A multi-scale simulation of hot spot initiation of detonation utilizing experimental measurements

Empirical and phenomenological hydrodynamic reactive flow models, such as the ignition-and-growth and Johnson–Tang–Forest models, have been effective in predicting the shock initiation and detonation characteristics of various energetic substances. These models utilize the compression and pressure properties of the reacting mixture to quantify its reaction rate. However, it has long been known that the shock initiation of detonation is controlled by local reaction sites called ‘hot spots’. In this study, a hot-spot model based on the temperature-dependent Arrhenius reaction rate is developed. The complex reaction process of the target explosive is addressed by conducting differential scanning calorimetry experiments whereas the reaction rate is determined using the Friedman isoconversional method. The hot spot is approximated by the region of high pressure accumulation due to multiple shock reverberations within the polymer binder, which is surrounded by the bulk explosive. The mesoscale smoothed particle hydrodynamic simulation is adopted to identify the peak temperatures within the hot spots. These peak temperatures obtained from the mesoscale level are then used to initialize the random sites of heat release prior to conducting the full-scale hydrodynamic simulation of the shock-to-detonation transition (SDT). To validate the simulation, the distance to detonation is compared with the reported experimental value to validate the initiation process of the proposed model and an 18-mm-radius rate stick is experimentally tested to confirm the reproducibility of the detonation properties. The comparison shows that the detonation properties and the initiation process of the explosive are well characterized, while no-go conditions are observed if no mesoscale hot-spot model is included in the hydrodynamic simulation. Therefore, the SDT process can be well described by the present model based on multi-scale hot-spot initiation.