本研究以數值方法探討二維穩態預混火焰在一階突擴階梯管內的火焰行為及火焰穩定極限。文中使用完整的納威爾-史托克方程式和簡化的甲烷四步驟反應模擬化學反應。在入口流場模式為Poiseuille速度分佈及等溫壁條件下觀察並分析預混層流火焰在突擴階梯管中穩定存在。參數探討平均入口速度、預混氣體當量比、管徑擴張比和壁溫對於再附著點長度、火焰位置、火焰形狀機制、氣體莫耳分率分佈、火焰穩定極限的影響。
緊鄰階梯突擴處後方所形成的滯流區中的渦流，會劇烈影響流場並直接改變燃燒反應機制及火焰形狀，而火焰位置也會間接影響流場流動分佈。本文研究了三種管徑擴張比(分別為1.67、2.5和5)，探討不同的入口流速下，涵蓋在計算域內所有可能的火焰位置。當ER=5時，研究發現有三種火焰形狀機制，分別是蕈狀火焰、鬱金香型火焰和非對稱-鬱金香型火焰；當ER=2.5時，則發現有四種火焰形狀機制，分別為蕈狀火焰、鬱金香型火焰、非對稱-鬱金香型火焰和傾斜型火焰;最後當ER=1.67時，發現有五種火焰形狀機制，分別為微弱火焰、蕈狀火焰、鬱金香型火焰、非對稱-鬱金香型火焰和傾斜型火焰。
研究結果顯示在等溫冷壁、低當量比條件下，火焰穩定極限範圍縮小，火焰形狀機制種類減少，火焰位置移動幅度較大; 反之，在等溫熱壁、高當量比條件下，火焰穩定極限範圍增廣，火焰形狀機制種類增加，火焰位置移動幅度較小。

Flame behaviors and stability limits of the two-dimensional steady premixed flame in one-step tubes are investigated numerically in this study. In this study, the complete Navier-Stokes equations are used in the mathematical formulation and the flame chemistry is modeled by a simplified four-step reduced reaction mechanism of methane-air mixture. The steady premixed flames in the one-step tubes are studied. Parametric investigations are carried out to understand the effect of average inflow velocity, mixture equivalence ratio, expansion ratio of the tube and wall-temperature on reattachment length, flame position, flame shape, distribution of gas mole fraction and flame stability limits.
It was observed that the recirculation zone, created due to sudden flow expansion, at the backward step significantly modifies the flow velocity profile and directly changes the combustion reaction mechanism, however the flame position will indirectly affect the distribution of the flow field. The inflow velocity is varied so as to cover all possible flame positions inside the domain. Three expansion ratio, 1.67, 2.5, 5, have been considered. Three flame behaviors have been observed when ER is 5, which are mushroom-shaped flame, tulip-shaped flame and asymmetrical tulip-shaped flame. Four flame behaviors have been observed when ER is 2.5, which are mushroom-shaped flame, tulip-shaped flame, asymmetrical tulip-shaped flame and slant-shaped flame. Five flame behaviors have been observed when ER is 1.67, which are weak flame, mushroom-shaped flame, tulip-shaped flame, asymmetrical tulip-shaped flame and slant-shaped flame.
Results show that the lower the wall-temperature and the mixture equivalence ratio, the smaller the flame stability limits range are, the fewer the types of flame shape are and the larger the increments of flame displacement become, and vice versa.

致謝 ii
摘要 iii
Abstract iv
總目錄 vi
圖目錄 ix
表目錄 xiii
符號說明 xiv
第一章 前言 1
1.1 研究動機 1
1.2 文獻回顧 5
1.3 研究目的 12
第二章 數學模型和求解方法 22
2.1 模型假設與統御方程式 22
2.2物理化學性質 24
2.3 化學反應機制 28
2.4 邊界條件 30
2.5求解方法和收斂標準 30
第三章 結果與討論 33
3.1 各種火焰形狀類型介紹 34
3.1.1 微弱火焰(weak flame) 35
3.1.2 蕈狀火焰(mushroom-shaped flame) 37
3.1.3 鬱金香型火焰(tulip-shaped flame) 38
3.1.4 非對稱-鬱金香型火焰(asymmetrical tulip-shaped flame) 40
3.1.5 傾斜型火焰(slant-shaped flame) 42
3.1.6 參數對火焰形狀的影響 44
3.2 當量比Ф對火焰燃燒機制的影響 45
3.2.1 當量比Ф對火焰穩定極限的影響 45
3.2.2當量比Ф對火焰形狀機制的影響 48
3.2.3當量比Ф對火焰位置的影響 50
3.3 ER對火焰及流場之間交互作用的影響 51
3.3.1 ER對無反應徑向流速分布在不同軸向位置之影響 52
3.3.2 ER對Xr分布的影響 54
3.4入口速度Ua對火焰燃燒機制的影響 60
3.4.1 入口速度Ua對火焰位置的影響 60
3.4.2入口速度Ua對火焰形狀機制的影響 62
3.4.3入口速度Ua對火焰形狀機制和火焰位置的影響 64
3.4.4入口速度Ua對中間產物一氧化碳的影響 66
3.5等溫熱壁(Tw3=600K)對火焰燃燒機制的影響 68
3.5.1等溫熱壁(Tw3=600K)對火焰穩定極限的影響 68
3.5.2等溫熱壁(Tw3=600K)時當量比Ф對火焰形狀機制的影響 71
3.5.3等溫熱壁(Tw3=600K)時當量比Ф對火焰位置的影響 72
3.5.4等溫熱壁(Tw3=600K)對火焰及流場之間交互作用的影響 73
3.5.5 等溫熱壁(Tw3=600K)條件下不同入口速度Ua對火焰燃燒機制的影響 78
3.5.6等溫熱壁(Tw3=600K)條件下Ua對一氧化碳的影響 82
第四章 結論與展望 84
參考文獻 86

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