the characteristics of these two flow structures with the action of the horizontal magnetic field are investigated in detail through the velocity information obtained from three ultrasonic sensors.

Key words: thermal convection, liquid metal, magnetohydrodynamics, single roll convection, double oscillation roll convection

中图分类号:

O359+.1

程有基, 陈新元, 阳倦成, 倪明玖. 液态金属热对流典型流动结构实验研究[J]. 中国科学院大学学报, 2023, 40(2): 155-164.

CHENG Youji, CHEN Xinyuan, YANG Juancheng, NI Mingjiu. Experimental investigation on the typical flow structures of liquid metal thermal convection[J]. Journal of University of Chinese Academy of Sciences, 2023, 40(2): 155-164.

参考文献

[1] Brent A D, Voller V R, Reid K J. Enthalpy-porosity technique for modeling convection-diffusion phase change:application to the melting of a pure metal[J]. Numerical Heat Transfer, 1988, 13(3):297-318.DOI:10.1080/10407788808913615.
[2] Hartmann D L, Moy L A, Fu Q. Tropical convection and the energy balance at the top of the atmosphere[J]. Journal of Climate, 2001, 14(24):4495-4511.
[3] McKenzie D P, Roberts J M, Weiss N O. Convection in the earth's mantle:towards a numerical simulation[J]. Journal of Fluid Mechanics, 1974, 62(3):465.
[4] Bénard H. Les tourbillons cellulaires dans une nappe liquid[J]. Revue Générale des Sciences Pures et Appliquées, 1900, 11:1261-1271.
[5] Rayleigh L. LIX. On convection currents in a horizontal layer of fluid, when the higher temperature is on the under side[J]. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 1916, 32(192):529-546.DOI:10.1080/14786441608635602.
[6] Chandrasekhar S. Hydrodynamic and hydromagnetic stability[M]. New York:Oxford University Press, 1961.
[7] Oberbeck A. Ueber Die Wärmeleitung der Flüssigkeiten Bei berücksichtigung der strömungen infolge von temperaturdifferenzen[J]. Annalen Der Physik Und Chemie, 1879, 243(6):271-292.
[8] Grossmann S, Lohse D. Scaling in thermal convection:a unifying theory[J]. Journal of Fluid Mechanics, 2000, 407:27-56.DOI:10.1017/50022112099007545.
[9] Grossmann S, Lohse D. Thermal convection for large Prandtl numbers[J]. Physical Review Letters, 2001, 86(15):3316-3319.DOI:10.1103/PhysRevLett.86.3316.
[10] Grossmann S, Lohse D. Prandtl and Rayleigh number dependence of the Reynolds number in turbulent thermal convection[J]. Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, 2002, 66(1 pt 2):016305.DOI:10.1103/PhysRevE.66.016305.
[11] Zhou Q, Xia K Q. Physical and geometrical properties of thermal plumes in turbulent Rayleigh-Bénard convection[J]. New Journal of Physics, 2010, 12(7):075006.DOI:10.1088/1367-2630/12/7/075006.
[12] 周全, 夏克青. Rayleigh-Bénard湍流热对流研究的进展、现状及展望[J]. 力学进展, 2012, 42(3):231-251.DOI:10.6052/1000-0992/11-163.
[13] Sun C, Xia K Q. Scaling of the Reynolds number in turbulent thermal convection[J]. Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, 2005, 72(6 Pt 2):067302.DOI:10.1103/PhysRevE.72.067302.
[14] Yanagisawa T, Yamagishi Y, Hamano Y, et al. Structure of large-scale flows and their oscillation in the thermal convection of liquid gallium[J]. Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, 2010, 82(1 Pt 2):016320.DOI:10.1103/PhysRevE.82.016320.
[15] Busse F H,Clever R M. Stability of convection rolls in the presence of a vertical magnetic field[J]. The Physics of Fluids, 1982, 25(6):931-935.DOI:10.1063/1.863845.
[16] 荣升. 导电流体热对流中磁场的致稳作用[J]. 力学学报, 1993, 25(6):658-664.
[17] Busse F H. The oscillatory instability of convection rolls in a low Prandtl number fluid[J]. Journal of Fluid Mechanics, 1972, 52(1):97-112.
[18] Clever R M, Busse F H. Transition to time-dependent convection[J]. Journal of Fluid Mechanics, 1974, 65(4):625-645.
[19] Fauve S, Laroche C, Libchaber A, et al. Effect of a horizontal magnetic field on convective instabilities in mercury[J]. Journal De Physique Lettres, 1981, 42(21):455-457.
[20] Libchaber A, Fauve S, Laroche C. Two-parameter study of the routes to chaos[J]. Physica D:Nonlinear Phenomena, 1983, 7(1/2/3):73-84.DOI:10.1016/0167-2789(83)90117-3.
[21] Lehnert B, Little N C. Experiments on the effect of inhomogeneity and obliquity of a magnetic field in inhibiting convection[J]. Tellus, 1957, 9(1):97-103.DOI:10.3402/tellusa.v9il.9063.
[22] Yu X X, Zhang J, Ni M J. Numerical simulation of the Rayleigh-Bénard convection under the influence of magnetic fields[J]. International Journal of Heat and Mass Transfer, 2018, 120:1118-1131.DOI:10.1016/j.ijheatmasstransfer.2017.11.151.
[23] Horanyi S, Krebs L, Müller U. Turbulent Rayleigh-Bénard convection in low Prandtl-number fluids[J]. International Journal of Heat and Mass Transfer, 1999, 42(21):3983-4003.DOI:10.1016/s0017-9310(99)00059-9.
[24] Burr U, Müller U. Rayleigh-Bénard convection in liquid metal layers under the influence of a vertical magnetic field[J]. Physics of Fluids, 2001, 13(11):3247-3257.DOI:10.1063/1.1404385.
[25] Aurnou J M, Olson P L. Experiments on Rayleigh-Bénard convection, magnetoconvection and rotating magnetoconvection in liquid gallium[J]. Journal of Fluid Mechanics, 2001, 430:283-307.
[26] Takeshita T, Segawa T, Glazier J A, et al. Thermal turbulence in mercury[J]. Physical Review Letters, 1996, 76(9):1465-1468.DOI:10.1103/PhysRevLett.76.1465.
[27] 周仲凯,王增辉,陈然. 强磁场下液态金属在竖直平板外的自由对流换热[J]. 中国科学院大学学报, 2020, 37(1):13-19.DOI:10.7523/j.issn.2095-6134.2020.01.003.
[28] Yanagisawa T, Yamagishi Y, Hamano Y, et al. Detailed investigation of thermal convection in a liquid metal under a horizontal magnetic field:Suppression of oscillatory flow observed by velocity profiles[J]. Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, 2010, 82(5 pt 2):056306.DOI:10.1103/PhysRevE.82.056306.
[29] Yanagisawa T, Yamagishi Y, Hamano Y, et al. Spontaneous flow reversals in Rayleigh-Bénard convection of a liquid metal[J]. Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, 2011, 83(3 Pt 2):036307.DOI:10.1103/PhyRevE.83.036307.
[30] Vogt T, Horn S, Grannan A M, et al. Jump rope vortex in liquid metal convection[J]. Proceedings of the National Academy of Sciences of the United States of America, 2018, 115(50):12674-12679.DOI:10.1073/pnas.1812260115.
[31] Vogt T, Ishimi W, Yanagisawa T, et al. Transition between quasi-two-dimensional and three-dimensional Rayleigh-Bénard convection in a horizontal magnetic field[J]. Physical Review Fluids, 2018, 3:013503.DOI:10.1103/physrevfluids.3.013503.
[32] Akashi M, Yanagisawa T, Tasaka Y, et al. Transition from convection rolls to large-scale cellular structures in turbulent Rayleigh-Bénard convection in a liquid metal layer[J]. Physical Review Fluids, 2019, 4(3):033501.DOI:10.1103/PhysRevFluids.4.033501.
[33] Zürner T, Schindler F, Vogt T, et al. Combined measurement of velocity and temperature in liquid metal convection[J]. Journal of Fluid Mechanics, 2019, 876:1108-1128.DOI:10.1017/jfm2019.556.
[34] Lim Z L, Chong K L, Ding G Y, et al. Quasistatic magnetoconvection:Heat transport enhancement and boundary layer crossing[J]. Journal of Fluid Mechanics, 2019, 870:519-542.DOI:10.1017/jfm.2019.232.
[35] Shang X D, Xia K Q. Scaling of the velocity power spectra in turbulent thermal convection[J]. Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, 2001, 64(6 Pt 2):065301.DOI:10.1103/PhysRevE.64.065301.