*Large-Eddy Simulation Modeling of Diesel Sprays*. University of Wisconsin-Madison, 2017.

The goal of this study is to develop/improve physical models for large-eddy simulations of Diesel sprays. The stochastic Kelvin-Helmholtz/Rayleigh-Taylor (KH-RT) atomization and breakup model, the synthetic eddy injection model, the droplet rotation model, and the sub-grid scale (SGS) dispersion model were developed and tested. Using the classical KH-RT model, it was found that simulation results are sensitive to several model parameters such as length and time scales of instability waves. The idea of the stochastic KH-RT model is to determine these parameters stochastically and dynamically. This is an attempt to reduce the sensitivity of the model parameters partly resulting from the incapability of predicting breakup mechanisms other than wave instabilities in the classical KH-RT model. The synthetic eddy injection model predicts fluctuations of the Lagrangian parcel initial velocity. The model attempts to simulate turbulence at the nozzle exit without the need of internal nozzle flow simulations, by superimposing a number of virtual coherent structures. The performance of these two newly developed models was compared to the original ones, namely the classical KH-RT and the cone angle injection models. Two experimental databases, the Engine Combustion Network (ECN) constant-volume sprays and the Engine Research Center optical engine sprays were used to validate the models. A number of simulated quantities such as liquid projected mass density, liquid and vapor penetrations, fuel vapor profiles, ignition delays, and lift-off lengths, were compared against the data. The stochastic KH-RT model improved the prediction of the projected mass density downstream and liquid penetrations in a range of operating conditions (errors within 5 %) without tuning the model constants case by case. The synthetic eddy injection model improved the prediction of vapor penetrations at early stage of injection since the development of instability modes and turbulent transport in the near-nozzle region were better resolved. The model also shows less grid sensitivity. Overall, using these two new models overcomes some limitations in the original models and makes LES as a more predictive tool for Diesel sprays.

The droplet rotation model considers droplet force and torque due to relative rotational motions between droplets and gas. Simulation results of the ECN non-vaporizing and vaporizing sprays with and without using the rotation model were compared. It was found that the droplet rotation has negligible effect. This is because the droplet response time scale to the rotational motion is much smaller than that to the translational motion. That is, slip angular velocity approaches to zero much faster, resulting in much smaller rotational force than the drag force.

The SGS dispersion model considers the effect of sub-grid motions on Diesel spray dispersion. The model assumes that the SGS dispersion velocity is decomposed into the deterministic and the stochastic parts. The deterministic part is modeled by the approximate deconvolution method and the stochastic part is assumed to be isotropic and Gaussian distributed. It was found that the two model parameters, variance of the Gaussian distribution and turbulence correlation time, have a critical effect on the spatial distribution of droplets with small inertia downstream of the spray. Larger variance or longer turbulence correlation time predicts wider liquid spray angle. However, they have small effect on predicting resolved gas-phase statistics. The primary reason for this is that the motion of high-momentum liquid blobs in the near-nozzle region leading to air entrainment and subsequent gas jet development is little influenced by the SGS dispersion. Moving further downstream a quasi-equilibrium is established between the two phases, resulting in relatively small slip velocities. Therefore, it was found that the spray momentum source term in the gas momentum equation is much smaller than the other terms in the downstream region.