激波与火焰相互作用发展过程的数值模拟
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摘要
本文主要研究激波与火焰相互作用过程中爆轰的产生问题,课题源于国家自然科学基金青年科学基金项目(10802077/A020403)——激波与火焰相互作用与爆燃转爆轰强化机制的数值模拟。本文分别对此进行了理论研究,模型建立,程序编制和数值模拟。
理论研究部分介绍了对激波与火焰相互作用起重要作用的三种不稳定性现象和成因, Richtmyer-Meshkov不稳定性、Kelvin-Helmholtz不稳定性和Rayleigh-Taylor不稳定性,尤其是R-M不稳定性。分析了斜压效应的产生以及它对涡量和R-M不稳定性的发展影响,推导说明了K-H和R-T联合不稳定性对流体界面失稳的影响,还介绍了界面不稳定性的五个发展阶段,着重讨论了界面不稳定的非线性发展阶段。
计算模型是常温常压下,在一个无限长的激波管中,充满一定化学当量比的氢气和空气可燃混合气,在管道中轴线上有一个正在燃烧的球形火焰,管道左侧有一入射激波向右传播,当到达火焰面时,激波开始与火焰相互作用。文章还采用了在流场中加入小火焰和障碍物的计算模型。
本文采用二维非定常带化学反应的Euler方程作为控制方程,详细氢氧9组分20步基元反应为化学反应模型,时空守恒方法为计算方法。利用FORTRAN语言编制计算程序,并在曙光PHPC100型高性能计算机上运行程序。
通过对结果的研究,找出了爆轰形成关键参数:激波马赫数和火焰半径。马赫数为1.4不会发生爆轰现象;马赫数为2.0时,半径大的火焰可以产生爆轰。马赫数为2.3时,所有半径的火焰都可以产生爆轰。火焰半径决定了反向透射激波的形成和传播方向。能量聚集区和激波多重诱导区最容易产生爆轰。流场加入小火焰和障碍物增大了两种区域的产生机会,缩短爆轰形成的时间和空间跨度。
This paper is concerned with research into the generation of detonation during the process of shock-flame interaction. It is a part of the Natural Science Foundation of China project (10802077 / A020403): The Simulation of Shock-Flame Interaction and Mechanism of Deflagration-to-Detonation Transition (DDT). Theoretical models, computational program and numerical simulations are presented.
The theoretical analysis introduced three instability phenomena including their generative mechanisms: Richtmyer-Meshkov instability, Kelvin-Helmholtz instability and Rayleigh-Taylor instability, particularly the R-M. The generative reasons for the baroclinic effect and the role it plays in the process of the generation and development of vortices and R-M instability is discussed, and the analysis of K-H and R-T joint instability and its impact on fluid interface instability was introduced. Five phases of the development of instabilities were introduced, particularly the nonlinearity processes of the instability. A mathematical model was established. The mathematical model consisted of a long shock tube, maintained at normal temperature and atmospheric pressure, filled with a hydrogen-air mixture. A burning orbicular flame was fixed in the pipe with its central axis just cross the center of flame, an incident shock wave was introduced at left side of the tube, and the shock-flame interaction began once the shock reached flame. Models of adding small flames and obstacles into the flow field were adopted.
2-dimensional Euler equations coupled with chemical reactions were used as control equations. Numerical simulation of the process was performed using the space-time conservation method. The detailed hydrogen-oxygen chemical mechanism, which included 9 species and 20 element reactions, was included. The computational program was written using FORTRAN, and run on a high performance computer.
An analysis of the results indicated two key parameters Mach number and flame radius for the generation of detonation. When the Mach number was below 1.4, detonation would never appear. A flame with larger radius would generate detonation, when the Mach number was increased to 2.0, but for Mach numbers of 2.3 or larger, all the flames were able to generate detonation no matter how big the flame radius was. Flame radius plays an important role in shock reflection formation and its direction of propagation. Detonation was easily generated in the regions where energy gathered or where there were multiply shocks. The addition of small flames or obstacles to the flow field could increase the chance of these two areas’generation, hence the process of the generation of detonation was shortened in terms of space and time.
理论研究部分介绍了对激波与火焰相互作用起重要作用的三种不稳定性现象和成因, Richtmyer-Meshkov不稳定性、Kelvin-Helmholtz不稳定性和Rayleigh-Taylor不稳定性,尤其是R-M不稳定性。分析了斜压效应的产生以及它对涡量和R-M不稳定性的发展影响,推导说明了K-H和R-T联合不稳定性对流体界面失稳的影响,还介绍了界面不稳定性的五个发展阶段,着重讨论了界面不稳定的非线性发展阶段。
计算模型是常温常压下,在一个无限长的激波管中,充满一定化学当量比的氢气和空气可燃混合气,在管道中轴线上有一个正在燃烧的球形火焰,管道左侧有一入射激波向右传播,当到达火焰面时,激波开始与火焰相互作用。文章还采用了在流场中加入小火焰和障碍物的计算模型。
本文采用二维非定常带化学反应的Euler方程作为控制方程,详细氢氧9组分20步基元反应为化学反应模型,时空守恒方法为计算方法。利用FORTRAN语言编制计算程序,并在曙光PHPC100型高性能计算机上运行程序。
通过对结果的研究,找出了爆轰形成关键参数:激波马赫数和火焰半径。马赫数为1.4不会发生爆轰现象;马赫数为2.0时,半径大的火焰可以产生爆轰。马赫数为2.3时,所有半径的火焰都可以产生爆轰。火焰半径决定了反向透射激波的形成和传播方向。能量聚集区和激波多重诱导区最容易产生爆轰。流场加入小火焰和障碍物增大了两种区域的产生机会,缩短爆轰形成的时间和空间跨度。
This paper is concerned with research into the generation of detonation during the process of shock-flame interaction. It is a part of the Natural Science Foundation of China project (10802077 / A020403): The Simulation of Shock-Flame Interaction and Mechanism of Deflagration-to-Detonation Transition (DDT). Theoretical models, computational program and numerical simulations are presented.
The theoretical analysis introduced three instability phenomena including their generative mechanisms: Richtmyer-Meshkov instability, Kelvin-Helmholtz instability and Rayleigh-Taylor instability, particularly the R-M. The generative reasons for the baroclinic effect and the role it plays in the process of the generation and development of vortices and R-M instability is discussed, and the analysis of K-H and R-T joint instability and its impact on fluid interface instability was introduced. Five phases of the development of instabilities were introduced, particularly the nonlinearity processes of the instability. A mathematical model was established. The mathematical model consisted of a long shock tube, maintained at normal temperature and atmospheric pressure, filled with a hydrogen-air mixture. A burning orbicular flame was fixed in the pipe with its central axis just cross the center of flame, an incident shock wave was introduced at left side of the tube, and the shock-flame interaction began once the shock reached flame. Models of adding small flames and obstacles into the flow field were adopted.
2-dimensional Euler equations coupled with chemical reactions were used as control equations. Numerical simulation of the process was performed using the space-time conservation method. The detailed hydrogen-oxygen chemical mechanism, which included 9 species and 20 element reactions, was included. The computational program was written using FORTRAN, and run on a high performance computer.
An analysis of the results indicated two key parameters Mach number and flame radius for the generation of detonation. When the Mach number was below 1.4, detonation would never appear. A flame with larger radius would generate detonation, when the Mach number was increased to 2.0, but for Mach numbers of 2.3 or larger, all the flames were able to generate detonation no matter how big the flame radius was. Flame radius plays an important role in shock reflection formation and its direction of propagation. Detonation was easily generated in the regions where energy gathered or where there were multiply shocks. The addition of small flames or obstacles to the flow field could increase the chance of these two areas’generation, hence the process of the generation of detonation was shortened in terms of space and time.
引文
[1] Joseph Yang, Toshi Kubota, Edward E Zukoski. Application of Shock-Induced Mixing to Supersonic Combustion. AIAA Journal. 1993(31): 854-862
[2] Khokhlov A M, Oran E S, Chtchelkanova A Y, Wheeler J C. Interaction of a Shock with a Sinusoidally Perturbed Flame [J]. Combustion and Flame. 1999(117): 99-116
[3] Kull A E, etal. Experimental Studies of Super detonative Ram Accelerator Modes. AIAA paper 89-0431, 1989
[4] Hertzberg A, Brucher A P. Ram Accelerator: A New Chemical Method for Accelerating Projectile to Ultrahigh Velocities. AIAA Journal. 1988(26): 195-203
[5] Salamandra G D, ARS J. 1960,30-73
[6] Salamandra G D, Sevast’yanova I K. Sov. Phys. Tech. Phys. 1960.4: 1250
[7] Eder A, Brehm N. Analytical and Experimental Insights into Fast Deflagrations, Detonations, and the Deflagration-to-Detonation Transition Process. Heat and Mass Transfer. 2001(37): 543-548
[8] Markstein G H, Schwartz D. Jet Propulsion. 1955, 25-173
[9] Markstein G H, Sixth Symposium (Intermational) on Combustion, Rheingold, New York, 1957, page. 387
[10] Markstein G H, Nonsteady Flame Propagation. Macmillan, NY, 1964, Chapter D
[11] Markstein G H, Rudinger G. Shock Wave and Flame Interactions. Combustion and Propulsion. Third AGARD Colloquium. Pergamon Press, NY, 1958, page. 153
[12] Thomas G, Richard Bambrey, Caren Brown. Experimental Observations of Flame Acceleration and Transition to Detonation Following Shock-Flame Interaction. Combustion Theory And Modelling.2001(5): 573-594
[13]靳建明.火焰在激波诱导下稳定性问题的数值模拟和实验验证[D],硕士论文,南京:南京理工大学,2004
[14] G. Lacaze, B Cuenot , T Poinsot, M Oschwald. Large eddy simulation of laser ignition and compressible reacting flow in a rocket-like configuration. Combustion and Flame. 2009 (156): 1166–1180
[15] F. Williams, Combustion Theory, Benjamin Cummings, Menlo Park, CA, 1985
[16] I. Glassman, Combustion, Academic Press, New York, 1987
[17] M. Champion, B. Deshaies, G. Joulin, K. Kinoshita, Combust. Flame 1986 (65): 319–337
[18] Vadim N. Gamezo, Alexei M Khokhlov, Elain S Oran. The Influence of Shock Bifurcationon Shock-Flame Interactions and DDT. Combustion Institute 2001(29):1810-1826
[19] Elain S Oran, V N Gamezo, A M Khokhlov, Effects of boundary layers and wakes on shock-flame interactions and DDT, AIAA. 2002, 0776
[20] Elain S Oran, V N Gamezo, A M Khokhlov, Three-dimensional reactive shock bifurcations. Proceedings of the Combustion Institute 2005. (30): 1841–1847
[21]范宝春,江强,董刚,叶经方.激波与火焰相互作用过程.爆炸与冲击. 2003.23(6):488-492
[22]范宝春,叶经方,董刚,江强.激波与火焰相互作用的化学动力学模拟.自然科学进展. 2004. 14(3):312-318
[23]董刚,刘宏伟,陈义良.通用甲烷层流预混火焰半详细化学动力学机理.燃烧科学与技术. 2002. 8(1): 44-48
[24]董刚,范宝春,谢波.温度梯度影响爆燃装爆轰的数值模拟.中国安全生产科学技术2007. 6(3): 39-43
[25]程军波,傅德薰,马延文. Richtmyer-Meshkov失稳的数值模拟.计算物理. 2001. 18(5): 390-396
[26]孙锦山,朱建士.理论爆轰物理.国防工业出版社,第一版1995
[27]王继海.二维非定常流和激波.北京:科学出版社,1994
[28] Lewis D J. Taylor Instability of Liquid Surfaces When Accelerated in A Direction Perpendicular to Their Planes II. Proc. Roy. Soc. London, 1950, A202(1068): 81-98
[29] Birkhoff G. Taylor Instability and Laminar Mixing. LA1862, Los Alamos: Los Alamos Scientific Lab., 1954.76
[30] Birkhoff G. Helmholtz and Taylor Instability. In: Birkhoff G, Bellman R, Lin C C ed. Hydrodynamic Instability, Am. Math. Soc., New York, 1962: 52-76
[31] Kee R J, Rupley F M, Miller J A. The CHEMKIN Thermodynamic Data Base[R]. Sandia National Laboratories Report SAND87-8215B, 1990
[32] Bonnie J. McBride, Michael J. Zehe, and Sanford Gordon NASA Glenn Coefficients for Calculating Thermodynamic Properties of Individual Species. NASA, TP-2002-211556
[33]翁春生, Jay. Gore. P. CE/SE方法在非定常爆轰计算中的应用.空气动力学学报, 2003, 3 :301-310
[34] Chang S. C. The Method of Space-Time Conservation Element and Solution Element - A New Approach for Solving the Navier-Stokes and Euler Equations[J]. Journal of Computational Physics, 1995, 119(2)
[35] Zhang Z C, Yu S T. A Modified Space-Time Conversation Element and Solution ElementMethod for Euler and Navier-Stokes Equations. 1999.AIAA: 99-327
[36]董刚,范宝春.氢气-空气混合物种瞬态爆轰过程的二维数值模拟[J].高压物理学报2004. 18(1):40-46
[37]陈绍仲.一个理想的爆燃转爆轰过程[J].宁波大学学报. 2002, 15(4): 1-6
[38]陈永刚,何立明,刘建勋.时空守恒元和解元方法的爆震波一维数值模拟.推进技术2005(26):256-259
[39]王超,施红辉.激波诱导燃烧转爆轰数值模拟[C],第十四届全国激波与激波管学术会议论文集, 2010: 164-167
[40] Zhang Z C, Yu S T. A Modified Space-Time Conversation Element and Solution Element Method for Euler and Navier-Stokes Equations. 1999.AIAA: 99-327
[41]施红辉,卓启威。Richtmyer-Meshkov不稳定性流体混合区发展的实验研究[J]。力学学报。2007,29(3):417-421
[42]卓启威.气液界面R-M不稳定性实验研究[D].硕士论文,北京:中国科学院力学研究所.2006
[43]卓启威,施红辉。气液界面上Richtmyer-Meshkov不稳定性的实验研究[J]。实验流体力学。2007,21(1):25-30
[44]张鸣远,景思睿,李国君.高等工程流体力学[M].西安交通大学出版社. 2006
[45] Alexei M Khokhlov, Elain s Oran. Numerical Simulation of Detonation Initiation in a Flame Brush: The Role of Hot Spots. Combustion and Flame 1999,16: 400-416
[46] Mark, A Avest, D F Griffithst and Desmond J Hingam. Runge-Kutta Solutions of Hyperbolic Conservation Law with Source Term. SIAM. J. SCI. COMPUT. Vol. 22, No. 1, PP. 20-38
[47]王超.脉冲爆轰发动机中波的动力过程分析[D],博士论文,北京:中国科学院力学研究所,2003
[48] Manabu Hishida , Toshi Fujiwara, PiotrWolanski. Fundamentals of rotating detonations[J]. Shock Waves. 2009, 19:1–10
[49] J S Grondin, John H S Lee. Experimental observation of the onset of detonation downstream of a perforated plate disturbance[J]. Shock Waves. 2010, 20: 381–386
[50] James Meredith, Hoi Dick Ng, John H S Lee. Detonation diffraction from an annular channel[J]. Shock Waves. 2010, 20: 449–455
[51] Alexandra Camargo, Hoi Dick Ng, Jenny Chao, John H S Lee. Propagation of near-limit gaseous detonationsin small diameter tubes[J]. Shock Waves. 2010, 20: 499–508
[52] Rémy Sorin, Ratiba Zitoun, Boris Khasainov, Daniel Desbordes. Detonation diffraction through different geometries[J]. Shock Waves. 2009, 19: 11–23
[53] F Virot, B Khasainov, D Desbordes, H N Presles. Two-cell detonation: losses effects on cellular structure and propagation in rich H2–NO2/N2O4–Ar mixtures[J]. Shock Waves. 2010, 20: 457–465
[54] A V Fedorov , T A Khmel, Y V Kratova. Cellular detonation diffraction in gas–particle mixtures[J]. Shock Waves. 2010, 20: 509–519
[55] A Emelianov, A Eremin. Detonation wave initiated by explosive condensation of supersaturated carbon vapor[J]. Shock Waves. 2010, 20: 491–498
[2] Khokhlov A M, Oran E S, Chtchelkanova A Y, Wheeler J C. Interaction of a Shock with a Sinusoidally Perturbed Flame [J]. Combustion and Flame. 1999(117): 99-116
[3] Kull A E, etal. Experimental Studies of Super detonative Ram Accelerator Modes. AIAA paper 89-0431, 1989
[4] Hertzberg A, Brucher A P. Ram Accelerator: A New Chemical Method for Accelerating Projectile to Ultrahigh Velocities. AIAA Journal. 1988(26): 195-203
[5] Salamandra G D, ARS J. 1960,30-73
[6] Salamandra G D, Sevast’yanova I K. Sov. Phys. Tech. Phys. 1960.4: 1250
[7] Eder A, Brehm N. Analytical and Experimental Insights into Fast Deflagrations, Detonations, and the Deflagration-to-Detonation Transition Process. Heat and Mass Transfer. 2001(37): 543-548
[8] Markstein G H, Schwartz D. Jet Propulsion. 1955, 25-173
[9] Markstein G H, Sixth Symposium (Intermational) on Combustion, Rheingold, New York, 1957, page. 387
[10] Markstein G H, Nonsteady Flame Propagation. Macmillan, NY, 1964, Chapter D
[11] Markstein G H, Rudinger G. Shock Wave and Flame Interactions. Combustion and Propulsion. Third AGARD Colloquium. Pergamon Press, NY, 1958, page. 153
[12] Thomas G, Richard Bambrey, Caren Brown. Experimental Observations of Flame Acceleration and Transition to Detonation Following Shock-Flame Interaction. Combustion Theory And Modelling.2001(5): 573-594
[13]靳建明.火焰在激波诱导下稳定性问题的数值模拟和实验验证[D],硕士论文,南京:南京理工大学,2004
[14] G. Lacaze, B Cuenot , T Poinsot, M Oschwald. Large eddy simulation of laser ignition and compressible reacting flow in a rocket-like configuration. Combustion and Flame. 2009 (156): 1166–1180
[15] F. Williams, Combustion Theory, Benjamin Cummings, Menlo Park, CA, 1985
[16] I. Glassman, Combustion, Academic Press, New York, 1987
[17] M. Champion, B. Deshaies, G. Joulin, K. Kinoshita, Combust. Flame 1986 (65): 319–337
[18] Vadim N. Gamezo, Alexei M Khokhlov, Elain S Oran. The Influence of Shock Bifurcationon Shock-Flame Interactions and DDT. Combustion Institute 2001(29):1810-1826
[19] Elain S Oran, V N Gamezo, A M Khokhlov, Effects of boundary layers and wakes on shock-flame interactions and DDT, AIAA. 2002, 0776
[20] Elain S Oran, V N Gamezo, A M Khokhlov, Three-dimensional reactive shock bifurcations. Proceedings of the Combustion Institute 2005. (30): 1841–1847
[21]范宝春,江强,董刚,叶经方.激波与火焰相互作用过程.爆炸与冲击. 2003.23(6):488-492
[22]范宝春,叶经方,董刚,江强.激波与火焰相互作用的化学动力学模拟.自然科学进展. 2004. 14(3):312-318
[23]董刚,刘宏伟,陈义良.通用甲烷层流预混火焰半详细化学动力学机理.燃烧科学与技术. 2002. 8(1): 44-48
[24]董刚,范宝春,谢波.温度梯度影响爆燃装爆轰的数值模拟.中国安全生产科学技术2007. 6(3): 39-43
[25]程军波,傅德薰,马延文. Richtmyer-Meshkov失稳的数值模拟.计算物理. 2001. 18(5): 390-396
[26]孙锦山,朱建士.理论爆轰物理.国防工业出版社,第一版1995
[27]王继海.二维非定常流和激波.北京:科学出版社,1994
[28] Lewis D J. Taylor Instability of Liquid Surfaces When Accelerated in A Direction Perpendicular to Their Planes II. Proc. Roy. Soc. London, 1950, A202(1068): 81-98
[29] Birkhoff G. Taylor Instability and Laminar Mixing. LA1862, Los Alamos: Los Alamos Scientific Lab., 1954.76
[30] Birkhoff G. Helmholtz and Taylor Instability. In: Birkhoff G, Bellman R, Lin C C ed. Hydrodynamic Instability, Am. Math. Soc., New York, 1962: 52-76
[31] Kee R J, Rupley F M, Miller J A. The CHEMKIN Thermodynamic Data Base[R]. Sandia National Laboratories Report SAND87-8215B, 1990
[32] Bonnie J. McBride, Michael J. Zehe, and Sanford Gordon NASA Glenn Coefficients for Calculating Thermodynamic Properties of Individual Species. NASA, TP-2002-211556
[33]翁春生, Jay. Gore. P. CE/SE方法在非定常爆轰计算中的应用.空气动力学学报, 2003, 3 :301-310
[34] Chang S. C. The Method of Space-Time Conservation Element and Solution Element - A New Approach for Solving the Navier-Stokes and Euler Equations[J]. Journal of Computational Physics, 1995, 119(2)
[35] Zhang Z C, Yu S T. A Modified Space-Time Conversation Element and Solution ElementMethod for Euler and Navier-Stokes Equations. 1999.AIAA: 99-327
[36]董刚,范宝春.氢气-空气混合物种瞬态爆轰过程的二维数值模拟[J].高压物理学报2004. 18(1):40-46
[37]陈绍仲.一个理想的爆燃转爆轰过程[J].宁波大学学报. 2002, 15(4): 1-6
[38]陈永刚,何立明,刘建勋.时空守恒元和解元方法的爆震波一维数值模拟.推进技术2005(26):256-259
[39]王超,施红辉.激波诱导燃烧转爆轰数值模拟[C],第十四届全国激波与激波管学术会议论文集, 2010: 164-167
[40] Zhang Z C, Yu S T. A Modified Space-Time Conversation Element and Solution Element Method for Euler and Navier-Stokes Equations. 1999.AIAA: 99-327
[41]施红辉,卓启威。Richtmyer-Meshkov不稳定性流体混合区发展的实验研究[J]。力学学报。2007,29(3):417-421
[42]卓启威.气液界面R-M不稳定性实验研究[D].硕士论文,北京:中国科学院力学研究所.2006
[43]卓启威,施红辉。气液界面上Richtmyer-Meshkov不稳定性的实验研究[J]。实验流体力学。2007,21(1):25-30
[44]张鸣远,景思睿,李国君.高等工程流体力学[M].西安交通大学出版社. 2006
[45] Alexei M Khokhlov, Elain s Oran. Numerical Simulation of Detonation Initiation in a Flame Brush: The Role of Hot Spots. Combustion and Flame 1999,16: 400-416
[46] Mark, A Avest, D F Griffithst and Desmond J Hingam. Runge-Kutta Solutions of Hyperbolic Conservation Law with Source Term. SIAM. J. SCI. COMPUT. Vol. 22, No. 1, PP. 20-38
[47]王超.脉冲爆轰发动机中波的动力过程分析[D],博士论文,北京:中国科学院力学研究所,2003
[48] Manabu Hishida , Toshi Fujiwara, PiotrWolanski. Fundamentals of rotating detonations[J]. Shock Waves. 2009, 19:1–10
[49] J S Grondin, John H S Lee. Experimental observation of the onset of detonation downstream of a perforated plate disturbance[J]. Shock Waves. 2010, 20: 381–386
[50] James Meredith, Hoi Dick Ng, John H S Lee. Detonation diffraction from an annular channel[J]. Shock Waves. 2010, 20: 449–455
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