Skip to main content
SpringerLink
Log in

Numerical study on shock–dusty gas cylinder interaction

  • Research Paper
  • Published:
Acta Mechanica Sinica Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Zhang, F., Frost, D.L., Thibault, P.A., et al.: Explosive dispersal of solid particles. Shock Waves 10, 431–443 (2001)

    Article  MATH  Google Scholar 

  2. Popel, S.I., Gisko, A.A.: Charged dust and shock phenomena in the solar system. Nonlinear Process. Geophys. 13, 223–229 (2006)

    Article  Google Scholar 

  3. 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)

    Article  Google Scholar 

  4. Balakrishnan, K.: On bubble and spike oscillations in a dusty gas Rayleigh–Taylor instability. Laser Part. Beams 30, 633–638 (2012)

    Article  Google Scholar 

  5. Ranjan, D., Oakley, J., Bonazza, R.: Shock–bubble interactions. Annu. Rev. Fluid Mech. 43, 117–140 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  6. Ou, J., Zhai, Z.: Effects of aspect ratio on shock–cylinder interaction. Acta Mech. Sin. 35, 61–69 (2019)

    Article  Google Scholar 

  7. Zhai, Z., Si, T., Zou, L.: Jet formation in shock–heavy gas bubble interaction. Acta Mech. Sin. 29, 24–35 (2013)

    Article  Google Scholar 

  8. Rudinger, G., Somers, L.M.: Behaviour of small regions of different gases carried in accelerated gas flows. J. Fluid Mech. 7, 161–176 (1960)

    Article  MATH  Google Scholar 

  9. Haas, J.F., Sturtevan, B.: Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities. J. Fluid Mech. 181, 41–76 (1987)

    Article  Google Scholar 

  10. Collins, B.D., Jacobs, J.W.: PLIF flow visualization and measurements of the Richtmyer–Meshkov instability of an air/SF6 interface. J. Fluid Mech. 464, 113–136 (2002)

    Article  MATH  Google Scholar 

  11. Jacobs, J.W.: The dynamics of shock accelerated light and heavy gas cylinders. Phys. Fluids A 5, 2239–2247 (1993)

    Article  Google Scholar 

  12. Layes, G., Le Métayer, O.: Quantitative numerical and experimental studies of the shock accelerated heterogeneous bubbles motion. Phys. Fluids 19, 042105 (2007)

    Article  MATH  Google Scholar 

  13. Ou, J., Ding, J., Luo, X., et al.: Effects of Atwood number on shock focusing in shock–cylinder interaction. Exp. Fluids 59, 29–39 (2018)

    Article  Google Scholar 

  14. Zou, L., Liao, S., Liu, C., et al.: Aspect ratio effect on shock–accelerated elliptic gas cylinders. Phys. Fluids 28(3), 297–319 (2016)

    Article  Google Scholar 

  15. Ding, J., Si, T., Chen, M., et al.: On the interaction of a planar shock with a three-dimensional light gas cylinder. J. Fluid Mech. 828, 289–317 (2017)

    Article  MathSciNet  Google Scholar 

  16. Ding, J., Liang, Y., Chen, M., et al.: Interaction of planar shock wave with three-dimensional heavy cylindrical bubble. Phys. Fluids 30, 106109 (2018)

    Article  Google Scholar 

  17. Balakrishnan, K., Menon, S.: On the role of ambient reactive particles in the mixing and afterburn behind explosive blast waves. Combust. Sci. Technol. 182, 186–214 (2010)

    Article  Google Scholar 

  18. Boiko, V.M., Kiselev, V.P., Kiselev, S.P., et al.: Shock wave interaction with a cloud of particles. Shock Waves 7, 275–285 (1997)

    Article  MATH  Google Scholar 

  19. Kiselev, V.P., Kiselev, S.P., Vorozhtsov, E.V.: Interaction of a shock wave with a particle cloud of finite size. Shock Waves 16, 53–64 (2006)

    Article  MATH  Google Scholar 

  20. Ota, O.A., Barton, C.J., Holder, D.A.: Shock tube experiment: half-height dense gas region. Phys. Scr. T 132, 014015 (2008)

    Article  Google Scholar 

  21. Ukai, S., Balakrishnan, K., Menon, S.: On Richtmyer–Meshkov instability in dilute gas–particle mixtures. Phys. Fluids 22, 104103 (2010)

    Article  Google Scholar 

  22. Vorobieff, P., Anderson, M., Conroy, J., et al.: Vortex formation in a shock–accelerated gas induced by particle seeding. Phys. Rev. Lett. 106, 184503 (2011)

    Article  Google Scholar 

  23. Rudinger, G.: Some properties of shock relaxation in gas flows carrying small particles. Phys. Fluids 7, 658–663 (1964)

    Article  MathSciNet  Google Scholar 

  24. Saito, T., Marumoto, M., Takayama, K.: Numerical investigations of shock waves in gas–particle mixtures. Shock Waves 13, 299–322 (2003)

    Article  MATH  Google Scholar 

  25. Yin, J., Ding, J., Luo, X.: Numerical study on dusty shock reflection over a double wedge. Phys. Fluids 30, 013304 (2018)

    Article  Google Scholar 

  26. 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)

    Article  MATH  Google Scholar 

  27. Crowe, C.T.: Drag coefficient of particles in a rocket nozzle. AIAA J. 5, 1021–1022 (1967)

    Article  Google Scholar 

  28. Hermsen, R.W.: Review of particle drag models. In: JANAF Performance Standardization Subcommittee 12th Meeting Minutes. CPIA Publication, vol. 113 (1979)

  29. Gilbert, M., Davis, L., Altman, D.: Velocity lag of particles in linearly accelerated combustion gases. Jet Propuls. 25, 26–30 (1955)

    Article  Google Scholar 

  30. Knudsen, J.G., Katz, D.L.: Fluid Mechanics and Heat Transfer. McGraw-Hill, New York (1958)

    MATH  Google Scholar 

  31. 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)

    Article  Google Scholar 

  32. 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)

  33. Sauer, F.M.: Convective heat transfer from spheres in a free-molecular flow. J. Aeronaut. Sci. 18, 353–354 (1951)

    Article  MATH  Google Scholar 

  34. 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)

    Article  Google Scholar 

  35. Richtmyer, R.D.: Taylor instability in shock acceleration of compressible fluids. Commun. Pure Appl. Math. 13, 297–319 (1960)

    Article  MathSciNet  Google Scholar 

  36. 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)

    Article  MATH  Google Scholar 

  37. Picone, J.M., Boris, J.P.: Vorticity generation by shock propagation through bubbles in a gas. J. Fluid Mech. 189, 23–51 (1988)

    Article  Google Scholar 

  38. 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)

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grants 11802304 and 11625211) and the Science Challenging Project (Grant TZ2016001).

Author information

Authors and Affiliations

  1. Beijing Institute of Applied Physics and Computational Mathematics, Beijing, 100094, China

    Jingyue Yin & Xin Yu

  2. Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei, 230026, China

    Juchun Ding & Xisheng Luo

Authors
  1. Jingyue Yin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Juchun Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xisheng Luo
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xin Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Juchun Ding.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yin, J., Ding, J., Luo, X. et al. Numerical study on shock–dusty gas cylinder interaction. Acta Mech. Sin. 35, 740–749 (2019). https://doi.org/10.1007/s10409-019-00861-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10409-019-00861-2

Keywords

Search

Navigation