Hostname: page-component-77f85d65b8-pztms Total loading time: 0 Render date: 2026-04-14T06:42:12.507Z Has data issue: false hasContentIssue false
  • English
  • Français

Unveiling scaling laws, dispersal morphologies and phase diagrams in gas–particle systems under blast-supersonic flow coupling

Published online by Cambridge University Press:  06 April 2026

Kuilong Chen Open the ORCID record for Kuilong Chen [Opens in a new window] ,
Baoqing Meng  and
Baolin Tian
Kuilong Chen
Affiliation:
State Key Laboratory of High Temperature Gas Dynamics, Institute of Mechanics, Chinese Academic of Sciences, Beijing 100190, PR China School of Engineering Science, University of Chinese Academy of Sciences , Beijing 100049, PR China
Baoqing Meng*
Affiliation:
State Key Laboratory of High Temperature Gas Dynamics, Institute of Mechanics, Chinese Academic of Sciences, Beijing 100190, PR China School of Engineering Science, University of Chinese Academy of Sciences , Beijing 100049, PR China
Baolin Tian
Affiliation:
School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, PR China
*
Corresponding author: Baoqing Meng, mengbaoqing92@foxmail.com
Get access Rights & Permissions [Opens in a new window]

Abstract

In compressible gas–particle flows the dispersion of particle clouds driven by a blast is widely observed in extreme natural and engineering scenarios. Whereas prior research has primarily focused on planar shock or blast-driven configurations, this study investigates a gas–particle system combining a finite-source blast with supersonic inflow. Accordingly, the compressible multiphase particle-in-cell method is employed to simulate the flow. The resulting waves including main shock, contact surface and secondary shock are parametrically investigated, where the main shock radius follows an approximate power law to time. Driven primarily by the drag force, a simplified two-stage scaling law for spanwise leading particle dispersion is derived: a time-squared dependence during the blast-dominated stage and growth behaviour ranging from linear to logarithmic in the subsequent flow-impingement stage. Furthermore, four dispersion morphologies are identified: compressed, uniform, eroded and jetting, each explained by specific wave–particle interaction mechanisms. Finally, a phase diagram correlating these morphologies with the inflow Mach number, Stokes number and pressure ratio is constructed. These findings reveal the coupled mechanisms in gas–particle systems driven by a blast and supersonic inflow, providing a predictive basis for impulse effects and particle dispersion.

JFM classification

Multiphase and Particle-laden Flows: Multiphase and Particle-laden Flows Compressible Flows: Supersonic flow Compressible Flows: Detonation waves

Information

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1032 , 10 April 2026 , A59
Check for updates
Copyright
© The Author(s), 2026. 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

Baby, V.Y., Paramanantham, V. & Rajesh, G. 2024 Regular reflection to Mach reflection (RR–MR) transition in short wedges. J. Fluid Mech. 998, A38.10.1017/jfm.2024.826CrossRefGoogle 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 (6), 861–889.10.1016/0301-9322(86)90033-9CrossRefGoogle Scholar
Balachandar, S. & Eaton, J.K. 2010 Turbulent dispersed multiphase flow. Annu. Rev. Fluid Mech. 42 (2010), 111–133.10.1146/annurev.fluid.010908.165243CrossRefGoogle Scholar
Balakrishnan, K. 2014 Explosion-driven Rayleigh–Taylor instability in gas-particle mixtures. Phys. Fluids 26 (4), 43303-1–43303-15.10.1063/1.4873175CrossRefGoogle Scholar
Black, W.J., Denissen, N. & McFarland, J.A. 2018 Particle force model effects in a shock-driven multiphase instability. Shock Waves 28 (3), 463–472.10.1007/s00193-017-0790-0CrossRefGoogle Scholar
Brandt, V., Grabowski, J., Jurtz, N., Kraume, M. & Kruggel-Emden, H. 2023 A benchmarking study of different DEM coarse graining strategies. Powder Technol. 426, 118629.10.1016/j.powtec.2023.118629CrossRefGoogle Scholar
Brode, H.L. 1959 Blast wave from a spherical charge. Phys. Fluids 2 (2), 217–229.10.1063/1.1705911CrossRefGoogle Scholar
Capecelatro, J. 2022 Modeling high-speed gas–particle flows relevant to spacecraft landings. Intl J. Multiphase Flow 150, 104008.10.1016/j.ijmultiphaseflow.2022.104008CrossRefGoogle Scholar
Capecelatro, J. & Wagner, J.L. 2024 Gas–particle dynamics in high-speed flows. Annu. Rev. Fluid Mech. 56 (2024), 379–403.10.1146/annurev-fluid-121021-015818CrossRefGoogle Scholar
Cardona, V., Joussot, R. & Lago, V. 2021 Shock/shock interferences in a supersonic rarefied flow: experimental investigation. Exp. Fluids 62, 135.10.1007/s00348-021-03225-4CrossRefGoogle Scholar
Casey, D.T., et al. 2015 Performance and mix measurements of indirect drive Cu-doped Be implosions. Phys. Rev. Lett. 114 (20), 205002.10.1103/PhysRevLett.114.205002CrossRefGoogle ScholarPubMed
Chen, H., Yin, J., Li, X., Yang, D. & Lu, W. 2022 A numerical study on the blast wave distribution and propagation characteristics of cylindrical explosive in motion. Math. Probl. Engng 2022(1), 6446164.Google Scholar
Cigala, V., Kueppers, U., Fernández, J.J.P. & Dingwell, D.B. 2021 Linking gas and particle ejection dynamics to boundary conditions in scaled shock-tube experiments. Bull. Volcanol. 83 (8), 53.10.1007/s00445-021-01473-0CrossRefGoogle ScholarPubMed
Crowe, C.T. (Ed.) 2012 Multiphase lows with Droplets and Particles, 2nd edn. CRC Press.Google Scholar
Dahal, J. & McFarland, J.A. 2017 A numerical method for shock driven multiphase flow with evaporating particles. J. Comput. Phys. 344, 210–233.10.1016/j.jcp.2017.04.074CrossRefGoogle Scholar
Daniel, K.A. & Wagner, J.L. 2022 The shock-induced dispersal of particle curtains with varying material density. Intl J. Multiphase Flow 152, 104082.10.1016/j.ijmultiphaseflow.2022.104082CrossRefGoogle Scholar
Daoud, T., Briney, S., Couture, A., Balachandar, S. & Jackson, T.L. 2025 Recent advances in point-particle force modeling for Euler-Lagrange simulations in explosively-driven multiphase environments. In AIAA 2025-1883. AIAA SCITECH 2025 Forum. American Institute of Aeronautics and Astronautics.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, 881–895.10.1017/jfm.2019.550CrossRefGoogle Scholar
Drake, R.P., Kuranz, C.C., Miles, A.R., Muthsam, H.J. & Plewa, T. 2009 Stellar explosions, instabilities, and turbulence. Phys. Plasmas 16 (4), 041004.10.1063/1.3101816CrossRefGoogle Scholar
Drew, D.A. & Lahey, R.T. 1987 The virtual mass and lift force on a sphere in rotating and straining inviscid flow. Intl J. Multiphase Flow 13 (1), 113–121.10.1016/0301-9322(87)90011-5CrossRefGoogle Scholar
Friedman, M.P. 1961 A simplified analysis of spherical and cylindrical blast waves. J. Fluid Mech. 11 (1), 1–15.10.1017/S0022112061000810CrossRefGoogle 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 (9), 091109.10.1063/1.4751876CrossRefGoogle Scholar
Gurney, R.W. 1943 The initial velocities of fragments from bombs, shell, grenades. Tech. Rep. DTIC ADA289704. Defense Technical Information Center .10.21236/ADA289704CrossRefGoogle 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 (9), 093301.10.1063/5.0015190CrossRefGoogle Scholar
Lee, T.D. 1951 Difference between turbulence in a two-dimensional fluid and in a three-dimensional fluid. J. Appl. Phys. 22 (4), 524–524.10.1063/1.1699997CrossRefGoogle Scholar
Li, J., He, J., Meng, B. & Tian, B. 2022 Investigation of dust lifting by a moving shock wave based on compressible multiphase particle-in-cell method. Phys. Fluids 34 (10), 103316.10.1063/5.0112056CrossRefGoogle Scholar
Li, Y., Ren, D., Bo, Z., Huang, W., Ye, Q. & Cui, Y. 2019 Gas-Particle Two-Way Coupled Method for Simulating the Interaction Between a Rocket Plume and Lunar Dust. Acta Astronautica.10.1016/j.actaastro.2018.12.024CrossRefGoogle Scholar
Li, Z. & Zhang, H. 2009 Gas-kinetic numerical studies of three-dimensional complex flows on spacecraft re-entry. J. Comput. Phys. 228, 1116–1138.10.1016/j.jcp.2008.10.013CrossRefGoogle Scholar
Ling, Y. & Balachandar, S. 2018 a Asymptotic scaling laws and semi-similarity solutions for a finite-source spherical blast wave. J. Fluid Mech. 850, 674–707.10.1017/jfm.2018.475CrossRefGoogle Scholar
Ling, Y. & Balachandar, S. 2018 b Simulation and scaling analysis of a spherical particle-laden blast wave. Shock Waves 28 (3), 545–558.10.1007/s00193-017-0799-4CrossRefGoogle Scholar
Ling, Y., Haselbacher, A. & Balachandar, S. 2011 a Importance of unsteady contributions to force and heating for particles in compressible flows: part 1: modeling and analysis for shock–particle interaction. Intl J. Multiphase Flow 37 (9), 1026–1044.10.1016/j.ijmultiphaseflow.2011.07.001CrossRefGoogle Scholar
Ling, Y., Haselbacher, A. & Balachandar, S. 2011 b Importance of unsteady contributions to force and heating for particles in compressible flows. Part 2: application to particle dispersal by blast waves. Intl J. Multiphase Flow 37 (9), 1013–1025.10.1016/j.ijmultiphaseflow.2011.07.002CrossRefGoogle Scholar
Ling, Y., Wagner, J.L., Beresh, S.J., Kearney, S.P. & Balachandar, S. 2012 Interaction of a planar shock wave with a dense particle curtain: modeling and experiments. Phys. Fluids 24 (11), 113301.10.1063/1.4768815CrossRefGoogle Scholar
Lingeman, J.E., McAteer, J.A., Gnessin, E. & Evan, A.P. 2009 Shock wave lithotripsy: advances in technology and technique. Nat. Rev. Urol. 6 (12), 660–670.10.1038/nrurol.2009.216CrossRefGoogle ScholarPubMed
Loiseau, J., Pontalier, Q., Milne, A.M., Goroshin, S. & Frost, D.L. 2018 Terminal velocity of liquids and granular materials dispersed by a high explosive. Shock Waves 28 (3), 473–487.10.1007/s00193-018-0822-4CrossRefGoogle Scholar
Lube, G., Breard, E., Esposti-Ongaro, T., Dufek, J. & Brand, B. 2020 Multiphase flow behaviour and hazard prediction of pyroclastic density currents. Nat. Rev. Earth Environ. 1, 348–365.10.1038/s43017-020-0064-8CrossRefGoogle Scholar
Ma, X., Kong, D. & Shi, Y. 2023 Experimental and numerical investigation of blast loads induced by moving charge explosion. Structures 47, 2037–2049.10.1016/j.istruc.2022.12.042CrossRefGoogle 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 (2), 024105.10.1063/1.4941131CrossRefGoogle Scholar
Miao, L., Li, J. & Xue, K. 2024 Multiscale understanding of structural effect on explosive dispersal of granular media. J. Fluid Mech. 999, A46.10.1017/jfm.2024.745CrossRefGoogle 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 (6), 98.10.1007/s00348-018-2547-7CrossRefGoogle 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 (3), 559–577.10.1007/s00193-017-0741-9CrossRefGoogle Scholar
Ouellet, F., Rollin, B., Koneru, R.B., Garno, J. & Balachandar, S. 2021 Effects of perturbing the particle volume fraction distribution in blast-driven multiphase instability. Shock Waves 31 (4), 337–360.10.1007/s00193-021-01023-9CrossRefGoogle Scholar
Parmar, M., Haselbacher, A. & Balachandar, S. 2009 Modeling of the unsteady force for shock–particle interaction. Shock Waves 19 (4), 317–329.10.1007/s00193-009-0206-xCrossRefGoogle Scholar
Parmar, M., Haselbacher, A. & Balachandar, S. 2010 Improved drag correlation for spheres and application to shock-tube experiments. AIAA J. 48 (6), 1273–1277.10.2514/1.J050161CrossRefGoogle Scholar
Prentice, J. 1968 Dimensional problem of the power law in rheology. Nature 217, 157.10.1038/217157a0CrossRefGoogle Scholar
Raman, K.S., et al. 2014 An in-flight radiography platform to measure hydrodynamic instability growth in inertial confinement fusion capsules at the national ignition facility. Phys. Plasmas 21 (7), 072710.10.1063/1.4890570CrossRefGoogle 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 (1), 29–45.10.1007/s001930050096CrossRefGoogle Scholar
Sano, T. et al. 2021 Laser astrophysics experiment on the amplification of magnetic fields by shock-induced interfacial instabilities. Phys. Rev. E 104, 035206.10.1103/PhysRevE.104.035206CrossRefGoogle ScholarPubMed
Shi, S., Jiang, B. & rui Meng, X. 2018 Assessment of gas and dust explosion in coal mines by means of fuzzy fault tree analysis. Intl J. Mining Sci. Technol. 28 (6), 991–998.10.1016/j.ijmst.2018.07.007CrossRefGoogle Scholar
Si, Y., Li, S., Meng, B., Wang, C. & Tian, B. 2024 A dominant dimensionless number and theoretical model for the evolution of multiphase Richtmyer–Meshkov instability. Phys. Fluids 36 (1), 013314.10.1063/5.0180793CrossRefGoogle Scholar
Si, Y., Shuai, L., Qian, C., Baoqing, M., Chun, W. & Baolin, T. 2023 Heat transfer effects on multiphase Richtmyer–Meshkov instability of dense gas–particle flow. Phys. Fluids 35 (5), 053339.Google Scholar
Snider, D.M. 2001 An incompressible three-dimensional multiphase particle-in-cell model for dense particle flows. J. Comput. Phys. 170 (2), 523–549.10.1006/jcph.2001.6747CrossRefGoogle Scholar
Sugiyama, Y., Ando, H., Shimura, K. & Matsuo, A. 2019 Numerical investigation of the interaction between a shock wave and a particle cloud curtain using a CFD–DEM model. Shock Waves 29 (4), 499–510.10.1007/s00193-018-0878-1CrossRefGoogle Scholar
Teh, E. & Johansen, C. 2016 Effect of particle momentum transfer on an oblique-shock-wave/laminar-boundary-layer interaction. Acta Astronaut. 128, 431–439.10.1016/j.actaastro.2016.08.004CrossRefGoogle Scholar
Theofanous, T.G. & Chang, C.-H. 2017 The dynamics of dense particle clouds subjected to shock waves. Part 2. Modeling/numerical issues and the way forward. Intl J. Multiphase Flow 89, 177–206.10.1016/j.ijmultiphaseflow.2016.10.004CrossRefGoogle Scholar
Theofanous, T.G., Mitkin, V. & Chang, C.-H. 2016 The dynamics of dense particle clouds subjected to shock waves. Part 1. Experiments and scaling laws. J. Fluid Mech. 792, 658–681.10.1017/jfm.2016.97CrossRefGoogle 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
Vasco, D.-W., Curtis, M.W., Almuhna Sahir, R. & McFarland Jacob, A. 2021 Evaporation and breakup effects in the shock-driven multiphase instability. J. Fluid Mech. 908 (1), A13.Google Scholar
Wagner, J.L., Beresh, S.J., Kearney, S.P., Pruett, B.O.M. & Wright, E.K. 2012 Shock tube investigation of quasi-steady drag in shock-particle interactions. Phys. Fluids 24 (12), 123301.10.1063/1.4768816CrossRefGoogle Scholar
Wang, Z. & de Yan, H. 2019 Unified gas-kinetic scheme for the monodisperse gas-particle flow and its application in the shock-driven multiphase instability. Intl J. Multiphase Flow 115, 95–107.10.1016/j.ijmultiphaseflow.2019.07.010CrossRefGoogle Scholar
Wu, Q., Zhang, Y., Meng, B., Shi, Y. & Tian, B. 2024 Freeze out of multi-mode Richtmyer–Meshkov instability using particles. Phys. Fluids 36 (6), 063342.10.1063/5.0213952CrossRefGoogle Scholar
Xu, Q.P., Su, J.J., Li, Z.R., Liu, Y., Jiang, H.Y. & Huang, F.L. 2020 Air blast pressure characteristics of moving charge. J. Phys.: Conf. Series 1507 (3), 032052.Google Scholar
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
Yang, X., Shyy, W. & Xu, K. 2024 Unified gas-kinetic wave–particle method for polydisperse gas–solid particle multiphase flow. J. Fluid Mech. 983, A37.10.1017/jfm.2024.80CrossRefGoogle 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, L., Feng, Z., Sun, M., Guan, H., Jin, H. & Shi, H. 2023 Modeling of long-term shock interaction with a movable particle curtain in a rectangular tube based on a dense discrete phase model. Powder Technol. 415, 118116.10.1016/j.powtec.2022.118116CrossRefGoogle Scholar
Zhou, Y., Sadler, J.D. & Hurricane, O.A. 2025 Instabilities and mixing in inertial confinement fusion. Annu. Rev. Fluid Mech. 57 (1), 197–225.10.1146/annurev-fluid-022824-110008CrossRefGoogle Scholar