## 3 Model Validation
### Rail Pressure Effects  
To ensure that the effects of rail pressure changes are captured by the model when predicting the spray's behavior between the start of the injection (lamping up) and the end of the injection (lamping down), the experimental conditions from previous ECN work under operating conditions No. 2, 3, and 4 (as described in Table 2) are studied in this section. Figures 7 and 8 show a comparison of the spray shape and equivalence ratio between the simulation results and the experimental data of the rail pressure under 100 MPa and 50 MPa conditions, respectively. The gray background images show the experimental data obtained from high-speed videos using the Schlieren video technique. The white background images show the simulation results. The gradient color region represents the equivalence ratio data, with values shown on the gradient color bar in the right corner. Figure 5: Comparison of the initial spray penetration (0.0–0.3 ms) of the experimental result [23] and the simulation result under different ambient temperatures. (**a**) Maximum vapor penetration, (**b**) liquid spray penetration and (**c**) injection mass flow rate. The black particles are the liquid fuel data from the simulation, which the cut-plane from the direction of the spray then rotates 90\({}^{\circ}\) to the left (which is similar to the display in case No. 2, as mentioned in the previous section (Figure 3)). From these comparisons, the results of the simulation show a better prediction under high rail pressure conditions (150 MPa and 100 MPa) than under a low rail pressure condition (50 MPa). The results of the spray penetration and spray distribution angle (Figures 9 and 10) shown in the red, blue, and yellow colors indicate the results for rail pressures of 150, 100, and 50 MPa, respectively. The dots and solid lines represent the experimental and simulation results, respectively. The results of vapor penetration are shown in the top graphs of Figures 9 and 10, while the middle and bottom graphs show the liquid penetration and injection rates, respectively. Figure 6: Comparison of the spray distribution angle for different ambient temperatures. (**a**) Spray angle and (**b**) spray cone angle. Figure 7: Comparison of the spray shapes and the equivalence ratio histories of the experimental result [23] and the simulation result under a rail pressure of 100 MPa. Figure 8: Comparison of the spray shapes and equivalence ratio histories of the experimental results [23] and simulation results for a rail pressure of 50 MPa. Figure 9: Comparison of the spray penetration of the experiment results [23] and the simulation results for different rail pressures. (**a**) Maximum vapor penetration, (**b**) liquid spray penetration and (**c**) injection mass flow rate. Figure 9 shows that the model predictions for the penetration length under high rail pressure conditions are longer than those under low rail pressure conditions, which is consistent with the experimental data. Figure 10 shows the initial spray penetration (0.0-0.3 ms); even under the rail pressure conditions in all three cases, these data cannot properly capture the initial ramp for both vapor and liquid penetration. The simulation results show a trend that is consistent with the experimental data. The spray model and other sub-parameters make this model more effective in its predictions, which is consistent with experimental data. The rail pressure directly affected the air fluctuation in the injected fuel due to the impulse exchange between the gas and the liquid. The spraying behavior under high rail pressure caused the cavitation flow to efficiently accelerate at the nozzle exit. The high rail pressure cavity also increased the spray distribution angle [22]. Figure 11 shows a comparison of the spray angles (left graph) and the spray cone angles (right graph) for different rail pressures, in which the spray distribution angle is measured by the same technique described in the previous section.