Hostname: page-component-857557d7f7-v48vw Total loading time: 0 Render date: 2025-11-26T09:11:39.080Z Has data issue: false hasContentIssue false
  • English
  • Français

Modelling external particle jet formation in explosive granular dispersal systems

Published online by Cambridge University Press:  26 November 2025

Yifeng He Open the ORCID record for Yifeng He [Opens in a new window] ,
Junsheng Zeng ,
Baolin Tian  and
Yue Yang Open the ORCID record for Yue Yang [Opens in a new window]
Yifeng He
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, School of Mechanics and Engineering Science, Peking University, Beijing 100871, PR China HEDPS-CAPT, Peking University, Beijing 100871, PR China
Junsheng Zeng
Affiliation:
School of Aeronautic Science and Engineering, Beihang University, Beijing, PR China Shanghai Zhangjiang Institute of Mathematics, Shanghai, PR China
Baolin Tian*
Affiliation:
School of Aeronautic Science and Engineering, Beihang University, Beijing, PR China Shanghai Zhangjiang Institute of Mathematics, Shanghai, PR China
Yue Yang*
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, School of Mechanics and Engineering Science, Peking University, Beijing 100871, PR China HEDPS-CAPT, Peking University, Beijing 100871, PR China
*
Corresponding authors: Yue Yang, yyg@pku.edu.cn; Baolin Tian, tianbaolin@buaa.edu.cn
Corresponding authors: Yue Yang, yyg@pku.edu.cn; Baolin Tian, tianbaolin@buaa.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

We investigate the evolution of an external particle jet in a dense particle bed subjected to a radially divergent air-blast. Both random and single-mode perturbations are considered. By analysing the particle dynamics, we show that the Rayleigh–Taylor instability (RTI), the Richtmyer–Meshkov instability (RMI) and large particle inertia contribute to the formation of the external jet. The external particle jet exhibits a spike-like structure at its top and a bubble-like structure near its bottom. As the expanding particle bed lowers the internal gas pressure, particles near the bubble experience strong inward coupling forces and undergo RTI with variable acceleration. Meanwhile, particles in the spike experience weak gas–particle coupling and collision forces due to large particle inertia and low particle volume fraction, respectively. Consequently, the particles in the spike retain a nearly constant velocity, in contrast to the accelerating spikes observed in cylindrical RTI. To investigate the contributions of RMI to the particle jet growth, we track the trough-near particles in the single-mode perturbation case. It is revealed that the trough-near particles accelerate under the perturbation-induced pressure gradient, overtaking the crest-near particles and inducing phase inversion, thereby resulting in an increase in jet length. We establish a linear-growth model for the jet length increment, similar to the planar Richtmyer–Meshkov impulsive model. Combined with the jet-length-increment model, we propose an external-particle-jet-length model that is consistent with both numerical and experimental results for diverse initial gas pocket central pressures and particle bed thicknesses.

JFM classification

Compressible Flows: Shock waves

Information

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1024 , 10 December 2025 , A5
Check for updates
Copyright
© The Author(s), 2025. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Annamalai, S., Rollin, B., Ouellet, F., Neal, C., Jackson, T.L. & Balachandar, S. 2016 Effects of initial perturbations in the early moments of an explosive dispersal of particles. J. Fluids Engng. 138, 070903.10.1115/1.4030954CrossRefGoogle Scholar
Baer, M.R. & Nunziato, J.W. 1986 A two–phase mixture theory for the deflagration–to–detonation transition (ddt) in reactive granular materials. Int. J. Multiph. Flow 12, 861–889.10.1016/0301-9322(86)90033-9CrossRefGoogle Scholar
Balakrishnan, K. & Menon, S. 2010 On turbulent chemical explosions into dilute aluminum particle clouds. Combust. Theory Model. 14, 583–617.10.1080/13647830.2010.502974CrossRefGoogle Scholar
Barba, F.D. & Picano, F. 2018 Clustering and entrainment effects on the evaporation of dilute droplets in a turbulent jet. Phys. Rev. Fluids 3 (3), 034304.10.1103/PhysRevFluids.3.034304CrossRefGoogle Scholar
Bell, G.I. 1951 Taylor instability on cylinders and spheres in the small amplitude approximation. Report No. LA-1321, LANL. vol. 1321, pp. 91873–91879,Google Scholar
Bender, J.D. et al. 2021 Simulation and flow physics of a shocked and reshocked high–energy–density mixing layer. J. Fluids Mech. 915, A84.10.1017/jfm.2020.1122CrossRefGoogle Scholar
Berk, T. & Coletti, F. 2021 Dynamics of small heavy particles in homogeneous turbulence: a Lagrangian experimental study. J. Fluids Mech. 917, A47.10.1017/jfm.2021.280CrossRefGoogle Scholar
Britan, A. & Ben-Dor, G. 2006 Shock tube study of the dynamical behavior of granular materials. Int. J. Multiph. Flow 32, 623–642.10.1016/j.ijmultiphaseflow.2006.01.007CrossRefGoogle Scholar
Calvo-Rivera, A., Huete, C. & Velikovich, A.L. 2022 The stability of expanding reactive shocks in a van der Waals fluid. Phys. Fluids 34 (4), 046106.10.1063/5.0087073CrossRefGoogle Scholar
Calvo-Rivera, A., Velikovich, A.L. & Huete, C. 2023 On the stability of piston-driven planar shocks. J. Fluids Mech. 964, A33.10.1017/jfm.2023.373CrossRefGoogle Scholar
Capecelatro, J. 2022 Modeling high–speed gas–particle flows relevant to spacecraft landings. Int. J. Multiph. Flow 150, 104008.10.1016/j.ijmultiphaseflow.2022.104008CrossRefGoogle Scholar
Capecelatro, J. & Desjardins, O. 2013 Eulerian–Lagrangian modeling of turbulent liquid–solid slurries in horizontal pipes. J. Comput. Phys. 55, 64–79.Google Scholar
Capecelatro, J. & Wagner, J.L. 2024 Gas–particle dynamics in high–speed flows. Annu. Rev. Fluid Mech. 56, 379–403.10.1146/annurev-fluid-121021-015818CrossRefGoogle Scholar
Chiapolino, A. & Saurel, R. 2020 Numerical investigations of two–phase finger–like instabilities. Comput. Fluids 206, 104585.10.1016/j.compfluid.2020.104585CrossRefGoogle Scholar
Crowe, C., Sommerfield, M. & Tsuji, Y. 1998 Multiphase Flows with Droplets and Particles. CRC Press.Google Scholar
Crowl, D.A. 2003 Understanding Explosions. Wiley.10.1002/9780470925287CrossRefGoogle Scholar
Ding, J., Fan, C., Zhou, Z. & Luo, X. 2025 Instability at imploding gas layer impacted by convergent shock. J. Fluids Mech. 1008, A9.10.1017/jfm.2025.178CrossRefGoogle Scholar
Ding, J., Si, T., Yang, J., Lu, X., Zhai, Z. & Luo, X. 2017 Measurement of a Richtmyer–Meshkov instability at an air-SF 6 interface in a semiannular shock tube. Phys. Rev. Lett. 119, 014501.10.1103/PhysRevLett.119.014501CrossRefGoogle Scholar
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. J. Fluids Engng. 141, 091302.10.1115/1.4043055CrossRefGoogle Scholar
Frost, D.L. 2018 Heterogeneous/particle–laden blast waves. Shock Waves 28, 439–449.10.1007/s00193-018-0825-1CrossRefGoogle Scholar
Frost, D.L., Grégoire, Y., Petel, O., Goroshin, S. & Zhang, F. 2012 Particle jet formation during explosive dispersal of solid particles. Phys. Fluids 24, 091109.10.1063/1.4751876CrossRefGoogle Scholar
He, Y., Meng, B., Tian, B. & Yang, Y. 2024 Shock–induced instability of dual–layer dilute gas–particle mixture. Phys. Rev. Fluids 9, 124301.10.1103/PhysRevFluids.9.124301CrossRefGoogle Scholar
He, Y., Peng, N., Li, H., Tian, B. & Yang, Y. 2023 Formation of the cavity on a planar interface subjected to a perturbed shock wave. Phys. Rev. Fluids 8 (6), 063402.10.1103/PhysRevFluids.8.063402CrossRefGoogle Scholar
Huete, C., Velikovich, A.L., Martinez-Ruiz, D. & Calvo-Rivera, A. 2021 Stability of expanding accretion shocks for an arbitrary equation of state. J. Fluids Mech. 927, A34.10.1017/jfm.2021.781CrossRefGoogle Scholar
Hughes, K.T., Balachandar, S., Diggs, A., Haftka, R., Kim, N.H. & Littrell, D. 2020 Simulation–driven design of experiments examining the large–scale, explosive dispersal of particles. Shock Waves 30, 325–347.10.1007/s00193-019-00927-xCrossRefGoogle Scholar
Hughes, K.T., Charonko, J.J., Prestridge, K.P., Kim, N.H., Haftka, R.T. & Balachandar, S. 2021 Proton radiography of explosively dispersed metal particles with varying volume fraction and varying carrier phase. Shock Waves 31, 75–88.10.1007/s00193-020-00983-8CrossRefGoogle 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, 093301.10.1063/5.0015190CrossRefGoogle Scholar
Lai, S., Houim, R.W. & Oran, E.S. 2018 Effects of particle size and density on dust dispersion behind a moving shock. Phys. Rev. Fluids 3, 064306.10.1103/PhysRevFluids.3.064306CrossRefGoogle Scholar
Li, J., Ding, J., Si, T. & Luo, X. 2020 Convergent Richtmyer–Meshkov instability of light gas layer with perturbed outer surface. J. Fluids Mech. 884, R2.10.1017/jfm.2019.989CrossRefGoogle Scholar
Li, J., Xue, K., Zeng, J., Tian, B. & Guo, X. 2022 Shock–induced interfacial instabilities of granular media. J. Fluid Mech. 930, A22.10.1017/jfm.2021.912CrossRefGoogle Scholar
Li, J., Wang, H., Zhai, Z. & Luo, X. 2023 a Richtmyer–Meshkov instability of a single–mode heavy–light interface in cylindrical geometry. Phys. Fluids 35, 106112.10.1063/5.0167248CrossRefGoogle Scholar
Li, J., Zeng, J. & Xue, K. 2023 b Pressure evolution in shock–compacted granular media. Pet. Sci. 20 (6), 3736–3751.10.1016/j.petsci.2023.04.017CrossRefGoogle Scholar
Liu, H., Tafti, D.K. & Li, T. 2014 Hybrid parallelism in MFIX CFD–DEM using OpenMP. Powder Technol. 259, 22–29.10.1016/j.powtec.2014.03.047CrossRefGoogle Scholar
Loth, E. 2008 Compressibility and rarefaction effects on drag of a spherical particle. AIAA J. 46, 2219–2228.10.2514/1.28943CrossRefGoogle Scholar
Lozano, E., Roehl, D., Celes, W. & Gattass, M. 2016 An efficient algorithm to generate random sphere packs in arbitrary domains. Comput. Math. Appl. 71, 1586–1601.10.1016/j.camwa.2016.02.032CrossRefGoogle Scholar
Lube, G., Breard, E.C.P., Esposti-Ongaro, T., Dufek, J. & Brand, B. 2020 Multiphase flow behaviour and hazard prediction of pyroclastic density currents. Nat. Rev. Earth Environ. 1 (7), 348–365.10.1038/s43017-020-0064-8CrossRefGoogle Scholar
Luo, X., Liu, L., Liang, Y., Ding, J. & Wen, C. 2020 Richtmyer–Meshkov instability on a dual–mode interface. J. Fluids Mech. 905, A5.10.1017/jfm.2020.732CrossRefGoogle 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, 024105.10.1063/1.4941131CrossRefGoogle Scholar
McGrath, T.P., Clair, J.G.S. & Balachandar, S. 2016 A compressible two–phase model for dispersed particle flows with application from dense to dilute regimes. J. Appl. Phys. 119, 174903.10.1063/1.4948301CrossRefGoogle 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 (7), 074102.10.1063/1.5099996CrossRefGoogle Scholar
Meshkov, E.E. 1969 Instability of the interface of two gases accelerated by a shock wave. Fluid Dyn. 4, 101–104.10.1007/BF01015969CrossRefGoogle Scholar
Michael, D.H. 1965 Kelvin–Helmholtz instability of a dusty gas. Math. Proc. Camb. Philos. Soc. 61, 569–571.10.1017/S030500410000414XCrossRefGoogle Scholar
Middlebrooks, J.B., Avgoustopoulos, C.G., Black, W.J., Allen, R.C. & McFarland, J.A. 2018 Droplet and multiphase effects in a shock-driven hydrodynamic instability with reshock. Exp. Fluids 59 (98), 1–16.10.1007/s00348-018-2547-7CrossRefGoogle Scholar
Mikaelian, K.O. 2005 Rayleigh–Taylor and Richtmyer–Meshkov instabilities and mixing in stratified cylindrical shells. Phys. Fluids 17, 094105.10.1063/1.2046712CrossRefGoogle Scholar
Milne, A.M. 2016 Gurney analysis of porous shells. Propellants Explos. Pyrotech. 41, 665–671.10.1002/prep.201600016CrossRefGoogle Scholar
Milne, A., Parrish, C. & Worland, I. 2010 Dynamic fragmentation of blast mitigants. Shock Waves 20, 41–51.10.1007/s00193-009-0235-5CrossRefGoogle Scholar
Milne, A.M., Floyd, E., Longbottom, A.W. & Taylor, P. 2014 Dynamic fragmentation of powders in spherical geometry. Shock Waves 24, 501–513.10.1007/s00193-014-0511-xCrossRefGoogle Scholar
Osnes, A.N., Vartdal, M., Khalloufi, M., Capecelatro, J. & Balachandar, S. 2023 Comprehensive quasi-steady force correlations for compressible flow through random particle suspensions. Int. J. Multiph. Flow 165, 104485.10.1016/j.ijmultiphaseflow.2023.104485CrossRefGoogle Scholar
Osnes, A.N., Vartdal, M. & Reif, B.A.P. 2018 Numerical simulation of particle jet formation induced by shock wave acceleration in a Hele-Shaw cell. Shock Waves 28, 451–461.10.1007/s00193-017-0778-9CrossRefGoogle Scholar
Papalexandris, M.V. 2004 Numerical simulation of detonations in mixtures of gases and solid particles. J. Fluids Mech. 507, 95–142.10.1017/S0022112004008894CrossRefGoogle Scholar
Peng, N., Yang, Y., Wu, J. & Xiao, Z. 2021 a Mechanism and modelling of the secondary baroclinic vorticity in the Richtmyer–Meshkov instability. J. Fluids Mech. 911, A56.10.1017/jfm.2020.1080CrossRefGoogle Scholar
Peng, N., Yang, Y. & Xiao, Z. 2021 b Effects of the secondary baroclinic vorticity on the energy cascade in the Richtmyer–Meshkov instability. J. Fluids Mech. 925, A39.10.1017/jfm.2021.687CrossRefGoogle Scholar
Pontalier, Q., Loiseau, J., Goroshin, S. & Frost, D.L. 2018 Experimental investigation of blast mitigation and particle–blast interaction during the explosive dispersal of particles and liquids. Shock Waves 28, 489–511.10.1007/s00193-018-0821-5CrossRefGoogle Scholar
Posey, J.W., Roque, B., Guhathakurta, S. & Houim, R.W. 2021 Mechanisms of prompt and delayed ignition and combustion of explosively dispersed aluminum powder. Phys. Fluids 33, 113308.10.1063/5.0065312CrossRefGoogle Scholar
Rana, U., Abadie, T., Chapman, D., Joiner, N. & Matar, O.K. 2024 Richtmyer–Meshkov instability at high Mach number: non–Newtonian effects. Phys. Fluids 36, 066104.10.1063/5.0209843CrossRefGoogle Scholar
Renzo, A.D., Napolitano, E.S. & Maio, F.P.D. 2021 Coarse–grain dem modelling in fluidized bed simulation: a review. Processes 9 (2), 279.10.3390/pr9020279CrossRefGoogle Scholar
Richtmyer, R.D. 1960 Taylor instability in shock acceleration of compressible fluids. Commun. Pure Appl. Maths 13, 297–319.10.1002/cpa.3160130207CrossRefGoogle Scholar
Rodriguez, V., Saurel, R., Jourdan, G. & Houas, L. 2013 Solid–particle jet formation under shock-wave acceleration. Phys. Rev. E 88, 063011.10.1103/PhysRevE.88.063011CrossRefGoogle ScholarPubMed
Rodriguez, V., Saurel, R., Jourdan, G. & Houas, L. 2014 External front instabilities induced by a shocked particle ring. Phys. Rev. E 90, 043013.10.1103/PhysRevE.90.043013CrossRefGoogle ScholarPubMed
Rodriguez, V., Saurel, R., Jourdan, G. & Houas, L. 2017 Impulsive dispersion of a granular layer by a weak blast wave. Shock Waves 27, 187–198.10.1007/s00193-016-0658-8CrossRefGoogle Scholar
Rogue, X., Rodriguez, G., Haas, J.F. & Saurel, R. 1998 Experimental and numerical investigation of the shock–induced fluidization of a particles bed. Shock Waves 8, 29–45.10.1007/s001930050096CrossRefGoogle Scholar
Shallcross, G.S., Fox, R.O. & Capecelatro, J. 2020 A volume–filtered description of compressible particle–laden flows. Int. J. Multiph. Flow 122, 103138.10.1016/j.ijmultiphaseflow.2019.103138CrossRefGoogle Scholar
Si, T., Jiang, S., Cai, W., Wang, H. & Luo, X. 2025 Shock–tube experiments on strong–shock–driven single–mode Richtmyer–Meshkov instability. J. Fluids Mech. 1006, R1.10.1017/jfm.2025.36CrossRefGoogle Scholar
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, 109602.10.1016/j.jcp.2020.109602CrossRefGoogle Scholar
Ukai, S., Balakrishnan, K. & Menon, S. 2010 On Richtmyer–Meshkov instability in dilute gas–particle mixtures. Phys. Fluids 22, 104103.10.1063/1.3507318CrossRefGoogle 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 (18), 184503.10.1103/PhysRevLett.106.184503CrossRefGoogle Scholar
Wang, Z., Liu, M. & Yang, X. 2020 A four-way coupled CFD-DEM modeling framework for charged particles under electrical field with applications to gas insulated switchgears. Powder Technol. 373, 433–445.10.1016/j.powtec.2020.06.086CrossRefGoogle 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, 4422–4431.10.1039/C8SM00209FCrossRefGoogle ScholarPubMed
Xue, K., Miu, L., Li, J., Bai, C. & Tian, B. 2023 Explosive dispersal of granular media. J. Fluid Mech. 959, A17.10.1017/jfm.2023.117CrossRefGoogle Scholar
Xue, K., Sun, L. & Bai, C. 2016 Formation mechanism of shock–induced particle jetting. Phys. Rev. E. 94 (2), 022903.10.1103/PhysRevE.94.022903CrossRefGoogle ScholarPubMed
Zeng, J., Meng, B., Ye, X. & Tian, B. 2024 Closed equation model for cavity evolution in granular media. J. Fluids Mech. 996, A15.10.1017/jfm.2024.759CrossRefGoogle Scholar
Zhang, F., Damjanac, B. & Huang, H. 2013 Coupled discrete element modeling of fluid injection into dense granular media. J. Geophys. Res.-Solid Earth 118, 2703–2722.10.1002/jgrb.50204CrossRefGoogle Scholar
Zhang, F., Frost, D.L., Thibault, P.A. & Murray, S.B. 2001 Explosive dispersal of solid particles. Shock Waves 10 (6), 431–443.10.1007/PL00004050CrossRefGoogle Scholar
Zhang, F., Ripley, R.C., Yoshinaka, A., Findlay, C.R., Anderson, J. & Rosen, B.V. 2015 Large–scale spray detonation and related particle jetting instability phenomenon. Shock Waves 25, 239–254.10.1007/s00193-014-0525-4CrossRefGoogle Scholar
Zhou, Y. 2017 a Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. I. Phys. Rep. 720–722, 1–136.Google Scholar
Zhou, Y. 2017 b Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. II. Phys. Rep. 723–725, 1–160.Google Scholar
Zhou, Y. et al. 2021 Rayleigh–Taylor and Richtmyer–Meshkov instabilities: a journey through scales. Physica D 423, 132838.10.1016/j.physd.2020.132838CrossRefGoogle Scholar
Zou, L., Liu, J., Liao, S., Zheng, X., Zhai, Z. & Luo, X. 2017 Richtmyer–Meshkov instability of a flat interface subjected to a rippled shock wave. Phys. Rev. E 95, 013107.10.1103/PhysRevE.95.013107CrossRefGoogle ScholarPubMed