Shock Waves

, Volume 19, Issue 1, pp 67–81 | Cite as

Transient phenomena in one-dimensional compressible gas–particle flows

  • Y. Ling
  • A. HaselbacherEmail author
  • S. Balachandar
Original Article


The transient behavior of compressible gas– particle flows produced in shock tubes with particle-laden driver section is studied. Particular attention is focused on the time scales with which the solution approaches the equilibrium state. Theoretical estimates indicate that the gas and particle contact surfaces equilibrate first, followed by the shock wave, and finally by the expansion fan. The estimates are in good agreement with numerical simulations. The simulations also show that the approach to equilibrium condition of the shock speed is non-monotonic (monotonic) if the mass fraction of particles initially located in the driver section is below (above) a particle-diameter dependent critical value. For the speed of the particle contact surface, the reverse trends are observed.


Gas–particle flow Unsteady flow Shock tube 


47.55.Kf 47.37.+Q 47.11.Df 


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  1. 1.
    Barth, T.J.: A 3d upwind Euler solver for unstructured meshes. AIAA Paper 91-1548 (1991)Google Scholar
  2. 2.
    Carrier G.F.: Shock waves in a dusty gas. J. Fluid Mech. 4, 376–382 (1958)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Clift, R., Gauvin, W.H.: The motion of particles in turbulent gas streams. In: Proceedings of Chemeca’70, vol. 1, pp. 14–28 (1970)Google Scholar
  4. 4.
    Elperin T., Igra O., Ben-Dor G.: Rarefaction waves in dusty gases. Fluid Dyn. Res. 4, 229–238 (1988)CrossRefGoogle Scholar
  5. 5.
    Ferry J., Balachandar S.: A fast Eulerian method for disperse two-phase flow. Int. J. Multiphase Flow 27, 1199–1226 (2001)zbMATHCrossRefGoogle Scholar
  6. 6.
    Haselbacher, A.: A WENO reconstruction algorithm for unstructured grids based on explicit stencil construction. AIAA Paper 2005-0879 (2005)Google Scholar
  7. 7.
    Haselbacher, A.: On constrained reconstruction operators. AIAA Paper 2006-1274 (2006)Google Scholar
  8. 8.
    Haselbacher, A., Najjar, F.: Multiphase flow simulations of solid-propellant rocket motors on unstructured grids. AIAA Paper 2006-1292 (2006)Google Scholar
  9. 9.
    Haselbacher A., Najjar F., Ferry J.: An efficient and robust particle-localization algorithm for unstructured grids. J. Comput. Phys. 225(2), 2198–2213 (2007)zbMATHCrossRefGoogle Scholar
  10. 10.
    Haselbacher, A., Najjar, F.M., Balachandar, S., Ling, Y.: Lagrangian simulations of shock-wave diffraction at a right-angled corner in a particle-laden gas. In: Proceedings of the 6th International Conference on Multiphase Flow (2007)Google Scholar
  11. 11.
    Jiang G.S., Shu C.W.: Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126, 202–228 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Kriebel A.R.: Analysis of normal shock waves in particle laden gas. J. Basic Eng-T. ASME 86, 655–665 (1964)Google Scholar
  13. 13.
    Larrouturou B.: How to preserve the mass fraction positivity when computing compressible multi-component flows. J. Comput. Phys. 95, 59–84 (1991)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Marble F.E.: Dynamics of a dusty gas. Annu. Rev. Fluid Mech. 2, 397–446 (1970)CrossRefGoogle Scholar
  15. 15.
    Miura, H., Glass, I.I.: On a dusty-gases shock tube. In: Proceedings of the Royal Society A, vol. 382, pp. 373–388 (1982)Google Scholar
  16. 16.
    Roe P.L.: Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comput. Phys. 250–258, 357–372 (1981)CrossRefMathSciNetGoogle Scholar
  17. 17.
    Rudinger G.: Some properties of shock relaxation in gas flows carrying small particles. Phys. Fluids 7, 658–663 (1964)CrossRefMathSciNetGoogle Scholar
  18. 18.
    Rudinger G., Chang A.: Analysis of nonsteady two-phase flow. Phys. Fluids 7, 1747–1754 (1964)zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Saito T.: Numerical analysis of dusty-gas flows. J. Comput. Phys. 176, 129–144 (2002)zbMATHCrossRefGoogle Scholar
  20. 20.
    Sommerfeld M.: The unsteadiness of shock waves propagating through gas–particle mixture. Exp. Fluids 3, 197–206 (1985)CrossRefGoogle Scholar
  21. 21.
    Soo S.L.: Gas dynamic processes involving suspended solids. AIChE J. 3, 384–391 (1961)CrossRefGoogle Scholar
  22. 22.
    Thompson P.A.: Compressible-Fluid Dynamics, 1st edn. McGraw-Hill, Inc., New York (1972)zbMATHGoogle Scholar
  23. 23.
    Whitaker S.: Forced convection heat transfer correlations for flow in pipes, past flat plates, single spheres, and for flow in packed beds and tube bundles. AIChE J. 18, 361–371 (1972)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of Mechanical and Aerospace EngineeringUniversity of FloridaGainesvilleUSA
  2. 2.Department of Mechanical and Aerospace EngineeringUniversity of FloridaGainesvilleUSA
  3. 3.Department of Mechanical and Aerospace EngineeringUniversity of FloridaGainesvilleUSA

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