Linear Stability Analysis of Thermocapillary Flow in Rotating Shallow PoolsHeated from Inner Wall  

作　　者：TIAN Zu-an ZENG Zhong LIU Hao YIN Linmao ZHANG Liangqi QIAO Long 

机构地区：[1]State Key Laboratory of Coal Mine Disaster Dynamics and Control(Chongqing University),Chongqing 400044,China [2]Department of Engineering Mechanics,College of Aerospace Engineering,Chongqing University,Chongqing 400044,China [3]Department of Engineering Mechanics,College of Mathematics and Physics,Chongqing University of Science and Technology,Chongqing 401331,China

出　　处：《Journal of Thermal Science》2020年第1期251-259,共9页热科学学报（英文版）

基　　金：supported by the National Natural Science Foundation of P. R. China (No. 11572062);Program for Changjiang Scholars and Innovative Research Team in University (No. IRT_17R112)

摘　　要：Thermocapillary flow of silicon melt(Pr=0.011)in shallow annular pool heated from inner wall was simulated at the dimensionless rotation ratewranging from 0 to 7000.The effect of pool rotation on the stability of the thermocapillary flow was investigated.The steady axisymmetric basic state was solved by using the spectral element method;the critical stability parameters were determined by linear stability analysis;the mechanism of the flow instability was explored by the analysis of energy balance.A stability diagram,exhibiting the variation of the critical Marangoni number versus the dimensionless rotation ratewwas presented.The results reveal that only one Hopf bifurcation point appeared in the intervals ofω<3020 andω>3965,and the corresponding instability was caused by the shear energy,which was provided by the thermocapillary force and pool rotation,respectively.In addition,the competition between thermocapillary force and pool rotation leads to three Hopf bifurcation points in the range of 3020<ω<3965 with the increase of Marangoni number.Thermocapillary flow of silicon melt(Pr=0.011) in shallow annular pool heated from inner wall was simulated at the dimensionless rotation rate ω ranging from 0 to 7000. The effect of pool rotation on the stability of the thermocapillary flow was investigated. The steady axisymmetric basic state was solved by using the spectral element method; the critical stability parameters were determined by linear stability analysis; the mechanism of the flow instability was explored by the analysis of energy balance. A stability diagram, exhibiting the variation of the critical Marangoni number versus the dimensionless rotation rate ω was presented. The results reveal that only one Hopf bifurcation point appeared in the intervals of ω<3020 and ω>3965, and the corresponding instability was caused by the shear energy, which was provided by the thermocapillary force and pool rotation, respectively. In addition, the competition between thermocapillary force and pool rotation leads to three Hopf bifurcation points in the range of 3020<ω<3965 with the increase of Marangoni number.

关 键 词：annular pool thermocapillary flow instability spectral element method linear stability analysis 

分 类 号：O363.2[理学—流体力学]