Modelling non-ideal detonations in commercial explosives

Highly non-ideal explosives usually react expressively below their ideal velocities of detonation. In these cases, dimensional effects and product heterogeneities become important to proper model their respective detonation state. Although Direct Numerical Simulation (DNS) techniques can provide a complete and exact solution for this problem, their actual computation cost are still not practical for industrial applications. In order to minimize these constrains, a simplified two-dimensional steady non-ideal detonation model for cylindrical stick explosives is presented. Based on an ellipsoidal shock shape approach (ESSA), the proposed model combines the quasi-one-dimensional theory for the axial flow solution with the unconfined sonic post-flow conditions at the edge of the explosive. Once calibrated, the model offers the possibility to predict the non-ideal detonation state for any charge diameter, resulting in a full mapping of the diameter-effect curve of the explosive. In addition, the effect of the inert confiner on the detonation flow is calculated by coupling a mechanistic confinement approach with the ESSA model. Thus, the proposed engineering approach is used to model the main properties of one of the most common ammonium nitrate-based explosive used in mining and quarrying industries, including the complete axial flow solution.