The depressurization of the surrounding chamber or superheating of the injected liquid is responsible for the flashing of the sprays, which promotes micro-explosion of many bubbles near free-surface and thereby leading to primary atomization of sprays. In this work, we propose a mathematical model, and the Dirichlet hyperboloids are used to explain the micro-explosion process while the external flashing phenomenon is observed in superheated liquid jets. The developed mathematical model is implemented in the Lagrangian framework to study the spray structure, and the results of numerical simulations are found to be in good agreement with the experimental results from the literature. In the onset region of a fully flashing regime, the bell-shaped spray structure becomes eminent due to increased drag on the high radial-velocity ejected droplets. However, at a lower degree of superheat, the droplet size is found to increase with a decrease in ambient pressure. Whereas the opposite trend is observed at a higher degree of superheat.