Jones-Wilkins-Lee equation of state

The Jones-Wilkins-Lee equation of state is used for the fully reacted state of explosives .

${\displaystyle p=A\cdot \left(1-{\frac {\omega }{R_{1}\cdot V}}\right)\cdot \exp(-R_{1}\cdot V)+B\cdot \left(1-{\frac {\omega }{R_{2}\cdot V}}\right)\cdot \exp(-R_{2}\cdot V)+{\frac {\omega \cdot e_{0}}{V}}}$

It is with = density of the explosive and = density of the detonation products. The parameters , , , and are tabular works can be seen (see Fig. Dobratz et al.). There you will also find information about the initial density , detonation speed , Chapman-Jouguet pressure and the chemical energy contained in the explosive required for the selected explosive . The JWL equation of state can be easily adapted to test results and is determined by a sum at constant energy, i.e. H. the isentropic is the basis for the equation of state. The isentropic is a first approximation of the equation of state at low pressures. ${\displaystyle V=\rho _{e}/\rho }$ ${\displaystyle \rho _{e}}$ ${\displaystyle \rho }$ ${\displaystyle A}$ ${\displaystyle B}$ ${\displaystyle R_{1}}$ ${\displaystyle R_{2}}$ ${\displaystyle \omega }$ ${\displaystyle \rho _{0}}$ ${\displaystyle V_{D}}$ ${\displaystyle P_{CJ}}$ ${\displaystyle e_{0}}$ ${\displaystyle p_{S}=\sum \phi _{i}(\nu )}$

Examples of parameters of the JWL equation of state

TNT

${\displaystyle \rho _{0}=1{,}630\,\mathrm {g/cm} ^{3}}$ ; ; ; ; ; ; ; ; ${\displaystyle v_{D}=6930\,\mathrm {m/s} }$ ${\displaystyle p_{CJ}=21{,}0\,\mathrm {GPa} }$ ${\displaystyle A=373{,}8\,\mathrm {GPa} }$ ${\displaystyle B=3{,}747\,\mathrm {GPa} }$ ${\displaystyle R_{1}=4{,}15}$ ${\displaystyle R_{2}=0{,}90}$ ${\displaystyle \omega =0{,}35}$ ${\displaystyle e_{0}=6{,}00\,\mathrm {GPa} }$

Composition B

${\displaystyle \rho _{0}=1{,}717\,\mathrm {g/cm} ^{3}}$; ; ; ; ; ; ; ; ${\displaystyle v_{D}=7980\,\mathrm {m/s} }$ ${\displaystyle p_{CJ}=29{,}5\,\mathrm {GPa} }$ ${\displaystyle A=524{,}2\,\mathrm {GPa} }$ ${\displaystyle B=7{,}678\,\mathrm {GPa} }$ ${\displaystyle R_{1}=4{,}20}$ ${\displaystyle R_{2}=1{,}10}$ ${\displaystyle \omega =0{,}35}$ ${\displaystyle e_{0}=8{,}50\,\mathrm {GPa} }$

literature

• BMDobratz, PC Crawford: LLNL Explosives Handbook: Properties of Chemical Explosives and Explosive Simulants , University of California ; Lawrence Livermore National Laboratory ; Report UCRL-5299; Rev.2; 1985