James M. Short

The chemistry of detonations. VII. A simplified method for predicting explosive performance in the cylinder test

A simple equation is derived for predicting explosive performance in the cylinder test. The equation takes the form, V (mm/μsec)=0.368φ0.54ρ0.840(R−R0)0.212 0.065ρ0 , φ=NM12Q12 where V is the wall velocity, R − R0 the radial expansion in cm, ρ0 the loading density, N the number of moles of gaseous detonation products per gram of explosive, M the average molecular weight of these gases, and Q the heat of detonation in calories per gram. The equation is shown to predict wall velocities with a precision of approximately 1% for CHNO explosives and CHNOF explosives which produce HF but not CF4 in their detonations. An “HFCF4H2OCO2 arbitrary” is used to predict detonation products of fluoroexplosives.

A computational technique for the evaluation of dynamic effects of exothermic reactions

Abstract The paper presents a computational technique for the analysis of nonsteady flow fields generated by exothermic reactions in a compressible medium. This is obtained by numerical integration of the set of rate equations of chemical kinetics combined with the set of conservation equations of nonsteady gasdynamics expressed in a Lagrangian form. Under the hypothesis that the power pulse of exothermic energy is so short that the effects of diffusion, viscosity, and conductivity are, during its effective life span, negligible, the place where it is generated can be restricted to a discrete Lagrangian cell, and, consequently, the chemical kinetic set expressed in terms of ordinary differential equations. The computational model devised in this manner is referred to as the exothermic center. Conceptually, it is a simple flow field, which consists of a kernel, confined within a single Lagrangian cell around the center where the exothermic reaction takes place, and of inert surroundings through which the pressure wave generated by the expanding kernel propagates, the two separated from each other by an impermeable interface. The computations yield the characteristic features of the power pulse of work done by the kernel on the surroundings. On the basis of this information, complex flow fields, where exothermic processes occur, can be analyzed as a nonsteady (diabatic) flow subject to energy (heat) supply that is furnished at a predetermined rate and given as a function of local thermodynamic state parameters, as demonstrated in the companion paper presented at the 15th Symposium (International) on Combustion.

The chemistry of detonations. VIII. Energetics relationships on the detonation isentrope

The ratio of energy delivered at seven volumes expansion compared with two volumes expansion on the detonation isentrope is obtained from the square of the ratio of cylinder wall velocities at 20 mm expansion and 6 mm expansion in the Lawrence Livermore National Laboratory cylinder test. The velocities fit the relationship (V20V62=1.9197−0.327ϱo−0.44 [MF(H2O)]2 , where MF(H2O) is the mole fraction of water in the detonation gas mixture, as calculated using an “H2OCO2 arbitrary.” The relationship applies to CHNO, CHNOF, CNO, and HNO explosives with a standard deviation which compares favorably with the experimental precision of the measurements. The correlation described here will serve as a benchmark against which we will later test whether nonideal explosives are still reacting in the time frame of the cylinder test.

Dynamics of the exothermic process in combustion

The paper presents an attempt to provide a link between chemical kinetics of exothermic processes in a combustion system and the gasdynamic phenomena they are capable of generating. For this purpose experiments were performed using the reflected shock technique with a mixture of 2H 2 +O 2 +27A, while gasdynamic phenomena were observed by means of high-speed cinematographic laser schlieren photography and laser-shear interferometry. The analysis, based on the most recently available kinetic rate data for the hydrogen-oxygen system, was carried out by the use of a numerical technique especially developed for handling properly the “stiff” differential equations describing the rates of chemical reactions, combined with an appropriate numerical technique for the integration of the partial differential equations of non-steady, inviscid gasdynamics in Lagrangian form. The agreement between experimental and analytical results is quite satisfactory, providing thus, on one hand, a rationalization for the observed gasdynamic effects of exothermic reactions, and, on the other, an experimental check of the validity of currently available chemical kinetic rate data for the hydrogen-oxygen system with respect to the macroscopic effects of its reaction mechanism.

Improved prediction of cylinder test energies

Abstract Energies delivered at 7 volumes expansion in the cylinder test are well correlated for 16 typical and atypical explosives. The criterion for a typical explosive is that it have approximately 0.40 mole fraction of water vapor in the detonation products. The correlation equation is (V 20 ) 2 = 0.200 ϕp 0 1.50 [1.104 − 0.265 MF(H 2 O) ], with ϕ = NM 1 2 Q 1 2 where V20 is the cylinder wall velocity in mmμs at 20 mm expansion in the 1-in. cylinder test, ϱ0 is the loading density, N is the number of moles of gaseous detonation products per gram of explosive (calculated by the H2OCO2 arbitrary), M is the average molecular weight of the gases, Q is the heat of detonation in cal/g, and MF(H2O) is the mole fraction of water vapor in the detonation products. For reasons that are not now known, the insensitive explosives TATB and nitroguanidine underperform by about 15% relative to the above equation.

A comparison of calculations of detonation pressures for a homologous series of polynitroaliphatic explosives by different equations of state

Detonation pressures of a homologous series of bis (2,2,2-trinitroethyl) alkanedioates, C(NO/sub 2/)/sub 3/CH/sub 2/-O-CO-(CH/sub 2/)/sub n/ x CO-O-C-(NO/sub 2/)/sub 3/, n = 0-15, are calculated by means of the Kamlet-Jacobs equation, the STRETCH-BKW computer code with RDX and TNT parameters, BKW(RUBY), BKWR, and JCZ-3. Calculations at a constant density of 1.7 g/cm/sup 3/ show that the BKWR code and the Kamlet-Jacobs equation track one another reasonably well, and that using STRETCH-BKW with either set of parameters predicts P/sub J/ to be almost invariant with oxygen balance. All of the calculational methods show reasonably similar variations of P/sub J/ with loading density. Effects of changing the assumed heat of formation of solid carbon are shown to be quite different for BKW(RUBY) and BKWR.

Estimation of the efficiency of nonideal explosives

Abstract Cylinder test energies of nonideal explosives are calculated on the basis of the following two assumptions: (a) that the detonation products of the overbalanced and underbalanced explosives have equilibrated completely to form the free energy-minimized detonation product composition at 7 volumes expansion; and (b) that each component has gone to its own detonation products, with no mixing or equilibration of the detonation species. From these calculations and the experimental cylinder test energy, the extent of interreaction is estimated. For the most efficient of the nonideal explosives tested, interreaction efficiencies approach 70%.