The evolution of the temperature field during cavity collapse in liquid nitromethane. Part II: reactive 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 r\ ole 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 the first part of this work we focused on the hydrodynamic effects in the collapse process by switching off the reaction te\ rms in the mathematical formulation. In this part, we reinstate the reactive terms and study the collapse of the cavity in the presence of chemical reactions. By using a multi-phase formulation which ove\ rcomes current challenges of cavity collapse modelling in reactive media we account for the large density difference across the material interface without generating spurious temperature peaks thus allow\ ing the use of a temperature-based reaction rate law. The mathematical and physical models are validated against experimental and analytic data. In Part I, we demonstrated that, compared to experiments, the generated hot spots have a more complex topologica\ l structure and additional hot spots arise in regions away from the cavity centreline. Here, we extend this by identifying which of the previously-determined high-temperature regions in fact lead to igni\ tion and comment on the reactive strength and reaction growth rate in the distinct hot spots. We demonstrate and quantify the sensitisation of nitromethane by the collapse of the isolated cavity by compa\ ring the ignition times of nitrometane due to cavity collapse and the ignition time of the neat material. The ignition in both the centreline hot spots and the hot spots generated by Mach stems occurs in\ less than half the ignition time of the neat material. We compare two- and three-dimensional simulations to examine the change in topology, temperatures and reactive strength of the hot spots by the thi\ rd dimension. It is apparent that belated ignition times can be avoided by the use of three-dimensional simulations. The effect of the chemical reactions on the topology and strength of the hot spots in \ the timescales considered is also studied, in a comparison between inert and reactive simulations where maximum temperature fields and their growth rates are examined