## 3 Results and Discussion
### Optimization Process Results
The geometrical parameters 4 and 5 are responsible for adjusting the curvature between the points GP2 and GP3 (shown in Figure 4) and the alignment between GP1 and GP2, respectively. The GP4 has values in the middle of the parameter range in order to obtain a smoother bowl shape with a lower objective function. Then, the GP5 was conducted to the maximum value of the range, again avoiding the re-entrant shape. The last parameter, the GP6, is capable of updating the bowl centre depth. The results for this parameter converge close to the maximum value possible. Figure 8: Evolution of constraints and objectives outputs toward the optimized value. Figure 10 summarizes the distribution of the objective function in the domain of each parameter related to the injection system and the swirl number. Analogous to previous figures, the blue dots represent each simulated case, and the red dot is the best configuration found for the oxy-fuel concept. The top-left graph shows that the most suitable number of oriifics is the minimum in the studied range, leading to a big orifice diameter. This preference for fewer oriifics is related to the reduction of the CO emissions, in agreement with the results of [PERSON] et al. in [41]. Furthermore, the PSO-NS algorithm explores all the possible ranges for the spray angle value. The best case is located in the spray angle value that matches the piston geometry [42]. Regarding the injection settings, the best case moves to the maximum level in the explored range, which is related to the fact that higher injection pressure improves the atomization and evaporation of the fuel, enhancing the mixture and the ability to react with the oxygen present in the combustion chamber [43]. Moreover, the SOI distribution during the optimization evidences that when the injection is advanced, the combustion performance deteriorated, because it promotes a longer ignition delay with a higher gap between fuel injection and the start of combustion. Thus, the heat release rate had a large peak in the premixed combustion phase, and a maximum in-cylinder pressure value beyond the constraint of the optimization process [44]. On the other hand, when the SOI moves toward the top dead center, the ignition delay is reduced, with a smoother start of combustion. Lastly, the reduction of the swirl number is related to the increment of the bowl diameter that will reduce the gas velocity in the bowl, and at the same time, could reduce heat transfer and other energy losses [45]. Figure 9: Objective function value for the geometrical parameters. The plots in Figure 11 corroborate the fact that the best case (the red dot with the minimum objective function), is obtained for the lowest soot level and the maximum efficiency, which were the objectives of the optimization process. Also, the constraints are respected, with a high reduction of CO emissions, associated with the maximum efficiency trend. Figure 11: Objective function value evolution for the constraints and objective parameters. Figure 10: Objective function value for inputs of the injection system and swirl number. The Pareto fronts can be seen in the left side of Figure 12 where the initial diesel reference case is the black dot and the optimum case is represented with the red dot. In both plots, the vertical dashed line represents the efficiency of the baseline case, and the horizontal dashed lines indicate the respective levels for the constraints. In both graphs, several cases meet the constraints (are below the horizontal dashed lines), and provide a better efficiency than the oxy-fuel baseline case. Because the objective function is composed by four parameters with different coefficients that define the optimization priorities, the best solution is the combination between the constraints and the objectives with a best trade-off between all these outputs simultaneously. The plots on the right side of Figure 12 illustrate how the optimum case tries to reach the lowest HC level maximizing the efficiency.