Development of a fractal engine simulation model in a multidimensional simulation for the cold start process of a gasoline direct injection engine

Abstract

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.