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Improved Gurney Formulas for Exploding Cylinders and Spheres using “Hard Core” Approximation
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.19860110303
Subject(s) - explosive material , kinetic energy , spheres , radius , mechanics , core (optical fiber) , limiting , mach number , physics , volume (thermodynamics) , geometry , optics , classical mechanics , thermodynamics , mathematics , chemistry , engineering , mechanical engineering , computer security , organic chemistry , astronomy , computer science
The final liner velocity predicted by the Gurney formulas for sandwich cylindrical and spherical configurations for very light liners (small M/C values) are (6E) 1/2 , (4E) 1/2 and (10E/3) 1/2 respectively. The existance of these differences among the limiting velocity values contradicts the well known fact that the explosive products' escape velocity does not depend on the initial geometry of the explosive when no Mach waves are formed. An improvement to the Gurney formulas for exploding cylinders and spheres is suggested which corrects this basic inconsistancy. It is based on the observation that light liners are accelerated to their final velocity in a short time getting their kinetic energy mainly from that part of the explosive which is in contact with them. It is shown that by excluding from the explosive mass the inner volume and replacing it with an infinitely hard core the experimentally measured liner velocities for the cylindrical and spherical geometrics are more accurately reproduced. The core radius is found by maximizing the liner velocity, thus getting the fastest transformation of the gas potential energy to kinetic energy which is possible within the model assumptions. The improved formulas predict for the limit of very small M/C the same velocity, (6E) 1/2 for all the above mentioned geometries. The comparison of the improved formulas with available experimental data reveals how the accuracy of the Gurney model is limited at the large and the small values of M/C.