底部加热平面Poiseuille流中的局部行波结构  

Localized traveling wave convection in plan Poiseuille flow heated from below

作　　者：赵秉新[1,2] 田振夫[1] 

机构地区：[1]复旦大学力学与工程科学系,上海200433 [2]宁夏大学数学计算机学院,银川750021

出　　处：《水动力学研究与进展（A辑）》2012年第6期649-658,共10页Chinese Journal of Hydrodynamics

基　　金：国家自然科学基金资助项目(10972058;10662006);宁夏自然科学基金资助项目(NZ0938)~~

摘　　要：利用高精度紧致差分格式,模拟研究了物性参数对底部均匀加热平面Poiseuille流动系统中行波对流结构的影响。取与实验相同的参数条件下,获得的数据与实验结果吻合较好,验证了格式的有效性。当雷诺数为定值时,随着傅汝德数Fr的逐渐减小,流场中依次出现了传导状态、局部行波对流(LTW)状态和充分发展的行进波对流(TW)状态。LTW状态的存在受雷诺数和傅汝德数的共同影响,局部对流区域的宽度及对流涡卷数随着傅汝德数的增加而减小。此外,探讨了普朗特数对局部行波结构的影响,进一步给出了不同普朗特数下雷诺数和弗汝德数的倒数与产生涡旋的关系。分析表明:在给定雷诺数时,LTW状态发生的临界傅汝德数的倒数随着普朗特数Pr的增大而以指数形式减小;在Pr 2/3时,LTW状态存在的傅汝德数的范围为最小。Based on a High-order compact （HOC） difference scheme proposed for the two-dimensional hydrodynamic equations, the behavior of plane Poiseuille flows heated uniformly from below was investigated with various physical parameters. The numerical results, in excellent agreement with experimental ones at the same conditions, prove the effectiveness of the HOC scheme. With the fixed Reynolds number Re and the decreasing of Froude Fr, it occurred in sequence the conduction, localized traveling wave （LTW） convection and fully developed traveling wave convection. LTW convection isaffected remarkably by both Re and Fr, and with the increasing ofFr, the vortex number and the width of localized convection field decreased. In addition, some analysis on the influence of Prandtl number Pr on the LTW convection was made and found that the critical value of 1/Fr decreased exponentially with the increase ofPr, and that the range of Fr in which the localized traveling wave convection exist is smallest at Pr = 2/3 for the fixed Reynolds. In the end, the critical relation curves between Re and 1/Fr of the vortex producing for numbers of Pr are also shown.

关 键 词：Poiseuille流动 行进波 高精度 稳定性 

分 类 号：O357[理学—流体力学]