Reactive burn modeling of non-ideal explosives

Abstract

Detonations in non-ideal explosives are highly dependent on the initial state of reactants, explosive charge size, and confining material properties. Most phenomenological reactive burn models are constructed at specific densities. Thus, they lack a predictive capability when applied to explosive systems that differ from the calibration experiments. This research develops a reactive burn model that incorporates the initial charge compaction as parameter in the continuum-level representation. Thermochemical, hydrodynamic, and experimental analyses were conducted for a stoichiometric mixture of ammonium nitrate and fuel oil (ANFO) at different initial densities. Thermochemical calculations revealed strong variations in mole fractions and equilibrium states for the detonation products species. Chapman-Jouguet (CJ) states were used to devise a reactive, chemistry-implicit equation of state based on a pseudo-polytropic form. The non-equilibrium chemistry was modeled using a global pressure-dependent rate law whose rate parameters track experimental size effect data. This new reactive burn model matches CJ states and products release isentropes down to 1% of the CJ pressure, and replicates the non-monotonic relation between detonation velocity and reactants density at finite radii.This work culminates in a multimaterial numerical framework to solve the reactive Euler equations in confined, multidimensional high-explosive systems. The Ghost Fluid Method (GFM) is used to handle the dynamic material interfaces for the detonation products, confining materials, and surrounding medium. The solution sensitivity to different interface boundary conditions is analyzed by replacing the original GFM with two Riemann solver-based strategies. A novel method for defining the left and right states of the interfacial Riemann problem eliminates the need for sorting or nodal interpolation during the projection along the material interface. Numerical tests indicate that populating the interface node values using the Riemann solution mitigate overheating errors but at additional computational cost. Solution convergence and computational efficiency are also explored as a function of the spatial and temporal order of the numerical discretization schemes. Large-scale aquarium experiments are presented for ANFO encased in polymethyl methacrylate (PMMA) using explosive grade and agricultural grade ammonium nitrate prills. The time-resolved image data provided information on the detonation velocity, products expansion, and inert shock wave in the water. Computational results for these aquarium tests using the devised reactive burn model agree within 1% in terms to front velocities and reaction products expansions. The proposed model and numerical framework, in conjunction with high-fidelity experimental data, provides a reliable computational tool for simulating non-ideal explosive systems in a wide range of geometries, confinement, and pressing densities.