## 2 Methodology
### CFD Model Description and Model Validation  
The CFD simulations were carried out by using the OpenFOAM(r) technology CFD software [24] with the Lib-ICE [25] code coupled to perform the combustion system simulation including a complete pack of solvers for internal combustion engine simulations. The model was built reproducing the real geometry of the cylinder, considering an axi-symmetric sector of the combustion chamber defined in function of the number of holes of the injector in order to reduce the computational time required to perform all the simulations. For the simulations of the experimental case, named as a reference case in this work, the sector represents \(1/10\) of the combustion chamber. A dynamic mesh layering technique was used to reproduce the movement of the piston, which is available in in Lib-ICE tools [25,26]. This model uses n-heptane as a fuel diesel surrogate in order to reproduce the experimental data of the engine. The spray characteristics were modeled by using a Lagrangian particle approach that assumes a \"blob\" injection model [27,28]. The liquid atomization, break-up, and evaporation model were modeled by using Kelvin-Helmholtz (KH) and Ryleigh-Taylor (RT) algorithms [29,30]. Also, the rate of injection (ROI) was obtained from an in-house model [31]. This model reproduces the injection profile as a function of the injection pressure, number of nozzle holes and engine speed. The CFD model then groups the liquid droplet into parcels inside the combustion chamber, thus serving as the spray field. Turbulence modelling was performed by the Reynolds-averaged Navier Stokes (RANS) approach with a re-normalized group (RNG _k_-_e_) [32]. The Angelberger model [33] was used to model the engine heat transfer. The detailed chemistry is represented by a \begin{table}
\begin{tabular}{l l} \hline Engine type & DI Diesel engine \\ Compression ratio [-] & 16:1 \\ Number of cylinders [-] & 4 \\ Bore/stroke [mm] & 85/96 \\ Volume [L] & 22 \\ Injector number of orifices & 10 \\ Spray angle [deg] & 154 \\ \hline \end{tabular}
\end{table} 
Table 1: Engine specifications. reduced chemical kinetic mechanism implemented by N-heptane that contains 162 species and 1543 reactions. To perform the simulation of the combustion phenomenon, a representative interactive flamelet (RIF) model was implemented. The RIF model considers the flame structure as an unsteady laminar diffusion flame, and assumes that the length and turbulent scales are much larger than the chemical ones. Its evolution is calculated in the mixture fraction region where energy and species equations are solved and the effects of mixing are covered in the scalar dissipation rate [26]. The models and sub-models used in this study are listed in Table 2.  
The values for the boundary conditions were gathered from the experimental data through an in-house methodology developed by [PERSON] et al. in [34] and are presented in Table 3. The boundary conditions at the edges of the segments were calculated by using a similar approach than the other walls of the combustion chamber. Specifically, at this region the temperature was the same than the wall temperature and the species concentration is the same as inside the combustion chamber. An initial simulation using a well-refined mesh was performed by searching for a good agreement between experimental and simulation results with high accuracy in terms of in-cylinder pressure and heat-release rate. This well-refined mesh, named fine mesh, is presented in Figure 1 where the (a) and (b) images represent the fine mesh in the side and top view, respectively, and counts with 52,000 cells at top dead center (TDC). In addition, with the fine mesh already defined, a different mesh configuration was tested. A coarse mesh, which is a simplified version of the fine mesh, was used to evaluate a reduction in computational time while maintaining the same accuracy for the results. This coarse mesh counts with 26,900 cells at TDC are also shown in Figure 1, where images (c) and (d) shows the side and top view.