RM不稳定过程中预混火焰界面演化及混合区增长预测

汪洋; 董刚

doi:10.6052/0459-1879-20-278

RM不稳定过程中预混火焰界面演化及混合区增长预测

doi: 10.6052/0459-1879-20-278

汪洋,
董刚^2), ,

南京理工大学瞬态物理重点实验室, 南京 210094

基金项目: 1) 国家自然科学基金资助项目(11872213)

详细信息

作者简介:
2) 董刚, 研究员, 主要研究方向: 可压缩反应流的数值模拟. E-mail: gdong@njust.edu.cn

通讯作者:
董刚

中图分类号: O362
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出版历程
- 收稿日期: 2020-08-10
- 刊出日期: 2020-12-10

INTERFACE EVOLUTIONS AND GROWTH PREDICTIONS OF MIXING ZONE ON PREMIXED FLAME INTERFACE DURING RM INSTABILITY

Wang Yang,
Dong Gang^{2)
, ,}

Key Laboratory of Transient Physics, Nanjing University of Science and Technology, Nanjing 210094, China

摘要

摘要: 预混火焰界面的RM (Richtmyer-Meshkov)不稳定导致的界面混合区增长过程在自然界和工程实践中十分常见,但化学反应对其增长的影响机理仍不明确,反应性界面混合区增长速率的预测也未见报道, 因此,开展RM不稳定过程中火焰界面演化和混合区预测的研究十分必要.本文采用带单步化学反应的Navier-Stokes方程和高精度数值格式,研究了正弦形预混火焰界面在平面入射激波及其反射激波作用下的RM不稳定过程.结果表明, 在入射激波作用后的阶段,除RM不稳定本身导致的界面演化为"钉-帽"和"泡"形结构外,化学反应一方面以预混火焰传播的方式促进了界面中"泡"结构的增长,另一方面通过与涡结构的复杂相互作用促进了"钉-帽"结构的增长.化学反应活性越强, 火焰界面的"泡" 结构和"钉-帽"结构的增长越快.在第一次反射激波作用后的阶段,化学反应以相同的火焰传播方式对"泡"和"钉-帽"结构产生影响, 两者效应相抵,因而导致反射激波作用后的阶段中界面混合区增长不受化学反应活性的影响.根据以上分析,分别针对入射激波和第一次反射激波作用后的火焰界面混合区增长速率提出了相应的预测模型,为探索反应性RM不稳定过程的理论预测方法提供了有益参考.
- RM不稳定 /
- 预混火焰界面 /
- 混合区增长 /
- 数值模拟 /
- 预测
Abstract: Growth of mixing zone on premixed flame interface induced by Richtmyer-Meshkov (RM) instability occurs frequently in natural phenomena and in engineering applications. The effect of chemical reaction on the growth mechanism of mixing zone on the interface still remains unknown, and the predictions on growth rate of mixing zone on reactive interface were seldom reported. Therefore, it is necessary to study the interface evolutions and the predictions of mixing zone on the premixed flame interface during the RM instability. The present study adopted the Navier-Stokes equations with a single-step reaction and the computational scheme with high resolutions to numerically research the RM instability of flame interface with sinusoidal pattern, induced by a planar incident shock wave and its reflected shock wave. The results in present study show that during the stage after the passage of incident shock wave, besides the RM instability mechanism which leads to the "spike-cap" and "bubble" structures of the interface, the chemical reaction not only promotes the "bubble" structure growth in the form the premixed flame propagation, but also gives rise to the growth of "spike-cap" structure through the interaction with vortices structure. The more reactive the premixed gases, the rapider the growth for both "spike-cap" and "bubble" structures. The results also show that during the stage after the passage of first reflected shock wave, the chemical reaction has the same effects on the developments of both "spike-cap" and "bubble" structures in the mode of premixed flame propagation. The counteraction between both effects results in the independence of mixing zone growth on the chemical reaction. Based on above analyses, the predicted models for the stages after passages of incident shock wave and reflected shock wave are proposed, respectively, in order to provide a useful method for predictions of mixing zone growth during the reactive RM instability.
- RM instability /
- premixed flame interface /
- mixing zone growth /
- numerical simulation /
- prediction

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参考文献(1)

[1]	Poludnenko AY, Chambers J, Ahmed K, et al. A unified mechanism for unconfined deflagration-to-detonation transition in terrestrial. Science, 2019, 366(6465), eaau7365
[2]	Yang J, Kubota T, Zukoski EE. Applications of shock-induced mixing to supersonic combustion. AIAA Journal, 1994,31:854-862
[3]	徐建于, 黄生洪. 圆柱形汇聚激波诱导Richtmyer-Meshkov不稳定的SPH模拟. 力学学报, 2019,51(4):998-1011
[3]	( Xu Jianyu, Huang Shenghong. Numerical simulation of cylindrical converging shock induced Richtmyer-Meshkov instability with SPH. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(4):998-1011 (in Chinese))
[4]	Oran ES, Gamezo VN. Origins of the deflagration-to-detonation transition in gas-phase combustion. Combustion and Flame, 2007,148:4-47
[5]	Richtmyer RD. Taylor instability in shock acceleration of compressible fluids. Communications on Pure and Applied Mathematics, 1960,13(2):297-319
[6]	Zhang Q, Sohn S. Non-linear theory of unstable fluid mixing driven by shock wave. Physics of Fluids, 1997,9:1106-1124
[7]	Sohn S. Simple potential-flow model of Rayleigh-Taylor and Richtmyer-Meshkov instabilities for all density ratios. Physical Review E, 2003,67:026301
[8]	Mikaelian KO. Explicit expressions for the single-mode Rayleigh-Taylor and Richtmyer-Meshkov instabilities at arbitrary Atwood numbers. Physical Review E, 2003,67:026319
[9]	Brouillette M, Sturtevant B. Experiments on the Richtmyer-Meshkov instability: small-scale perturbations on a plane interface. Physics of Fluids, 1993,A5(4):916-930
[10]	Mikaelian KO. Turbulent mixing generated by Rayleigh-Taylor and Richtmyer-Meshkov instabilities. Physica D, 1989,36:343-357
[11]	Mikaelian KO. Extended model for Richtmyer-Meshkov mix. Physica D, 2011,240:935-942
[12]	Ukai S, Balakrishnan K, Menon S. Growth rate predictions of single- and multi-mode Richtmyer-Meshkov instability with reshock. Shock Waves, 2011,21:533-546
[13]	Zhou Y. Rayleigh-Taylor and Richtmyer-Meshkov instability induced flow, turbulence and mixing. I. Physics Reports, 2017, 720-722:1-136
[14]	Vetter M, Sturtevant B. Experiments on the Richtmyer-Meshkov instability of an air/SF$_6$ interface. Shock Waves, 1995,4(5):247-252
[15]	Leinov E, Malamud G, Elbaz Y, et al. Experimental and numerical investigation of the Richtmyer-Meshkov instability under re-shock conditions. Journal of Fluid Mechanics, 2009,626:449-475
[16]	Zou LY, Liu JH, Liao SF, et al. Richtmyer-Meshkov instability of a flat interface subjected to a rippled shock wave. Physical Review E, 2017,95:013107
[17]	刘金宏, 邹立勇, 曹仁义等. 绕射激波和反射激波作用下N$_{2}$/SF$_{6}$界面R-M不稳定性实验研究. 力学学报, 2014,46(3):475-479
[17]	( Liu Jinhong, Zou Liyong, Cao Renyi, et al. Experimentally study of the Richtmyer-Meshkov instability at N$_{2}$/SF$_{6}$ flat interface by diffracted incident shock waves and reshock. Chinese Journal of Theoretical and Applied Mechanics, 2014,46(3):475-479 (in Chinese))
[18]	Liang Y, Zhai Z, Ding J, et al. Richtmyer-Meshkov instability on a quasi-single-mode interface. Journal of Fluid Mechanics, 2019,872:729-751
[19]	Guo X, Ding J, Luo X, et al. Evolution of shocked multi-mode interface with sharp corners. Physical Review Fluids, 2018,3:114004
[20]	Luo X, Dong P, Si T, et al. The Richtmyer-Meshkov instability of a 'V' shaped air/SF$_{6}$ interface. Journal of Fluid Mechanics, 2016,802:186-202
[21]	Bai J, Liu J, Wang T, et al. Investigation of the Richtmyer-Meshkov instability with double perturbation interface in nonuniform flows. Physical Review E, 2010,81:056302
[22]	蒋华, 董刚, 陈霄. 小扰动界面形态对RM 不稳定性影响的数值分析. 力学学报, 2014,46(4):544-552
[22]	( Jiang Hua, Dong Gang, Chen Xiao. Numerical study on the effects of small-amplitude initial perturbations on RM instability. Chinese Journal of Theoretical and Applied Mechanics, 2014,46(4):544-552 (in Chinese))
[23]	蒋华, 董刚, 朱跃进等. 界面初始扰动形态影响RM不稳定过程的数值研究. 工程力学, 2013,31(11):244-250
[23]	( Jiang Hua, Dong Gang, Zhu Yuejin, et al. Numerical study on influence of initial perturbations on RM instability. Engineering Mechanics, 2013,31(11):244-250 (in Chinese))
[24]	Schilling O, Latini M, Don WS. Physics of reshock and mixing in single-mode Richtmyer-Meshkov instability. Physical Review E, 2007,76:026319
[25]	Thornber B, Drikakis D, Youngs DL, et al. Physics of the single-shocked and reshocked Richtmyer-Meshkov instability. Journal of Turbulence, 2012,13(10):1-17
[26]	Lombardini M, Pullin DI, Meiron DI. Transition to turbulence in shock-driven mixing: A Mach number study. Journal of Fluid Mechanics, 2012,690:203-226
[27]	Tritschler VK, Olson BJ, Lele SK, et al. On the Richtmyer- Meshkov instability evolving from a deterministic multimode planar interface. Journal of Fluid Mechanics, 2014,755:429-462
[28]	Khokhlov AM, Oran ES, Chtchelkanova AY, et al. Interaction of a shock with a sinusoidally perturbed flame. Combustion and Flame, 1999,117:99-116
[29]	Kilchyk V, Nalim R, Merkle C. Laminar premixed flame fuel consumption rate modulation by shocks and expansion waves. Combustion and Flame, 2011,158:1140-1148
[30]	Massa L, Jha P. Linear analysis of the Richtmyer-Meshkov instability in shock-flame interactions. Physics of Fluids, 2012,24:056101
[31]	Jiang H, Dong G, Chen X, et al. Numerical simulations of the process of multiple shock-flame interactions. Acta Mechanica Sinica, 2016,32(4):659-669
[32]	Jiang H, Dong G, Chen X, et al. A parameterization of the Richtmyer-Meshkov instability on a premixed flame interface induced by the successive passages of shock waves. Combustion and Flame, 2016,169:229-241
[33]	Chen X, Dong G, Li B. Numerical study of three-dimensional developments of premixed flame induced by multiple shock waves. Acta Mechanica Sinica, 2018,34(6):1035-1047
[34]	Attal N, Ramaprabhu P. Numerical investigation of a single-mode chemically reacting Richtmyer-Meshkov instability. Shock Waves, 2015,25:307-328
[35]	Thomas GO, Bambrey R, Brown C. Experimental observations of flame acceleration and transition to detonation following shock-flame interaction. Combustion and Theory Modelling, 2001,5(4):573-594
[36]	Balsara DS, Shu CW. Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy. Journal of Computational Physics, 2000,160:405-452
[37]	Khokhlov AM, Austin JM, Pintgen F, et al. Numerical study of the detonation wave structure in ethylene-oxygen mixtures// 42nd AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, USA, 2004. 1. 5-8, 792
[38]	Kuo KK. Principles of Combustion, 2nd Edition. Hoboken, New Jersey, John Wiley & Sons, Inc., 2005