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Shock-induced interfacial instabilities of granular media

Published online by Cambridge University Press:  11 November 2021

Jiarui Li Open the ORCID record for Jiarui Li [Opens in a new window] ,
Kun Xue ,
Junsheng Zeng ,
Baolin Tian  and
Xiaohu Guo
Jiarui Li
Affiliation:
State Key Laboratory of Explosive Science and Technology, Explosion Protection and Emergency Disposal Technology Engineering Research Center of the Ministry of Education, Beijing Institute of Technology, Beijing 100081, China
Kun Xue*
Affiliation:
State Key Laboratory of Explosive Science and Technology, Explosion Protection and Emergency Disposal Technology Engineering Research Center of the Ministry of Education, Beijing Institute of Technology, Beijing 100081, China
Junsheng Zeng
Affiliation:
Intelligent Energy Lab, Frontier Research Center, Peng Cheng Laboratory, Shenzhen 518000, China
Baolin Tian
Affiliation:
Institute of Applied Physics and Computational Mathematics, Beijing 1000871, China
Xiaohu Guo
Affiliation:
Daresbury Laboratory, Warrington WA4 4AD, UK
*
† Email address for correspondence: [email protected]
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Abstract

This paper investigates the shock-induced instability of the interfaces between gases and dense granular media with finite length via the coarse-grained compressible computational fluid dynamics–discrete parcel method. Despite generating a typical spike-bubble structure reminiscent of the Richtmyer–Meshkov instability (RMI), the shock-driven granular instability (SDGI) is governed by fundamentally different mechanisms. Unlike the RMI arising from baroclinic vorticity deposition on the interface, the SDGI is closely associated with the interfacial and bulk granular dynamics, which evolve with the transient coupling between particles and gases. Consequently, the SDGI follows a growth law distinctly different from that of the RMI, namely a semilinear slow regime followed by an exponentially expedited regime and a quadratic asymptotic regime. We further establish the instability criteria of the SDGI for granular media with infinite and finite lengths, which do not exist in the RMI. A scaling growth law of the SDGI for dense granular media with finite length is derived by normalizing the time with the rarefaction propagation time, which successfully collapses the data from cases with varying shock strength, particle column length and particle volume fraction and ought to hold for granular media with varying particle parameters. The effect of the initial perturbation magnitude can be properly considered in the scaling growth law by incorporating it into the length normalization.

JFM classification

Multiphase and Particle-laden Flows: Particle/fluid flow Granular media: Dry granular material Compressible Flows: Shock waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 930 , 10 January 2022 , A22
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

Aglitskiy, Y. et al. 2010 Basic hydrodynamics of Richtmyer–Meshkov-type growth and oscillations in the inertial confinement fusion-relevant conditions. Phil. Trans. R. Soc. A: Math. Phys. Engng Sci. 368, 1739–1768.CrossRefGoogle ScholarPubMed
Apte, S., Mahesh, K. & Lundgren, T. 2003 A Eulerlan-Lagrangian model to simulate two-phase/particulate flows. Center for Turbulence Research Annual Research Briefs, 161–171.Google Scholar
Baer, M.R. & Nunziato, J.W. 1986 A two-phase mixture theory for the deflagration-to-detonation transition (ddt) in reactive granular materials. Intl J. Multiphase Flow 12, 861–889.CrossRefGoogle Scholar
Ben-Dor, G., Britan, A., Elperin, T., Igra, O. & Jiang, J.P. 1997 Experimental investigation of the interaction between weak shock waves and granular layers. Exp. Fluids 22, 432–443.CrossRefGoogle Scholar
Britan, A., Shapiro, H. & Ben-Dor, G. 2007 The contribution of shock tubes to simplified analysis of gas filtration through granular media. J. Fluid Mech. 586, 147–176.CrossRefGoogle Scholar
Carmouze, Q., Saurel, R., Chiapolino, A. & Lapebie, E. 2020 Riemann solver with internal reconstruction (RSIR) for compressible single-phase and non-equilibrium two-phase flows. J. Comput. Phys. 408, 109176.CrossRefGoogle Scholar
Chiapolino, A. & Saurel, R. 2020 Numerical investigations of two-phase finger-like instabilities. Comput. Fluids 206, 104585.CrossRefGoogle Scholar
Cho, G.C., Dodds, J. & Santamarina, J.C. 2006 Particle shape effects on packing density, stiffness, and strength: natural and crushed sands. J. Geotech. Geoenviron. Engng 133, 591–602.CrossRefGoogle Scholar
Crowe, C.T., Schwarzkopf, J.D., Sommerfeld, M. & Tsuji, Y. 2012 Multiphase Flows with Droplets and Particles. CRC Press.Google Scholar
David, L.F., Yann, G., Oren, P., Samuel, G. & Fan, Z. 2012 Particle jet formation during explosive dispersal of solid particles. Phys. Fluids 24, 091109.Google Scholar
DeMauro, E.P., Wagner, J.L., DeChant, L.J., Beresh, S.J. & Turpin, A.M. 2019 Improved scaling laws for the shock-induced dispersal of a dense particle curtain. J. Fluid Mech. 876, 881–895.CrossRefGoogle Scholar
Di Felice, R. 1994 The voidage function for fluid-particle interaction systems. Intl J. Multiphase Flow 20, 153–159.CrossRefGoogle Scholar
Duke-Walker, V., Maxon, W.C., Almuhna, S.R. & McFarland, J.A. 2021 Evaporation and breakup effects in the shock-driven multiphase instability. J. Fluid Mech. 908, A13.CrossRefGoogle Scholar
Eriksen, F.K., Toussaint, R., Turquet, A.L., Måløy, K.J. & Flekkøy, E.G. 2018 Pressure evolution and deformation of confined granular media during pneumatic fracturing. Phys. Rev. E 97, 012908.CrossRefGoogle ScholarPubMed
Fernández-Godino, M.G., Ouellet, F., Haftka, R.T. & Balachandar, S. 2019 Early time evolution of circumferential perturbation of initial particle volume fraction in explosive cylindrical multiphase dispersion. Trans. ASME J. Fluids Engng 141, 091302.CrossRefGoogle Scholar
Formenti, Y., Druitt, T.H. & Kelfoun, K. 2003 Characterisation of the 1997 Vulcanian explosions of Soufrière Hills Volcano, Montserrat, by video analysis. Bull. Volcanol. 65, 587–605.CrossRefGoogle Scholar
Frost, D.L. 2018 Heterogeneous/particle-laden blast waves. Shock Waves 28, 439–449.CrossRefGoogle Scholar
Han, P., Xue, K. & Bai, C. 2021 Explosively driven dynamic compaction of granular media. Phys. Fluids 33, 023309.CrossRefGoogle Scholar
Inoue, T., Yamazaki, R. & Inutsuka, S.-I. 2009 Turbulence and magnetic field amplification in supernova remnants: interactions between a strong shock wave and multiphase interstellar medium. Astrophys. J 695, 825–833.CrossRefGoogle Scholar
Kandan, K., Khaderi, S.N., Wadley, H.N.G. & Deshpande, V.S. 2017 Surface instabilities in shock loaded granular media. J. Mech. Phys. Solids 109, 217–240.CrossRefGoogle Scholar
Koneru, R.B., Rollin, B., Durant, B., Ouellet, F. & Balachandar, S. 2020 A numerical study of particle jetting in a dense particle bed driven by an air-blast. Phys. Fluids 32, 093301.CrossRefGoogle Scholar
Kruggel-Emden, H., Sturm, M., Wirtz, S. & Scherer, V. 2008 Selection of an appropriate time integration scheme for the discrete element method (DEM). Comput. Chem. Engng 32, 2263–2279.CrossRefGoogle Scholar
Li, J., Ding, J., Si, T. & Luo, X. 2020 Convergent Richtmyer–Meshkov instability of light gas layer with perturbed outer surface. J. Fluid Mech. 884, R2.CrossRefGoogle Scholar
Liu, X.D., Osher, S. & Chan, T. 1994 Weighted essentially non-oscillatory schemes. J. Comput. Phys. 115, 200–212.CrossRefGoogle Scholar
Luo, X., Li, M., Ding, J., Zhai, Z. & Si, T. 2019 Nonlinear behaviour of convergent Richtmyer–Meshkov instability. J. Fluid Mech. 877, 130–141.CrossRefGoogle Scholar
McFarland, J.A., Black, W.J., Dahal, J. & Morgan, B.E. 2016 Computational study of the shock driven instability of a multiphase particle-gas system. Phys. Fluids 28, 024105.CrossRefGoogle Scholar
Meng, B., Zeng, J., Tian, B., Li, L., He, Z. & Guo, X. 2019 Modeling and verification of the Richtmyer–Meshkov instability linear growth rate of the dense gas-particle flow. Phys. Fluids 31, 074102.Google Scholar
Milne, A., Parrish, C. & Worland, I. 2010 Dynamic fragmentation of blast mitigants. Shock Waves 20, 41–51.CrossRefGoogle Scholar
Milne, A.M., Floyd, E., Longbottom, A.W. & Taylor, P. 2014 Dynamic fragmentation of powders in spherical geometry. Shock Waves 24, 501–513.CrossRefGoogle Scholar
Mo, H., Lien, F.-S., Zhang, F. & Cronin, D.S. 2018 A numerical framework for the direct simulation of dense particulate flow under explosive dispersal. Shock Waves 28, 559–577.CrossRefGoogle Scholar
Mo, H., Lien, F.-S., Zhang, F. & Cronin, D.S. 2019 A mesoscale study on explosively dispersed granular material using direct simulation. J. Appl. Phys. 125, 214302.CrossRefGoogle Scholar
Osnes, A.N., Vartdal, M. & Pettersson Reif, B.A. 2017 Numerical simulation of particle jet formation induced by shock wave acceleration in a Hele-Shaw cell. Shock Waves 28, 451–461.CrossRefGoogle Scholar
Rodriguez, V., Saurel, R., Jourdan, G. & Houas, L. 2013 Solid-particle jet formation under shock-wave acceleration. Phys. Rev. E 88, 063011.CrossRefGoogle ScholarPubMed
Rycroft, C.H. 2009 VORO++: A three-dimensional Voronoi cell library in C++. Chaos 19, 041111.CrossRefGoogle ScholarPubMed
Sundaresan, S., Ozel, A. & Kolehmainen, J. 2018 Toward constitutive models for momentum, species, and energy transport in gas–particle flows. Annu. Rev. Chem. Biomol. Engng 9, 61–81.CrossRefGoogle ScholarPubMed
Tian, B., Zeng, J., Meng, B., Chen, Q., Guo, X. & Xue, K. 2020 Compressible multiphase particle-in-cell method (CMP-PIC) for full pattern flows of gas-particle system. J. Comput. Phys. 418, 109602.CrossRefGoogle Scholar
Toro, E.F. 2009 Riemann Solvers and Numerical Methods for Fluid Dynamics. The HLL and HLLC Riemann Solvers.CrossRefGoogle Scholar
Ukai, S., Balakrishnan, K. & Menon, S. 2010 On Richtmyer–Meshkov instability in dilute gas-particle mixtures. Phys. Fluids 22, 104103.CrossRefGoogle Scholar
Vorobieff, P., Anderson, M., Conroy, J., White, R., Truman, C.R. & Kumar, S. 2011 Vortex formation in a shock-accelerated gas induced by particle seeding. Phys. Rev. Lett. 106, 184503.CrossRefGoogle Scholar
Xue, K., Du, K., Shi, X., Gan, Y. & Bai, C. 2018 Dual hierarchical particle jetting of a particle ring undergoing radial explosion. Soft Matter 14, 4422–4431.CrossRefGoogle ScholarPubMed
Xue, K., Li, F. & Bai, C. 2013 Explosively driven fragmentation of granular materials. Eur. Phys. J. E 36, 1–16.CrossRefGoogle ScholarPubMed
Xue, K., Shi, X., Zeng, J., Tian, B., Han, P., Li, J., Liu, L., Meng, B., Guo, X. & Bai, C. 2020 Explosion-driven interfacial instabilities of granular media. Phys. Fluids 32, 084104.CrossRefGoogle Scholar
Yan, G., Yu, H.S. & Mcdowell, G. 2009 Simulation of granular material behaviour using DEM. Procedia Earth Planet. Sci. 1, 598–605.CrossRefGoogle Scholar
Zhang, Y., He, Z., Xie, H.S., Xiao, M.J. & Tian, B.L.J.J.o.F.M. 2020 Methodology for determining coefficients of turbulent mixing model. 905, A26.Google Scholar
Zhou, Y. et al. 2021 Rayleigh–Taylor and Richtmyer–Meshkov instabilities: a journey through scales. Physica D 423, 132838.CrossRefGoogle Scholar