## 7 Conclusions  
A research on supersonic ejectors for refrigeration application using computational fluid dynamics (CFD) and one-dimensional analytical models has been conducted. Several ejectors with varying radius of converging mixing section inlet were studied. The objective was to show that the ejector one-dimensional analytical model can be improved by considering wall pressure variation in the converging mixing section. Typically, the pressure on this wall is assumed to be constant and equal to the secondary flow inlet pressure. Two turbulence models, i.e., k-omega SST and transition SST, have been tested to find which  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Sim. no. **} & \multirow{2}{*}{\(P_{0}\) [kPa]} & \multicolumn{3}{c}{**Secondary Mass Flow Rate, \(\hat{m}_{s}\) [kg/s]**} & \multicolumn{3}{c}{**Increase of \(\hat{m}_{s}\) Relative to that of Ejector G2 [\%]**} \\ \cline{2-7}  & & **Ejector G2** & **Ejector G2.1** & **Ejector G2.2** & **Ejector G2.1** & **Ejector G2.2** \\ \hline
0′ & 618 & 0.00997 & 0.01014 & 0.01096 & 1.71 & 9.93 \\
1′ & 584 & 0.01066 & 0.01092 & 0.01163 & 2.44 & 9.10 \\
2′ & 549 & 0.01182 & 0.01215 & 0.01269 & 2.79 & 7.36 \\
3′ & 515 & 0.01193 & 0.01227 & 0.01340 one gives the closest results to the experimental data. The predicted secondary mass flow rates, \(\dot{m}_{s}\), obtained from the one-dimensional model have been compared before and after incorporating the above-mentioned pressure variation into the model. The conclusions of this work are summarized as follows:  
1. In the CFD analysis, the transition SST turbulence model is better than the k-omega SST model in terms of how close the predicted \(\dot{m}_{s}\) is to the experimental data. Most of the transition SST model results are within the experimental uncertainty of [PERSON]'s work [9], i.e., no greater than 4%. On the other hand, many of the errors of k-omega SST results are ranging from 7% to 9%. These results are obtained when the ejector is operating in the critical region. 2. The authors have found that the effect of wall pressure variation in the converging mixing section is actually prominent in the prediction of the one-dimensional model. Even a small amount of change in the converging wall pressure can result in a significant improvement of the model prediction of \(\dot{m}_{s}\), especially at high \(P_{0}\). However, regardless of the operating conditions, the sensitivity of \(\dot{m}_{s}\) is high with respect to the change of the converging wall pressure, i.e., a small change in the pressure can result in a high change in \(m_{s}\). It has also been found that, in general, the inclusion of the wall pressure variation will improve the trend (slope) of the predicted \(\dot{m}_{s}\). Based on these findings, this wall pressure variation should be considered in future modeling of ejectors. 3. The pressure increase on the wall of the converging mixing section is due to the impingement of the secondary flow on that wall. This happens because the shock train of the primary jet partially blocks the secondary flow as it tries to enter the ET. On the other hand, the pressure decrease at the end of that converging wall is due to the acceleration of the secondary flow as it enters the ET. The effects of these two phenomena compete each other that result in the increase or decrease of the average wall pressure. Moreover, we have also found that the behaviors of these two phenomena are linked to the primary jet speed, and the cell size and position of the shock train. 4. The CFD results show that the secondary mass flow rate increases as the angle of the converging mixing section decreases. However, due to the limited range of angles simulated, the current results have not verified the existence of an optimum angle value that has been observed by other researchers.