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

Abstract

Detonations in non-ideal explosives tend to propagate significantly below the nominal one-dimensional detonation speed. In these cases, multi-dimensional effects within the reaction zone are important. A streamlinebased approach to steady-state non-ideal detonation theory is developed. It is shown in this study that, given the streamline shapes, the two-dimensional problem reduces to an ordinary differential equation eigenvalue problem along each streamline, the solution of which determines the local shock shape that, in turn, leads to the solution of the detonation speed as a function of charge diameter. A simple approximation of straight but diverging streamlines is considered. The results of the approximate theory are compared with those of high-resolution direct numerical simulations of the problem. It is shown that the straight streamline approximation is remarkably predictive of highly non-ideal explosive diameter effects. It is even predictive of failure diameters. Given this predictive capability, one potential use of the method is in the determination of rate law parameters by fitting to data from unconfined rate stick experiments. This is illustrated by using data for ammonium nitrate fuel oil explosives.

Numerical modelling of steady detonations with the CREST reactive burn model

“…It can be seen that the DNS results lie between those from the DSD approximation and SSA. This is consistent with results obtained by [14], who found that the SSA model gives too large a detonation velocity. At small radii the disparity between the DNS results and the SSA is significant and SSA gives a failure radius of (∼ 0.83 mm) compared to (∼ 1.25 mm) for the DNS calculations.…”

“…Watt et al [14] have developed a more sophisticated model, the Straight Streamline Approximation (SSA) model. This makes no assumptions about the shock front curvature, instead it assumes that the post-shock streamlines are straight.…”

“…Watt et al [14] have developed an approximate model for detonations in cylindrical charges which make an assumption about the shape of the streamlines and then solves the equations along the streamlines. The simplest approximation is to assume that the post-shock streamlines are straight, the straight streamline approximation (SSA).…”

“…where α, m and n are constants [14]. These show the post-shock streamline curvature as a function of shock slope for SSA calculations in slab geometry for different detonation velocities.…”

Diameter Effect on the Propagation of Curved Detonation Waves in Micro‐Channel Charges Within a Strong Confinement

“…Therefore, the propagation of detonation waves in micro-channel charges is determined by nonlinear couplings between multidimensional effects and chemical kinetics, which makes the theoretical research very complex. Watt [17] et al studied the detonation velocities in detonation wave propagation by approximating the streamline in straight lines, but the result was found to be better when the charge was unconstrained. Xu [18] et al studied the detonation velocities of detonation waves in micro-channel explosives, but it was assumed that the curved detonation wave front is flat, which is not true.…”