JWL equation of state

All reactive flow models require as a minimum two equations of state, one for the unreacted explosive and one for its reaction products a reaction rate law for the conversion of explosive to products and a mixture rule to calculate partially reacted states in which both explosive and products are present. The Ignition and Growth reactive flow model [60] uses two Jones-Wilkins-Lee (JWL) equations of state, one for the unreacted explosive and another one for the reaction products, in the temperature dependent form ... 

MAT HIGH EXPLOSIVE BURN as the key word is adopted in the code to describe explosive with Jones-Wilkins-Lee (JWL) equation of state to model the pressure generated by the expansion of the detonation product ... 

Where A, B, Rj and are material constants in JWL equation of state, P = the pressure of detonation products, V = the specific volume and E = initial value of the specific energy. 

Dynamic load applied using JWL equation of state for 2D axisymmetric models having 100 mm blasthole diameter in elasto-plastic rock obeying metal plasticity rules. Volumetric strain (scalar quantity) apportioned by statistical fracture mech principals used for fractures representation. 

Besides, on the basis of the cylinder test data, if the detonation parameters at the CJ point as the initial point of the products expansion are known, it is possible to deduce constants in the Jones-Wilkins-Lee equation (known as JWL equation of state) of the detonation products isentropic expansion. 

Figure 5.18. Flowchart of possible calculation procedure to obtain parameters in the JWL equation of state...

Miller, P.J., and Carlson, K.E. Determination JWL Equation of State Parameters Using the Gurney Equation Approximation, 9th Symposium (Intmiational) on Detonation, Portland, MD, 1989, pp. 930-936. 

The BKW equation of state was shown earlier in this chapter to be adequate to describe the expansion of an explosion under water from several hundred kilobars to a tenth of a bar. The BKW equation of state was also shown to be adequate to describe the plate dent test from over 500 kbars to less than 10 kbars. While it increases the confidence in using the BKW equation of state for describing such integral experiments, there is nothing unique about the BKW equation of state. The experimental data is also described, within experimental error, by explosive equations of state that describe the pressure-volume-temperature-energy relationship for detonation products quite differently. The cylinder test is used to calibrate the JWL equation of state for PBX-9404/9501 assuming C-J pressures varying from 380 to 305 kbars in the Livermore explosive data compendium. They all are forced to fit the cylinder test data ... 

As described in Chapter 5, section 5.4, the cylinder test consists of detonating a cylinder of explosive confined by copper and measuring the velocity of the expanding copper wall until it fractures. The cylinder test is commonly used to evaluate explosive performance using the JWL fitting form. The numerical model required to interpret cylinder wall expansion experiments must include a realistic description of build-up of detonation, Forest Fire burn and resulting wave curvature. That first became possible with the development of the NOBEL code. All previous calibrations of the JWL equation of state from cylinder test expansion data used explosive models without the essential detonation build-up to and of detonation. 

The lack of adequate detonation physics models in the codes used for calibrating the JWL equation of state from cylinder test data is one of the reasons that William C. Davis concluded JWL fit to a cylinder test may be useful for describing that particular cylinder test, but it will not be useful for describing anything else. While the JWL fitting form is the most unphysical equation of state used for describing explosives, calibrating any explosive equation of state with experimental data without build-up to and of detonation models will result in similar limitations to its usefulness. 

Experimental method to measure the effectiveness of an explosive. The radial expansion on detonation of a metallic cylinder (usually copper) filled with a high explosive is observed. A streak camera or a laser method might be used. The detonation velocity is determined simultaneously, using for example time-of-arrival pins. The -> Equation of State (EOS) which is often the Jones-Wilkins-Lee (JWL) EOS of the detonation products is derived using Gurney theory. 

In this simulation, three kinds of equation of state, linear, shook, JWL, and Compaction are applied. 

The JWL (Johns-Wilkins-Lee) equation of state (EOS), which is suited for hydrod5mamic of explosive detonation products, is employed as the EOS of TNT explosive in this study. The JWL EOS can be expressed as... 

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