The detonation of solid explosives: the equilibrium conditions in the detonation wave-front and the adiabatic expansion of the products of detonation

Abstract

Assuming chemical and thermal equilibrium to be maintained in the detonation wave-front, and using the equation of state in the form of the virial expansion, the velocity of detonation has been determined as a function of the loading density. In the absence of data at sufficiently high pressures and temperatures for the products of detonation of T.N.T., it has been assumed that the virial coefficients are constant and their values have been determined to give agreement with the measured values of the detonation velocity for loading densities less than 1.5 g.cm. -3 . The pressure-volume-temperature relation in the detonation wave-front can then be determined. The pressure in the detonation wave-front is found- to be of the order of 2 x 10 11 dyne cm. -2 for a loading density of 1.5 g.cm. -3 , compared with the value of 9.4 x 10 11 dyne cm. -2 given in the earlier work of other authors using the co-volume method. With the equation of state adopted in this paper it is found that at a high loading density only negligibly small amounts of hydrogen and carbon monoxide are present in the detonation wave-front, a fact which facilitates the calculation of the adiabatic relations in this case. It is shown (part B) that these gases do, however, develop rapidly during the initial stages of the adiabatic expansion. The calculation of the equilibrium conditions in the detonation wave-front with the adopted equation of state (part A) determines the initial conditions for the calculation of the adiabatic relations for a high loading density. The chemical composition of the gases during the adiabatic expansion and the external work done during it have been calculated for a loading density of 1.5 g.cm. -3 (part B). It is shown that the large amount of chemical energy released in the early stages of the expansion is to be correlated with the high effective value of the exponent in the adiabatic in this region, and this is due to the dominant role of the repulsive forces between the molecules of the tightly compressed gases during the early stages of the expansion. The same effect is also observed in the case of a low loading density (part C). The difference with regard to the amounts of hydrogen and carbon monoxide present in the detonation w ave-front for a low loading density complicates the solution of the equations in this case. In part C it is shown how this can be done for a loading density of 1.0 g.cm. -3 , and the detonation velocity and the pressure, density and temperature in the wave-front have been determined using the same equation of state as in parts A and B. The adiabatic pressure-volume relation for the expansion of the products of detonation, and the chemical com position during, and up to the end of, the adiabatic expansion have also been determined. Compared with the results for a high loading density, there is considerably more carbon monoxide and less carbon dioxide and a substantial rise in the total number of moles of gas pro­duced per mole of explosive. The ratio is found to be sensitive to the pressure in the detonation wave-front, from which, by comparison with the observed values of this ratio, independent evidence is obtained for the detonation pressure calculated in part A. The chemical energy released per gram of explosive is less for a loading density of 1.0 g .cm -3 than for a loading density of 1.5 g.cm -3 , and the external work done is also less in the former than in the latter case. The amounts of ammonia and of hydrocyanic acid in chemical equilibrium with the other gases are determined and they are found to be negligibly small. It is concluded that these gases, observed in experiments, are probably formed by catalytic action with the bomb fragments during the cooling period after the adiabatic expansion has been completed. The calculations have been compared with the available experimental data and are in reasonable agreement with it. An explanation is suggested for the observed difference in the composition of the gaseous products of the detonation of T.N.T., initiated at a given loading density, with detonators of different power.