Understanding of Diesel Engine Combustion Process via Mathematical Modeling: Part 2 — Results
Authors: Danov Stanislav N. , Gupta Ashwani K. 
Published: February 2021

Abstract
In the companion Part 1 of this two part series paper a mathematical model of combustion process in a diesel engine was presented having both premixed and diffusion flame. The combustion of fuel vaporized during the self-ignition delay period is modeled according to the conditions of premixed flame. A kinetic differential equation has been created for modeling this kind of combustion. The combustion of fuel during the injection process is modeled according to the theory of diffusion flames. This process is strongly influenced by processes of fuel injection, vaporization and diffusion. The atomization process is taken into account by means of the Sauter mean diameter (SMD) of fuel droplets. The instantaneous vaporization rate is defined by the current value of temperature, pressure, concentration of fuel vapors and the mean fuel droplet size in terms of the SMD. The mathematical model includes differential equations describing the processes of fuel injection, vaporization, heat transfer and combustion in both premixed and diffusion flame that occurs in the engine cylinder. The above equations are solved together with the differential equation of the first law of thermodynamics expressing the energy conversion process in the cylinder of diesel engine. The fourth-order Runge-Kutta method is applied for obtaining numerical solution of the system of differential equations. The model is calibrated and validated for two different turbocharged diesel engines — 8DKRN 74/160 and Sulzer-6RLB-66. The analysis is performed on a PC using FORTRAN 90. The comparison between the experimental data and numerical results shows very good agreement.
Numerical experiments have been carried out for examining the combustion behavior in the cylinder of a marine DI diesel engine Sulzer 6RLB-66 having a cylinder diameter of 0.66 m bore and stroke of 1.4 m. The influence of the quality of fuel atomization process, estimated via the SMD, on the fuel vaporization rate and overall combustion rate has been evaluated. This influence is quantified and the results show very strong influence of SMD on the vaporization and combustion process, both with respect to the maximum rates and the duration of the processes. In addition numerical experiments have been carried out for determining the effect of duration of fuel injection and the beginning of fuel injection (degrees of crank angle rotation before TDC) on subsequent combustion parameters and integral indicator parameters of the engine. These results show that ratio: “amount of fuel burnt under the premixed flame conditions / amount of fuel burnt under diffusion flame conditions” for one cycle varies significantly with the change in fuel injection duration. The model provides both the instantaneous values of engine parameters in the cylinder (i.e., temperature, pressure, current air-gas mixture composition, heat transfer rate, thermo-physical properties of the air-gas mixture, etc.) and integral indicator engine parameters (mean indicated pressure, specific fuel consumption, efficiency, etc.). A comparison between experimental and modeling data show gratifying results.