The interaction of a planar shock wave with a dusty-gas cylinder is numerically studied by a compressible multi-component solver with an adaptive mesh refinement technique. The influence of non-equilibrium effect caused by the particle relaxation, which is closely related to the particle radius and shock strength, on the evolution of particle cylinder is emphasized. For a very small particle radius, the particle cloud behaves like an equilibrium gas cylinder with the same physical properties as those of the gas–particle mixture. Specifically, the transmitted shock converges continually within the cylinder and then focuses at a region near the downstream interface, producing a local high-pressure zone followed by a particle jet. Also, noticeable secondary instabilities emerge along the cylinder edge and the evident particle roll-up causes relatively large width and height of the shocked cylinder. As the particle radius increases, the flow features approach those of a frozen flow of pure air, e.g., the transmitted shock propagates more quickly with a weaker strength and a smaller curvature, resulting in an increasingly weakened shock focusing and particle jet. Also, particles would escape from the vortex core formed at late stages due to the larger inertia, inducing a greater particle dispersion. It is found that a large particle radius as well as a strong incident shock can facilitate such particle escape. The theory of Luo et al. (J. Fluid Mech., 2007) combined with the Samtaney–Zabusky (SZ) circulation model (J. Fluid Mech., 1994) can reasonably explain the high dependence of particle escape on the particle radius and shock strength.
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This work was supported by the National Natural Science Foundation of China (Grants 11802304 and 11625211) and the Science Challenging Project (Grant TZ2016001).
Zhang, F., Frost, D.L., Thibault, P.A., et al.: Explosive dispersal of solid particles. Shock Waves 10, 431–443 (2001)CrossRefzbMATHGoogle Scholar
Popel, S.I., Gisko, A.A.: Charged dust and shock phenomena in the solar system. Nonlinear Process. Geophys. 13, 223–229 (2006)CrossRefGoogle Scholar
Jenkins, C.M., Ripley, R.C., Wu, C.Y., et al.: Explosively driven particle fields imaged using a high speed framing camera and particle image velocimetry. Int. J. Multiphase Flow 51, 73–86 (2013)CrossRefGoogle Scholar
Balakrishnan, K.: On bubble and spike oscillations in a dusty gas Rayleigh–Taylor instability. Laser Part. Beams 30, 633–638 (2012)CrossRefGoogle Scholar
Saito, T., Marumoto, M., Takayama, K.: Numerical investigations of shock waves in gas–particle mixtures. Shock Waves 13, 299–322 (2003)CrossRefzbMATHGoogle Scholar
Yin, J., Ding, J., Luo, X.: Numerical study on dusty shock reflection over a double wedge. Phys. Fluids 30, 013304 (2018)CrossRefGoogle Scholar
Saito, T., Saba, M., Sun, M., et al.: The effect of an unsteady drag force on the structure of a non-equilibrium region behind a shock wave in a gas–particle mixture. Shock Waves 17, 255–262 (2007)CrossRefzbMATHGoogle Scholar
Crowe, C.T.: Drag coefficient of particles in a rocket nozzle. AIAA J. 5, 1021–1022 (1967)CrossRefGoogle Scholar
Gilbert, M., Davis, L., Altman, D.: Velocity lag of particles in linearly accelerated combustion gases. Jet Propuls. 25, 26–30 (1955)CrossRefGoogle Scholar
Knudsen, J.G., Katz, D.L.: Fluid Mechanics and Heat Transfer. McGraw-Hill, New York (1958)zbMATHGoogle Scholar
Drake, R.M.: Discussion: ’forced convection heat transfer from an isothermal sphere to water’ (Vliet, GC, and Leppert, G., 1961, ASME J. Heat Transfer, 83, 163–170). J. Heat Transf. 83, 170–172 (1961)CrossRefGoogle Scholar
Gottlieb, J.J., Coskunses, C.E.: Effects of particle volume on the structure of a partly dispersed normal shock wave in a dusty gas. NASA STI/Recon Technical Report N, vol. 86 (1985)Google Scholar
Sauer, F.M.: Convective heat transfer from spheres in a free-molecular flow. J. Aeronaut. Sci. 18, 353–354 (1951)CrossRefzbMATHGoogle Scholar
Wang, X., Yang, D., Wu, J., et al.: Interaction of a weak shock wave with a discontinuous heavy-gas cylinder. Phys. Fluids 27, 064104 (2015)CrossRefGoogle Scholar
Luo, X., Lamanna, G., Holten, A.P.C., et al.: Effects of homogeneous condensation in compressible flows: Ludwieg-tube experiments and simluations. J. Fluid Mech. 572, 339–366 (2007)CrossRefzbMATHGoogle Scholar
Picone, J.M., Boris, J.P.: Vorticity generation by shock propagation through bubbles in a gas. J. Fluid Mech. 189, 23–51 (1988)CrossRefGoogle Scholar
Samtaney, R., Zabusky, N.J.: Circulation deposition on shock-accelerated planar and curved density-stratified interfaces: models and scaling laws. J. Fluid Mech. 269, 45–78 (1994)CrossRefGoogle Scholar