## 4 Mesh Independence and Validation of the CFD Simulation
### Validation  
To ensure the validity of the CFD simulations, a comparison with experimental data was conducted. The experimental results used for this comparison were those of [PERSON] [9]. The data selected were only those when the ejector was operating in the critical mode. This was done because the current work focuses on an ejector operating at this mode. Comparing with the experimental data, it was found that the \(\dot{m}_{s}\) from CFD results using the transition SST turbulence model agree better than those using the k-omega SST model. This finding confirms the results of [PERSON] et al. [27]. The comparison can be seen in Table 3. It should be noted that [PERSON] [9] has found experimentally that \(P_{0}=308\) kPa is the minimum pressure at which the secondary flow started to choke. Therefore, at this pressure or above, the ejector operates in critical mode. [PERSON] [9] mentioned that the uncertainty of the measured mass flow rates was no greater than 4%. Hence, almost all of the CFD results using the transition SST model are within the experimental uncertainty while it is the opposite for those using the k-omega SST (Table 3). Regarding the \(\dot{m}_{p}\), the results of CFD using the transition SST model are comparable to those using the k-omega SST. The difference between the CFD results and the experimental data is less than 6% for all operating conditions and the average is only around 4.2% (Table 4). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & \multicolumn{2}{c}{**Primary Mass Flow Rate, \(\dot{m}_{p}\) [kg/s]**} & \multicolumn{2}{c}{\(\Delta\dot{m}_{p, CFD}\) **1 [\%]**} \\ \cline{3-7}
**Sim. No.** & \(P_{0}\) [kPa] & \multirow{2}{*}{**Exp.**} & **Transition** & **k-Omega** & **Transition** & **k-Omega** \\  & & & **SST** & **SST** & **SST** & **SST** \\ \hline
0 & 618 & 0.06713 & 0.07108 & 0.07104 & 5.88 & 5.82 \\
1 & 584 & 0.06464 & 0.06717 & 0.06713 & 3.91 & 3.85 \\
2 & 549 & 0.06087 & 0.06314 & 0.06310 & 3.73 & 3.66 \\
3 & 515 & 0.05716 & 0.05923 & 0.05919 & 3.62 & 3.55 \\
4 & 480 & 0.05325 & 0.05520 & 0.05516 & 3.66 & 3.59 \\
5 & 446 & 0.04931 & 0.05129 & 0.05125 & 4.02 & 3.93 \\
6 & 412 & 0.04543 & 0.04738 & 0.04733 & 4.29 & 4.18 \\
7 & 377 & 0.04150 & 0.04335 & 0.04331 & 4.46 & 4.36 \\
8 & 343 & 0.03768 & 0.03943 & 0.03940 & 4.64 & 4.56 \\
9 & 308 & 0.03397 & 0.03540 & 0.03537 & 4.21 & 4.12 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of the primary mass flow rates obtained from CFD and experiments. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & \multicolumn{2}{c}{**Secondary Mass Flow Rate, \(\dot{m}_{s}\) [kg/s]**} & \multicolumn{2}{c}{\(\Delta\dot{m}_{s, CFD}\) **1 [\%]**} \\ \cline{3-7}
**Sim. no. ** & \(P_{0}\) [kPa] & \multirow{2}{*}{**Exp. **} & **Transition** & **k-Omega** & **Transition** & **k-Omega** \\  & & & **SST** & **SST** & **SST** & **SST** \\ \hline
0 & 618 & 0.01189 & 0.01157 & 0.01211 & -2.69 & 1.85 \\
1 & 584 & 0.01206 & 0.01195 & 0.01315 & -0.91 & 9.04 \\
2 & 549 & 0.01240 & 0.01177 & 0.01284 & -5.08 & 3.55 \\
3 & 515 & 0.01286 & 0.01204 & 0.0129 Based on the above comparison, the transition SST turbulence model was chosen over the k-omega SST for the CFD study in this work. However, it should be noted that although the \(\dot{m}_{s}\) obtained from CFD using k-omega SST are less accurate, they also show a similar trend compared to those from the experiments. Moreover, their discrepancies are not too bad, i.e., only around 9% or less, concerning the complexity of the flow. This means that the k-omega SST turbulence model should not be excluded as an option in predicting an ejector flow. Ideally, to increase the soundness of the CFD simulations, comparison between the CFD results and experimental data should also be done for other variables such as wall pressure or axis Mach number distribution. However, such data are not available in the work of [PERSON] [9].