本研究完成了以數值模擬火焰行為在二維一階突擴通道的模型，並以非中心線對稱的假設做全模型模擬。本研究主要著重在突擴比為2(β =2)的情況下且壁保持等溫冷壁300K，改變入口流速，發現了四種火焰行為，穩態蕈狀火焰、穩態鬱金香形火焰、簡單週期性震盪火焰，及複雜週期性震盪火焰。其中鬱金香形火焰為穩態與非穩態火焰的過渡火焰，其穩定原因是由於壁對火焰的熄滅效應。簡單週期性震盪火焰是由於入口流速增加，造成火焰不穩定(Landau-Darrieus flame instability)，隨著入口平均流速增加，週期愈大(頻率愈小)，火焰長度也愈長。複雜週期性震盪火焰其週期長度約為週期性震盪火焰的6~10倍，由於火焰本身的不穩定機制，與一階突擴通道的流場不穩定機制之間的交互作用所造成。另外也比較了不同突擴比並尋找不同流速下的火焰行為及火焰的存在極限，並且發現了不同的火焰傳播行為: 不穩定震動火焰。本研究中發現使不同火焰存在的原因不僅與入口平均流速、壁對火焰的熄滅效應、火焰本身不穩定，亦和流場對稱性有關。

Flame behaviors in a mesoscale one-stepped sudden-expansion channel are numerically investigated by a two-dimensional model without symmetry assumption at centerline. The channel expansion ratio β is equal to 2. The isothermal wall boundary condition (300K) is set to eliminate the wall-flame thermal interaction. It is found four flame behaviors: the steady mushroom-shaped flame, the steady tulip-shaped flame, the simple periodically oscillating flame and the complex periodic oscillating flame. The tulip-shaped flame is a transition among the steady and unsteady flame, and it is stable due to the wall-quenching effect. As the velocity of inlet raise, the simple periodic oscillating flame is caused by Landau-Darrieus flame instability. Meanwhile, the flame period time becomes longer with the mean velocity increase, and the flame axial length also longer. The existence of complex periodic flame is due to the interaction between Landau-Darrieus instability and hydrodynamic instability. I also change expansion ratio to find out flame behaviors under various mean velocity of inlet, and investigate the flame existence limit. In addition, another flame behavior, unsteady shaking flame, is observed. In this study, the flames exists because of the mean velocity if inlet, wall-quenching effect, flame instability and symmetry of the flowfield.

論文審定書 i
誌謝 ii
摘要 iii
Abstract iv
目錄 v
圖目錄 viii
表目錄 x
符號說明 xi
第1章 序論 1
1.1 前言 1
1.2 文獻回顧 2
1.3 微小尺度燃燒系統 6
1.4研究目的 7
1.5本文架構 8
第2章 數學模型和求解方法 9
2.1 數學模型 9
2.2 邊界條件 11
2.3 模型假設與統御方程式 12
2.3.1 模型假設 12
2.3.2 統御方程式 12
2.3.3 數值方法 15
第3章 結果與討論 16
3.1 不同流速下之火焰形態分類 18
3.1.1 入口平均流速對火焰位置關係 19
3.2 穩態火焰(Steady flame) 21
3.2.1 穩態蕈狀火焰 21
3.2.2 穩態鬱金香形火焰機制 25
3.3 暫態非穩定火焰(Transient unsteady flame) 30
3.3.1 簡單週期性震盪火焰機制 30
3.3.2 複雜週期性震盪火焰機制 38
3.3.3 不同流速下簡單週期性震盪火焰之頻率 40
3.3.4 火焰軸向長度與頻率之關係 42
3.4 通道流場與燃燒流場比較 44
3.5 固定流速下不同Lewis number之影響 49
3.6 改變突擴比 之火焰存在極限比較 53
3.7 固定流量下不同突擴比 之比較 55
第4章 結論與未來展望 57
參考文獻 58

[1] 趙怡欽,許家睿,陳冠邦, “現階段微尺度燃燒科技發展簡介”, 燃燒季刊第十一卷 第三期(2002) pp.2-10
[2] Y. Yiguang, M. Kaoru, Technology development and fundamental research, Progress in Energy and Combustion Science 37, 2011, pp.669-715
[3] D. G. Norton, D. G. Vlachos, Combustion characteristics and flame stability at the microscale: a CFD study of premixed methane/air mixtures, Chemical Engineering Science 58, 2003, pp.4871 – 4882
[4] G. Pizza, C. E. Frouzakis, J. Mantzaras, A. G. Tomboulides, K. Boulouchos, Dynamics of premixed hydrogen/air flames in mesoscale channels, Combustion and Flame 155, pp. 2-20
[5] G. Pizza, C. E. Frouzakis, J. Mantzaras, A. G. Tomboulides, K. Boulouchos, Dynamics of premixed hydrogen/air flames in microchannels, Combustion and Flame 152, pp. 433–450
[6] Y. Ju, B. Xu, Effects of channel width and Lewis number on the multiple flame regimes and propagation limits in mesoscale, Combustion Science and Technology, Vol. 178, 2006, pp.1723-1753
[7] Y. Ju, B. Xu, Theoretical and experimental studies on mesoscale flame propagation and extinction, Proceedings of the Combustion Institute, Vol. 29,2002, pp.949-956
[8] K. Maruta, T. Kataoka, N.II. Kim, S. Minaev, R. Fursenko, Characteristics of combustion in a narrow channel with a temperature gradient, Proceedings of the Combustion Institute, Vol. 30, 2005, pp.2429-2436
[9] J. Daou, M. Matalon, Influence of conductive heat-losses on the propagation of premixed flames in channels, Combustion and Flame, Vol.126, 2002, pp.321-339
[10] C.H. Tsai, The asymmetric behavior of steady laminar flame propagation in ducts, Combustion Science and Technology, Vol.180, 2008, pp.533-545
[11] D.G.Norton, D.G.Vlachos, Combustion characteristics and stability at the microscale: a CFD study of premixed methane/air mixtures, Chemical Engineering Science, Vol.58, 2003, pp.4871-4882
[12] D.G.Norton, D.G.Vlachos, A CFD study of propane/air microflame stability, Combustion and Flame, Vol.138, 2004, pp.97-107
[13] N. Kim, K. Maruta, A numerical study on propagation of premixed flames in small tubes, Combustion and Flame, Vol.146, 2006, pp.283-301
[14] G. Pizza, C. E. Frouzakis, J. Mantzaras, A. G. Tomboulides, K. Boulouchos, Three-dimensional simulations of premixed hydrogen/air flames in microtubes, Journal of Fluid Mechanics, Vol. 658, 2010, pp. 463- 491
[15] M.J Kwon, B.J Lee, S.H Chung, An observation of near-planar spinning premixed flames in a sudden expansion tube, Combustion and Flame, Vol. 105,1996, pp.180-188
[16] Y. Ju, B. Xu, Experimental study of spinning combustion in a mesoscale divergent channel, Proceedings of the Combustion Institute, Vol. 31, pp.3285-3292
[17] Anil A. Deshpande, Sudarshan Kumar, On the formation of spinning flames and combustion completeness for premixed fuel-air mixtures in stepped tube microcombustors, Applied Thermal Engineering 51, 2013, pp.91-101
[18] Yong Fan, Yuji Suzuki, Nobuhide Kasagi, Expermental study of a micro-scale premixed flame in quartz channels, Proceedings of the Combustion Institute, Vol.32, 2009, pp.3083-3090
[19] Subhadeep Chakraborty, Achintya Mukhopadhyay, Swarnendu Sen, Interaction of Lewis number and heat loss effects for a laminar premixed flame propagating in a channel, International Journal of Thermal Sciences, Vol.47, 2008, pp.84-92
[20] V. N. Kurdyumov, E. Ferna´Ndez-Tarrazo, Lewis number effect on the propagation of premixed laminar flames in narrow open ducts, Combustion and Flame, Vol.128, pp.382-394
[21] W. Cherdron, F. Durst, J. H. Whitelaw, Asymmetric flows and instabilities in symmetric ducts with sudden expansions, J. Fluid Mech.,Vol.84, 1978, pp.13-31
[22] B.F. Armaly, F. Dursts, J.C.F.Pereira, B.Schonung, Experimental and theoretical investigation of backward-facing step flow, J. Fluid Mech.,Vol.127,1983, pp.473-496
[23] F. Durst, J. C. F. Pereirat, C. Tropea, The plane symmetric sudden-expansion flow at low Reynolds numbers, J. Fluid Mech.,Vol.248,1993, pp.567-581
[24] J.H.Nie, B.F.Armaly, Three-dimensional convective flow adjacent to backward-facing step effects of step height, International Journal of Heat and Mass Transfer, Vol.45, 2002, pp.2431-2438
[25] Hiroshi Iwai, Kazuyoshi Nakabe, Kenjiro Suzuki, Flow and Heat transfer characteristics of backward-facing step laminar flow in a rectangular duct, International Journal of Heat and Mass Transfer, Vol.43, 2000, pp.457-471
[26] W.M. Yang, S.K. Chou, C. Shu, Z.W. Li, H. Xue, Combustion in micro-cylindrical combustors with and without a backward facing step, Applied Thermal Engineering, Vol.22, 2002, pp.1777-1787
[27] W.M. Yang, S.K. Chou, J. Li, Microthermophotovoltaic power generator with high power density, Applied Thermal Engineering, Vol.29, 2009, pp.3144-3148
[28] Valiev Damir, The role of Landau-Darrieus instability in flame dynamics and deflagration-to-detonation transition, 2007