Simplified theoretical model for vapor fraction prediction at the nozzle exit for flash boiling atomization

Flash boiling atomization differs from classic spraying strategies due to the transition of the primary breakup mechanism. It has been proven that the distribution pattern of different breakup modes is tightly associated with the vapor fraction at the nozzle exit. Existing investigations have proposed empirical equations to approximate this characteristic via data fitting, but the absence of a mechanistic analysis constrains its generalization to scenarios involving variable boundary conditions, including diversified geometries and injection parameters. In the present study, we establish a simplified theoretical formula for vapor fraction prediction at the nozzle exit under flash boiling conditions, which can be easily adapted to different boundary parameters. The constructed formula is justified with published experimental data covering parameters that are recognized to be dominant for the development of flash boiling atomization, and the prediction error is less than 10% for most of the studied cases. It is proposed that bubble nucleation, rather than bubble growth, is the major cause for the varying vapor fraction in nozzles with diversified designs. This investigation provides a powerful and convenient tool for precisely estimating the vapor developing tendency inside the nozzles, while also deepening the understanding of the complex flash boiling internal phase-change that decides the external spray characteristics.