# 臺灣博碩士論文加值系統

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 摘 要 本論文旨以理論建立一適用準則以律定當引用Burke-Schumann薄焰 假說處理有限速率擴散燃燒所需之最低燃率要求，其目的在使燃焰結構 解析與行為預測得以近似估算並維持可欲精度。文中分別探討平面靜域 與渦流場內有限燃率擴散焰，後者則係為檢驗流體應變效應而設。關於 準則建立係以燃燒產物分佈作為依據，而燃率計算則依 Arrhenius反應 定律為之，並以一反應參數 C作為適用指標。另者，亦定義一背景當量 比Φ以表述燃燒環境中燃料與助燃物的配置比例，並將渦漩強度、流元 位置與時間效應等項組成一參數ξ作為流體應變指標。根據研究發現： 此類燃焰具動態行為並受Φ與ξ值統制，當處於Φ>1條件下燃焰將朝助 燃物區位移，在Φ<1時將朝向燃料，而Φ=1則無明顯焰區位移。在流體 應變方面：於渦流近域之燃焰將具較大ξ值並承受較大拉伸應變，其焰 區因Φ所生位移將趨緩，但對遠域燃焰而言則結果完全相反。在適用準 則方面：於指定檢驗時刻及相同擴散條件與助燃環境下，Φ值越大合於 容差所需最小C值愈低；然ξ值越大則合於容差所需最小C值條件愈高。 本研究亦根據渦流運動與座標轉換，發展一套計算程式用以繪製渦流燃 燒結構圖作為現象探討之用。雖然為求理論解析之可行，本研究引用許 多基本假設，然所獲結果趨勢卻可對紊流燃燒與擴散焰理論的實驗研究 提供參考助益。
 ABSTRACT This thesis presents a theoretical study on seeking a criterion of validity for applying Burke-Schumann flame sheet postulate to deal with diffusion flame burning problems with a finite rate. The purpose is to provide an approximation basis for doing analysis of the burning structure and prediction of the flame behavior with desired accuracy. Two major topics studied are that flame burning in a quiescent field and that in a vortex flow field, while the latter is designed for examining the effect of variable flow strain on the flame burning. In deriving the criterion, the distributions of flame burning products were invoked as a base for judgments, and the rate of burning was assumed following Arrhenius law of reaction. In this way, a reaction parameter C was identified to be the criterion index, a background equivalence ratioΦ was defined to tell the proportions of fuel and oxidizer placed in the field, and a parameterξwas used as an indicator for the flow straining effect. According to the study, it was found that the behavior of flame burning is dynamic, governed byΦ andξ. The trend of behavior further shows that the flame zone will be shifted toward the oxidizer side whenΦ>1, toward the fuel side whenΦ<1, and will be stationary in the field whenΦ=1. As to the flow straining effect, it shows that the flame zone will be strongly strained and weakly shifted in the near field of the vortex, characterized with a large value ofξ, while in the far field the trend is totally reversed. About the criterion of validity, it was found that the larger the Φ, the smaller the minimal requirement of C for a good approximation, under given conditions of species diffusivity D, flame stoichiometry S, oxidizer concentration YOo, and the justification instant t. Besides, it was also found that the minimal C to qualify a good approximation will be increased withξ. In addition to the above, efforts were also done in developing a computer program which is based on vortex kinematics and coordinate transformations of the flow geometry. It was thus able to generate distribution data of the flame burning in the vortex field, and plots of the vortical flame burning structures were then obtained for illustrations. In all, the present theoretical study may for analysis convenience involve many simplifications and basic assumptions; however, the physical trends here observed would be useful for further experimental studies on the issue of turbulent combustion and diffusion flame theories, in the future.
 目 錄 1.前言........................................................1 1.1.問題起源................................................1 1.2.文獻研究................................................3 1.3.論文架構................................................5 2.平面靜域內有限速率擴散火焰燃燒之探討........................7 2.1.燃焰之Arrhenius動力理論模擬.............................7 2.1.1.問題描述與基本假設................................7 2.1.2.數學模式與時空條件................................9 2.1.3.數值方法與計算求解...............................12 2.2.燃焰之Burke-Schumann動力解.............................14 2.3.有限速率擴散燃焰結構與暫態行為.........................18 2.4.燃焰之Burke-Schumann解適用準則.........................22 2.4.1.比對流程.........................................27 2.4.2.趨勢分析.........................................29 3.平面單渦流場內有限速率擴散燃燒之區域探討...................31 3.1.區域焰元之Arrhenius動力理論模擬........................31 3.1.1.問題描述與基本假設...............................32 3.1.2.數學模式與時空條件...............................32 3.1.3.數值方法與計算求解...............................37 3.2.區域焰元之Burke-Schumann動力解.........................39 3.3.有限速率擴散焰元結構與暫態行為.........................42 3.4.區域焰元之Burke-Schumann解適用準則.....................46 3.4.1.比對流程.........................................46 3.4.2.趨勢分析.........................................48 4.平面單渦流場內有限速率擴散燃燒之整體探討...................51 4.1.區域焰元聚合方法與程式.................................51 4.2.勢渦流模擬之適用性探討.................................54 4.3.結果與趨勢分析.........................................57 5.結論.......................................................64 參考文獻.....................................................67 自傳.........................................................70
 參考文獻1. Burke, S. P., and Schumann, T. E. W., "Diffusion flame,"Industrial Engineering Chemistry, Vol.20, p998-1004 (1928).2. Mitchell, R. E., Sarofin, A. F. and Clomburg, L. A.,"Experimental and Numerical Investigation of ConfinedLaminar Diffusion Flames," Comb. & Flame, Vol.37, p227-244(1980).3. Williams, F. A., Combustion Theory, The Benjamin/CummingsPublishing Inc., 2nd ed. (1985).4. Greenberg, J. B., "The Burke-Schumann Diffusion FlameRevisited-with Fuel Spray Injection," Comb. & Flame, Vol.77,p229-240 (1989).5. Kim, J. B., "Diffusive Burning of Plane Liquid and SprayJets in a Coflowing Oxidizer Stream", Ph.D Thesis, TheUniversity of Michigan, Ann Arbor, USA (1988).6. Marble, F. E., "Growth of a Diffusion Flame in Field of aVortex," Advances in Aerospace Science, p395-413 (1985).7. Shiah, S. M., "Dynamic Behavior of a Dense Spray DiffusionFlame in a Potential Vortex," Ph.D Thesis, The Universityof Michigan, Ann Arbor, USA (1992).8. Shiah, S. M., "Analytical Diffusion Layer Structure of aConcentration Driving Nonstationary Diffusion Flame," Proc.of the 9th. Nat. Conf. on Mech. Eng., CSME, p383-390 (1992).9. Fendell, F., and Wu, F., "Unsteady Planar Diffusion Flames:Ignition, Travel, Burnout," NASA Technical Report, p357-362,Aug. 01 (1995).10. Carrier, G. F., Fendell, F. E., and Marble, F. E., "Effectsof Strain Rate on Diffusion Flames" SIAM J. of Appl. Math.,Vol.28, p453 (1975).11. Continillo, G., and Sirignano, W. A., "Counter-Flow SprayCombustion and Flame," Comb. & Flame, Vol.81, p453 (1991).12. Linan, A., "The Asymptotic Structure of Counter-flowDiffusion Flames for Large Activation Energies," ActaAstronautica, Vol.1, p1007-1039 (1974).13. Tsuji, H., and Yamaoka, I., "The Counter-flow DiffusionFlames in the Forward Stagnation Region of Porous Cylinder,"The 11th Symp on Comb., The Combustion Institute/Pittsburgh,p979-984 (1967).14. Schaefer, B. A., "Temperature and Optimum Ionization in theMicro Diffusion Flame," Comb. & Flame, Vol.50, p198-207(1983).15. Cetegen, B. M. ,and Sirignano, W. A., " Study of Mixing andReaction in the Field of a Vortex," Comb. Sci. & Tech.,Vol.72, p157-181 (1990).16. Zukoski, E. E., and Marble, F. E., " Experiments Concerningthe Mechanism of Flame from Bluff Bodies" Proc. of theNorthwestern Gasdynamics Symposium., Aug, p205-210 (1955).17. Rogers, D. E., and Marble, F. E., " A Mechanism forHigh-Frequency Oscillation in Ramjet Combustors andAfterburners" Jet Propulsion, Vol.26, p456 (1956).18. Karagozian, A. R., and Marble, F.E., " Study of DiffusionFlames in a Stretched Vortex," Comb. Sci. & Tech., Vol.45,p65-84 (1986).19. Karagozian, A. R., and Manda, B. V. S., " Flames Structureand Fuel Consumption in the Field of a Vortex pair," Comb.Sci. & Tech., Vol.49, p185-200 (1986).20. Manda, B. V. S., and Karagozian, A. R., " Effects of HeatTransfer on Diffusion Flames-Vortex pair Interaction," Comb.Sci. & Tech., Vol.61, p101-119 (1988).21. Laverdant, A. M., and Candel, S. M., " A Numerical Analysisof a Diffusion Flame-Vortex Interaction," Comb. Sci. & Tech.,Vol.60, p79-96 (1988).22. Rolon, J. C., Aguerre, F., Candel S., " Experiments on theInteraction between a Vortex and a Strained Diffusion Flame,"Comb. & Flame, Vol.100, No3, p79-96 (1988).23. Macarage, Michele G., Jackson, T. L., Hussaini, M. Y.,"Ignition Dynamics of a Laminar Diffusion Flame in theField of a Vortex embedded in a Shear Flow," Comb. Sci. &Tech., Vol.102, no.1-6, p231-253 (1994).24. Kozusko, F., Macarage, Michele G., " Study of Ignition of aDiffusion Flame in the Field of a Vortex Pair," Series inScience and Engineering., Vol.3, p275-284 (1994).
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