Calculating Overdriven Detonation for Reaction Product Shock States for Pressures Higher than those for Steady Detonation Waves

When detonation waves impact high impedance materials, are overdriven in gas gun or laser experiments, enter a converging geometry, etc., shock pressures much higher than steady, Chapman-Jouguet (C-J) detonation can be generated. Such measurements have steadily improved over the past 50 years as spacial and time resolution have improved. 1 So has reaction product equation of state modeling. The Jones-Wilkins-Lee (JWL) reaction product equations of state were originally fit only to product expansion below C-J and were too compressible at higher pressures. Urtiew and Hayes 2 showed that by raising R 1 , R 2 , and ω, they could improve fits to overdriven data, while still matching product expansion data below the C-J state.

In the 1990s, Nellis, Mitchell, et al 3 measured high pressure Hugoniots of dissociating liquid nitrogen, ionization of water, and CO/CO 2 equilibrium as functions of shock pressure. The shock temperatures of individual dimers and trimers are higher than those for detonation C-J waves, which distribute their internal energy over more product vibrational modes. Thus more N 2 dissociation, more H 2 O ionization, and different CO 2 /CO ratios occur in the Nellis experiments compared to detonation. The large dissociation energy of N 2 has the greatest effect on the CHEETAH chemical equilibrium calculations, as shown by Tarver 1 for HMX and TATB overdriven detonation waves.

References

1. Tarver, C.M., Journal of Physical Chemistry A, 124, 1399 (2020).

2. P. A. Urtiew and B. Hayes, Combustion, Explosion, and Shock Waves 27, 505–514 (1991)

3. W. J. Nellis et al. J. Chem. Phys. 94, 2244–2257 (1991)