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Development of G-Equation Combustion Model for Direct Injection SI Engine Simulations

An improved spark ignition model has been developed and implemented into the KIVA-3V code. In this model, the spark ignition kernel growth is tracked by Lagrangian particle markers. The effects of turbulent flow and spark discharge energy on the kernel growth are considered. After the ignition kernel size exceeds a critical size related to the integral turbulent length scale of the flow, the turbulent flame is considered to be fully developed. A G-equation model is used to track the mean turbulent flame evolution. By ignoring the detailed turbulent flame brush structure, fine numerical resolution is not required, thus making the model suitable for use in multidimensional simulations of SI engines. Combined with a characteristic time scale combustion model, the models were used to simulate the ignition and combustion processes of a small marine DISI two-stroke engine that features two-spark plugs, where the triple flame structure must be considered. The evolution of the two spark kernels and turbulent flames starting from the two spark plugs are modeled. Good agreements with measured cylinder pressure was also obtained Introduction The combustion in spark ignition engines is initiated by an electric discharge from the spark plug. The ignition process can be described by three successive phases  breakdown, arc and glow discharge [Heywood, 1988]. The breakdown phase always precedes the arc and glow discharge. During this phase, an electrically conductive column is created between the spark plug electrodes, where the temperature and pressure is high. Then a shock wave is created that propagates away from the plug. The duration of the initial breakdown phase is very short (~10ns) with high-energy transfer efficiency between the electrical energy supplied and the plasma (about 94%). During the early stage (0 to 5μs after the breakdown) of the ignition process, the plasma kernel expands violently and the mass and energy transfer processes are much dominated by the pressure wave and the chemical reaction contributes little to the kernel growth. Subsequently, the contribution of chemical reaction becomes significant [Kravchik et al., 1995]. Although the ignition process is important, it is not practical to resolve the process in detail in engine CFD simulations, because the typical grid-size and time step used is larger than that needed to describe this early stage of ignition precisely. Thus, a relatively simple sub-grid scale model is needed to predict the ignition process in 3-D engine calculations. The combustion in DISI engines can take place in premixed mixture conditions (early injection operating mode) or in partially premixed (stratified) mixture conditions (late injection operating mode). In the late injection mode, by controlling the spray and air-fuel mixing process, a stratified mixture can be obtained with a desirable mixture located near the spark plug. At this operating condition, the equivalence ratio of the stratified air-mixture ranges from rich to lean. The flame propagates with a higher speed along a surface of stoichiometric mixture and with lower speeds on the lean and rich sides. When the unburned intermediate species such as H2, H, CO diffuse from the rich premixed branch and meet and mix with the O and O2 surviving from the lean mixture branch, a diffusion flame is developed. Thus, a structure called a “triple flame” is formed, as schematically shown in Fig. 1. In the present study, this premixed combustion is modeled using the G-equation model, which is a kind of flamelet combustion model, and the diffusion combustion behind, controlled by turbulence mixing, is modeled by a characteristic time scale combustion model. The spray breakup is simulated by LISA [Linearized Instability Sheet Atomization] model [Schmidt et al, 1999]. The ignition and combustion models are implemented into the KIVA-3V code, which is used in this study. Lean premixed flame branch Rich premixed flame branch Diffusion flame O,O2,CO2,H2O,etc CO,H,OH,etc Diffusion flame Droplet Stoichiometric premixed flame Figure 1 Structure of a triple flame in DISI engines Ignition Model Development In the present work, the ignition model used the same approach as that used in the DPIK model of Fan et al. [1999]. The kernel surface position is marked by the particles, and the flame surface density is obtained from the number density of particles in each computational cell, as shown in Fig. 2. The ignition kernel is assumed to be spherical during the initial ignition process. When the kernel grows, the particles move outwards radially from the spark plug electrodes. The ignition particle’s speed, i.e., the kernel growth rate, is influenced by the flow turbulence and air-