不同高径比下浮区晶体生长熔体内对流不稳定性分析

人工晶体学报 ›› 2023, Vol. 52 ›› Issue (2): 220-228.

不同高径比下浮区晶体生长熔体内对流不稳定性分析

王苗苗¹, 张传成¹, 任浩¹, 唐绪兵¹, 丁守军¹, 邹勇¹, 黄护林²

1.安徽工业大学微电子与数据科学学院,马鞍山 243032;
2.南京航空航天大学航天学院,南京 210016

收稿日期:2022-11-02 出版日期:2023-02-15 发布日期:2023-03-08
通信作者: 丁守军,博士,副教授。E-mail:sjding@ahut.edu.cn邹勇,博士,副教授。E-mail:yongzou@ahut.edu.cn
作者简介:王苗苗(1999—),女,安徽省人,硕士研究生。E-mail:2352580049@qq.com
基金资助:
国家自然科学基金(51976080,52202001);安徽省科技重大专项(202203a07020002);安徽高校自然科学研究重点项目(KJ2021A0388);安徽高校研究生科学研究项目(YSJ20210361)

Analysis of Convective Instability in Melt of Floating Zone Crystal Growth with Different Aspect Ratio

WANG Miaomiao¹, ZHANG Chuancheng¹, REN Hao¹, TANG Xubing¹, DING Shoujun¹, ZOU Yong¹, HUANG Hulin²

1. School of Microelectronics and Data Science, Anhui University of Technology, Ma'anshan 243032, China;
2. College of Astronautics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Received:2022-11-02 Online:2023-02-15 Published:2023-03-08

摘要/Abstract

摘要： 本文通过数值模拟的方法,研究了零重力条件下半浮区液桥内熔体热毛细对流的演化规律。在液桥的高度L和温差ΔT保持不变的情况下,通过改变液桥的半径R来改变液桥的高径比(Ar=L/R)。随着高径比Ar的变化,液桥内的对流表现出不同的流动特征。在Ar=0.5时,热毛细对流处于三维稳态;在Ar=1时,流场和温度场从稳态模式向非稳态周期多频振荡模式转变,它们之间的频率关系满足倍频关系(f_n=nf₁);在Ar=1.25时,监测点的速度振荡频率增大,表现为较小幅度的振荡模式,且温度振荡消失。

关键词: 浮区法晶体生长, 液桥, 热毛细对流, 高径比, 数值模拟, 熔体

Abstract: In this paper, the evolution of thermocapillary convection in melt of half-floating zone liquid bridge under the condition of zero gravity was studied by means of numerical simulation. Under the condition that the height L of the liquid bridge and the temperature difference ΔT remain unchanged, the aspect ratio (Ar=L/R) of the liquid bridge can be changed by changing the radius R of the liquid bridge. The convection in the liquid bridge exhibits various flow characteristics with the change of the aspect ratio Ar. Thermocapillary convection is in a three-dimensional steady state when Ar=0.5. The flow field and temperature field change from the steady state mode to the unsteady periodic multi-frequency oscillation mode satisfying the frequency doubling relationship (f_n=nf₁) when Ar=1. When Ar=1.25, the velocity oscillation frequency of the monitoring point increases, showing a smaller amplitude oscillation mode, and the temperature oscillation disappears.

Key words: floating zone crystal growth, liquid bridge, thermocapillary convection, aspect ratio, numerical simulation, melt

中图分类号:

王苗苗, 张传成, 任浩, 唐绪兵, 丁守军, 邹勇, 黄护林. 不同高径比下浮区晶体生长熔体内对流不稳定性分析[J]. 人工晶体学报, 2023, 52(2): 220-228.

WANG Miaomiao, ZHANG Chuancheng, REN Hao, TANG Xubing, DING Shoujun, ZOU Yong, HUANG Hulin. Analysis of Convective Instability in Melt of Floating Zone Crystal Growth with Different Aspect Ratio[J]. JOURNAL OF SYNTHETIC CRYSTALS, 2023, 52(2): 220-228.

参考文献

[1] 李凯, 胡文瑞. 非均匀磁场对空间浮区法晶体生长的影响[J]. 中国科学(A辑), 2001, 31(5): 466-473.
LI K, HU W R. Effect of non-uniform magnetic field on crystal growth by space floating zone method[J]. Scientia Sinica (Mathematica), 2001, 31(5): 466-473(in Chinese).
[2] LYUBIMOVA T P, SKURIDYN R V. The influence of vibrations on the stability of thermocapillary flow in liquid zone[J]. International Journal of Heat and Mass Transfer, 2014, 69: 191-202.
[3] MINAKUCHI H, OKANO Y, DOST S. Effect of thermo-solutal Marangoni convection on the azimuthal wave number in a liquid bridge[J]. Journal of Crystal Growth, 2017, 468: 502-505.
[4] HUANG H L, ZHU G P, ZHANG Y. Effect of Marangoni number on thermocapillary convection in a liquid bridge under microgravity[J]. International Journal of Thermal Sciences, 2017, 118: 226-235.
[5] JIN C H, OKANO Y, MINAKUCHI H, et al. Numerical simulation of thermo-solutal Marangoni convection in a full floating zone with radiative heat transfer under zero gravity[J]. Journal of Crystal Growth, 2021, 570: 126204.
[6] JAYAKRISHNAN R, TIWARI S. Dynamic mode decomposition of oscillatory thermo-capillary flow in curved liquid bridges of high Prandtl number liquids under microgravity[J]. Advances in Space Research, 2021, 68(10): 4252-4273.
[7] VARAS R, SALGADO SÁNCHEZ P, PORTER J, et al. Thermocapillary effects during the melting in microgravity of phase change materials with a liquid bridge geometry[J]. International Journal of Heat and Mass Transfer, 2021, 178: 121586.
[8] KANG Q, WU D, DUAN L, et al. Space experimental study on wave modes under instability of thermocapillary convection in liquid bridges on Tiangong-2[J]. Physics of Fluids, 2020, 32(3): 034107.
[9] LE C C, LIU L J, LI Z Y. Thermocapillary instabilities in half zone liquid bridges of low Prandtl fluid with non-equal disks under microgravity[J]. Journal of Crystal Growth, 2021, 560/561: 126063.
[10] RYBICKI A, FLORYAN J M. Thermocapillary effects in liquid bridges. I. Thermocapillary convection[J]. The Physics of Fluids, 1987, 30(7): 1956-1972.
[11] VELTEN R, SCHWABE D, SCHARMANN A. The periodic instability of thermocapillary convection in cylindrical liquid bridges[J]. Physics of Fluids A: Fluid Dynamics, 1991, 3(2): 267-279.
[12] CHEN Q S, HU W R. Influence of liquid bridge volume on instability of floating half zone convection[J]. International Journal of Heat and Mass Transfer, 1998, 41(6/7): 825-837.
[13] FAN J G, LIANG R Q. Thermal-solutal capillary convection in binary mixture liquid bridge with various aspect ratios under microgravity[J]. Journal of Crystal Growth, 2022, 586: 126630.
[14] KUHLMANN H C, NIENHÜSER C. Dynamic free-surface deformations in thermocapillary liquid bridges[J]. Fluid Dynamics Research, 2002, 31(2): 103-127.
[15] KUHLMANN H C, NIENHÜSER C. The influence of static and dynamic free-surface deformations on the three-dimensional thermocapillary flow in liquid bridges[M]//Interfacial Fluid Dynamics and Transport Processes. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003: 213-239.
[16] DOLD P, CRÖLL A, LICHTENSTEIGER M, et al. Floating zone growth of silicon in magnetic fields:Ⅳ.Rotating magnetic fields[J]. Journal of Crystal Growth, 2001, 231(1/2): 95-106.
[17] WALKER J S, WITKOWSKI L M, HOUCHENS B C. Effects of a rotating magnetic field on the thermocapillary instability in the floating zone process[J]. Journal of Crystal Growth, 2003, 252(1/2/3): 413-423.
[18] 袁章福, 柯家骏, 李晶. 金属及合金的表面张力[M]. 北京: 科学出版社, 2006.
YUAN Z F, KE J J, LI J. Surface tension of metals and alloys [M]. Beijing: Science Press, 2006(in Chinese).
[19] 邹勇, 朱桂平, 李来, 等. 旋转磁场下辐射加热温度对空间浮区对流的影响[J]. 中国科学院大学学报, 2018, 35(2): 261-269.
ZOU Y, ZHU G P, LI L, et al. Influences of radiation temperature on convection of space floating zone under rotating magnetic field[J]. Journal of University of Chinese Academy of Sciences, 2018, 35(2): 261-269(in Chinese).
[20] LEVENSTAM M, AMBERG G. Hydrodynamical instabilities of thermocapillary flow in a half-zone[J]. Journal of Fluid Mechanics, 1995, 297: 357-372.