## 3 Model Validation
### Ambient Temperature Effects  
In this section, the low and high ambient temperature conditions are used for model calibration. To demonstrate the predictive efficiency of the model, the spray behavior under different ambient temperatures, as well as at different ambient pressures (case No. 1 and 2 in Table 2) is used as a case study. A comparison of the fuel spray injection in the cylinder at different ambient temperatures and ambient pressures shows the influence of evaporation and spray fuel diffusion. Figures 2 and 3 present a comparison of the spray shape and equivalence ratio between the experimental and simulation results for cases No. 1 and 2. The gray background images show the experimental data obtained from high-speed videos using the Schlieren video technique to represent the vapor and liquid for case No. 1. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Case No.**} & **Ambient** & **Ambient** & **Ambient** & **Fuel** & **Injection** & **Injection** & **Rail** \\  & **Composition** & **Temperature** & **Pressure** & **Temperature** & **Duration** & **Mass** & **Pressure** \\  & & **[K]** & **[MPa]** & **[K]** & **[ms]** & **[mg]** & **[MPa]** \\ \hline
1 & N\({}_{2}\) = 100.0 & 440 & 2.93 & 363 & 1.54 & 3.46 & 150 \\ \hline \multirow{4}{*}{2} & O\({}_{2}\) = 0.00; & & & & & & \\  & N\({}_{2}\) = 89.71; & 900 & 6.05 & 373 & 1.54 & 3.46 & 150 \\  & C\({}_{2}\) = 3.77 & & & & & & \\ \hline \multirow{4}{*}{3} & O\({}_{2}\) = 0.00; & & & & & & \\  & N\({}_{2}\) = 89.71; & 900 & 6.07 & 373 & 5.2 & 9.30 & 100 \\  & C\({}_{2}\) = 6.52; & & & & & & \\  & H\({}_{2}\)O = 3.77 & & & & & & \\ \hline \multirow{4}{*}{4} & O\({}_{2}\) = 0.00; & & & & & & \\  & N\({}_{2}\) = 89.71; & 900 & 6.07 & 373 & 5.65 & 6.90 & 50 \\ \cline{1-1}  & CO\({}_{2}\) = 6.52; & & & & & & \\ \cline{1-1}  & H\({}_{2}\)O = 3.77 & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The Operating Conditions of the Test Cases. For case No. 2, the experimental data image obtained from the high-speed video using the Schlieren video technique shows vapor and liquid regions, which are stored as MATLAB binary files. The white background images show the simulation result, in which the gradient color region represents the equivalence ratio data. The value of the equivalence ratio is represented by the gradient color bar in the right corner. The black particles are liquid fuel data from the simulation, which the cut-plane from the direction of the spray then rotates 90\({}^{\circ}\) to the left. Figures 2 and 3 illustrate the shape of the variance by using Re-Normalization Group Theory to determine the small movement effects, while the KH-ACT model calculation captures the impact of cavitation and turbulence on the primary cracks in addition to aerodynamic separation. The calculation results show a smoother distribution for the spray shape boundary simulation than for the experimental data due to the turbulence model's limitations in conjunction with the RNG k-\(\epsilon\) turbulence model, where the RNG k-\(\epsilon\) turbulence model is used for determining the smaller movements effects. Nonetheless, the simulation results are satisfactory, as these results indicate the effective grid resolution for this simulation. Each comparison image shows the exact thickness of the fuel mass distributed throughout and is consistent with the experimental data. The method of image analysis obtained from this model is sufficient for the study of spray behavior. The comparison results (Figure 4 and Figure 6) show the spray penetration and spray distribution angle. Black and red represent the results under ambient temperatures of 440 and 900 K, respectively, while dots and solid lines represent the experimental and simulation results, respectively. The results of vapor penetration are shown in the top graphs of Figures 4 and 5, while the middle and bottom graphs show the liquid penetration and injection rates, respectively.