The evolution of the temperature field during cavity collapse in liquid nitromethane. Part I: inert case

This work is concerned with the effect of cavity collapse in non-ideal explosives as a means of controlling their sensitivity. The main objective is to understand the origin of localised temperature peaks (hot spots) which play a leading order role at the early stages of ignition. To this end we perform two- and three-dimensional numerical simulations of shock induced single gas-cavity collapse in liquid nitromethane. Ignition is the result of a complex interplay between fluid dynamics and exothermic chemical reaction. In order to understand the relative contribution between these two processes, we consider in this first part of the work the evolution of the physical system in the absence of chemical reactions. We employ a multi-phase mathematical formulation which can account for the large density difference across the gas-liquid material interface without generating spurious temperature peaks. The mathematical and physical models are validated against experimental, analytic and numerical data. Previous inert studies have identified the impact of the upwind (relative to the direction of the incident shock wave) side of the cavity wall to the downwind one as the main reason for the generation of a hot-spot outside of the cavity, something which is also observed in this work. However, it is also apparent that the topology of the temperature field is more complex than previously thought and additional hot spots locations exist, which arise from the generation of Mach stems rather than jet impact. To explain the generation mechanisms and topology of the hot spots we carefully follow the complex wave patterns generated in the collapse process and identify specifically the temperature elevation or reduction generated by each wave. This allows to track each hot spot back to its origins. It is shown that the highest hot spot temperatures can be more than twice the post-incident shock temperature of the neat material and can thus lead to ignition. By comparing two-dimensional and three-dimensional simulation results in the context of the maximum temperature observed in the domain, it is apparent that three-dimensional calculations are necessary in order to avoid belated ignition times in reactive scenarios