Steady Non-ideal Detonations in Cylindrical Sticks of Explosives

Abstract

Abstract. Numerical simulations of detonations in cylindrical rate-sticks of highly non-ideal explosives are performed, using a simple model with a weakly pressure dependent rate law and a pseudo-polytropic equation of state. Some numerical issues with such simulations are investigated, and it is shown that very high resolution (hundreds of points in the reaction zone) are required for highly accurate (converged) solutions. High resolution simulations are then used to investigate the qualitative dependences of the detonation driving zone structure on the diameter and degree of confinement of the explosive charge. The simulation results are used to show that, given the radius of curvature of the shock at the charge axis, the steady detonation speed and the axial solution are accurately predicted by a quasi-one-dimensional theory, even for cases where the detonation propagates at speeds significantly below the Chapman-Jouguet speed. Given reaction rate and equation of state models, this quasi-one-dimensional theory offers a significant improvement to Wood-Kirkwood theories currently used in industry.

A streamline approach to two-dimensional steady non-ideal detonation: the straight streamline approximation

“…We also compare with a leading order DSD analysis where the resulting Q1D equations are solved numerically, as described in [7,10,11].…”

“…This gives of the order of 200 points in the DDZ length along the charge centre-line. The numerical setup is similar to that in [11,14]. The detonation is initiated by a high-pressure region at the base of the explosive, and the simulations are allowed to run for long time to ensure the steady state has been reached.…”

“…The method for finding the solution for confined detonations is similar as for the unconfined case. The slope of the shock front at the edge decreases in magnitude as the strength of the confiner increases [11,14], the value of which can be obtained using shock-polar matching [6,7]. The edge slope, y f,edge , can be found in relation to the edge angle, φ edge , determined by the shock polar match [7]: y f,edge = − tan φ edge .…”

“…An alternative approach is to perform direct numerical simulations (DNS) of the governing compressible reactive flow equations. However, accurate determination of VoD from DNS is computationally expensive due to requirement of high resolution [8,11]. Hence, DNS is impractical for large-scale parametric studies or for determining best fits of model parameters.…”

OPTIMEX: Measurement of Detonation Front Curvature with a Passive Fiber Optical System

“…The shape of the detonation front enables modellers to skip the problematic and computationally intensive description of the reaction zone structure, and, for example in the case of the simple detonation shock dynamics (DSD) approach, enables direct calibration of a particular explosive [1][2][3]. The information obtained from an experimentally determined detonation front shape may also be used for validation of higher order DSD or numerical simulations using full reactive Euler equations, even for highly non-ideal explosives [4]. Papers have also been presented using this information for the determination of reaction zone kinetics [5,6].…”