## 4 Results and Discussion  
Simulations were performed for all ROI shapes considered, using both fuels for both engine test conditions. The relative deviations presented in the comments of Figures 5-14 were calculated relative to the Top-Hat shape of ROI as reference. Figure 5 illustrates the values of the ignition delay dependent on the ROI shape. The ignition delay in a diesel engine represents the duration between the start of injection and the start of combustion (SOC). In this study, the SOC was defined by the zero value of the rate of heat release. As seen in the following figure, the ignition delay is slightly influenced by the ROI shape and confirms the results from [11]. As it depends on the physical parameters, namely the cylinder charge pressure and temperature during the injection timing, respectively on the chemical parameters, such as fuel chemical composition and structure, fuel cetane number, it can be noticed a very small variation of this parameter relative to the ROI shape. Because the percentage of biodiesel in the B20 composition is low and its cetane number is approximately the same as diesel fuel, the differences for ignition delay between these two fuels are small. Concerning the ignition delay in [18; 21], where the considered shapes of injection rates are somehow different relative to those from this study, not equivalent results have been obtained for diesel fuel, kerosene, and kerosene-diesel blends. In Figure 6 are shown the evolutions of the initial combustion phase relative to the ROI shape. The initial combustion stage is characterized by the combustion of the premixed charge, being considered as the period between the start of combustion and the event when 10% of the mass fraction is burned (MFB10%). This period is strongly influenced by the amount of fuel injected, accumulated, vaporized, and mixed with air during the ignition delay. For the R1 engine test condition, the minimum values are obtained using the BO1 shape with a reduction of 14.6% for diesel fuel and 13.9% for B20 relative to the considered reference shape (TH). For the R2 test condition, the minimum values are obtained when using the same BO1 shape with a reduction of 9.3% for diesel fuel and, respectively, 11.9% for B20. The maximum values on the R1 test condition are obtained using the BO2 shape with an increase of 20.9% for diesel fuel and 23.1% for B20, while on the R2 these are obtained using the TR3 shape with an increase of 36.4% for diesel fuel and 23.3% for B20. This finding could be explained by the lesser fuel quantity injected during the ignition delay. The values of the initial combustion stage are comparable, having approximately similar variations for both fuels. Figure 5: Ignition delay variation by different shapes of ROI. Figure 7 shows the values of total combustion duration versus the ROI shape. The combustion duration is considered as the interval between the start of combustion and the instant when 95% of the mass fraction is burned. The minimum values are obtained for the TR1 shape with a reduction of 34.8% for diesel fuel at both engine test conditions (R1 and R2) and 36% for B20 at R1, respectively, 34.3% at R2. It can thus be pointed out that triangular shapes ensure the fastest combustion by promoting the premixed phase, which clearly explains the occurrence of the highest peak in-cylinder temperatures among the studied ROI shapes (Figure 8). For both fuels, the maximum combustion duration is reached when using the TH shape. A constant fuel injection speed leads to a longer combustion duration because the fuel is evenly distributed throughout the whole injection process compared to a fast injection when a high amount of fuel concentrates over a certain part of the injection process, which causes a short combustion duration. In such conditions, the combustion process is shifted towards a slower mixing-controlled combustion phase. When using B20 instead of diesel, the fuel mass flow increases by 4.1% for R1 and only by 1.5% for R2.