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Simplified and Extended Gurney Formulas for Imploding Cylinders and Spheres
Author(s) -
Hirsch E.
Publication year - 1986
Publication title -
propellants, explosives, pyrotechnics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.56
H-Index - 65
eISSN - 1521-4087
pISSN - 0721-3115
DOI - 10.1002/prep.19860110103
Subject(s) - radius , spheres , explosive material , circular symmetry , simple (philosophy) , symmetry (geometry) , physics , mathematical analysis , mathematics , geometry , mechanics , computer science , philosophy , chemistry , computer security , organic chemistry , epistemology , astronomy
The usefulness of the Gurney formulas in application to one‐dimensional computer codes for shaped charge design has called for their extention to predict the asymptotic velocities of imploding cylinders. Two different approaches by Chou, Carleone, and Flis on 1981 and by Chanteret on 1983 have led to improvements which were shown to predict correctly two‐dimensional code simulations for unconfined charges. Both works did not lead however to simple formulas which retain the conveniency of the original Gurney formulas. In the work presented, closed form analytical solutions for both the cylindrical as well as the spherical geometries are derived. The solution for each geometry is presented in a way in which the symmetry between the inner liner and the confinement is easily recognized. The relation of each solution to the Gurney formula for asymmetrical sandwich is also obvious. The presented solutions reduce to all the known Gurney formulas for the more simple geometries at the appropriate limits. The accuracy of the predictions by the obtained formulas is limited however when the assumptions of the Gurney model do not describe the real physical situation closely. This happens in general in extreme cases, e.g. when the liners are very light comparing to the explosive mass or when the ratio between the confinement radius and the inner liner radius is very large comparing to unity.