Additional afterburning energy value to simulate fully confined trinitrotoluene explosions

Euler-Lagrange software packages are commonly employed in the analysis and design of chambers subjected to internal detonations of high explosives because they allow modeling the interaction between high-explosive gas products, air, liquid, and structures. In general, the expansion of high-explosive products is modeled by the Jones-Wilkinson and Lee equation of state, and additional extension methods such as the Miller or the additional energy release extensions are used to model the afterburning energy which is released after the detonation. These extension methods require that the additional energy by unit mass is predefined. Although the difference between the heat of combustion and the heat of detonation provides a specific value for the additional energy, for example, 10.01 MJ/kg TNT for trinitrotoluene charges detonated inside of chambers with rich oxygen, this value is generally inappropriate if high-explosive gas products and air are modeled separately, that is, by the Jones-Wilkinson and Lee equation of state and the ideal gas equation of state, respectively. This article explains how to determine an appropriate value for the specific additional energy value for use in the commercial software package AUTODYN for more reliable predictions of the quasi-static gas pressure in fully confined chambers subjected to trinitrotoluene explosion. The procedure detailed in this article can be applied to any kind of chamber geometries and chamber materials. A simplified chart for the afterburning energy as a function of the charge mass density is derived. The proposed approach in predicting the quasi-static gas pressure is validated with the quasi-static gas pressure described by the Unified Facilities Criteria's guideline and some experimental tests. A procedure to determine the additional afterburning energy that should be employed for highly deformable chambers is also explained.