The present paper gives a mathematical model for collapse and ignition of reactive gas-filled bubbles. Oxyhydrogen bubbles, which can be formed in high-temperalure reactor water, can present an explosion hazard. In addition to treating the classical features of bubble dynamics, energy balances for the liquid and gas phase, and the heat transfer between the gas and surrounding liquid are included in the model. The gas-phase thermodynamic properties and chemical reaction rates are assembled by incorporating a real-gas version of the CHEMKJN chemical kinetics package in which the Nobel-Abel equation of state is used. The liquid energy equation is solved by the integral method to yield an ordinary differential equation for interface temperature. Some typical numerical results and shock ignition thresholds, or critical shock pressures necessary to ignite the gas-phase mixture, under various conditions for argon-diluted hydrogen/oxygen bubbles in water and glycerin are presented. Comparison with experimental data indicates that the model can predict the process of bubble collapse and ignition accurately, especially if ignition occurs during the first cycle. Calculations show that initial bubble radius, temperature, pressure, and mixture composition have strong influences on bubble collapse and ignition. The ignition threshold decreases with increasing initial radius and temperature and decreasing initial gas pressure. Ignition is also favored by stoichiometric or fuel-rich mixture diluted by inert gas.
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