A sub-grid model accounting for the interaction of spray and sub-grid turbulence was developed and tested. The model predicts the sub-grid scale dispersion velocity used for calculating the slip velocity in Lagrangian–Eulerian Large-eddy simulation spray models. The dispersion velocity is assumed to be decomposed into a deterministic and a stochastic part, and it is updated in every turbulence correlation time for each computational parcel. The model was validated against two datasets: volume-of-fluid simulations and Engine Combustion Network experiments. The volume-of-fluid data showed that dispersion velocities at the centerline are anisotropic. This qualitative feature is well captured by the current model. For the Engine Combustion Network Spray A cases, it was found that sub-grid scale dispersion has profound impact on the prediction of the spatial distribution of liquid mass. Neglecting the sub-grid scale dispersion model results in underprediction of the width of the lateral projected liquid mass density profiles. Also, the prediction of the projected liquid mass density is sensitive to the two model constants determining the sub-grid scale dispersion velocity magnitude and turbulence time scale. However, the predictions of resolved gas-phase statistics are relatively insensitive to different sub-grid scale dispersion model setups. The primary reason for this was investigated. It was found that the motion of high-momentum liquid blobs in the near-nozzle region leading to air entrainment and subsequent gas jet development is minimally influenced by sub-grid scale dispersion. The importance of sub-grid scale dispersion inversely correlates with drag force magnitude: the larger the drag force, the less critical the sub-grid scale dispersion. Moving further downstream, quasi-equilibrium between the two phases is established, resulting in relatively small slip velocity and drag force.

Three time integration schemes and four finite volume interpolation schemes for the convection term in momentum equation were tested under turbulent planar gas jet and Sandia non-reacting vaporizing Spray-H cases. The three time integration schemes are the first-order Euler implicit scheme, the second-order backward scheme, and the second-order Crank-Nicolson scheme. The four spatial interpolation schemes are cubic central, linear central, upwind, and vanLeer schemes. Velocity magnitude contour, centerline and radial mean velocity and Reynolds stress profiles for the planar turbulent gas jet case, and fuel vapor contour and liquid and vapor penetrations for the Diesel spray case predicted by the different numerical schemes were compared. The sensitivity of the numerical schemes to mesh resolution was also investigated. The non-viscosity based dynamic structure subgrid model was used. The numerical tool used in this study was OpenFOAM. Results showed that the first-order Euler implicit schemes predict wider range of length scales as seen in velocity and fuel vapor contour plots, while the second-order time integration schemes predict more small scale structures. The non-monotonic central schemes show less grid sensitivity than the monotonic schemes. Overall the cubic central scheme with the Euler implicit scheme gives the best performance. The first-order upwind scheme gave poor results, so it should be avoided to use in simulating high-pressure fuel injection process.

The Kelvin-Helmholtz/Rayleigh-Taylor (KH-RT) wave breakup model is a commonly used model in predicting primary and secondary atomization and breakup processes in Lagrangian-Eulerian Diesel spray simulations. Droplet sizes predicted by this model are dependent on several parameters. The parameters include fuel physical properties, such as density, viscosity, and surface tension, and a number of adjustable model constants, such as KH and RT time constants, KH and RT size constants, and the breakup length constant. The purpose of this study is to investigate the effects of these parameters on predicting spray motions using large-eddy simulation with the dynamic structure sub-grid stress model. The code used in this study is OpenFOAM. This study has three major parts. Firstly, effects of the model constants on the prediction of momentum exchange process were examined by comparing liquid and gas momentum fluxes. Drag Forces exerted on liquid spray by gas phase can be determined from the slopes of gas and liquid momentum fluxes plotted against axial distance. We found that the prediction of momentum exchange between gas and liquid is most sensitive to the KH time constant, B1, among the other model constants. Secondly, effects of fuel physical properties were investigated by using four different fuels in the simulations of non-vaporizing and vaporizing sprays. The four fuels used were n-dodecane, F76 fuel, n-hexadecane, and methyl tetradecanoate. The F76 fuel is a multi-component fuel containing twenty-one hydrocarbons. Global spray quantities such as liquid and vapor penetrations, Sauter mean diameter, total liquid mass, number of parcels, and breakup model quantities such as Ohnesorge number and KH wave speed were compared. The key finding is that not all of these quantities monotonically increase or decrease with fuel molecular weight. Lastly, effects of fuel physical properties on sensitivities of the breakup model constants were studied. We compared liquid penetration and vapor penetration for each fuel using different values of the model constants. We found that the prediction of vapor penetrations is more sensitive to the KH time constant B1 when a fuel with lighter molecular weight was used, and the prediction of liquid penetrations is sensitive to the breakup length constant, Cb, in all of the four fuels. The computational investigations in this study reveal some limitations of the current spray breakup model, and motivate us to develop more advanced models to overcome these limitations.

Large eddy simulation models are tested for use on high speed evaporating liquid sprays. Three models are tested: standard Smagorinsky, a one-equation viscosity based model, and the dynamic structure model. The models are tested using channel flow, planar gas jet, and a diesel spray. The motivation of the work is to evaluate the accuracy and suitability of LES models that can be used for internal combustion engine modeling with direct injection of fuel in which moderate mesh resolution is the norm. Results from the channel flow and the gas jet provide additional insight into model capabilities that impact performance in liquid spray simulations. Simulation results were analyzed using contour images to compare the general structure of the flows, and experimental data for comparison of ensemble averaged mean and rms velocity profiles, liquid and vapor penetration, and mass fraction profiles. Results show that all three models perform similarly in the channel flow with good matches on the mean velocity results and some under prediction of rms values. The dynamic structure model showed slightly steeper near wall rms values closer to the experimental data. In the jet flow, the one-equation model results showed unexpected flow structures in images of the velocity magnitude. Mean velocity profiles matched data well for all three models. But centerline velocity decay rates and rms velocity radial profiles matched data much better for the dynamic structure model results. In the liquid spray the one-equation model performed poorly when compared to experimental data. The Smagorinsky model gave reasonable results and the dynamic structure model gave very good results in these comparisons. The overall conclusion is that the dynamic structure model is the best of the three models for direct injection engine simulations. (C) 2014 Elsevier Ltd. All rights reserved.