Two streamline, ordinary differential equation (ODE) models for detonation, the Chan-Kirby model and the straight streamline approach of Watt et al., are extended to a multiphase system of equations. These multiphase equations, with realistic equations of state, are used to better capture the heterogeneities in non-ideal explosives used in mining applications.

Streamline ODE multidimensional models are normally obtained by reducing the partial differential equations (PDEs) describing the motion of the material to ODEs by making approximations about some of the physics of the problem. These models are referred to as reduced ODE models in this work and are the primary focus of this research into fast, efficient solutions of non-ideal explosives.

In the development of these reduced order forms, some terms in the full equations have been removed for analytical convenience. Although this is not always the result of a formal order of magnitude analysis, this somewhat empirical approach is justified by simulation studies. In particular, by demonstrating that in a variety of benchmark problems, the reduced order ODEs give similar results to those obtained from the much more complex, full order PDE models. Further support is obtained by comparing the reduced order solution with experimental results.

Comparisons with multiphase direct numerical simulations and experiments are undertaken to investigate the effect of the approximations and assumptions made in the derivation of the models. Both models produce comparable diameter effect curves for two different non-ideal explosives, EM120D and ANFO, in unconfined conditions. Empirical assumptions in the Chan-Kirby model can be eliminated but investigation shows that the straight streamline multiphase extension is based on better approximations for non-ideal explosives. This latter approach also gives better prediction of the diameter effect curve and detonation driving zone shape.

The multiphase straight streamline model is then extended to model confined multiphase detonations, with realistic equations of state for the confining material, and predicts most strong confinement examples well.

Future work of extending to curved streamlines and including confinement other than strong or weak is discussed.