Euler-Lagrange modeling of circular discrete orifices gas-liquid pintle injectors using blob injection

An Euler-Lagrange methodology under Unsteady Reynolds-Averaged Navier-Stokes closure is proposed for cold-flow atomization in gas-liquid pintle injectors with discrete circular orifices. No interface-resolving treatment of the primary breakup region is employed: blob injection initializes the dispersed phase, and the Madabhushi model governs the complete atomization cascade. Model constants are determined a priori from literature values and correlations as a function of the operating condition; in particular, the column-breakup constant is tied to operating-condition correlations rather than treated as a free parameter, which reduces the uncertainty associated with the breakup-model calibration with respect to a single, case-independent value. The approach is validated against four test configurations encompassing two sets of experimental Sauter mean diameter measurements at different ambient pressures and two LES VOF-to-DPM reference solutions at Weg=3500 and 8500. The radial Sauter Mean Diameter profiles are reproduced with good accuracy across all downstream stations; locally, the model tends to overpredict D 32 in the near-field and near-axis region and to underpredict it in the far field. As far as the comparison with LES is concerned, good agreement is obtained at Weg=3500 and 8500 for the diameter distributions, percentile diameters, and droplet velocity profiles, with local point-wise deviations along the transverse profiles. A preliminary effective column-phase drag correction is assessed through a ± 30% sensitivity study based on the spatially resolved transverse diameter profiles. Among the investigated values, the nominal coefficient provides the most consistent profile agreement, yielding the lowest D 32-profile NRMSE at both Weber numbers without a systematic benefit from a further increase. The correction is therefore retained as a preliminary effective-area projected closure for the present conditions rather than as a final or universal drag correlation. The results confirm that the proposed framework provides a physically consistent and computationally efficient description of spray statistics in pintle injectors across a wide throttling range, enabling a faster design with respect to interface- or scale-resolving methods.