## 3 Simulation Details  
The assessment of the injection rate shape effects on performance and emissions was made by simulation using the AVL BOOST software including the AVL MCC combustion model (mixing controlled combustion). This model evaluates the rate of heat release in direct injection compression ignition (DICI) engines [25]. The NOx formation is based on the extended Zeldovich mechanism coupled with three additional reactions for N2O formation. The Soot estimation is performed by a mechanism consisting of two reactions of formation and oxidation which are based on chemical kinetics. The AVL MCC model requires the introduction of specific values for some physical properties and several normalised model parameters. Figure 2 shows the symbolic model of the engine and the AVL MCC normalized parameters. The model calibration was performed for the Top-Hat (TH) shape of the rate of injection (ROI). Table 4 shows the values adopted and introduced in the AVL MCC combustion model for the normalized parameters and the physical data corresponding to both fuels and engine operating conditions. An initial stage of the simulation study consisted in the model calibration. This was done based on the comparison made between the experimental and simulated in-cylinder pressure traces and the values of engine parameters expressing performance (brake power-BP), efficiency (brake-specific fuel consumption (BSFC)) and emissions (nitrogen oxides-NO\({}_{\text{x}}\) and Soot). The relative deviations for all parameters considered relevant to the model calibration remained below 3% for both tested fuels and engine operating conditions, as shown in Table 5.  
Figure 2: Symbolic model of the diesel engine under test. The experimental pressure traces and the numerically determined temperature and pressure curves are revealed in Figure 3. It shows a normal variation of cylinder charge temperature by crankshaft position with the maximum values reached after TDC for both engine operating conditions and tested fuels. It can be noticed that the peak in-cylinder temperature has higher values for diesel fuel than for biodiesel B20, regardless of the engine operating condition. A next stage of the simulation work consisted in modifying the shape of the original injection rate (Top-Hat) by keeping the same area, initiation event (start of injection-SOI) and duration up to the end of the injection (EOI). The following acronyms of the ROI shapes are applied: Top-Hat (TH); Isosceles Trapezoid (IT); Right Trapezoid (RT); Triangle 1 (TR1); Triangle 2 (TR2); Triangle 3 (TR3); Boot 1 (BO1); Boot 2 (BO2). The ROI variations relative to the crankshaft angular position are illustrated in Figure 4. The start of injection and the end of injection (SOI/EOI) were considered as \(-5\,^{\circ}\)CA/11\(\,{}^{\circ}\)CA for R1 (full load, 1400 rpm) and, respectively, \(-5.5\,^{\circ}\)CA/13\(\,{}^{\circ}\)CA for R2 (full load, 2400 rpm). Both events were related to the top dead center end of compression (TDC). \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Operating Point** & **R1 (Full Load, 1400 rpm)** & **R2 (Full Load, 2400 rpm)** \\ \hline  & **Fuel** & **D100** & **B20** & **D100** & **B20** \\ \hline  & Ignition Delay Calibration Factor [-] & 0.68 & 0.62 & 0.5 & 0.49 \\  & Combustion Parameter [-] & 0.76 & 0.685 & 0.74 & 1.17 \\ Normalised Model & Turbulence Parameter [-] & 1 & 1 & 2 & 1 \\ Parameters & Dissipation Parameter [-] & 1 & 1 & 0.0001 & 1 \\  & Premixed Combustion Parameter [-] & 0.65 & 0.65 & 0.9 & 0.7 \\ \hline  & Number of Injector Holes [-] & & 5 & \\ Physical & Hole Diameter [mm] & & 0.24 & \\ Data & Discharge Coefficient [-] & & 0.5 & \\  & Rail Pressure [bar] & & 350 & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The values adopted for the normalized parameters and physical properties of the AVL MCC.