## 6 Results and Discussion
### Pressure Variation on the Wall of the Converging Mixing Section
Mach number contour lines of the primary flow for \(M\geq 1\) (black lines) are superimposed onto it to see the shock cells position and size. Figure 17: The secondary mass flow rates of ejector G2 obtained from various methods for different primary pressures. Figure 19: The secondary mass flow rates of eject G2.2 obtained from various methods for different primary pressures. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**Ejector G2**} & \multicolumn{3}{c}{**Ejector G2.1**} & \multicolumn{3}{c}{**Ejector G2.2**} \\ \cline{2-11}
**Sim no. ** & \(P_{0}\) [kPa] & \(\Delta P_{CV}\)1 [FOOTNOTE:1]Footnote 1: \(\Delta P_{CV}=\left(P_{CV,m_{\text{s,ID}}}-P_{2}\right)\times 100/\text{P}_{ \text{L}}\left[\%\right]\); where \(P_{2}=100.8\,\text{kPa}\) and \(P_{CV,m_{\text{s,ID}}}=P_{5}\) is the average wall pressure of the converging mixing section obtained from CFD. 2 \(\Delta\dot{m}_{\text{s,ID}}=\left(\dot{m}_{\text{s,ID}}-\dot{m}_{\text{s,CFD}} \right)\times 100/\dot{m}_{\text{s,CFD}}\) [\%]; \(\dot{m}_{\text{s,ID}}\) and \(\dot{m}_{\text{s,CFD}}\) are the secondary mass flow rates obtained from the one-dimensional model and CFD, respectively. \begin{tabular}{c c c c c c c c c c c} \hline \hline  & & & \multicolumn{3}{c}{**Ejector G2**} & \multicolumn{3}{c}{**Ejector G2.1**} & \multicolumn{3}{c}{**Ejector G2.2**} \\ \cline{3-11}
**Sim no. ** & \(P_{0}\) [kPa] & \(\Delta P_{CV}\)1 [FOOTNOTE:1]Footnote 1: \(\Delta P_{CV}=\left(P_{CV,m_{\text{s,erg}}}-P_{2}\right)\times 100/\text{P}_{ \text{L}}\left[\%\right]\); where \(P_{2}=100.8\,\text{kPa}\) and \(P_{5}\),\(m_{\text{s,IFD}}\) are the average wall pressure of the converging mixing section obtained from CFD. 2 \(\Delta\dot{m}_{\text{s,ID}}=\left(\dot{m}_{\text{s,ID}}-\dot{m}_{\text{s,CFD}} \right)\times 100/\dot{m}_{\text{s,CFD}}\) [\%]; \(\dot{m}_{\text{s,ID}}\) and \(\dot{m}_{\text{s,CFD}}\) are the secondary mass flow rates obtained from the one-dimensional model and CFD, respectively. The fact that there is only a slight improvement at lower \(P_{0}\) leads to the following conclusions. Firstly, the pressure variation on the converging wall is too small which means that the average (area-weighted) pressure is close to \(P_{2}\). This can be seen in Table 5 above. Secondly, it means that other phenomena, which are beyond the scope of this research, play a more significant role in this pressure region. Despite the slight improvement in the lower \(P_{0}\) region, it is important to note that the one-dimensional prediction of \(\dot{m}_{s}\) is very sensitive to the change of the converging wall pressure, regardless what the \(P_{0}\) values are. Figure 20 helps to explain the statement. In Figure 20, \(\Delta P_{CV}\) has the same definition as that in Table 5. The \(\dot{m}_{s,1D,mod-std}\) is defined as \(\left(\dot{m}_{s,1D,mod}-\dot{m}_{s,1D,std}\right)\times 100/\dot{m}_{s, CFD}\) in percent where \(\dot{m}_{s,CFD}\) is the secondary mass flow rate obtained from CFD, and \(\dot{m}_{s,1D,std}\) and \(\dot{m}_{s,1D,mod}\) are the secondary mass flow rates obtained from the standard and modified one-dimensional models, respectively. In this figure, it can be concluded that the least sensitive ejector to wall pressure change is ejector G2.2. Yet, it is still something that cannot be ignored even at lower pressures. As an example, for the lowest \(P_{0}\) (308 kPa), when the converging wall pressure decreases by 2.25%, the predicted mass flow rate increases by 7.28%. The most sensitive to the wall pressure change is ejector G2. At the lowest \(P_{0}\) (308 kPa), an only 0.28% decrease in the wall pressure results in 3.30% increase in the predicted mass flow rate. These results suggest that, instead of simply assuming \(P_{CV,\mu\alpha\alpha\beta}\) to be equal to \(P_{2}\), a good estimate of the pressure should be found and utilized. This finding also proves what has been suggested by [PERSON] and [PERSON] (1998), i.e., more local flow phenomena should be included in the one-dimensional model to improve it further.