奇异摄动在层流预混火焰理论研究中的应用

陈正

doi:10.6052/0459-1879-18-243

奇异摄动在层流预混火焰理论研究中的应用

陈正^2), ,

北京大学工学院,湍流与复杂系统国家重点实验室,北京 100871

基金项目: 1) 国家自然科学基金资助项目(91741126, 91541204, 51322602).

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作者简介:
null

2) 陈正,研究员,主要研究方向：燃烧火焰动力学. E-mail: cz@pku.edu.cn

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陈正

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- 收稿日期: 2018-07-22
- 刊出日期: 2018-11-17

APPLICATION OF SINGULAR PERTURBATION IN THE ANALYSIS OF LAMINAR PREMIXED FLAMES

Chen Zheng^2), ,

State Key Laboratory of Turbulence and Complicated System, College of Engineering, Peking University,Beijing 100871, China

摘要

摘要: 奇异摄动被广泛应用于求取力学问题的近似解.一个典型问题就是流体力学中的边界层.郭永怀先生曾发展了适用于平板黏性流动边界层问题的奇异摄动理论.类似于流体力学中的边界层,燃烧研究中的层流预混火焰也可以通过奇异摄动理论进行分析,在燃烧研究中通常称其为大活化能渐近分析.本文介绍了大活化能渐近分析在一维平面预混火焰和球形传播火焰中的应用及相关研究进展.首先介绍了预混火焰结构及其涉及的不同特征尺度,分析了大活化能条件下出现的特征尺度分离,并给出了关于平面预混火焰大活化能渐近分析的详细推导,讨论了热辐射对火焰传播的影响;然后介绍了大活化能渐近分析在点火与球形传播火焰方面的应用,指出了只有能够同时描述点火与球形火焰传播的理论才能准确地预测临界点火条件,并讨论了考虑链式反应的点火与火焰传播理论,分析了热辐射对球形火焰传播的影响,给了关于火焰稳定性理论研究的发展趋势.最后,基于当前研究进展对未来的研究方向进行了展望,其中涉及多步化学反应、低温冷火焰、复杂流动、辐射重吸收等.
- 奇异摄动 /
- 层流预混火焰 /
- 点火 /
- 球形传播火焰 /
- 大活化能渐近分析
Abstract: Singular perturbation is widely used to obtain the approximate solutions for mechanical problems. A typical problem is the boundary layer in fluid mechanics. Yung-Huai Kuo has developed the singular perturbation theory for the boundary layer over a plate. Similar to the boundary layer in fluid mechanics, the laminar premixed flame in combustion can also be analyzed by the singular perturbation method, which is usually called as the large-activation-energy asymptotics. The laminar premixed flame structure consists of the preheat zone, reaction zone, and equilibrium zone. Under the limit of the large activation energy, the chemical reaction rate is very sensitive to the temperature and thereby chemical reaction only occurs in the very thin reaction zone. The ratio between the reaction zone thickness and the preheat zone thickness is a small parameter, based on which the asymptotic analysis can be conducted for a laminar premixed flame. This paper reviews the application and progress of the large-activation-energy asymptotic analysis in the one-dimensional planar premixed flame and spherically propagating flame. First, the structure of the premixed flame and its different characteristic length scales are introduced. The length scale separation due to large activation energy is analyzed. The detailed derivation of the large-activation-energy asymptotic analysis of a planar premixed flame is presented. The analytical solutions for the preheat zone, reaction zone, and equilibrium zone are first sepratedly obtained and then matched aound the interfaces among these three zones. The effects of radiation heat loss on premixed planar flames are discussed. Then, the application of the large-activation-energy asymptotic analysis to the ignition and spherically propagating flame is introduced. It is pointed out that in order to accurately predict the critical ignition conditions, the theory should be able to describe both the ignition kernel development and the spherical flame propagation afterwards. The ignition and flame propagation theory considering chain reactions is discussed, and the trend of theoretical research on flame instability is described. Moreover, the effects of radiation heat loss on spherical flame propagation are discussed. Finally, the future research directions are prospected based on the current research progress, which includes multi-step chemistry, low-temperature cool flame, complicated flow and radiation reabsorption.
- singular perturbation /
- laminar premixed flame /
- ignition /
- spherically propagating flame /
- large-activation-energy asymptotics

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[1]	Kuo YH.On the flow of an incompressible viscous fluid past a flat plate at moderate reynolds numbers. J Math Phys Camb, 1953, 32: 83-101
[2]	Tsien HS.The Poincare-Lighthill-Kuo method. Advan Appl Mech, 1956, 4: 241-349
[3]	Van Dyke M.Perturbation Methods in Fluid Mechanics. Stanford, CA: Parabolic Press, 1975
[4]	Zeldowitsch JB, Kamenetzki DAF.A theory of thermal propagation of flame. Acta Physicochimica Urss, 1938, 9: 341-50
[5]	Zeldovich YB, Barenblatt GI, Librovich VB, et al.The Mathematical Theory of Combustion and Explosions. New York: Consultants Bureau, 1985
[6]	Bush WB, Fendell FE.Asymptotic analysis of laminar flame propagation for general Lewis numbers. Combust Sci Technol, 1970, 1: 421-8
[7]	Bush WB.Asymptotic analysis of laminar flame propagation-review and extension. Int J Eng Sci, 1979, 17: 597-613
[8]	Williams FA.Theory of combustion in laminar flows. Annu Rev Fluid Mech, 1971, 3: 171
[9]	Linan A.Asymptotic structure of counterflow diffusion flames for large activation-energies. Acta Astronautica, 1974, 1: 1007-1039
[10]	Buckmaster JD, Lundford GSS.Theory of Laminar Flames Cambridge: Cambridge University Press, 1982
[11]	Williams FA. Combustion Theory.Second edition ed: Benjamin-Cummins, Menlo Park, CA, 1985
[12]	Law CK. Combustion Physics.Cambridge: Cambridge University Press, 2006
[13]	Clavin P, Searby G.Combustion Waves and Fronts in Flows. Cambridge: Cambridge University Press, 2016
[14]	Poinsot T, Veynante D.Theoretical and Numerical Combustion. 2nd ed R.T. Edwards, Inc, 2005
[15]	Mallard E, Le Chatelier HL. Combustion des melanges gaseux explosifs. ,Ann Mines,, 1883, 4: 379-568
[16]	Mitani T.Propagation velocities of 2-reactant flames. Combust Sci Technol, 1980, 21: 175-177
[17]	Holmes MH.Introduction to Perturbation Methods. 2nd ed. New York: Springer, 2013
[18]	Joulin G, Clavin P.Linear-stability analysis of non-adiabatic flames-diffusional-thermal model. Combust Flame, 1979, 35: 139-153
[19]	Spalding DB.A Theory of inflammability limits and flame-quenching. Philos Trans R Soc London, Ser A, 1957, 240: 83-100
[20]	Landau L.On the theory of slow combustion. Acta Phys Chim, 1944, 19: 77-85
[21]	Sivashinsky GI.Diffusional-thermal theory of cellular flames. Combust Sci Technol, 1977, 15: 137-146
[22]	Pelce P, Clavin P.Influence of hydrodynamics and diffusion upon the stability limits of laminar premixed flames. J Fluid Mech, 1982, 124: 219-237
[23]	Matalon M, Matkowsky BJ.Flames as gas-dynamic discontinuities. J Fluid Mech, 1982, 124: 239-259
[24]	Clavin P.Dynamic behavior of premixed flame fronts in laminar and turbulent flows. Prog Energy Combust Sci, 1985, 11: 1-59
[25]	Law CK, Sung CJ.Structure, aerodynamics, and geometry of premixed flamelets. Prog Energy Combust Sci, 2000, 26: 459-505
[26]	Sivashinsky GI.Instabilities, pattern-formation, and turbulence in flames. Annu Rev Fluid Mech, 1983, 15: 179-199
[27]	Clavin P.Premixed combustion and gasdynamics. Annu Rev Fluid Mech, 1994, 26: 321-352
[28]	Buckmaster J, Clavin P, Linan A, et al.Combustion theory and modeling. Proc Combust Inst, 2005, 30: 1-19
[29]	Matalon M.Intrinsic flame instabilities in premixed and nonpremixed combustion. Annu Rev Fluid Mech, 2007, 39: 163
[30]	Matalon M.Flame dynamics. Proc Combust Inst, 2009, 32: 57-82
[31]	Jin W, Wang JH, Zhang WJ, et al.Investigation of the heat loss effect on cellular flames via proper orthogonal decomposition. Combust Sci Technol, 2018, 190: 803-822
[32]	Eng JA, Zhu DL, Law CK.On the structure, stabilization, and dual response of flat-burner flames. Combust Flame, 1995, 100: 645-652
[33]	Matthews MT, Dlugogorski BZ, Kennedy EM.Influence of upstream versus downstream heat losson the structure and stability of planar premixed burner-stabilized flames. Combust Sci Technol, 2006, 178: 1373-1410
[34]	Chao BH.Instability of burner-stabilized flames with volumetric heat loss. Combust Flame, 2001, 126: 1476-1488
[35]	Kurdyumov VN, Matalon M.The porous-plug burner: Flame stabilization, onset of oscillation, and restabilization. Combust Flame, 2008, 153: 105-118
[36]	Kurdyumov VN, Sanchez-Sanz M.Influence of radiation losses on the stability of premixed flames on a porous-plug burner. Proc Combust Inst, 2013, 34: 989-996
[37]	Matalon M.On flame stretch. Combust Sci Technol, 1983, 31: 169-181
[38]	Candel SM, Poinsot TJ.Flame stretch and the balance equation for the flame area. Combust Sci Technol, 1990, 70: 1-15
[39]	Sivashinsky GI.Converging spherical flame front. Int J Heat Mass Transfer, 1974, 17: 1499-1506
[40]	Sivashinsky GI.Hydrodynamic theory of flame propagation in an enclosed volume. Acta Astronautica, 1979, 6: 631-645
[41]	Clavin P, Williams FA.Effects of molecular-diffusion and of thermal-expansion on the structure and dynamics of premixed flames in turbulent flows of large-scale and low intensity. J Fluid Mech, 1982, 116: 251-282
[42]	Frankel ML, Sivashinsky GI.On effects due to thermal-expansion and Lewis number in spherical flame propagation. Combust Sci Technol, 1983, 31: 131-138
[43]	Frankel ML, Sivashinsky GI.On quenching of curved flames. Combust Sci Technol, 1984, 40: 257-268
[44]	Bechtold JK, Cui C, Matalon M.The role of radiative losses in self-extinguishing and self-wrinkling flames. Proc Combust Inst, 2005, 30: 177-184
[45]	Matalon M, Bechtold JK.A multi-scale approach to the propagation of non-adiabatic premixed flames. J Eng Math, 2009, 63: 309-326
[46]	Clavin P, Grana-Otero JC.Curved and stretched flames: the two Markstein numbers. J Fluid Mech, 2011, 686: 187-217
[47]	Kelley AP, Jomaas G, Law CK. On the critical radius for sustained propagation of spark-Ignited spherical flames. AIAA Paper 2008-1054, 2008
[48]	Lewis B, Von Elbe G.Combustion Flames and Explosive of Gases. 2nd edtion, New York: Academic Press, 1961
[49]	Deshaies B, Joulin G.On the initiation of a spherical flame kernel. Combust Sci Technol, 1984, 37: 99-116
[50]	Champion M, Deshaies B, Joulin G, et al.Spherical flame initiation-Theory versus experiments for lean propane-air mixtures. Combust Flame, 1986, 65: 319-337
[51]	Champion M, Deshaies B, Joulin G.Relative influences of convective and diffusive transports during sphericla flame initiation. Combust Flame, 1988, 74: 161-170
[52]	He L, Law CK.On the dynamics of transition from propagating flame to stationary flame ball. AIAA 99--0325, 1999
[53]	He LT.Critical conditions for spherical flame initiation in mixtures with high Lewis numbers. Combust Theory Model, 2000, 4: 159-172
[54]	Chen Z, Ju Y.Theoretical analysis of the evolution from ignition kernel to flame ball and planar flame. Combust Theory Model, 2007, 11: 427-453
[55]	Chen Z, Burke MP, Ju Y.On the critical flame radius and minimum ignition energy for spherical flame initiation. Proc Combust Inst, 2011, 33: 1219-1226
[56]	Kelley AP, Jomaas G, Law CK.Critical radius for sustained propagation of spark-ignited spherical flames. Combust Flame, 2009, 156: 1006-1013
[57]	Taylor SC.Burning velocity and the influence of flame stretch. [Ph D Thesis]. University of Leeds, 1991
[58]	Tseng LK, Ismail MA, Faeth GM.Laminar burning velocities and markstein numbers of hydrocarbon/air flames. Combust Flame, 1993, 95: 410-426
[59]	Tse SD, Zhu DL, Law CK.Morphology and burning rates of expanding spherical flames in H-2/O-2/inert mixtures up to 60 atmospheres. Proc Combust Inst, 2000, 28: 1793-1800
[60]	Chen Z, Qin X, Ju YG, et al.High temperature ignition and combustion enhancement by dimethyl ether addition to methane-air mixtures. Proc Combust Inst, 2007, 31: 1215-1222
[61]	Huang Z, Zhang Y, Zeng K, et al.Measurements of laminar burning velocities for natural gas-hydrogen-air mixtures. Combust Flame, 2006, 146: 302-311
[62]	Halter F, Tahtouh T, Mouna$\ddot{i}$m-Rousselle C. Nonlinear effects of stretch on the flame front propagation. Combust Flame, 2010, 157: 1825-1832
[63]	Chen Z.Effects of radiation and compression on propagating spherical flames of methane/air mixtures near the lean flammability limit. Combust Flame, 2010, 157: 2267-2276
[64]	Chen Z.On the accuracy of laminar flame speeds measured from outwardly propagating spherical flames: Methane/air at normal temperature and pressure. Combust Flame, 2015, 162: 2442-2453
[65]	Faghih M, Chen Z.The constant-volume propagating spherical flame method for laminar flame speed measurement. Sci Bull, 2016, 61: 1296-1310
[66]	Egolfopoulos FN, Hansen N, Ju Y, et al.Advances and challenges in laminar flame experiments and implications for combustion chemistry. Prog Energy Combust Sci, 2014, 43: 36-67
[67]	Wu Y, Chen Z.Asymptotic analysis of outwardly propagating spherical flames. Acta Mech Sinica, 2012, 28: 359-366
[68]	Ronney PD.On the mechanics of flame propagation limits and extinguishment processes at microgravity. Proc Combust Inst, 1988, 22: 1615-1623
[69]	Ronney PD, Sivashinsky GI.A theoretical-study of propagation and extinction of nonsteady spherical flame fronts. SIAM J Appl Math, 1989, 49: 1029-1046
[70]	Chen Z.On the extraction of laminar flame speed and Markstein length from outwardly propagating spherical flames. Combust Flame, 2011, 158: 291-300
[71]	Kelley AP, Bechtold JK, Law CK.Premixed flame propagation in a confining vessel with weak pressure rise. J Fluid Mech, 2012, 691: 26-51
[72]	Wu FJ, Liang WK, Chen Z, et al.Uncertainty in stretch extrapolation of laminar flame speed from expanding spherical flames. Proc Combust Inst, 2015, 35: 663-670
[73]	Liang WK, Wu FJ, Law CK.Extrapolation of laminar flame speeds from stretched flames: Role of finite flame thickness. Proc Combust Inst, 2017, 36: 1137-1143
[74]	Li XT, Hu EJ, Meng X, Peng C, et al.Effect of Lewis Number on nonlinear extrapolation methods from expanding spherical flames. Combust Sci Technol, 2017, 189: 1510-1526
[75]	Chen Z, Gou X, Ju Y.Studies on the outwardly and inwardly propagating spherical flames with radiative loss. Combust Sci Technol, 2010, 182: 124-142
[76]	Yu H, Han W, Santner J, et al.Radiation-induced uncertainty in laminar flame speed measured from propagating spherical flames. Combust Flame, 2014, 161: 2815-2824
[77]	Chen Z.Effects of radiation absorption on spherical flame propagation and radiation-induced uncertainty in laminar flame speed measurement. Proc Combust Inst, 2017, 37: 1129-1136
[78]	Chen Z.Effects of radiation on large-scale spherical flame propagation. Combust Flame, 2017, 183: 66-74
[79]	Dold JW, Weber RO, Thatcher RW, et al.Flame balls with thermally sensitive intermediate kinetics. Combust Theory Model, 2003, 7: 175-203
[80]	Dold JW.Premixed flames modelled with thermally sensitive intermediate branching kinetics. Combust Theory Model, 2007, 11: 909-948
[81]	Gubernov VV, Sidhu HS, Mercer GN.Combustion waves in a model with chain branching reaction and their stability. Combust Theory Model, 2008, 12: 407-431
[82]	Sharpe GJ.Effect of thermal expansion on the linear stability of planar premixed flames for a simple chain-branching model: The high activation energy asymptotic limit. Combust Theory Model, 2008, 12: 717-738
[83]	Sharpe GJ.Thermal-diffusive instability of premixed flames for a simple chain-branching chemistry model with finite activation energy. SIAM J Appl Math, 2009, 70: 866-884
[84]	Gubernov VV, Kolobov AV, Polezhaev AA, et al.Oscillatory thermal-diffusive instability of combustion waves in a model with chain-branching reaction and heat loss. Combust Theory Model, 2011, 15: 385-407
[85]	Sharpe GJ, Falle SAEG.Numerical simulations of premixed flame cellular instability for a simple chain-branching model. Combust Flame, 2011, 158: 925-934
[86]	Bai B, Chen Z, Zhang HW, et al.Flame propagation in a tube with wall quenching of radicals. Combust Flame, 2013, 160: 2810-2819
[87]	Zhang H, Chen Z.Effects of heat conduction and radical quenching on premixed stagnation flame stabilized by a wall. Combust Theory Model, 2013, 17: 682-706
[88]	Zhang H, Guo P, Chen Z.Outwardly propagating spherical flames with thermally sensitive intermediate kinetics and radiative loss. Combust Sci Technol, 2013, 185: 226-248
[89]	Zhang HW, Chen Z.Bifurcation and extinction limit of stretched premixed flames with chain-branching intermediate kinetics and radiative loss. Combust Theory Model, 2018, 22: 531-553
[90]	Zhang H, Chen Z.Spherical flame initiation and propagation with thermally sensitive intermediate kinetics. Combust Flame, 2011, 158: 1520-1531
[91]	Zhang H, Guo P, Chen Z.Critical condition for the ignition of reactant mixture by radical deposition. Proc Combust Inst, 2013, 34: 3267-3275
[92]	Han W, Chen Z.Effects of finite-rate droplet evaporation on the ignition and propagation of premixed spherical spray flame. Combust Flame, 2015, 162: 2128-2139
[93]	Han W, Chen Z.Effects of finite-rate droplet evaporation on the extinction of spherical burner-stabilized diffusion flames. Int J Heat Mass Transfer, 2016, 99: 691-701
[94]	Liang W, Chen Z, Yang F, et al.Effects of Soret diffusion on the laminar flame speed and Markstein length of syngas/air mixtures. Proceedings of the Combustion Instituete, 2013, 34: 695-702
[95]	Han W, Chen Z.Effects of Soret diffusion on spherical flame initiation and propagation. Int J Heat Mass Transfer, 2015, 82: 309-315
[96]	Bechtold JK, Matalon M.Hydrodynamic and diffusion effects on the stability of spherically expanding flames. Combust Flame, 1987, 67: 77-90
[97]	Bechtold JK, Matalon M. Some new results on Markstein number predictions. AIAA Paper 2000-0575, 2000
[98]	Matalon M, Cui C, Bechtold JK. Hydrodynamic theory of premixed flames: effects of stoichiometry, variable transport coefficients and arbitrary reaction orders . J Fluid Mech, 2003, 487: 179-210
[99]	Jomaas G, Law CK, Bechtold JK.On transition to cellularity in expanding spherical flames. J Fluid Mech, 2007, 583: 1-26
[100]	Bradley D, Cresswell TM, Puttock JS.Flame acceleration due to flame-induced instabilities in large-scale explosions. Combust Flame, 2001, 124: 551-559
[101]	Wu FJ, Jomaas G, Law CK.An experimental investigation on self-acceleration of cellular spherical flames. Proc Combust Inst, 2013, 34: 937-945
[102]	Yang S, Saha A, Wu FJ, et al.Morphology and self-acceleration of expanding laminar flames with flame-front cellular instabilities. Combust Flame, 2016, 171: 112-118
[103]	Kim WK, Mogi T, Kuwana K, et al.Self-similar propagation of expanding spherical flames in large scale gas explosions. Proc Combust Inst, 2015, 35: 2051-2058
[104]	Bauwens CR, Bergthorson JM, Dorofeev SB.Experimental study of spherical-flame acceleration mechanisms in large-scale propane-air flames. Proc Combust Inst, 2015, 35: 2059-2066
[105]	Kagan L, Sivashinsky G.Parametric transition from deflagration to detonation: Runaway of fast flames. Proc Combust Inst, 2017, 36: 2709-2715
[106]	Kagan L, Sivashinsky G.Transition to detonation of an expanding spherical flame. Combust Flame, 2017, 175: 307-311
[107]	Gostintsev YA, Istratov AG, Shulenin YV.Self-similar propagation of a free turbulent flame in mixed gas mixtures. Combust Explo Shock, 1988, 24: 563-569
[108]	Bauwens CR, Bergthorson JM, Dorofeev SB.Critical Peclet numbers for the onset of Darrieus-Landau instability in atmospheric-pressure methane-air flames. Proc 25th ICDERS, Leeds, UK, August 2-7, 20152015
[109]	Buckmaster J.Edge-flames. Prog Energy Combust Sci, 2002, 28: 435-475
[110]	Sanchez AL, Williams FA.Recent advances in understanding of flammability characteristics of hydrogen. Prog Energy Combust Sci, 2014, 41: 1-55
[111]	Williams FA.Progress in knowledge of flamelet structure and extinction. Prog Energy Combust Sci, 2000, 26: 657-682
[112]	de Goey LPH, Hermanns RTE, Bastiaans RJM. Analysis of the asymptotic structure of stoichiometric premixed CH$_4$-H-2-air flames. Proc Combust Inst, 2007, 31: 1031-1038
[113]	Seshadri K, Bai XS.Rate-ratio asymptotic analysis of the structure and extinction of partially premixed flames. Proc Combust Inst, 2007, 31: 1181-1188
[114]	Ju YG, Reuter CB, Won SH.Numerical simulations of premixed cool flames of dimethyl ether/oxygen mixtures. Combust Flame, 2015, 162: 3580-3588
[115]	Ju YG.On the propagation limits and speeds of premixed cool flames at elevated pressures. Combust Flame, 2017, 178: 61-69
[116]	Zhang WK, Faqih M, Gou XL, et al.Numerical study on the transient evolution of a premixed cool flame. Combust Flame, 2018, 187: 129-136
[117]	Chen Z, Qin X, Xu B, et al.Studies of radiation absorption on flame speed and flammability limit of CO2 diluted methane flames at elevated pressures. Proc Combust Inst, 2007, 31: 2693-2700

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奇异摄动在层流预混火焰理论研究中的应用

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2) 陈正,研究员,主要研究方向：燃烧火焰动力学. E-mail: cz@pku.edu.cn

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奇异摄动在层流预混火焰理论研究中的应用

作者简介: null2) 陈正,研究员,主要研究方向：燃烧火焰动力学. E-mail: cz@pku.edu.cn

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2) 陈正,研究员,主要研究方向：燃烧火焰动力学. E-mail: cz@pku.edu.cn

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