Numerical Simulations of Double-Diffusive Convection in Different Liquid Metals Under Magnetic Fields

CHEN Sisi; LI Xulong; ZHANG Chaonan; QIN Juanjuan; ZHAO Bingxin

doi:10.21656/1000-0887.440347

Volume 45 Issue 12

Dec. 2024

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2024 > 45(12): 1473-1482

CHEN Sisi, LI Xulong, ZHANG Chaonan, QIN Juanjuan, ZHAO Bingxin. Numerical Simulations of Double-Diffusive Convection in Different Liquid Metals Under Magnetic Fields[J]. Applied Mathematics and Mechanics, 2024, 45(12): 1473-1482. doi: 10.21656/1000-0887.440347

Citation:

PDF( 0 KB)

Numerical Simulations of Double-Diffusive Convection in Different Liquid Metals Under Magnetic Fields

doi: 10.21656/1000-0887.440347

1.
School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, P.R.China
2.
Ningxia Key Laboratory of Interdisciplinary Mechanics and Scientific Computing, Yinchuan 750021, P.R.China

Received Date: 2023-12-05
Rev Recd Date: 2024-03-20
Publish Date: 2024-12-01

Abstract

Abstract

With the high-precision and high-resolution numerical method, the dynamics of double-diffusive convection of different liquid metals in a long cavity under external magnetic fields in 2 directions was directly simulated, to reveal the influences of the fluid property parameter of Prandtl number Pr, the magnetic field direction and the magnetic field intensity on the flow and the heat and mass transfers. The results indicate that, within the range of the considered Pr values, the flow transitions from periodic to steady with the increase of Pr for weak magnetic fields. Specifically, when the Pr is 0.03, the convective system will have unsteady solution, and the flow will be periodic. The efficiency of heat and mass transfers initially increase rapidly, then slowly. For the moderately strong magnetic field, the flow remains steady, and the growth rate of the heat and mass transfer efficiency slows down further with Pr increasing. For the strong magnetic field, the flow is always steady, and the efficiency of the heat and mass transfer hardly changes with the Pr. Under the same magnetic field intensity, compared with the inclined magnetic field with a direction of 45° and the horizontal magnetic field, the vertical magnetic field has a weaker suppressive effect on the heat and mass transfer efficiency.
- double-diffusive convection,
- direct numerical simulation,
- high accuracy,
- magnetic field

FullText(HTML)

References(26)

References

[1]	IHLI T, BASU T K, GIANCARLI L M, et al. Review of blanket designs for advanced fusion reactors[J]. Fusion Engineering and Design, 2008, 83(7/9): 912-919.
[2]	倪明玖. 磁约束核聚变反应堆研发相关的金属流体力学问题研究[J]. 中国科学: 物理学力学天文学, 2013, 43(12): 1570-1578. NI Mingjiu. Liquid metal hydrodynamics relevant to R&D of magnetocondined fusion reactor[J]. Scientia Sinica: Physica, Mechanica & Astronomica, 2013, 43(12): 1570-1578. (in Chinese)
[3]	SUN Z H I, GUO M, VLEUGELS J, et al. Strong static magnetic field processing of metallic materials: a review[J]. Current Opinion in Solid State and Materials Science, 2012, 16(5): 254-267. doi: 10.1016/j.cossms.2012.08.001
[4]	RUDRAIAH N, BARRON R M, VENKATACHALAPPA M, et al. Effect of a magnetic field on free convection in a rectangular enclosure[J]. International Journal of Engineering Science, 1995, 33(8): 1075-1084. doi: 10.1016/0020-7225(94)00120-9
[5]	BURR U, MVLLER 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
[6]	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. doi: 10.1017/S0022112000002950
[7]	NANDUKUMAR Y, PAL P. Oscillatory instability and routes to chaos in Rayleigh-Bénard convection: effect of external magnetic field[J]. EPL (Europhysics Letters), 2015, 112(2): 24003. doi: 10.1209/0295-5075/112/24003
[8]	TASAKA Y, IGAKI K, YANAGISAWA T, et al. Regular flow reversals in Rayleigh-Bénard convection in a horizontal magnetic field[J]. Physical Review E, 2016, 93: 043109. doi: 10.1103/PhysRevE.93.043109
[9]	YU P X, XIAO Z, WU S, et al. High accuracy numerical investigation of double-diffusive convection in a rectangular cavity under a uniform horizontal magnetic field and heat source[J]. International Journal of Heat and Mass Transfer, 2017, 110: 613-628. doi: 10.1016/j.ijheatmasstransfer.2017.03.068
[10]	NAFFOUTI A, BEN-BEYA B, LILI T. Three-dimensional Rayleigh-Bénard magnetoconvection: effect of the direction of the magnetic field on heat transfer and flow patterns[J]. Comptes Rendus Mécanique, 2014, 342(12): 714-725. doi: 10.1016/j.crme.2014.09.001
[11]	SELIMLI S, RECEBLI Z, ARCAKLIOGLU E. Combined effects of magnetic and electrical field on the hydrodynamic and thermophysical parameters of magnetoviscous fluid flow[J]. International Journal of Heat and Mass Transfer, 2015, 86: 426-432. doi: 10.1016/j.ijheatmasstransfer.2015.02.074
[12]	YU X X, ZHANG J, NI M J. Numerical simulation of the Rayleigh-Benard 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
[13]	虞培祥. 不可压导电流体流动问题的流函数-速度型算法研究及应用[D]. 上海: 复旦大学, 2013. YU Peixiang. Research and application of streamfunction-velocity algorithm for incompressible conductive fluid flow problems[D]. Shanghai: Fudan University, 2013. (in Chinese)
[14]	YANAGISAWA T, HAMANO Y, MIYAGOSHI T, et al. Convection patterns in a liquid metal under an imposed horizontal magnetic field[J]. Physical Review E, 2013, 88(6): 063020. doi: 10.1103/PhysRevE.88.063020
[15]	BUSSE F H. Asymptotic theory of wall-attached convection in a horizontal fluid layer with a vertical magnetic field[J]. Physics of Fluids, 2008, 20(2): 024102. doi: 10.1063/1.2837175
[16]	仇建新. 外磁场作用下饱和多孔介质中液态金属流动与传热特性数值模拟[D]. 上海: 复旦大学, 2017. QIU Jianxin. Numerical simulation of liquid metal flow and heat transfer characteristics in saturated porous media under external magnetic field[D]. Shanghai: Fudan University, 2017. (in Chinese)
[17]	LIU W J, KRASNOV D, SCHUMACHER J. Wall modes in magnetoconvection at high Hartmann numbers[J]. Journal of Fluid Mechanics, 2018, 849: R2. doi: 10.1017/jfm.2018.479
[18]	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: 519-42. doi: 10.1017/jfm.2019.232
[19]	YAN M, CALKINS M A, MAFFEI S, et al. Heat transfer and flow regimes in quasi-static magnetoconvection with a vertical magnetic field[J]. Journal of Fluid Mechanics, 2019, 877: 1186-1206. doi: 10.1017/jfm.2019.615
[20]	ZVRNER T, SCHINDLER F, VOGT T, et al. Flow regimes of Rayleigh-Bénard convection in a vertical magnetic field[J]. Journal of Fluid Mechanics, 2020, 894: A21. doi: 10.1017/jfm.2020.264
[21]	TASAKA Y, YANAGISAWA T, FUJITA K, et al. Two-dimensional oscillation of convection roll in a finite liquid metal layer under a horizontal magnetic field[J]. Journal of Fluid Mechanics, 2021, 911: A19. doi: 10.1017/jfm.2020.1047
[22]	BENDARAA A, CHARAFI M M, HASNAOUI A. Numerical modeling of natural convection in horizontal and inclined square cavities filled with nanofluid in the presence of magnetic field[J]. The European Physical Journal Plus, 2019, 134(9): 468. doi: 10.1140/epjp/i2019-12814-8
[23]	MOOLYA S, SATHEESH A. Role of magnetic field and cavity inclination on double diffusive mixed convection in rectangular enclosed domain[J]. International Communications in Heat and Mass Transfer, 2020, 118: 104814. doi: 10.1016/j.icheatmasstransfer.2020.104814
[24]	REDDY N, MURUGESAN K. Magnetic field influence on double-diffusive natural convection in a square cavity: a numerical study[J]. Numerical Heat Transfer (Part A): Applications, 2017, 71(4): 448-475. doi: 10.1080/10407782.2016.1277922
[25]	YANG J Q, ZHAO B X. Numerical investigation of double-diffusive convection in rectangular cavities with different aspect ratio Ⅰ: high-accuracy numerical method[J]. Computers & Mathematics With Applications, 2021, 94: 155-169.
[26]	ZHAO B X, YANG J Q. Numerical investigation of 2D double-diffusive convection in rectangular cavities with different aspect ratios: heat and mass transfer and flow characteristics[J]. Physics of Fluids, 2022, 34(3): 034120. doi: 10.1063/5.0084537