側向加熱分層流體中鹽指對流的三維數值模擬

Abstract

本論文採用有限元素法軟體COMSOL Multiphysics來模擬側向加熱分層流體中三維雙擴散對流的流場結構，由於模擬為三維模擬，觀察流場的方向區分為橫面(Transverse plane)和縱面(longitudinal plane)，而在過去絕大多數的數值模擬均為觀察橫面的層狀對流，然而在縱面的雙擴散對流仍是不可忽略，在對流層中，當施加側壁溫度效應時，溫暖且富含溶質的流體沿著對流層的頂部從熱壁往冷壁流動，而冷且缺乏溶質的流體則沿著對流層的底部從冷壁往熱壁流動，這產生所謂的鹽指對流(salt-finger convection)，其在縱面的方向上能被觀察，故本論文著重於層狀對流在三維空間下隨時間的發展，並探討在不同邊界條件下，對流層內的流場結構。 研究結果顯示，當改變容器的幾何外型或邊界條件時，一旦產生完全發展的層狀對流，且層狀對流能夠穩定存在於溶液中，此時流場對應到穩定邊界圖(stability boundary)為B區(salt-finger regime)；然而，若是流場產生的層狀對流的厚度遠大於容器的高度時，流場的對流為單一環流，其類似於熱對流模型，此時流場對應到穩定邊界圖(stability boundary)為A區(thermal-diffusive regime)。在B區的流場中分別探討三個不同溫度差下，層狀對流隨時間的發展，結果顯示，當溫度差較小時，層狀對流的厚度相對較小，且達到完全發展時所需要的時間較長，而在縱面上會產生許多的小渦流，其軸平行於溫度梯度的方向；而當溫度差逐漸增加時，層狀對流的厚度相對變大，且達到完全發展時所需要的時間變得較短，由於層狀對流的厚度變大，在縱面上的小渦流有更多的空間在層狀對流發展，使得其形成長條狀渦流，且分布靠近上下水平邊界處。在A區的流場中，由於其類似於熱對流模型，故以單一環流呈現於流場中，而在縱面上的渦流則呈現一團紊亂，且其速度大小相對於橫面而言小很多。

This paper simulates and analyzes three dimensional double diffusive flow structure on a stratified fluid of lateral heating by the commercial software package－COMSOL Multiphysics using a finite element method. Since our studies are three dimensional simulations, we divide the flow field into the transverse plane and the longitudinal plane. In the past, most of numerical simulations generally studied the layered convection in the transverse plane. However, the double diffusive convection in the longitudinal plane is still not negligible. In each of the convection cells, after impulsively applying temperature difference, warm and solute-rich fluid flows from the hot to cold wall along the top of the cell while the return of the cool and solute-poor fluid is along the bottom of the cell. This situation is conducive to the so-called salt-finger convection and it can be observed in the longitudinal plane. Therefore, this paper focuses on the layered convection with the development of time in three dimensional space. And we discuss the flow structure of convection cell under different boundary conditions. The result shows that once a fully developed convection layer is generated with changing the geometric shape or boundary conditions of the tank, and layered convection can be stably present in the solution, the flow field corresponds to the stability boundary of B region (salt-finger regime). However, if the thickness of layered convection is larger than the height of the tank, convection is a single circulation over all the tank, which is similar to the thermal convection model. The flow field corresponds to the stability boundary of A region (thermal-diffusive regime). In B region, we discuss the layered convection with the development of time at three different temperature differences. The results show that when the temperature difference is small, the thickness of layered convection is relatively small, and the time for fully developed flow becomes longer. In the longitudinal plane, a horizontal row of small vortices are generated in layered convection, whose axes aligned in the direction of the temperature gradient. Nevertheless, when the temperature difference is gradually increased, the thickness of layered convection is relatively large. And small vortices have more space to grow in layered convection. The vortices form a long vortex and are present in the upper and lower horizontal boundaries. In A region, because the flow is similar to the thermal convection model, it is presented as a single circulation in the flow field. In the longitudinal plane, vortices are turbulent and their speeds are relatively smaller than the transverse plane.