臺灣博碩士論文加值系統

　　玻璃基板中殘留氣泡及夾雜物的多寡主要取決於玻璃熔解窯爐的澄清能力並對玻璃基板的品質有很大的影響。本研究針對玻璃熔解窯爐的熔融玻璃區發展一套三維數學模型，配合物理模型實驗，探討不同底吹氣體流量及電極加熱溫度下窯爐內的流動及熱傳行為，評估不同窯爐操作條件下的玻璃品質。

　　數學模型採用有限差分的數值解析方法，以SOLA-VOF計算流體力學技術計算窯爐內部的速度場、溫度場及窯爐使用分率等資訊。物理模型建構一縮小壓克力窯爐，利用矽油取代熔融玻璃，進行流動軌跡之觀測及最小滯留時間的量測，最後以最小滯留時間與窯爐使用分率作為評估玻璃品質的指標。

　　本研究分別探討三種底吹氣體流量與兩種電極加熱溫度，結果發現底吹氣體流量越大氣體攪拌環流及流動軌跡均越大，並有效提升最小滯留時間及窯爐使用分率，有助生產高品質的玻璃基板。電極加熱的操作條件僅小幅增加流動軌跡及窯爐使用分率卻大幅降低最小滯留時間，但由實驗觀測中可發現其可有效減少窯爐後段的懸浮氣泡濃度，因此需要更合適的玻璃品質評估指標來全面性評估玻璃品質。

　　The quantities of bubbles and inclusions that remain in glass substrate strongly depend on the refining ability of the glass melting furnace and have significant effects on the quality of glass substrate. This study, focused merely on the molten glass zone in the glass melting furnace, developed a mathematical model and a physical model to investigate fluid flow and heat transfer behaviors and to evaluate the glass qualities under different bubbling fluxes and heating temperatures.

　　By using finite difference method and a computational fluid dynamics technique, SOLA-VOF, the mathematical model could be used to analyze the velocity, temperature fields and active volume ratio of glass melting furnace. The physical model which executed in a reduced acrylic mold used silicon oil as a substitute for molten glass. The flow path and minimum residence time was recorded. The glass qualities under different operation conditions are evaluated by minimum residence time and active volume ratio of glass melting furnace in the end.

　　Three bubbling fluxes and two heating temperatures were investigated. The results showed that as the bubbling flux increases the bubbling circulation, flow path, and the minimum residence time and active volume ratio all increase. Therefore, the glass quality promotes as bubbling flux increases. To heating operating conditions, flow paths and active volume ratios are slightly raised, minimum residence times are significantly decreased, and suspended bubbles in the back zone of glass melting furnace are reduced. Therefore, the glass quality under heating should be evaluated by other appropriate glass quality indexes.

中文摘要.......................................I
Abstract......................................II
目錄.........................................III
表目錄........................................VI
圖目錄.......................................VII
符號說明.......................................X

第一章 導論....................................1
1.1 研究背景...................................1
1.2 玻璃窯爐研究之發展歷程.....................2
1.2.1 玻璃窯爐物理模型之發展進程...............2
1.2.2 玻璃窯爐數學模型之發展進程...............3
1.3 研究目的...................................5

第二章 研究方法................................8
2.1 數學模型...................................9
2.1.1 控制方程式...............................9
2.1.2 自由表面之處理..........................10
2.1.3 氣泡之處理..............................11
2.2 物理模式..................................12
2.2.1 油模實驗裝置之建構......................12
2.2.2 油模實驗流程............................13
2.3 玻璃品質評估指標..........................14

第三章 數值方法...............................18
3.1 網格分割與變數設置........................18
3.2 控制方程式之差分化........................19
3.2.1 能量方程式之顯性有限差分................19
3.2.2 動量方程式之顯性有限差分................19
3.2.3 連續方程式的差分化及流場壓力解法........20
3.3 自由表面追蹤之數值處理....................22
3.3.1 自由表面之建立/重建.....................22
3.3.2 自由表面之傳遞..........................26
3.3.3 流體體積重新分佈........................27
3.4 邊界條件..................................29
3.4.1 出入口邊界條件..........................29
3.4.2 自由表面邊界條件........................29
3.4.3 固體邊牆邊界條件........................30
3.4.4 氣泡邊界條件............................31
3.4.5 溫度場邊界條件..........................32
3.5 氣泡型態之追蹤............................33
3.6 穩定度的要求..............................34
3.7 數值計算流程..............................35

第四章 結果與討論.............................47
4.1 室溫下不同底吹氣體流量之流動現象..........47
4.1.1 氣泡型態之比較..........................48
4.1.2 流動軌跡及流場速度分佈..................49
4.2 底吹氣體流量固定時不同加熱溫度之流動現象..51
4.2.1 自然對流現象............................51
4.2.2 流動軌跡及流場速度分佈..................52
4.3 玻璃品質之評估............................54

第五章 結論...................................83

第六章 未來研究方向...........................85

參考文獻......................................86
附錄A 能量方程式之有限差分化..................89
附錄B 動量方程式之有限差分化..................90
附錄C 壓力與速度修正之推導....................95
附錄D 介面法向量之差分式......................99
附錄E 前向問題與逆向問題.....................100

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