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A fractal engine simulation (FES) sub-model was integrated into three-dimensional simulations for modeling turbulent combustion for a gasoline direct injection (GDI) engine. The FES model assumes that the effects of turbulence on flame propagation are to wrinkle and stretch the flame, and fractal geometry is used to predict the surface area increase and thus the turbulent burning velocity. Different formulas for the four sequential stages of combustion in SI engines are proposed to account for the changing effects of turbulence throughout the combustion process. However, most prior studies related to the FES model were quasi-dimensional simulations, with few found in multi-dimensional studies, and none under cold start conditions or stratified charges. This paper describes how the model was implemented into multidimensional simulations in CONVERGE CFD, and what the formulas are in the four sequential stages of combustion in SI engines. The capabilities of the FES model for simulating the cold start cases, under the conditions of the dramatically changing engine speed and mixture stratification in a complex engine geometry, are presented in this study. The FES model was able to not only simulate the steady-state cases with constant engine speed, but also predict the in-cylinder pressure traces in all four cylinders for the very first firing cycle with transient engine speed, and gave good agreement with the experimental measurements under these extremely transient conditions. The uncertain maximum fractal dimension was chosen as 2.37 in this research, and a simple linear correlation with engine speed was used to obtain the coefficient used in calculating the kernel formation time which controls the so-called combustion or ignition delay. 

A multi-dimensional model of the spark ignition process for SI engines was developed as a user defined function (UDF) integrated into the commercial engine simulation software CONVERGE CFD. The model simulates spark plasma movement in an inert flow environment without combustion. The UT model results were compared with experiments for arc movement in a crossflow and also compared with calorimeter measurements of thermal energy deposition under quiescent conditions. The arc motion simulation is based on a mean-free-path physical model to predict the arc movement given the contours of the crossflow velocity through the gap and the interaction of the spatially resolved electric field with the electrons making up the arc. A further development is the inclusion of a model for the thermal energy deposition of the arc as it is stretched by the interaction of the flow and the electric field. A novel feature of this model is that the thermal energy delivered to the gap at the start of the simulation is distributed uniformly along the arc rather than at discrete points along the arc, as is the case with the default CONVERGE CFD ignition models. This feature was found to greatly reduce the tendency of the arc to distort its shape and tangle itself in a non-physical way, as is the tendency when discrete energy input is used. It was found that the tangled distortion of the arc when using discrete energy input was due to perturbations along the arc caused by differential expansion of the gas along groups of adjacent mesh cells that either had energy input or did not. The distributed energy feature also gave arc temperature distributions that were more spatially uniform and had steeper temperature gradients, consistent with experimental arc images. The results are compared with experimental high-speed video images of arc movement for a spark plug of similar geometry and taken over a range of pressures and crossflow velocities in a high-pressure constant volume vessel. There is good agreement between the simulations and experimental images for the arc stretch distance in response to a crossflow. The simulations did not display as much lateral arc dispersion as seen in the experimental results, however, that were perhaps associated with flow recirculation zones downstream of the gap, present in the experiments. The influence of the electric field was shown by turning off the electric field effect in the simulations such that the arc movement was influenced by the flow field alone. The effect of the electric field was found to be more pronounced at lower crossflow velocities of 5 m/s and at lower pressures. 

A parametric study was carried out for the first firing cycle of a 4-cylinder, 2.0-liter, turbocharged gasoline direct injection (GDI) engine. The primary goal was to see how changes in the fuel injection parameters would affect the GDI engine combustion and emissions for the first four combustion events that constitute the first firing cycle. Experimental studies were carried out with a custom-designed powertrain control system to measure the HC emissions and pressure development for the first firing cycle. The quantitative experimental results were accompanied by simulations of the detailed temporal and spatial fuel concentration profiles using Converge CFD engine simulation software. An alternative calculation method was used to calculate the average combustion equivalence ratio for each of the four cylinders. This method showed that the majority of the cold start HC emissions during the first firing cycle was unburned gasoline and its possible decomposition products, which did not contribute significantly to the combustion and heat release. For the same amount of fuel injected into a cylinder, increased fuel rail pressure resulted in better evaporation and combustion, while slightly increasing the HC emissions during the cold start process. A multiple injection strategy was studied that split the fuel delivery between the intake stroke and the compression stroke with either one or two injections in each of those strokes (two or four injections total). The quadruple injection strategy led to better first cycle combustion, with higher engine IMEP and lower HC emissions. This resulted from a richer fuel mixture in the region near the spark plug due to better fuel evaporation and a better spatial fuel distribution. While increasing fuel rail pressure with either injection strategy failed to significantly lower the HC emissions given the same amount of injected fuel mass, higher rail pressure with the quadruple injection strategy resulted in higher IMEP for the same amount of injected fuel; this may provide the possibility to reduce the total fuel injection mass which may have benefits for both fuel consumption and emissions.