## 4 Effect of the Injection Rate Shape
### Microscopic Spray Characteristics  
In spraying simulations, the turbulent distribution has a significant impact on the spray parameters. The spray penetration distance depends on the surrounding conditions, including the injection rate, the injection time, the injected mass quantity, and others. The injection rate design affects the spray penetration and spray distribution angle. This section presents the spray penetration distance consisting of liquid and vapor penetration both during the injection time (0-1.54 ms) and after the EOI, by comparing the results of different injection rate shapes and using these shapes to analyze their effects on the microscopic spray characteristics. Figure 14 shows the simulation results of the spray penetrations. The black, red, blue, and yellow lines represent the simulation results for the RECT, QIGD, GIGD, and GIGD injection rates, respectively. The results of vapor penetration are shown in the top graph, while the middle and bottom graphs show the liquid penetration and injection mass flow rates, respectively. Figure 14 (top graph) shows the vapor penetration for the four injection rates with different shapes. The QIGD injection rates show the longest vapor penetration (approximately 25 mm), with an injection rate of around 4.5 mg/ms. Vapor penetration lengths with the same peak injection rates will ultimately lead to the same vapor penetrations. This occurs because, during injection, vapor penetration increases with the injection acceleration rate. After the EOI, the vapor penetration distance increases along with the injection rate at the EOI, when the spray penetration distance is affected by the momentum flux ratio. For the GIGD injection rate shape after the EOI, the vapor penetration continues to increase continuously, and a high injection rate results in rapid fuel movement, while the vapor penetration of the QIGD injection rate shape decreases continuously because of the injection rate at the EOI. Figure 14 (middle graph) shows the liquid spray penetration, for which the different injection rates also have a significant impact on liquid penetration. The QIGD injection rate provides the longest initial liquid penetration due to having the highest injection rate, while the GIGD injection rate shows the opposite. Liquid spray penetration increases relative to the injection rate shape and terminates at the end of injection. The liquid spray penetration results show the same trend as the injection rate for all cases. Since the greatest penetration distance is primarily affected by the momentum flux ratio, the liquid penetration distance  
Figure 13: Comparison spray cone angle for different rail pressures. will increase when the injection rate increases and decrease when the injection rate decreases. This is due to slowdown in the movement of the liquid fuel. In addition, because the spray penetration is a phenomenon that occurs in conjunction with the spray distribution, the spray distribution angle is an important parameter that affects the spray mixing process and is important for the analysis of spray performance. Therefore, the spray distribution angle was investigated by measuring the distribution angle via the spray shape obtained from the simulation. Figure 15 shows the spray distribution angles from the simulation results, where the black, red, blue, and yellow dots represent the measurement results of the RECT, QIGD, GIGD, and GIQD injection rates, respectively. As shown in the Figure 14, comparisons were made between the spray angle (left graph) and spray cone angle (right graph) under different injection rate shapes. Similar techniques to those in the previous section were used to measure the spray distribution angles. Figure 14: Comparison of the simulated spray penetration with different injection rate shapes. (**a**) Maximum vapor penetration, (**b**) liquid spray penetration and (**c**) injection mass flow rate.