Steady thermocapillary-buoyant convection in a shallow annular pool. Part 1: Single layer fluid
Steady thermocapillary-buoyant convection in a shallow annular pool. Part 1: Single layer fluid
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DOI：
10.1007/s10409-011-0450-6
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发表时间：
2011-05
影响因子：
3.5
通讯作者：
You-Rong Li;Shuang Wang;Chuang Wu
中科院分区：
文献类型：
--
作者：
You-Rong Li;Shuang Wang;Chuang Wu
本文研究了在径向温度梯度作用下环形浅池中的定常热毛细浮力对流。采用匹配渐近理论得到了小纵横比情况下的流场和热场的渐近解。小纵横比定义为层厚与差距宽度之比。将流动区域划分为远离筒壁的核心区和靠近筒壁的两端区。通过分别求解核心流和末端流，然后通过匹配的渐近展开将它们连接起来，在核心区域获得渐近解。对于硅熔体系统，将渐近解与数值模拟结果进行了比较。结果表明，对于小的深宽比，两种解在芯区有很好的一致性。随着深宽比的增大，现有渐近解的适用性逐渐降低。
This paper examines the steady thermocapillarybuoyant convection in a shallow annular pool subjected to a radial temperature gradient. A matched asymptotic theory is used to obtain the asymptotic solutions of the flow and thermal fields in the case of small aspect ratios, which is defined as the ratio of the layer thickness to the gap width. The flow domain is divided into the core region away from the cylinder walls and two end regions near each cylinder wall. Asymptotic solutions are obtained in the core region by solving the core and end flows separately and then joining them through matched asymptotic expansions. For the system of silicon melt, the asymptotic solutions are compared with the results of numerical simulations. It is found that the two kinds of solutions have a good agreement in the core region for a small aspect ratio. With the increase of aspect ratio, the applicability of the present asymptotic solutions decreases gradually.