## 6 Results and Discussion  
### Pressure Variation on the Wall of the Converging Mixing Section  
Figure 15 shows the pressure variation along the wall of the converging mixing section (\(80.7\leq x\leq 110\) mm) of ejector G1. The wall of the converging mixing section consists of two contour patterns. One is the linear/straight contour with a steeper slope (\(80.7\) mm \(\leq x\leq 97\) mm) and the other is the curved contour with a decreasing slope (\(97\) mm \(\leq x\leq 110\) mm). In general, all these pressure curves have the same pattern. They start to increase to reach a peak and then decrease, except for some curves, most notably the curves of sim 01 and 02. Note that the operating conditions for sim 00 to 09 in Figure 15 correspond to simulation no. 0 to 9 in Table 3, respectively. After the peak, these two curves decrease relatively a little and then increase again to finally decrease. Hence, there are two peaks. Such a pattern also exists, but is less obvious, in sim 03 and 05. This different pattern (the two peaks pattern) is mainly because of the different position and size of the shock train cells. Figure 16 compares simulation results having one peak pressure variation (sim 00) to that having two peaks (sim 01). The first pressure peak that occurs on the converging wall is due to the impingement of the secondary flow on the wall. After the impingement, part of the fluid flows into the ET and the remaining diverted into the steep converging wall to form a circulation. Regarding the second peak that exists on the other curves (ex: sim 01 in Figure 15), it is due to the different position and size of the cells of the shock train. The outer surface of the shock train and the ejector wall create a hypothetical annular duct that is continuously expanding and contracting along the \(x\)-direction. When the cross-sectional area of this annular duct increases (the duct diverges), the flow inside it will decelerate and, hence, the wall pressure increases (see the second pressure peak in Figure 16). The opposite will happen if the cross-sectional area of the duct decreases (the duct converges). Figure 15: Pressure variation along the wall of the converging mixing section (\(80.7\) mm \(\leq x\leq 110\) mm) of ejector G1 (top) and the geometrical contour of the converging mixing section wall (bottom). The operating conditions of sim 00 to 09 can be seen in Table 3 (corresponding to simulation no. 0 to 9). A similar phenomenon is also seen in the flow of ejectors G2, G2.1, and G2.2, which will be presented next. In the parametric study, the standard and the modified one-dimensional models were applied to the three ejectors (G2, G2.1, and G2.2), and the results were compared. All these ejectors were simulated at the critical conditions (\(P_{0}\geq 308\) kPa). The results of the modified model are encouraging. From Figures 17-19, there are two important observations to point out. Firstly, looking at the curves in general, one can see that the \(\dot{m}_{s}\) from CFD simulation decreases as the \(P_{0}\) increases. This means that it has a negative slope. On the other hand, the standard model shows the opposite, i.e., a positive slope. However, the curve slope of the modified model gets closer to that of the CFD results. This means that the one-dimensional model is improved. The second observation to point out is that, at high \(P_{0}\), the modified model improves the prediction of \(\dot{m}_{s}\) significantly. Interestingly, such improvement is obtained by only a slight change in the average pressure of the converging mixing section wall as can be seen in Table 5. As an example, for simulation no. 0\({}^{\prime}\) of ejector G2, a pressure difference of only 1.91% leads to 31.59% improvement on the one-dimensional model prediction of the secondary mass flow rate. Figure 16: Streamlines plot (colored by pressure) started from the secondary flow inlet for ejector G1 with operating conditions of sim 00 (\(P_{0}=618\) kPa; top), and 01 (\(P_{0}=584\) kPa; bottom).