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A recently introduced stochastic model for reduced numerical simulation of primary jet breakup is evaluated by comparing model predictions to DNS results for primary jet breakup under diesel conditions. The model uses onedimensional turbulence (ODT) to simulate liquid and gas time advancement along a lateral line of sight. This one-dimensional domain is interpreted as a Lagrangian object that is advected downstream at the jet bulk velocity, thus producing a flow state expressed as a function of streamwise and lateral location. Multiple realizations are run to gather ensemble statistics that are compared to DNS results. The model incorporates several empirical extensions of the original ODT model that represent the phenomenology governing the Weber number dependence of global jet structure. The model as previously formulated, including the assigned values of tunable parameters, is used here without modification in order to test its capability to predict various statistics of droplets generated by primary breakup. This test is enabled by the availability of DNS results that are suitable for model validation. Properties that are examined are the rate of bulk liquid mass conversion into droplets, the droplet size distribution, and the dependence of droplet velocities on droplet diameter. Quantities of greatest importance for engine modeling are found to be predicted with useful accuracy, thereby demonstrating a more detailed predictive capability by a highly reduced numerical model of primary jet breakup than has previously been achieved.

Previous studies have predicted $We^{-2/5}$ dependence of the streamwise location at which primary breakup of turbulent liquid jets begins and $We^{-3/5}$ dependence of the Sauter mean diameter (SMD) of droplets released at that location, where $We$ is the jet Weber number. Measured deviations from these predictions were attributed to measurement uncertainties and to the simplicity of the analysis, which invoked turbulence inertial-range phenomenology. Here, it is proposed that breakup onset is instead controlled by the residual presence of the boundary-layer structure of the nozzle flow in the near field of the jet. Assuming that the size of the breakup-inducing eddy is within the scale range of the log-law region, $We^{-1}$ dependence of both the onset location and the SMD at onset is predicted. These dependences agree with the available measurements more closely than those previously predicted. To predict the dependences on the Reynolds number $Re$, either the friction velocity in conjunction with the Blasius friction law or the bulk velocity can be used, where the former yields $Re^{3/8}$ and $Re^{1/4}$ dependence of the onset location and the SMD at onset respectively, while the latter implies no $Re$ dependence of either. The latter result is consistent with the available measurements, but the boundary-layer analysis indicates that the velocity scaling should be based on the friction velocity rather than the bulk velocity, so the origin of the measured lack of $Re$ dependence merits further investigation. A plausible hypothesis is that pressure effects associated with the transition from wall-bounded nozzle flow to jet free-slip boundary conditions induce a transient large-scale flow modification that counteracts the $Re$ dependence of the nozzle flow while preserving the logarithmic flow structure near the jet surface. Notwithstanding the absence of direct evidence supporting this hypothesis, the new analysis and comparisons of its predictions with measurements suggest that transient effects such as the residual influence of the nozzle-flow structure are the likely explanations of the observed parameter dependences.

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