Spray Atomization

Eulerian-Lagrangian (E-L) Spray Modeling

In the Eulerian-Lagrangian (E-L) based multiphase modeling framework, a Lagrangian coordinate system is adopted to describe a cloud of liquid/solid particles, while the continuum gas phase flow is resolved by a set of relevant transport equations, such as Reynolds-Averaged Navier-Stokes (RANS) equations, on the Eulerian grid coordinate as depicted on the left. Its popularity comes from how well it balances accuracy, computational cost, and physical fidelity when simulating multiphase flow systems.

The E-L framework easily incorporates sub-models for:

Primary/secondary breakup (KH-RT, TAB, etc.)
Collision and coalescence
Evaporation and fuel vapor mixing
Wall interaction (impingement, rebound, film formation)

Under the notion that a liquid jet emerging from an injector nozzle initially constitutes a continuum body at high velocity, disintegration of the turbulent liquid jet is appreciated as a key process of atomization forming a cloud of ligaments and small-scale droplets. Such a disintegration of continuum liquid mass is often referred to as primary breakup. The subsequent event of single droplet bursting into smaller droplets in dispersed phase nature is then termed secondary breakup. The following sub-chapters outlines newly developed primary/secondary breakup models centered on liquid spray atomization process.

Primary Breakup Models

When liquid is injected, it forms a jet that undergoes disintegration in the so-called primary breakup regime. In many industrial and engineering approaches, this phenomenon has been described as a surface wave instability developing along the liquid jet, which eventually causes the jet surface to fragment into a cloud of droplets. This mechanism reflects the aerodynamic interaction between the surrounding gas and the liquid phase. Such an understanding of primary breakup was first established by Reitz [1] and laid the groundwork for the aerodynamically driven breakup approach known as the Kelvin–Helmholtz (KH) model.

Nozzle-Generated Turbulence Primary Breakup Model

Development of Multi-Physics Turbulence (MPT) Model

Although the classic KH model has been widely incorporated in many CFD software for the last three decades, its usefulness has been relatively limited under conventional engine operating conditions. In contrast, under modern engine-relevant scenarios—especially those involving low-temperature combustion—the internal nozzle flow and the resulting turbulent structures have a dominant influence on spray atomization. To address this effect, my dissertation introduces a new primary breakup model that accounts for nozzle-generated turbulence. This model builds upon the previously established hybrid breakup framework, named KH-Faeth model [2], and further enhances its predictive accuracy.

Formulations in the new primary breakup model accounts for detailed physics of primary breakup mechanisms that incorporates the following three distinctive breakup regimes:

Non-aerodynamic (i.e., turbulence) primary breakup
Aerodynamically enhanced turbulence primary breakup
Merged primary/secondary breakup

By integrating the detailed physics discussed above, the MPT model serves as an enhanced extension of the KH-Faeth framework. The theoretical background and model formulations are presented in detail in my dissertation [2].

X-Ray Diagnostics

X-ray diagnostics offer a distinct advantage in quantifying spray mass and surface area distributions, particularly within optically dense regions where traditional optical methods face significant limitations. This approach establishes a reliable foundation for evaluating the predictive accuracy of developed models. To pursue this, our research group at Georgia Tech collaborated with Argonne National Laboratory, utilizing the Advanced Photon Source (APS) facility. Specifically, we employed the ultra-small angle x-ray scattering (USAXS) technique, which enables measurements of projected mass density (PMD) as well as the Sauter mean diameter (SMD) of droplets within dense spray plumes.

Assessment on the Model's Prediction Accuracy

The comparative analysis was carried out using the USAXS technique, which provides SMD measurements. The results, presented below, demonstrate the notable improvement achieved with the MPT model. However, complete verification of the model may have not been obtained yet since the results exhibit some degree of deviation of SMD predictions off the measurement. There may also be uncertainties in SAMR measurements as well inherently due to the challenge in injector alignment issue.

Modeling the Secondary Droplet Dynamics

Experimental support for modeling the single drop breakup and aerodynamic drag effect

To verify the developed model's prediction accuracy, microscopic single drop behavior was visualized using the high-speed camera. Characteristics of drop atomization and size and velocity distribution under the high speed cross-flow stream was obtained by utilizing PDPA (Phase Doppler Particle Analyzer) as illustrated in the figure below. The model assessment process was undergone for improving the model in capturing the droplet deformation rate and droplet breakup time. The test were carried using two different fuel types: conventional diesel-like fuel and bio-diesel (soybean oil) as table-listed below. Developed models are implemented in KIVA-3V and OpenFOAM CFD code.

Evaluation of drop dynamics: deformation and aerodynamic drag effect

Characteristics of secondary drop breakup: size distribution (Sauter Mean Diameter) measurement

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