臺灣博碩士論文加值系統

本文使用數值方法研究火焰在絕熱容器內非穩態傳播的現象，燃燒化學反應區以薄火焰模式簡化為一界面，燃燒速度則隨著未燃氣熱力性質和火焰面曲率的改變而變化，等位面(level set)G方程式用來描述此界面隨時間的運動。計算結果和實驗及DNS計算方法所得的結果非常相似。研究內容首先是探討管長、管徑、初始點火形狀、燃燒速度和圓管轉速等參數對火焰傳播的影響，結果顯示蕈狀形(mushroom shape)和鬱金香形(tulip shape)火焰都能在封閉管內穩定地傳播，而火焰成形機制主要是受到流體動力的影響。其次發現當點火端邊界由封閉口改為開放口時，計算的火焰形狀大部份沒有定性上的改變。最後在對火焰傳播進行穩定分析時，結果指出降低密度比、增加燃燒速度和縮短擾動波長皆會助長Darrieus-Landau 不穩定性，重力對火焰不穩定性亦有很大的影響。

Unsteady flames propagating in an adiabatic enclosure are investigated by a numerical method. The use of thin flame model simplifies the combustion chemical reaction zone as a flame sheet, of which the burning velocity is a function of unburned gas thermodynamic properties and the flame curvature. A level set G equation is employed to describe kinematics of the interface. Computational results are similar to those obtained by experimental and DNS numerical methods. In this study, the effects of tube length and diameter, initial flame shape, burning velocity, and tube rotating speed on flame propagation are analyzed first. Results show that both mushroom shape and tulip shape flames can propagate steadily in a closed tube. The mechanisms of flame shape formation are affected by hydrodynamics strongly. As the boundary of ignition side is changed from the closed end to the open end, there is no qualitative change of the flame shape for most flames. The flame stability analysis reveals that lowering the density ratio, increase in the burning velocity, and decrease in the disturbance wave number will amplify Darrieus-Landau instability. The gravity force also has the great effects on the flame stability.

目 錄
誌謝………………………………………………………..ⅰ
摘要………………………………………………………..ⅱ
英文摘要…………………………………………………..ⅲ
表目錄……………………………………………………..ⅳ
圖目錄……………………………………………………..ⅴ
符號說明…………………………………………………..ⅺ
目錄………………………………………………………ⅹⅸ
第1章 前言……………………………………………..1
1-1研究動機………………………………………….1
1- 2文獻回顧…………………………………………2
1- 3研究說明…………………………………………6
第2章 數學模型…………………………………………8
2-1 統制方程式………………………………………..9
2- 2火焰面運動方程式………………………………11
2-3初始條件和邊界條件……………………………..13
第3章 數值方法………………………………………….15
3- 1流場計算方法……………………………………..15
3-1.1格點系統……………………………….…….16
3-1.2流場差分方程式的建立………………….….17
3-1.3壓力修正量差分式的建立……………….….19
3-1.4初始條件和邊界條件之差分式……………..23
3-1.5時間間隔和收歛標準………………………..24
3-1.6促進收斂的技巧……………………………..25
3-2壓力方程式和體積源項之處理……………………27
3-3 G方程式的計算…………………………………….29
3-3.1 G方程式的格點系統………………………...29
3-3.2 G差分式的建立……………………………...30
3-3.3 初始條件和邊界條件的差分式………….….31
3-3.4時間間隔………………………………………33
3-3.5一維層流火焰燃燒速度之處理……………….34
第4章 層流火焰在絕熱封閉圓管內傳播………………….37
4-1火焰在不同長度圓管內傳播……………………….37
4-2圓管管徑對火焰傳播的影響………………………..42
4-3火焰面曲率對火焰傳播的影響……………………..44
4-4初始火焰形狀對火焰傳播的影響…………………...46
4-5圓管旋轉速度對火焰傳播的影響…………………….47
4-6火焰在封閉管內傳播的結論………………………….50
第5章火焰在絕熱圓管內由開口端向封閉端傳播之數值研究
……………………………………………………………...52
5-1本文計算結果與DNS計算結果的比較………………53
5-2初始火焰形狀對一端開口管火焰傳播的影響………..54
5-3管徑對一端開口管火焰傳播的影響…………………..55
5-4圓管轉速對一端開口管火焰傳播的影響……………..56
5-5火焰由開口端向閉口端傳播的結論……………..……58
第6章 火焰DARRIEUS-LANDAU與RAYLEIGH-
TAYLOR不穩定性的數值研究……………………………..60
6-1數學方程式…………………………………………….…61
6-2 初始條件和邊界條件…………………………………63
6-3 出口、計算網格和時間間隔的處理……………………65
6-4結果與討論……………………………………………….67
6-5穩定分析的結論…………….…………………………….71
第7章結論與展望…………………………………………………73
7-1結論……………………………………………………….73
4- 2未來展望…………………………………………….…..74
參考文獻……………………………………………………….…..76
附表………………………………………………………………..84
附圖………………………………………………………………..89
附錄A…………………………………………………………….126
附錄B…………………………………………………………….129
附錄C…………………………………………………………….131

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