| Summary: | The coupling of Eulerian and Lagrangian methods in the Eulerian–Lagrangian Spray Atomization (ELSA) approach is critical. This study proposes an equation for the primary breakup particle diameter <i>D</i> of a diesel fuel spray and adopts it as a key transition criterion for coupling. A three-dimensional diesel spray is modeled by the large-eddy simulation (LES) approach. This improved ELSA simulation was conducted using various transition criteria for particle diameter <i>D<sub>cr</sub></i>. The results show that fuel spray experiences two stages: stage I, when a liquid column appears without a dispersed phase, and stage II, when primary breakup occurs with many discrete particles. Although <i>D<sub>cr</sub></i> has little influence on the macro-spray characteristics, such as top penetration distance <i>S</i> and spray cone angle <i>θ</i>, it has significant effects on discrete particles, such as their number, average diameter, distribution and location, and spray cone area. <i>D<sub>cr</sub></i> should be determined on the basis of actual operating conditions.
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