本研究建立一新模型探討微小管內火焰被反覆點燃熄滅的傳播動態行為。此新模型主要忽略微小管中垂直流道方向的速度變化，因此在小管內入口為Poiseullie flow分佈的流場中，各流線符合質量守恆，即氣體溫度升高後，僅以流道方向膨脹，速度增加。
文中比較了此模型與常密度模型(CDM)對火焰傳播現象的分析的差異。研究發現兩者對於火焰點燃熄滅震盪的頻率、火焰形狀以及到達管道上游時間，都有非常大的差異。在CDM模型中，火焰在傳遞的過程不容易受到管壁熱散失的影響進入震盪現象。在新建立的模型中，火焰在初始點燃後，有延遲震盪現象，並且在震盪現象中震盪頻率密集，反應速率大小差異不大。
在路易士數改變的研究中，當路易士數提升時，在CDM中，火焰傳播過程震盪現象中，出現了震盪行為的時間增加的特性；而在新模型中，震盪行為減少，傳播時間下降。
氣體入口溫度改變的研究中，當溫度提升時，在CDM中，火焰震盪傳播時間縮短，震盪波長增加;在新模型中，提前產生震盪，反應速率下降。

A new model to discuss the behavior of flame repetitive ignition/quenching spread in a tiny tube is established in this study. This new model mainly ignores the velocities perpendicular to the flow direction, and therefore, each streamline meets the conservation of mass flow rate with the Poiseullie flow distribution at the entrance. In other words, as the gas temperatures increase, the gas expand and the velocities increase only in the channel direction.
In this study, we compare the new model with the CDM(Constant Density Model) and analyze the difference of the simulation results of the two models. The results show that the ignition/quenching frequencies, flame structures, and propagation speed are obviously of great differences.
In CDM, the reaction is easily quenched by the wall and oscillation happens earlier; in the new model, reaction is harder to be quenched by the wall after ignition, and small differences are in the reaction rate.
In the investigation of the Lewis number effect, when the Lewis number increases, the oscillation and time increase in CDM model; However , in the new model, the oscillation behavior and time decrease.
In the investigation of the inlet temperature effect, when temperature increases, oscillation decrease and in the oscillation process, wavelength expand .However, in the new model, the time is reduced into oscillation and reaction rates decrease.

總目錄
致謝 ii
中文摘要 iii
Abstract iv
總目錄 v
圖表目錄 vii
符號說明 x
第一章 序論 1
1.1 前言 1
1.2 文獻回顧 2
1.3 研究目的 6
第二章 數學模型和求解方法 13
2-1:幾何圖形和邊界條件 13
2-2 數值模型與統御方程式 15
2-3:模型無因次簡化 17
2-4:求解方法和收斂標準 19
第三章 結果與討論 20
3-1:CDM行為下火焰傳播過程 22
3-2:VDM行為下火焰傳播過程 27
3-3:路易士數對CDM行為的影響 33
3-4:路易士數對VDM行為的影響 39
3-5:入口溫度對CDM行為的影響 44
3-6:入口溫度對VDM行為的影響 50
第四章 結論 56
參考文獻 57

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