## 2 Numerical Models
### 3D Engine Combustion Model  
In order to get an accurate assessment of the changes in emission levels with CDA operation, a three-dimensional CFD model for the combustion chamber of the diesel engine D-49 was constructed in software FIRE ESE DIESEL, allowing to perform model settings, injection, and combustion analysis in diesel engines reliably and accurately [52]. In the diesel engine D-49, the injector with ten nozzles is placed centrally over the top of the piston. Given the symmetrical location of the injector at the combustion chamber, the 36\({}^{\circ}\) sector is selected as a computational domain (Figure 3). The total number of cells is 144,436 at TDC (top dead center). The calculation time step is 0.2 \({}^{\circ}\)CA. The calculation starts from 541 \({}^{\circ}\)CA (the beginning of compression) and ends at 841 \({}^{\circ}\)CA (the end of combustion). The boundary conditions and initial conditions are taken from the calculated results in GT-SUITE. The development of fuel spray was modeled with a Wave breakup model based on the instability of the surface wave [53]. In this model, breakup size-constant C1 decides the size of fuel droplets after crushing, and breakup time-constant C2 influences the characteristic breakup time, whose range is 5.0-60 in view of the different nozzle. The Dukowicz model [54] was used to calculate the evaporation of fuel droplets by applying semi-empirical functions for the heat transfer combined with a heat-mass transfer analogy. In this model, heat transfer-constant E1 is multiplied by the heat transfer coefficient calculated by the Ranz and Marshall correlation [55]. The k-\(\xi\)-f model was employed for turbulence modeling [56]. The extended coherent flame model-3 zone (ECFM-3Z) [57]  
Figure 2: Mechanical model of piston-connecting rod group.  
was chosen to calculate the combustion process. ECFM-3\(Z\) is a combustion model based on a flame surface density transport equation for the premixed combustion and a mixing model that can describe inhomogeneous turbulent diffusion combustion. Mixing model parameters influences the transfer of fuel from the pure fuel zone to the mixed zone. Auto ignition time is calculated by Two-Stag model, in which the Auto-ignition delay time for cool flame ignition and the main ignition is interpolated from tabulated values, which was created based on a n-heptane mechanism with 159 species and 770 reactions [58]. The Extended Zeldovich model is used to predict NOx emission and calculate the formation of nitrogen, oxygen, and hydrocarbon radicals, and this mechanism is solved in a sequential method for computational effectiveness. The kinetic model [59] was used to describe soot formation and oxidation. The model parameters have been tuned to ensure good consistency between the calculated results and experimental data.  
In this work, the 1D simulation results (initial air pressure and temperature in cylinder, chamber wall temperature, etc.) and the injection profile are substituted into the 3D CFD model as boundary conditions to calculate the combustion heat release rate and cylinder pressure curve, which are used to validate 1D combustion modeling in turn. The parameters of engine performance are obtained from the 1D simulation, and the emission characteristics are converted according to the 3D calculation results.