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Dynamics of cellular flame deformation after a head-on interaction with a shock wave: reactive Richtmyer–Meshkov instability

Published online by Cambridge University Press:  02 August 2021

Hongxia Yang Open the ORCID record for Hongxia Yang [Opens in a new window]  and
Matei Ioan Radulescu Open the ORCID record for Matei Ioan Radulescu [Opens in a new window]
Hongxia Yang*
Affiliation:
Fire & Explosion Protection Laboratory, Northeastern University, Shenyang 110819, PR China Department of Mechanical Engineering, University of Ottawa, 161 Louis-Pasteur, Ottawa K1N 6N5, Canada
Matei Ioan Radulescu
Affiliation:
Department of Mechanical Engineering, University of Ottawa, 161 Louis-Pasteur, Ottawa K1N 6N5, Canada
*
†Email address for correspondence: yang.hongxia@foxmail.com
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Abstract

Shock-flame interactions are fundamental problems in many combustion applications ranging from flame acceleration to flame control in supersonic propulsion applications. The present paper seeks to quantify the rate of deformation of the flame surface and burning velocity caused by the interaction and to clarify the underlying mechanisms. The interaction of a single shock wave with a cellular flame in a Hele-Shaw shock tube configuration was studied experimentally, numerically and theoretically. A mixture of stoichiometric hydrogen-air at sub-atmospheric pressure was chosen such that large cells can be isolated and their deformation studied with precision subsequent to the interaction. Following passage of the incident shock and vorticity deposition along the flame surface, the flame cusps are flattened and reversed backwards into the burned gas. The reversed flame then goes through four stages. At times significantly less than the characteristic flame burning time, the flame front deforms as an inert interface due to the Richtmyer–Meshkov instability with nonlinear effects becoming noticeable. At times comparable to the laminar flame time, dilatation due to chemical energy release amplifies the growth rate of the Richtmyer–Meshkov instability. This stage is abruptly terminated by the transverse burnout of the resulting flame funnels, followed by a longer front re-adjustment to a new cellular flame evolving on the cellular time scale of the flame. The proposed flame evolution model permits us to predict the evolution of the flame geometry and burning rate for arbitrary shock strength below the shock-induced auto-ignition point and flames with unit Lewis number in two dimensions.

JFM classification

Reacting Flows: Flames Compressible Flows: Shock waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 923 , 25 September 2021 , A36
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Boust, B., Sotton, J. & Bellenoue, M. 2012 Unsteady contribution of water vapor condensation to heat losses at flame-wall interaction. In 6th European Thermal Sciences Conference (Eurotherm), Journal of Physics Conference Series, vol. 395. IOP Publishing.CrossRefGoogle Scholar
Brouillette, M. 2002 The Richtmyer-Meshkov instability. Annu. Rev. Fluid Mech. 34 (1), 445–468.CrossRefGoogle Scholar
Chen, X., Dong, G. & Li, B. 2018 Numerical study of three-dimensional developments of premixed flame induced by multiple shock waves. Acta Mechanica Sin. 34 (6), 1035–1047.CrossRefGoogle Scholar
Chue, R.S., Clarke, J.F. & Lee, J.H. 1993 Chapman-Jouguet deflagrations. Proc. R. Soc. Lond. Ser. A: Math. Phys. Sci. 441 (1913), 607–623.Google Scholar
Ciccarelli, G., Johansen, C.T. & Parravani, M. 2010 The role of shock–flame interactions on flame acceleration in an obstacle laden channel. Combust. Flame 157 (11), 2125–2136.CrossRefGoogle Scholar
Dong, G., Fan, B. & Ye, J. 2008 Numerical investigation of ethylene flame bubble instability induced by shock waves. Shock Waves 17 (6), 409–419.CrossRefGoogle Scholar
Egolfopoulos, F.N. & Law, C.K. 1990 Chain mechanisms in the overall reaction orders in laminar flame propagation. Combust. Flame 80 (1), 7–16.CrossRefGoogle Scholar
Falle, S.A.E.G., Giddings, J.R., Morton, K.W. & Baines, M.J. 1993 Numerical Methods for Fluid Dynamics 4.Google Scholar
Goncharov, V.N. 1999 Theory of the ablative Richtmyer-Meshkov instability. Phys. Rev. Lett. 82 (10), 2091–2094.CrossRefGoogle Scholar
Jiang, H., Dong, G., Chen, X. & Li, B. 2016 A parameterization of the Richtmyer–Meshkov instability on a premixed flame interface induced by the successive passages of shock waves. Combust. Flame 169, 229–241.CrossRefGoogle Scholar
Jomaas, G., Law, C.K. & Bechtold, J.K. 2007 On transition to cellularity in expanding spherical flames. J. Fluid Mech. 583, 1–26.CrossRefGoogle Scholar
Ju, Y., Shimano, A. & Inoue, O. 1998 Vorticity generation and flame distortion induced by shock flame interaction. In Symposium (International) on Combustion, vol. 27, pp. 735–741. Elsevier.CrossRefGoogle Scholar
Khokhlov, A.M., Oran, E.S., Chtchelkanova, A.Y. & Wheeler, J.C. 1999 Interaction of a shock with a sinusoidally perturbed flame. Combust. Flame 117 (1–2), 99–116.CrossRefGoogle Scholar
Kilchyk, V., Nalim, R. & Merkle, C. 2013 Scaling interface length increase rates in Richtmyer–Meshkov instabilities. J. Fluids Engng 135 (3), 031203.CrossRefGoogle Scholar
Li, J., Zhao, Z., Kazakov, A. & Dryer, F.L. 2004 An updated comprehensive kinetic model of hydrogen combustion. Intl J. Chem. Kinet. 36 (10), 566–575.CrossRefGoogle Scholar
Lutoschkin, E., Rose, M.G. & Staudacher, S. 2013 Pressure-gain combustion using shock–flame interaction. J. Propul. Power 29 (5), 1181–1193.CrossRefGoogle Scholar
Markstein, G.H. 1957 A shock-tube study of flame front-pressure wave interaction. In Symposium (International) on Combustion, vol. 6, pp. 387–398. Elsevier.CrossRefGoogle Scholar
Massa, L. & Jha, P. 2012 Linear analysis of the Richtmyer-Meshkov instability in shock-flame interactions. Phys. Fluids 24 (5), 056101.CrossRefGoogle Scholar
Maxwell, B., Pekalski, A. & Radulescu, M. 2018 Modelling of the transition of a turbulent shock-flame complex to detonation using the linear eddy model. Combust. Flame 192, 340–357.CrossRefGoogle Scholar
Meyer, K.A. & Blewett, P.J. 1972 Numerical investigation of the stability of a shock-accelerated interface between two fluids. Phys. Fluids 15 (5), 753–759.CrossRefGoogle Scholar
Mikaelian, K.O. 2003 Explicit expressions for the evolution of single-mode Rayleigh–Taylor and Richtmyer-Meshkov instabilities at arbitrary atwood numbers. Phys. Rev. E 67 (2), 026319.CrossRefGoogle ScholarPubMed
Oran, E.S. & Gamezo, V.N. 2007 Origins of the deflagration-to-detonation transition in gas-phase combustion. Combust. Flame 148 (1-2), 4–47.CrossRefGoogle Scholar
Oron, D., Arazi, L., Kartoon, D., Rikanati, A., Alon, U. & Shvarts, D. 2001 Dimensionality dependence of the Rayleigh–Taylor and Richtmyer–Meshkov instability late-time scaling laws. Phys. Plasmas 8 (6), 2883–2889.CrossRefGoogle Scholar
Rakotoarison, W., Maxwell, B., Pekalski, A. & Radulescu, M.I. 2019 Mechanism of flame acceleration and detonation transition from the interaction of a supersonic turbulent flame with an obstruction: experiments in low pressure propane–oxygen mixtures. Proc. Combust. Inst. 37 (3), 3713–3721.CrossRefGoogle Scholar
Richtmyer, R.D. 1960 Taylor instability in shock acceleration of compressible fluids. Commun. Pure Appl. Maths 13 (2), 297–319.CrossRefGoogle Scholar
Rudinger, G. 1958 Shock wave and flame interactions. In Combustion and Propulsion, Third AGARD Colloquium, p. 153–182. Pergamon Press.Google Scholar
Sadot, O., Erez, L., Alon, U., Oron, D., Levin, L.A., Erez, G., Ben-Dor, G. & Shvarts, D. 1998 Study of nonlinear evolution of single-mode and two-bubble interaction under Richtmyer-Meshkov instability. Phys. Rev. Lett. 80 (8), 1654–1657.CrossRefGoogle Scholar
Scarinci, T., Lee, J.H., Thomas, G.O., Bambrey, R. & Edwards, D.H. 1993 Amplification of a pressure wave by its passage through a flame front. Prog. Astronaut. Aeronaut. 152, 3–24.Google Scholar
Sharpe, G.J. & Falle, S.A.E.G. 2006 Nonlinear cellular instabilities of planar premixed flames: numerical simulations of the reactive Navier–Stokes equations. Combust. Theor. Model. 10 (3), 483–514.CrossRefGoogle Scholar
Sharpe, G.J., Falle, S.A.E.G. & Billingham, J. 2008 Numerical solutions of a model for the propagation of a surface-catalysed flame in a tube. IMA J. Appl. Math. 73 (1), 107–122.CrossRefGoogle Scholar
Sivashinsky, G.I. 1983 Instabilities, pattern formation, and turbulence in flames. Annu. Rev. Fluid Mech. 15 (1), 179–199.CrossRefGoogle Scholar
Strehlow, R.A. 1984 Combustion Fundamentals. McGraw-Hill College.Google Scholar
Thomas, G., Bambrey, R. & Brown, C. 2001 Experimental observations of flame acceleration and transition to detonation following shock-flame interaction. Combust. Theor. Model. 5 (4), 573–594.CrossRefGoogle Scholar
Travnikov, O.Y., Liberman, M.A. & Bychkov, V.V. 1997 Stability of a planar flame front in a compressible flow. Phys. Fluids 9 (12), 3935–3937.CrossRefGoogle Scholar
Urtiew, P.A. & Oppenheim, A.K. 1968 Transverse flame-shock interactions in an explosive gas. Proc. R. Soc. Lond. A. Math. Phys. Sci. 304 (1478), 379–385.Google Scholar
Wei, H., Zhao, J., Zhou, L., Gao, D. & Xu, Z. 2017 Effects of the equivalence ratio on turbulent flame–shock interactions in a confined space. Combust. Flame 186, 247–262.CrossRefGoogle Scholar
Wijeyakulasuriya, S.D. & Mitra, S. 2014 Analyzing three-dimensional multiple shock-flame interactions in a constant-volume combustion channel. Combust. Sci. Technol. 186 (12), 1907–1927.CrossRefGoogle Scholar
Zhang, Q. & Guo, W. 2016 Universality of finger growth in two-dimensional Rayleigh–Taylor and Richtmyer–Meshkov instabilities with all density ratios. J. Fluid Mech. 786, 47–61.CrossRefGoogle Scholar
Zhang, Q. & Sohn, S.-I. 1999 Quantitative theory of Richtmyer-Meshkov instability in three dimensions. Z. Angew. Math. Phys. 50 (1), 1–46.CrossRefGoogle Scholar
Zhou, Y. 2017 a Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. II. Phys. Rep. 723, 1–160.Google Scholar
Zhou, Y. 2017 b Rayleigh–Taylor and Richtmyer-Meshkov instability induced flow, turbulence, and mixing. I. Phys. Rep. 720, 1–136.Google Scholar
Zhu, Y., Dong, G. & Liu, Y. 2013 Three-dimensional numerical simulations of spherical flame evolutions in shock and reshock accelerated flows. Combust. Sci. Technol. 185 (10), 1415–1440.CrossRefGoogle Scholar

Yang and Radulescu supplementary movie 1

The experimental result of the Interaction of a Ms = 1.9 incident shock wave with stoichiometric hydrogen-air flame

Download Yang and Radulescu supplementary movie 1(Video)
Video 2 MB

Yang and Radulescu supplementary movie 2

The experimental result of the Interaction of a Ms = 1.75 incident shock wave with stoichiometric hydrogen-air flame

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Video 2.3 MB

Yang and Radulescu supplementary movie 3

The experimental result of the Interaction of a Ms = 1.53 incident shock wave with stoichiometric hydrogen-air flame

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Video 2.3 MB

Yang and Radulescu supplementary movie 4

The initial numerical setup and cellular flame development

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Video 116.5 KB

Yang and Radulescu supplementary movie 5

Density profiles illustrating the numerical result of flame evolution subsequent to the interaction with the Ms=1.9 shock

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Video 388.2 KB

Yang and Radulescu supplementary movie 6

Density profiles illustrating the numerical result of inert interface evolution subsequent to the interaction with the Ms=1.9 shock

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Video 215.7 KB

Yang and Radulescu supplementary movie 7

Density profiles illustrating the numerical result of flame evolution subsequent to the interaction with the Ms=2.5 shock

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Video 382.9 KB

Yang and Radulescu supplementary movie 8

Density profiles illustrating the numerical result of flame evolution subsequent to the interaction with the Ms=1.75 shock

Download Yang and Radulescu supplementary movie 8(Video)
Video 408.9 KB

Yang and Radulescu supplementary movie 9

Density profiles illustrating the numerical result of flame evolution subsequent to the interaction with the Ms=1.53 shock

Download Yang and Radulescu supplementary movie 9(Video)
Video 463.3 KB

Yang and Radulescu supplementary movie 10

Density profiles illustrating the flame evolution subsequent to the interaction with the Ms=1.9 shock with the numerical refinement level of 6

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Video 241.9 KB