Pr数对环形浅液池热毛细对流的影响  

EFFECT OF PRANDTL NUMBER ON THERMOCAPILLARY CONVECTION IN SHALLOW ANNULAR POOLS

作　　者：石万元[1] 李友荣[1] 彭岚[1] 

机构地区：[1]重庆大学动力工程学院,重庆400044

出　　处：《工程热物理学报》2011年第2期250-254,共5页Journal of Engineering Thermophysics

基　　金：国家自然科学基金资助项目(No.50976128);教育部留学回国人员启动基金(教外司留(2009)1001-1);重庆市自然科学基金项目(CSTC2008BB4301);中国博士后基金项目(No.20080440694)

摘　　要：为了解流体普朗特数(Pr)对热毛细对流的影响,通过线性稳定性分析,确定了环形浅液池内硅熔体(Pr=0.011)和几种硅油(Pr数从6.7至57.9)热毛细对流失稳的临界条件,获得了它们在临界条件下的热流体波,特别是高Pr数硅油的热流体波。结果发现:当Pr≤15.9时,临界Ma数随Pr数的增加迅速上升,此时环形池内只有一组热流体波,呈连续条纹状。当Pr>15.9后,临界Ma数随Pr数的增加变缓,环形池内由波数相同、强弱和传播角不同的两组热流体波组成,二者相互干涉形成忽明忽暗、断断续续的条纹。随着Pr数的增加,其中占据主要地位的一组热流体波变得越来越长,传播角越来越小。临界波数m_c和临界相速ω_c随Pr数的增加而降低。In order to understand the effect of Prandtl （Pr） number on thermocapillary convection instability, the thermocapillary convection in shallow annular pools of silicon melt （Pr = 0.011） and silicone oils with Pr number ranging from 6.7 to 57.9 are investigated using linear stability analysis. The hydrothermal waves （HW） and their critical conditions for the incipience of HWs are determined, especially for those at high value of Pr number. The results indicate that the Mac increases sharply with increasing Pr number when Pr≤15.9, while it increases slightly with increasing Pr number when Pr 〉 15.9. When Pr≤15.9, there is only one group of HW in the pool. However, two groups of HW coexist in the pool and they interfere each other when Pr 〉 15.9. With increasing Pr number, the arms of the main group of HW become longer and their propagation angles decrease gradually. The critical wave number mc and critical phase velocity wc decrease with increasing Pr number.

关 键 词：热毛细对流 普朗特数 线性稳定性分析 热流体波 

分 类 号：TK124[动力工程及工程热物理—工程热物理]