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湍流热对流Prandtl数效应的数值研究

         

摘要

The high-resolution numerical simulations of two-dimensional (2D) turbulent Rayleigh-Bénard convection are con-ducted by using the Parallel direct method of DNS (PDM-DNS) with Ra = 1010 and Pr in a range from 0.05 to 20. Using the flow visualization technique, the effects of P r on the structure of plumes and large scale circulation (LSC) are investigated. With P r decreasing, plumes become more active and the flow turns more turbulent. When P r>4.3, pronounced LSC and corner vortex exist. The thickness of thermal boundary layer varies slightly with the value of Pr changing, which obeys a scaling law. Nusselt number (N u) increases with P r value increasing when P r value is low and becomes independent when P r value is high. Furthermore, two definitions of Reynolds number (Re) are given. The Re〈u〉 is calculated from the fluctuation of horizontal velocity near the center of bottom plate, and the ReU max is calculated from maximal horizontal velocity in the mean field. Both of them follow the same scaling Re~P r0.81.%本文采用直接数值模拟的并行直接求解方法,计算了Ra=1010,0.05≤P r≤20的系列Prandtl(P r)数二维湍流热对流.通过流动显示技术,讨论了P r数对羽流形态和大尺度环流结构的影响.在Ra=1010时,随着Pr数减小,羽流的运动和分布表现出更强的湍流性质,较高Pr数的羽流则表现出较强的规律性,当P r>4.3时,流场中存在明显的大尺度环流和角涡结构.不同P r数的温度边界层厚度差异不大,并随P r数存在标度率变化关系.当P r数较低时,系统的传热Nusselt(N u)数随着P r数增加而增加,当P r数较高时,Nu数随Pr数的变化不敏感.靠近底板处速度脉动随Pr数有显著的变化,Pr数越低速度波动越剧烈.通过底板中心位置水平脉动速度和平均场水平速度最大值给出的雷诺数Re〈u〉和ReU max,两种Re数随P r数的变化满足同一标度律,为Re~P r-0.81.

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