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Viscous jetting and Mach stem bifurcation in shock reflections: experiments and simulations

Published online by Cambridge University Press:  07 December 2020

S. S.-M. Lau-Chapdelaine Open the ORCID record for S. S.-M. Lau-Chapdelaine [Opens in a new window] ,
Q. Xiao  and
M. I. Radulescu Open the ORCID record for M. I. Radulescu [Opens in a new window]
S. S.-M. Lau-Chapdelaine*
Affiliation:
Department of Mechanical Engineering, University of Ottawa, 161 Louis Pasteur Pvt., Ottawa, OntarioK1N 6N5, Canada
Q. Xiao
Affiliation:
Department of Mechanical Engineering, University of Ottawa, 161 Louis Pasteur Pvt., Ottawa, OntarioK1N 6N5, Canada
M. I. Radulescu
Affiliation:
Department of Mechanical Engineering, University of Ottawa, 161 Louis Pasteur Pvt., Ottawa, OntarioK1N 6N5, Canada
*
Email address for correspondence: shem.lau-chapdelaine@rmc.ca
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Abstract

Shock reflection experiments are performed to study the large-scale convective mixing created by the forward jetting phenomenon. Experiments are performed at a wedge angle of $\theta _{{w}} = 30^{\circ }$ in nitrogen, propane–oxygen and hexane with incident shock Mach numbers up to $M = 4$. Experiments are complemented by shock-resolved viscous simulations of triple-point reflection in hexane for $M = 2.5$ to $6$. Inviscid simulations are performed over a wider range of parameters. Reynolds numbers up to $Re \lesssim 10^3$ are covered by simulations and Reynolds numbers of $Re \sim 10^5$ are covered by experiments. The study shows that as the isentropic exponent is lowered, and as the Mach number and Reynolds number are increased, the forward jet approaches the Mach stem, forms a vortex, deforms the shock front and in some cases bifurcates the Mach stem. Experiments show that Kelvin–Helmholtz instabilities in the vortex cause large-scale convective mixing behind the Mach stem at low isentropic exponents ($\gamma \le 1.15$). The limits of Mach stem bifurcation (triple Mach–White reflection) in inviscid simulations are plotted in the phase space of $M$–$\theta _{{w}}$–$\gamma$. A maximum isentropic exponent of $\gamma \approx 1.3$ is found beyond which bifurcation does not occur (at $\theta _{{w}} = 30^{\circ }$). This closely matches the boundary between irregular and regular detonation cellular structures.

JFM classification

Compressible Flows: Detonation waves Compressible Flows: Gas dynamics Compressible Flows: Shock waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 908 , 10 February 2021 , A18
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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Footnotes

†

Present address: Department of Chemistry and Chemical Engineering, Royal Military College, 11 Crerar Crescent, Kingston, Ontario K7K 7B4, Canada.

References

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Lau-Chapdelaine et al. supplementary movie 1

Schlieren video experiment 1 (nitrogen, $M_{\mathrm{c}}=2.4$, $\gamma_0 = 1.4$, $\theta_{\mathrm{w}} = 30^{\circ}$)

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Video 198.2 KB

Lau-Chapdelaine et al. supplementary movie 2

Schlieren video experiment 2 (nitrogen, $M_{\mathrm{c}}=3.0$, $\gamma_0 = 1.4$, $\theta_{\mathrm{w}} = 30^{\circ}$)

Download Lau-Chapdelaine et al. supplementary movie 2(Video)
Video 235 KB

Lau-Chapdelaine et al. supplementary movie 3

Schlieren video experiment 3 (nitrogen, $M_{\mathrm{c}}=3.5$, $\gamma_0 = 1.4$, $\theta_{\mathrm{w}} = 30^{\circ}$)
Download Lau-Chapdelaine et al. supplementary movie 3(Video)
Video 192 KB

Lau-Chapdelaine et al. supplementary movie 4

Schlieren video experiment 4 (propane-oxygen, $M_{\mathrm{c}}=2.4$, $\gamma_0 = 1.15$, $\theta_{\mathrm{w}} = 30^{\circ}$)

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Video 717.1 KB

Lau-Chapdelaine et al. supplementary movie 5

Schlieren video experiment 5 (propane-oxygen, $M_{\mathrm{c}}=2.9$, $\gamma_0 = 1.15$, $\theta_{\mathrm{w}} = 30^{\circ}$)

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Video 646.3 KB

Lau-Chapdelaine et al. supplementary movie 6

Schlieren video experiment 6 (propane-oxygen, $M_{\mathrm{c}}=3.5$, $\gamma_0 = 1.15$, $\theta_{\mathrm{w}} = 30^{\circ}$)

Download Lau-Chapdelaine et al. supplementary movie 6(Video)
Video 668.1 KB

Lau-Chapdelaine et al. supplementary movie 7

Schlieren video experiment 7 (hexane, $M_{\mathrm{c}}=2.5$, $\gamma_0 = 1.06$, $\theta_{\mathrm{w}} = 30^{\circ}$)

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Video 1.3 MB

Lau-Chapdelaine et al. supplementary movie 8

Schlieren video experiment 8 (hexane, $M_{\mathrm{c}}=2.7$, $\gamma_0 = 1.06$, $\theta_{\mathrm{w}} = 30^{\circ}$)

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Video 955.1 KB

Lau-Chapdelaine et al. supplementary movie 9

Schlieren video experiment 9 (hexane, $M_{\mathrm{c}}=3.4$, $\gamma_0 = 1.06$, $\theta_{\mathrm{w}} = 30^{\circ}$)

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Video 880.8 KB

Lau-Chapdelaine et al. supplementary movie 10

Schlieren video experiment 10 (propane--oxygen, $M_{\mathrm{c}} = 4.0$, $\gamma_0 = 1.15$, $\theta_{\mathrm{w}} = 30^{\circ}$)

Download Lau-Chapdelaine et al. supplementary movie 10(Video)
Video 1.5 MB

Lau-Chapdelaine et al. supplementary movie 11

Schlieren video experiment 11 (hexane, $M_{\mathrm{c}} = 4.0$, $\gamma_0 = 1.06$, $\theta_{\mathrm{w}} = 30^{\circ}$)

Download Lau-Chapdelaine et al. supplementary movie 11(Video)
Video 1.4 MB