Hostname: page-component-5c6d5d7d68-7tdvq Total loading time: 0 Render date: 2024-08-24T21:06:08.630Z Has data issue: false hasContentIssue false
  • English
  • Français

The blast waves from asymmetrical explosions

Published online by Cambridge University Press:  12 April 2006

K. W. Chiu ,
J. H. Lee  and
R. Knystautas
K. W. Chiu
Affiliation:
Department of Mechanical Engineering, McGill University, Montreal, Canada
J. H. Lee
Affiliation:
Department of Mechanical Engineering, McGill University, Montreal, Canada
R. Knystautas
Affiliation:
Department of Mechanical Engineering, McGill University, Montreal, Canada
Get access Rights & Permissions [Opens in a new window]

Abstract

From Whitham's ray-shock theory and the Brinkley-Kirkwood theory of shock propagation, a general theory for the propagation of asymmetrical blast waves of arbitrary shapes and strengths is developed in this paper. The general theory requires the simultaneous numerical solution of a set of partial differential equations and a pair of ordinary differential equations. If the shock shape is assumed to be known and remains invariant with time then the geometrical and the dynamical relationships in the theory can be decoupled. In this case the solution simply requires the integration of the ordinary differential equations governing the dynamics of the blast motion since the geometry is already known. As a specific example the asymmetrical blast waves generated by the rupture of a pressurized ellipsoid are studied. The peak pressure is calculated by assuming that the shock surface remains ellipsoidal for all times and that the peak overpressure decay rate of the blast depends on the local curvature. For weak shocks, it is found that the degree of directionality is more pronounced than for stronger shocks. For weak blasts the present theory agrees with the solution based on acoustic theory. Experimental results on the shock trajectories for asymmetrical blast waves generated by exploding wires are found to agree with the present theory.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 82 , Issue 1 , 19 August 1977 , pp. 193 - 208
Copyright
© 1977 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bach, G. G., Chiu, K. W. & Lee, J. H. 1975 Contribution to the propagation of non-ideal blast waves. I. Far field equivalency. 5th Int. Coll. Gasdynamics of Explosions and Reactive Systems, Bourges, France.
Brinkley, S. R. 1972 Principles of explosive behavior. Engineering Design Handbook. U.S. Army Material Command Headquarters: AMC pamphlet AMCP 706–180.
Brinkley, S. & Kirkwood, J. G. 1947 Theory of the propagation of shock waves. Phys. Rev. 71, 606.Google Scholar
Brode, H. 1955 Numerical solution of spherical blast waves. J. Appl. Phys. 26, 766.Google Scholar
Chester, W. 1954 The quasi cylindrical shock tube. Phil. Mag. 45, 1293.Google Scholar
Chisnell, R. F. 1957 The motion of a shock wave in a channel with applications to cylindrical and spherical shock waves. J. Fluid Mech. 2, 286.Google Scholar
Gottlieb, J. J. 1974 Simulation of travelling sonic boom in a pyramidal horn. UTIAS Rep. no. 196.Google Scholar
Gottlieb, J. J. & Glass, I. I. 1974 Recent development in sonic boom simulation using shock tubes. Can. J. Phys. 52, 207.Google Scholar
Landau, L. D. 1948 On shock waves at large distances from the place of their origin. J. Phys. USSR 9, 496.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1966 Fluid Mechanics. Pergamon.
Laumbach, D. D. & Probstein, R. F. 1969 A point explosion in a cold exponential atmosphere. J. Fluid Mech. 35, 513.Google Scholar
Panarella, E. & Savic, P. 1968 Blast waves from a laser-induced spark in air. Can. J. Phys. 46, 183.Google Scholar
Strehlow, R. A. & Baker, W. E. 1975 The characterization and evaluation of accidental explosions. N.A.S.A. Contractor Rep. no. 134779.Google Scholar
Whitham, G. B. 1956 On the propagation of weak shock waves. J. Fluid Mech. 1, 290.Google Scholar
Whitham, G. B. 1957a New approach to problems of shock dynamics. Part 1. Two-dimensional problems. J. Fluid Mech. 2, 146.Google Scholar
Whitham, G. B. 1957b On the propagation of shock waves through regions of non-uniform area or flow. J. Fluid Mech. 4, 337.Google Scholar
Whitham, G. B. 1959 New approach to problems of shock dynamics. Part 2. Three-dimensional problems. J. Fluid Mech. 5, 369.Google Scholar