Abstract
The numerical treatment of very strong spherical shock waves is the subject matter of this chapter. The Lagrangian equations in normalized form with artificial viscosity included are presented for spherical symmetric flow while radial distances are normalized with respect to a length based on the total blast energy and ambient air pressure. Two specific numerical procedures are presented; one in relation to the point source explosion and the second in relation to the expansion of very hot high-pressure isothermal sphere into the surrounding atmosphere. In relation to the point source explosion, Taylor’s strong shock solution was taken as initial conditions with an initial pressure of 1000 atmospheres and the equations are numerically integrated over a time interval where the pressure at the shock front drops to just a few atmospheres. The isothermal sphere had a starting pressure of 1000 atmospheres and the numerical procedure was run over a time interval where the overpressure at the shock front was down to less than 0.2 atmospheres. Several plots of pressure, density and particle velocity are presented.
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Notes
- 1.
Partial derivatives are used here to indicate the changes in position and time of specific particles; nonetheless, it should be understood that these partial derivatives imply that we are in fact following the path taken by a specific particle according to the Lagrangian description.
References
Y.B. Zel’dovich, Y.P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena (Dover Publications, Inc., Mineola, New York, 2002), Chapter 1
J. von Neumann, The Point Source Solution, Collected Works, vol 6 (Pergamon Press, New York, 1976), p. 219
H.L. Brode, Numerical Solutions of Spherical Blast Waves. J. Appl. Phys. 26, 766 (1955)
H.L. Brode, The Blast from a Sphere of High Pressure Gas, Report No. P-582 (Rand Corporation, Santa Monica, California, January 1955)
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Prunty, S. (2019). Numerical Treatment of Spherical Shock Waves. In: Introduction to Simple Shock Waves in Air . Shock Wave and High Pressure Phenomena. Springer, Cham. https://doi.org/10.1007/978-3-030-02565-6_6
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DOI: https://doi.org/10.1007/978-3-030-02565-6_6
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