JWL Calculating

The JWL is a standard equation of state used worldwide to describe the pressure-volume-energy behavior of a detonating explosive. Even so, not many people are very good at working with it. So I list all the various equations that describe how it works, then give one way that the solution can be obtained in an iterative manner. I have collaborated with Sedat Esen for several years. I am indebted to him for supplying almost all of our collection of dynamite data. He now works with ammonium nitrate/fuel oil, which is another area of interest to us

Analytic Model of Reactive Flow

A simple analytic model allows prediction of rate constants and size effect behavior before a hydrocode run if size effect data exists. At infinite radius, it defines not only detonation velocity but also average detonation rate, pressure and energy. This allows the derivation of a generalized radius, which becomes larger as the explosive becomes more non-ideal. The model is applied to near-ideal PBX 9404, in-between ANFO and most non-ideal AN. The power of the pressure declines from 2.3, 1.5 to 0.8 across this set. The power of the burn fraction, F, is 0.8, 0 and 0, so that an F-term is important only for the ideal explosives. The size effect shapes change from concave-down to nearly straight to concave-up. Failure is associated with ideal explosives when the calculated detonation velocity turns in a double-valued way. The effect of the power of the pressure may be simulated by including a pressure cutoff in the detonation rate. The models allows comparison of a wide spectrum of explosives providing that a single detonation rate is feasible

Porting Inition and Failure to Linked Cheetah

Linked CHEETAH is a thermo-chemical code coupled to a 2-D hydrocode. Initially, a quadratic-pressure dependent kinetic rate was used, which worked well in modeling prompt detonation of explosives of large size, but does not work on other aspects of explosive behavior. The variable-pressure Tarantula reactive flow rate model was developed with JWL++ in order to also describe failure and initiation, and we have moved this model into Linked CHEETAH. The model works by turning on only above a pressure threshold, where a slow turn-on creates initiation. At a higher pressure, the rate suddenly leaps to a large value over a small pressure range. A slowly failing cylinder will see a rapidly declining rate, which pushes it quickly into failure. At a high pressure, the detonation rate is constant. A sequential validation procedure is used, which includes metal-confined cylinders, rate-sticks, corner-turning, initiation and threshold, gap tests and air gaps. The size (diameter) effect is central to the calibration

Initiation Pressure Thresholds from Three Sources

Pressure thresholds are minimum pressures needed to start explosive initiation that ends in detonation. We obtain pressure thresholds from three sources. Run-to-detonation times are the poorest source but the fitting of a function gives rough results. Flyer-induced initiation gives the best results because the initial conditions are the best known. However, very thick flyers are needed to give the lowest, asymptotic pressure thresholds used in modern models and this kind of data is rarely available. Gap test data is in much larger supply but the various test sizes and materials are confusing. We find that explosive pressures are almost the same if the distance in the gap test spacers are in units of donor explosive radius. Calculated half-width time pulses in the spacers may be used to create a pressure-time curve similar to that of the flyers. The very-large Eglin gap tests give asymptotic thresholds comparable to extrapolated flyer results. The three sources are assembled into a much-expanded set of near-asymptotic pressure thresholds. These thresholds vary greatly with density: for TATB/LX-17/PBX 9502, we find values of 4.9 and 8.7 GPa at 1.80 and 1.90 g/cm{sup 3}, respectively

Kinetic information from detonation front curvature

The time constants for time-dependent modeling may be estimated from reaction zone lengths, which are obtained from two sources One is detonation front curvature, where the edge lag is close to being a direct measure The other is the Size Effect, where the detonation velocity decreases with decreasing radius as energy is lost to the cylinder edge A simple theory that interlocks the two effects is given A differential equation for energy flow in the front is used, the front is described by quadratic and sixth-power radius terms The quadratic curvature comes from a constant power source of energy moving sideways to the walls Near the walls, the this energy rises to the total energy of detonation and produces the sixth-power term The presence of defects acting on a short reaction zone can eliminate the quadratic part while leaving the wall portion of the cuvature A collection of TNT data shows that the reaction zone increases with both the radius and the void fractio

Estimated refractive index and solid density of DT, with application to hollow-microsphere laser targets

The literature values for the 0.55-$mu$m refractive index N of liquid and gaseous H$sub 2$ and D$sub 2$ are combined to yield the equation (N - 1) = [(3.15 +- 0.12) x 10$sup -6$]rho, where rho is the density in moles per cubic meter. This equation can be extrapolated to 300$sup 0$K for use on DT in solid, liquid, and gas phases. The equation is based on a review of solid-hydrogen densities measured in bulk and also by diffraction methods. By extrapolation, the estimated densities and 0.55-$mu$m refractive indices for DT are given. Radiation-induced point defects could possibly cause optical absorption and a resulting increased refractive index in solid DT and T$sub 2$. The effect of the DT refractive index in measuring glass and cryogenic DT laser targets is also described. (auth

Detonation in Shocked Homogeneous High Explosives

We have studied shock-induced changes in homogeneous high explosives including nitromethane, tetranitromethane, and single crystals of pentaerythritol tetranitrate (PETN) by using fast time-resolved emission and Raman spectroscopy at a two-stage light-gas gun. The results reveal three distinct steps during which the homogeneous explosives chemically evolve to final detonation products. These are (1) the initiation of shock compressed high explosives after an induction period, (2) thermal explosion of shock-compressed and/or reacting materials, and (3) a decay to a steady-state representing a transition to the detonation of uncompressed high explosives. Based on a gray-body approximation, we have obtained the CJ temperatures: 3800 K for nitromethane, 2950 K for tetranitromethane, and 4100 K for PETN. We compare the data with various thermochemical equilibrium calculations. In this paper we will also show a preliminary result of single-shot time-resolved Raman spectroscopy applied to shock-compressed nitromethane

The Energy Diameter Effect

We explore various relations for the detonation energy and velocity as they relate to the inverse radius of the cylinder. The detonation rate-inverse slope relation seen in reactive flow models can be used to derive the familiar Eyring equation. Generalized inverse radii can be shown to fit large quantities of cylinder results. A rough relation between detonation energy and detonation velocity is found from collected JWL values. Cylinder test data for ammonium nitrate mixes down to 6.35 mm radii are presented, and a size energy effect is shown to exist in the Cylinder test data. The relation that detonation energy is roughly proportional to the square of the detonation velocity is shown by data and calculation