Skip to main content
SpringerLink
Log in

Weak discontinuities in a non-equilibrium flow of a dusty gas

  • Contributed Papers
  • Published:
Acta Mechanica Aims and scope Submit manuscript

Summary

The behavior of a discontinuity in flow gradients at the head of a disturbance propagating through a homogeneous mixture of gas and small dust particles has been studied. It is shown that the presence of dust particles results in increasing the shock formation time as compared with a similar pure-gas case. When the disturbance is arbitrarily small in amplitude, the solution to the first order in the whole disturbed domain is constructed and analysed. It is found that the concentration of solid particles has a decaying, effect on the shock strength as one, might expect.

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

Similar content being viewed by others

References

  1. Campbell, I. J., Pitcher, A. S.: Shock waves in a liquid containing gas bubbles. Proc. Roy. Soc. LondonA243, 534–545 (1958).

    Google Scholar 

  2. Rudinger, G.: Relaxation in gas-particle flow, chapter 3. In: Non-equilibrium flows, vol. 1 pt. 1 (Wegener, P. P., ed.). New York: Marcel Dekker 1969.

    Google Scholar 

  3. Coespo, A.: Sound and shock waves in liquids containing bubbles. Phys. Fluids12, 2274–2282 (1969).

    Google Scholar 

  4. Pai, S. I., Menon, S., Fan, Z. Q.: Similarity solutions of a strong shock wave propagation in a mixture of a gas and dusty particles. Int. J. Eng. Sci.8, 1365–1373 (1980).

    Google Scholar 

  5. Pai, S. I., Sharma, V. D., Menon, S.: Time evolution of discontinuities at the wave head in a non-equilibrium two-phase flow of a mixture of a gas and dusty particles. Acta Mech.46, 1–13 (1983).

    Google Scholar 

  6. Clarke, J. F.: Small amplitude gasdynamic disturbances in an exploding atmosphere. J. Fluid Mech.89, 343–355 (1978).

    Google Scholar 

  7. Marble, F. E.: Dynamics of dusty gases. Ann. Rev. Fluid Mech.2, 397–447 (1970).

    Google Scholar 

  8. Chu, B. T.: Weak nonlinear waves in non-equilibrium flows, chapter 2. In: Nonequilibrium flows, pt. II (Wegener, P. P., ed.). New York: Marcel Dekker 1970.

    Google Scholar 

  9. Clarke, J. F.: Lectures on plane waves in reacting gases. Ann. Phys. For.9, 211–306 (1984).

    Google Scholar 

  10. Whitham, G. B.: Linear and nonlinear waves. New York: Wiley 1974.

    Google Scholar 

Download references

Author information

Author notes

  1. V. D. Sharma

    Present address: Department of Mathematics, I.I.T., Powai, Bombay, India

  2. B. D. Pandey

    Present address: Department of Mathematics, The Ohio State University, 43302, Marion, OH, USA

  3. R. R. Sharma

    Present address: Department of Applied Mathematics, I.T., B.H.V., 221005, Varanasi, India

Authors and Affiliations

    Authors
    1. V. D. Sharma
      View author publications

      You can also search for this author in PubMed Google Scholar

    2. B. D. Pandey
      View author publications

      You can also search for this author in PubMed Google Scholar

    3. R. R. Sharma
      View author publications

      You can also search for this author in PubMed Google Scholar

    Rights and permissions

    Reprints and permissions

    About this article

    Cite this article

    Sharma, V.D., Pandey, B.D. & Sharma, R.R. Weak discontinuities in a non-equilibrium flow of a dusty gas. Acta Mechanica 99, 103–111 (1993). https://doi.org/10.1007/BF01177238

    Download citation

    • Received:

    • Issue Date:

    • DOI: https://doi.org/10.1007/BF01177238

    Keywords

    Search

    Navigation