On the Propagation of Planar Blast Waves Through Nonuniform Channels

  • J. T. Peace
  • F. K. Lu
Conference paper

Abstract

The propagation of shock waves through nonuniform channels with slowly varying cross sections has been studied analytically from the 1950s.

Nomenculture

a

Sound speed, m/s

A

Channel cross-sectional area, \(\mathrm{m}^{2}\)

M

Mach number

p

Pressure, \(\mathrm{N}/\mathrm{m}^{2}\)

Q

\(\partial p / \partial t + \rho a \partial u / \partial t\), kg/m-s\(^3\)

t

Time coordinate, s

u

Velocity, m/s

W

Shock wave velocity, m/s

x

Axial coordinate, m

\(\alpha \)

Coefficient function

\(\beta \)

Coefficient function

\(\gamma \)

Ratio of specific heats

\(\rho \)

Density, \(\mathrm{kg}/\mathrm{m}^{3}\)

Subscripts

0

Initial or undisturbed gas state

s

Property on the shock

References

  1. 1.
    Chester, W.: The quasi-cylindrical shock tube. Phil. Mag. 45, 1293–1301 (1954)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Chisnell, R.F.: The motion of a shock wave in a channel, with applications to cylindrical and spherical shock waves. J. Fluid Mech. 2, 286–298 (1957)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Whitham, G.B.: On the propagation of shock waves through regions of non-uniform area or flow. J. Fluid Mech. 4, 337–360 (1958)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Whitham, G.B.: A new approach to problems of shock dynamics Pt. I Two dimensional problems. J. Fluid Mech. 2, 145–171 (1957)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Best, J.P.: A generalization of the theory of geometrical shock dynamics. Shock Waves 4, 251–273 (1991)CrossRefMATHGoogle Scholar
  6. 6.
    Kirkwood J.G., Bethe H.A., Progress report on the pressure wave produced by an underwater explosion I. OSRD Rept. 588 (1942)Google Scholar
  7. 7.
    Sharma, V.D., Ram, R., Sachdev, P.L.: Uniformly valid analytical solution to the problem of a decaying shock wave. J. Fluid Mech. 185, 153–170 (1987)CrossRefMATHGoogle Scholar
  8. 8.
    Sedov, L.I.: Similarity and Dimensional Methods in Mechanics. Academic Press, New York, NY (1959)MATHGoogle Scholar
  9. 9.
    Bethe, H.A., Fuchs, K., Hirschfelder, J.O., Magee, J.L., Peierls, R.E., von Neumann, J.: Blast Waves. Los Alamos Scientific Laboratory Report, LA–2000 (1947)Google Scholar
  10. 10.
    Taylor, G.I.: The formation of a blast wave by a very intense explosion. In: Proceedings of Royal Society of London, A–201, pp. 159–174 (1950)Google Scholar
  11. 11.
    Han, Z., Yin, X.: Shock Dynamics. Kluwer Academic Publisher, Beijing, China (1993)CrossRefMATHGoogle Scholar
  12. 12.
    Kamm, J.R.: Evaluation of the Sedov-von Newman-Taylor Blast Wave Solution. Los Alamos Scientific Laboratory Report, LA–UR–00–6055 (2000)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • J. T. Peace
    • 1
  • F. K. Lu
    • 1
  1. 1.Mechanical and Aerospace Engineering DepartmentAerodynamics Research Center, University of Texas at ArlingtonArlingtonUSA

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