High-Order Numerical Methods and Reaction Rate Law for Non-Ideal Detonation Modeling

摘要

This study demonstrates the ability of high-order, shock-capturing methods to simulate detonation wave propagation in right circular cylinders of non-ideal explosives. 2-D axisymmetric, reactive Euler equations were solved for the detonation of the highly non-ideal explosive ammonium nitrate-fuel oil (ANFO) using a simple pressure-dependent rate law and perfect gas equation of state. The fractional step method was applied to the convection and reaction operators using a 2nd-order Strang splitting. The flow solver consisted of a finite difference scheme where the flux is reconstructed by a modified fifth-order weighted essentially non-oscillatory (WENO5-Z) with local characteristic decomposition and local Lax-Friedrichs (LLF) flux splitting. Time integration was performed by a third order total variation diminishing (TVD) Runge-Kutta time discretization method, also known as the strong stability preserving (SSP) method.Large-scale aquarium experiments using cylindrical ANFO charges (with 176 mm(7 in) charge diameters) were used to measure propagation of detonation front and expansion of gaseous products with ultra high-speed imaging. Two different ammonium nitrate prill types were tested: explosive grade (EG) and agricultural grade (AG). The camera frames revealed a pulsating behavior in the detonation driving zone for both types of prills. The experimental data was used to calibrate the adiabatic exponent used in the simulations to match detonation propagation rates. The reduced numerical diffusion of WENO-Z schemes demonstrated the suitability of this kind of high-order methods to model the global dynamics of the detonation using coarse spatial discretizations and reduced simulation run times.