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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

REFERENCES

Ando, S. 1981 Pseudo-stationary oblique shock-wave reflection in carbon dioxide-domains and boundaries. Tech. Note 231. University of Toronto Institute for Aerospace Studies.Google Scholar
Austin, J. M. 2003 The role of instability in gaseous detonation. PhD thesis, California Institute of Technology.Google Scholar
Barbosa, F. J. & Skews, B. W. 2002 Experimental confirmation of the von Neumann theory of shock wave reflection transition. J. Fluid Mech. 472, 263–282.CrossRefGoogle Scholar
Ben-Dor, G. 2007 Shock Wave Reflection Phenomena. Springer.Google Scholar
Ben-Dor, G., Mazor, G., Takayama, K. & Igra, O. 1987 Influence of surface roughness on the transition from regular to Mach reflection in pseudo-steady flows. J. Fluid Mech. 176, 333–356.CrossRefGoogle Scholar
Bhattacharjee, R. R. 2013 Experimental Investigation of detonation re-initiation mechanisms following a mach reflection of a quenched detonation. Masters thesis, University of Ottawa.Google Scholar
Faghri, A. & Zhang, Y. 2006 Transport Phenomena in Multiphase Systems. Elsevier.Google Scholar
Falle, S. A. E. G. 1991 Self-similar jets. Mon. Not. R. Astron. Soc. 250 (3), 581–596.Google Scholar
Falle, S. A. E. G. & Giddings, J. R. 1992 Body capturing using adaptive Cartesian grids. In Numerical Methods for Fluid Dynamics (ed. K. W. Morton), pp. 335–342. Clarendon Press.Google Scholar
Falle, S. A. E. G. & Komissarov, S. S. 1996 An upwind numerical scheme for relativistic hydrodynamics with a general equation of state. Mon. Not. R. Astron. Soc. 278 (2), 586–602.Google Scholar
Fay, J. A. 1959 Two-dimensional gaseous detonations: velocity deficit. Phys. Fluids 2 (3), 283–289.Google Scholar
Glass, I. I. & Liu, W. S. 1978 Effects of hydrogen impurities on shock structure and stability in ionizing monatomic gases. Part 1. Argon. J. Fluid Mech. 84 (1), 55–77.CrossRefGoogle Scholar
Glaz, H. M., Colella, P., Glass, I. I. & Deschambault, R. L. 1985 a A detailed numerical, graphical, and experimental study of oblique shock wave reflections. Tech. Rep. LBL-20033. Lawrence Berkeley National Laboratory.Google Scholar
Glaz, H. M., Colella, P., Glass, I. I. & Deschambault, R. L. 1985 b A numerical study of oblique shock-wave reflections with experimental comparisons. Proc. R. Soc. Lond. A 398 (1814), 117–140.Google Scholar
Griffiths, R. W., Sandeman, R. J. & Hornung, H. G. 1976 The stability of shock waves in ionizing and dissociating gases. J. Phys. D: Appl. Phys. 9 (12), 1681–1691.Google Scholar
Grun, J., Stamper, J., Manka, C., Resnick, J., Burris, R., Crawford, J. & Ripin, B. H. 1991 Instability of Taylor–Sedov blast waves propagating through a uniform gas. Phys. Rev. Lett. 66 (21), 2738–2741.Google ScholarPubMed
Henderson, L. F. & Lozzi, A. 1975 Experiments on transition of Mach reflexion. J. Fluid Mech. 68 (1), 139–155.CrossRefGoogle Scholar
Henderson, L. F., Vasilev, E. I., Ben-Dor, G. & Elperin, T. 2003 The wall-jetting effect in Mach reflection: theoretical consideration and numerical investigation. J. Fluid Mech. 479, 259–286.CrossRefGoogle Scholar
Higashino, F., Henderson, L. F. & Shimizu, F. 1991 Experiments on the interaction of a pair of cylindrical weak blast waves in air. Shock Waves 1 (4), 275–284.CrossRefGoogle Scholar
Hornung, H. 1985 The effect of viscosity on the Mach stem length in unsteady strong shock reflection. In Flow of Real Fluids (ed. G. E. A. Meier & F. Obermeier), pp. 82–91. Springer.CrossRefGoogle Scholar
Hornung, H. 1986 Regular and Mach reflection of shock waves. Annu. Rev. Fluid Mech. 18, 33–58.CrossRefGoogle Scholar
Hornung, H. G. & Lemieux, P. 2001 Shock layer instability near the Newtonian limit of hypervelocity flows. Phys. Fluids 13 (8), 2394–2402.CrossRefGoogle Scholar
Lau-Chapdelaine, S. S. M. & Radulescu, M. I. 2013 Non-uniqueness of solutions in asymptotically self-similar shock reflections. Shock Waves 23 (6), 595–602.Google Scholar
Lau-Chapdelaine, S. S. M. & Radulescu, M. I. 2016 Viscous solution of the triple-shock reflection problem. Shock Waves 26 (5), 551–560.CrossRefGoogle Scholar
Lee, J. H. S. 2008 The Detonation Phenomenon. Cambridge University Press.Google Scholar
Li, H. & Ben-Dor, G. 1995 Reconsideration of pseudo-steady shock wave reflections and the transition criteria between them. Shock waves 5 (1–2), 59–73.Google Scholar
Li, H. & Ben-Dor, G. 1999 Analysis of double-Mach-reflection wave configurations with convexly curved Mach stems. Shock Waves 9 (5), 319–326.Google Scholar
Mach, P. 2011 Bifurcating mach shock reflections with application to detonation structure. Masters thesis, University of Ottawa.Google Scholar
Mach, P. & Radulescu, M. I. 2011 Mach reflection bifurcations as a mechanism of cell multiplication in gaseous detonations. Proc. Combust. Inst. 33 (2), 2279–2285.CrossRefGoogle Scholar
Maley, L. 2015 On shock reflections in fast flames. Masters thesis, University of Ottawa.Google Scholar
Maley, L., Bhattacharjee, R., Lau-Chapdelaine, S. S.-M. & Radulescu, M. I. 2015 Influence of hydrodynamic instabilities on the propagation mechanism of fast flames. Proc. Combust. Inst. 35 (2), 2117–2126.CrossRefGoogle Scholar
Mishin, G. I., Bedin, A. P., Iushchenkova, N. I., Skvortsov, G. E. & Riazin, A. P. 1981 Anomalous relaxation and instability of shock waves in gases. Sov. Phys. Tech. Phys. 26, 2315–2324.Google Scholar
Moen, I. O., Sulmistras, A., Thomas, G. O., Bjerketvedt, D. & Thibault, P. A. 1986 Influence of cellular regularity on the behavior of gaseous detonations. In Dynamics of Explosions (ed. J. R. Bowen, J.-C. Leyer & R. I. Soloukhin), pp. 220–243.Google Scholar
Ohnishi, N., Sato, Y., Kikuchi, Y., Ohtani, K. & Yasue, K. 2015 Bow-shock instability induced by Helmholtz resonator-like feedback in slipstream. Phys. Fluids 27 (6), 066103.Google Scholar
Quirk, J. J. 1992 A contribution to the great Riemann solver debate. ICASE Rep. No. 92-94. Springer.Google Scholar
Radulescu, M. I. & Lee, J. H. S. 2002 The failure mechanism of gaseous detonations: experiments in porous wall tubes. Combust. Flame 131 (1), 29–46.Google Scholar
Radulescu, M. I., Papi, A., Quirk, J. J., Mach, P. & Maxwell, B. M. 2009 The origin of shock bifurcations in cellular detonations. In 22nd International Colloquium on the Dynamics of Explosions and Reactive Systems.Google Scholar
Rikanati, A., Sadot, O., Ben-Dor, G., Shvarts, D., Kuribayashi, T. & Takayama, K. 2006 Shock-wave mach-reflection slip-stream instability: a secondary small-scale turbulent mixing phenomenon. Phys. Rev. Lett. 96 (17), 174503.Google ScholarPubMed
Rikanati, A., Sadot, O., Ben-Dor, G., Shvarts, D., Kuribayashi, T. & Takayama, K. 2009 A secondary small-scale turbulent mixing phenomenon induced by shock-wave Mach-reflection slip-stream instability. In Shock Waves (ed. K. Hannemann & F. Seiler), vol. 2, pp. 1347–1352. Springer.Google Scholar
Samtaney, R. & Pullin, D. I. 1996 On initial-value and self-similar solutions of the compressible Euler equations. Phys. Fluids 8 (10), 2650–2655.Google Scholar
Semenov, A. N., Berezkina, M. K. & Krasovskaya, I. V. 2009 a Classification of shock wave reflections from a wedge. Part 1. Boundaries and domains of existence for different types of reflections. Tech. Phys. 54 (4), 491–496.Google Scholar
Semenov, A. N., Berezkina, M. K. & Krasovskaya, I. V. 2009 b Classification of shock wave reflections from a wedge. Part 2. Experimental and numerical simulations of different types of Mach reflections. Tech. Phys. 54 (4), 497–503.CrossRefGoogle Scholar
Semenov, A. N., Berezkina, M. K. & Krassovskaya, I. V. 2012 Classification of pseudo-steady shock wave reflection types. Shock Waves 22 (4), 307–316.Google Scholar
Sharpe, G. J. & Falle, S. A. E. G. 2011 Numerical simulations of premixed flame cellular instability for a simple chain-branching model. Combust. Flame 158 (5), 925–934.Google Scholar
Shi, X., Zhu, Y., Luo, X. & Yang, J. 2017 Numerical study on double mach reflection of strong moving shock involving laminar transport. In 21st AIAA International Space Planes and Hypersonics Technologies Conference, Xiamen, China.Google Scholar
Shi, X., Zhu, Y., Yang, J. & Luo, X. 2019 Mach stem deformation in pseudo-steady shock wave reflections. J. Fluid Mech. 861, 407–421.CrossRefGoogle Scholar
Sirmas, N. & Radulescu, M. I. 2015 Evolution and stability of shock waves in dissipative gases characterized by activated inelastic collisions. Phys. Rev. E 91 (2).Google ScholarPubMed
Sirmas, N. & Radulescu, M. I. 2019 Structure and stability of shock waves in granular gases. J. Fluid Mech. 873, 568–607.CrossRefGoogle Scholar
Skews, B. W. 1967 The shape of a diffracting shock wave. J. Fluid Mech. 29 (2), 297–304.Google Scholar
Smith, W. R. 1959 Mutual reflection of two shock waves of arbitrary strengths. Phys. Fluids 2 (5), 533–541.Google Scholar
Sorin, R., Zitoun, R., Khasainov, B. & Desbordes, D. 2009 Detonation diffraction through different geometries. Shock Waves 19 (1), 11–23.CrossRefGoogle Scholar
Strehlow, R. A. & Biller, J. R. 1969 On the strength of transverse waves in gaseous detonations. Combust. Flame 13 (6), 577–582.CrossRefGoogle Scholar
Uribe, F. J. & Velasco, R. M. 2018 Shock-wave structure based on the Navier–Stokes–Fourier equations. Phys. Rev. E 97 (4), 043117.Google ScholarPubMed
Van Leer, B. 1977 Towards the ultimate conservative difference scheme. IV. A new approach to numerical convection. J. Comput. Phys. 23 (3), 276–299.CrossRefGoogle Scholar
Vasilev, E. I., Ben-Dor, G., Elperin, T. & Henderson, L. F. 2004 The wall-jetting effect in Mach reflection: Navier–Stokes simulations. J. Fluid Mech. 511, 363–379.Google Scholar
Vasilev, E. I., Elperin, T. & Ben-Dor, G. 2008 Analytical reconsideration of the von Neumann paradox in the reflection of a shock wave over a wedge. Phys. Fluids 20 (4), 046101.Google Scholar

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, $M_{\mathrm{c}}=3.0$, $\gamma_0 = 1.4$, $\theta_{\mathrm{w}} = 30^{\circ}$)

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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