Detonation equation of state at LLNL, 1995. Revision 3

Abstract

JWL's and 1-D Look-up tables are shown to work for "one-track'' experiments like cylinder tests, plate shots and the expanding sphere. They fail for "many-track" experiments like the compressed sphere. As long as the one-track experiment has dimensions larger than the explosive's reaction zone and the explosive is near-ideal, a general JWL with R1= 4.5 and R2 = 1.5 can be constructed, with both o and Eo being calculated from thermochemical codes. These general JWL's allow comparison between various explosives plus recalculation of the JWL for different densities. The Bigplate experiment complements the cylinder test by providing continuous oblique angles of shock incidence from Oo t o 70°. Explosive reaction zone lengths are determined from metal plate thicknesses, extrapolated run-to-detonation distances, radius size effects and detonation front curvature. Simple theories of the cylinder test, Bigplate, the cylinder size effect and detonation front curvature are given. The detonation front lag at the cylinder edge is shown t o be proportional to the half-power of the reaction zone length. By calibrating for wall blow-out, a full set of reaction zone lengths from PETN to ANFO are obtained. The 1800-2100 K freezing effect is shown to be caused by rapid cooling of the product gases. Compiled comparative data for about 80 explosives is listed. Ten Chapters plus an Appendix. Ps. = A(1e)exp(-Rlv) + B(1-*)exp(-%v) +-7 WE, R v Es is always positive, starting with a large number at Vj and declining to zero at some large volume. Also Es = Eo-Ed. We use the physicists' convention, where Eo is positive. Hence, the detonation energy, Ed, is negative for small volumes and positive for large volumes. At Vj, Ed equals the energy of compression, Ec. Eq. 19 requires the energy to be inserted at every time step, which makes codewriters feel better about its conservation. However, the energy is computed by adding or subtracting 1-7 increments on each cycle, so that the quality of conservation depends ultimately on the smallness of the steps. Eq. 19 is used only to set the pressure. The detonation velocity, D, is used to set the timing for the program burn part of the burn package. For the beta burn part, the code needs to be told the detonation point so it can calculate compression. One might give it the detonation volume Vj directly, which is what it really wants or Pj as is done in DYNA2D. Another common entry in LLNL production codes is rj + 1 sometimes called P or bhe, which is defined by, rj is the adiabatic gamma at the detonation point, and it varies only between 3.5 t o about 4.2. The "j" means that the detonation point is probably not a true C-J point but is an approximation depending on how it was generated. The hydrocode doesn't care if the actual detonation point is reached or not. It will be reached only in the case of heavy containment and with zoning to convergence. The energy dumped into the explosive is FEo, which rises to Eo d e r the shock wave has passed through. The reason why nobody cares about the detonation ...

Adding kinetics and hydrodynamics to the CHEETAH thermochemical code

“…After the sonic point, the system transitions to an adiabatic expansion. Note that the Von Neumann spike is higher in Figure 10 than is commonly supposed (C. Souers, private communication 14 ). This is due to the unreacted HMX equation of state.…”

Investigation of JWL Equation of State for Detonation Products at Low Pressure With Radio Interferometry

“…Moreover, the equation of state can be easily recalibrated in order to match the experimental results. The constants have often been determined with the cylinder test [4] where the lowest pressure reached is about 4 GPa. In this paper, parameters of the JWL equation of state are calibrated with the thermochemical code SIAME 1.0 (SImulation of Aerothermochemical of Mechanics of Explosives).…”

Determination of detonation products equation of state from cylinder test: Analytical model and numerical analysis

“…There are two ways to determine the JWL parameters of equation of state: (1) by use of a thermo-chemical equilibrium code, and (2) using some of the experimental tests. The former method implies the use of a mentioned semi-empirical computer program that has a JWL fitting procedure built in, e. g. [6,7], and will not be considered here. The latter approach, which is based on detonation products expansion physics, will be further investigated.…”

“…The most common source of experimental data to obtain explosive performance parameters is the cylinder test [7][8][9][10]. A copper tube is filled with the explosive of interest and the planar detonation wave (normal to the cylinder axis) is generated as shown in fig.…”