A combined analytical/numerical approach to the modelling of the processes leading to puffing and micro-explosion in a composite multi-component fuel/water droplet

Abstract

The previously developed analytical/numerical model for predicting heat transfer and component diffusion in composite multi-component droplets is adjusted for use in practical engineering applications related to the analysis of droplet heating and evaporation, and the onset of puffing and micro-explosions in those droplets. This adjustment allowed us to gain new insights into the previously developed models of these processes. The focus of the analysis is on kerosene/water droplets. It is demonstrated that the number of terms in the series in the analytical solution to the heat transfer equation can be reduced to just one or two to ensure that the maximal error of the model prediction does not exceed 1\%, unless we are interested in the processes at the very start of heating. At the same time, the minimal number of terms in the series in the analytical solution to the component diffusion equation should be at least seven to ensure that the errors of the prediction of the numerical code do not exceed 3\%. It is shown that, to ensure that the analytical/numerical code predicts physically consistent results, the maximal absolute error of calculation of the eigenvalues based on the bisection method cannot exceed 10^-7. It is shown that using these limiting values for each of these input parameters leads to about 50%-75% reduction in the CPU time required to obtain results close to those which were obtained using the non-optimised version of the numerical code. The overall reduction in CPU time can be as up to about 95%. The predictions of the adjusted analytical/numerical code are validated against in-house experimental data and data available in the literature.