垂直圓環柱體中雙擴散對流的三維數值模擬

Three dimensional simulation of double diffusive convection in a vertical annulus

洪藍擬(Lan-Ni Hung)

指導教授 ： 陳發林

國立臺灣大學/工學院/應用力學研究所/碩士(2021年)

https://doi.org/10.6342/NTU202101075

摘要

本論文利用有限元素法計算模擬軟體COMSOL Multipysics來模擬三維垂直圓環柱體中的雙擴散對流現象，以前人的垂直圓環柱雙擴散對流之流體穩定性數值分析為理論背景，來設定模擬軟體相關之物理現象研究問題和參數設定。以往的研究多著重於直角坐標系雙擴散現象之數值分析和數值模擬，圓柱座標系之研究通常會加上內壁旋轉使之產生泰勒渦旋(Taylor vortex)，並且討論轉速對產生對流層的影響。若內壁無旋轉，也多只有側向加熱之研究之實驗和數值分析，極少研究探討內壁無旋轉之雙擴散自然對流現象，故本論文致力於利用數值模擬的方式探討內壁無旋轉之雙擴散自然對流效應。
本研究主題為設想有兩同心圓環柱，兩圓環柱間為封閉的容器，並填入線性濃度分層之鹽水，故設定材料之無因次參數Pr=7 和 Le=100來模擬鹽水。溫度設定內壁固定為高溫，外壁固定為低溫，也就是有側向溫度差，而上下壁為熱絕緣，上下內外壁皆不通透。其中，濃度的初始條件將會分為兩個部份來探討，一是濃度線性分布垂直於溫度線性分布，濃度變化方向為圓環柱高度方向，而溫度變化方向為徑向方向，此初始條件是為了探討在圓環柱剖面側視圖(sectional side view)可觀察到的分層對流流場型態，且藉由改變內外圓環柱半徑比和溫度差來探討這兩個邊界條件之不同會如何影響分層對流流場結構；二是濃度線性梯度分布平行於溫度線性梯度分布，且溫度和濃度變化方向皆為徑向方向。由於前人使用此初始條件研究圓環柱線性流體穩定性之分析，並且得出不同半徑比其相對應之軸對稱和非軸對稱比較圖。而本研究將選取其半徑比0.8之軸對稱和非軸對稱比較圖，並在圖上選取10個重要的點來做暫態流場模擬，探討模擬結果之物理意義是否能與此比較圖相符且互相佐證。

關鍵字

數值模擬 ； 雙擴散對流 ； 圓柱座標系 ； 側向加熱 ； 層狀對流

並列摘要

This thesis uses the finite element method calculation simulation software COMSOL Multipysics to simulate the double-diffusion convection phenomenon in a three-dimensional vertical annulus. The previous numerical analysis of the fluid stability of the vertical toroidal double-diffusion convection is the theoretical background to set the simulation software related physical phenomena research issues and parameter settings. Previous studies have mostly focused on the numerical analysis and numerical simulation of the double-diffusion phenomenon in the rectangular coordinate system. The study of the cylindrical coordinate system usually adds the rotation of the inner wall to produce the Taylor vortex , and discusses how to influence the layered concevtion. If the inner wall doesn’t rotate, there are mostly experiments and numerical analysis of the study of lateral heating. Very few studies have explored the double-diffusion natural convection phenomenon without rotation of the inner wall. Therefore, this paper uses numerical simulation to explore the double-diffusion of the inner wall without rotation.
The theme of this research is to assume two concentric circular columns, a closed container between the two circular columns, and filled with linear concentration stratified brine, so set the dimensionless parameters of the material Pr=7 and Le=100 to simulate brine . Temperature setting in the inner wall is fixed at high temperature and the outer wall is fixed at low temperature, that is, there is a lateral temperature difference. The upper and lower walls are thermally insulated, and the upper, lower, inner and outer walls are impenetrable. The initial conditions of concentration will be discussed in two parts. First, the linear concentration distribution is perpendicular to the linear temperature distribution. The direction of the concentration change is the height of the circular column, and the direction of the temperature change is the radial direction. This initial condition is to explore the pattern of layered convection that can be observed in the sectional side view of the annulus, and to explore the difference between the two boundary conditions by changing the radius ratio and temperature difference of the inner and outer walls how to affect the structure of layered convection. Second, the linear concentration gradient distribution is parallel to the temperature linear gradient distribution, and the direction of temperature and concentration changes are both radial directions. Because the predecessors used this initial condition to study the analysis of the linear fluid stability of the annulus, and obtained the axisymmetric and non-axisymmetric comparison diagrams with different radius ratios. This study will select axisymmetric and non-axisymmetric comparison diagrams with a radius ratio of 0.8, and select 10 important points on the diagram for transient flow field simulation, and explore whether the physical meaning of the simulation results can be consistent with this comparison diagram and corroborate each other.

並列關鍵字

numerical simulation ； double diffusion convection ； cylindrical coordinate ； lateral heating ； layerd convection

參考文獻

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