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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: [email protected]
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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

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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