## 4 Results and Discussion
### The Effect of Air Leaking into the Primary Fluid on the Ejector Performance  
The ejector performance curves with different air mass fractions were obtained through numerical simulations and are shown in Figure 7. The entrainment rate of the ejector decreased as \(Y_{1}\) increased. The larger value of \(Y_{1}\) was, the smaller the entrainment rate. Therefore, the air leaking into the primary fluid impaired the steam ejector performance under specific operating conditions. The entrainment ratio under \(Y_{1}\) = 0.5 decreased by 10% compared with \(Y_{1}\) = 0; in addition, \(Y_{1}\) = 0 had a higher critical pressure than the others. Many factors affect the ejector performance, as mentioned in the Introduction. Among these factors, the physical parameters of the working fluid and the internal flow structure of the ejector were the focus of the following discussion, and the relationship between their changes and the performance of the ejector is established.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Test** & **Operating Condition (kPa)** & **Entrainment Ratio** & \multirow{2}{*}{**Error (\%)**} & \multirow{2}{*}{**Critical Back Pressure (kPa)**} & \multirow{2}{*}{**Error (\%)**} \\  & **Primary/Secondary Fluid** & & **Ref. [6]/CFD** & & **Ref. [6]/CFD** & **(\%)** \\ \hline
1 & 198/1.20 & 0.52/0.545 & \(-\)4.8 & 3.5/3.5 & 0 \\
2 & 270/1.20 & 0.39/0.398 & \(-\)2 & 4.6/4.6 & 0 \\
3 & 270/0.87 & 0.27/0.260 & 3.7 & 4.5/4.4 & 2.2 \\
4 & 270/1.23 & 0.54/0.556 & 2.9 & 4.6/4.9 & 6.5 \\
5 & 361/1.23 & 0.29/0.283 & 2.4 & 6.0/5.7 & 5 \\ \hline \end{tabular}
\end{table}
Table 4: Comparisons between [1] and CFD results in this study.  
Figure 7: Entrainment ratio of the ejector with different \(Y_{1}\) values.  
4.1.1. The Effect of Air Leaking into the Primary Fluid on the Working Fluid Physical Parameters  
We assumed the cross-section of the nozzle outlet as the initial mixing position of the primary and secondary fluids and obtained these parameters by taking the average value on this cross-section from the simulation results; these physical parameters are listed in Table 5.  
As indicated in Table 5, the velocity and sound speed of the primary fluid at the initial mixing position decreased as \(Y_{1}\) increased from 0.1 to 0.5, while the density increased. Except for the increase in velocity, the other physical parameters of the secondary fluid remained unchanged. Therefore, there was an essential connection between the change in these parameters and the decrease in the entrainment ratio. To more intuitively show the relationship between the entrainment ratio and the air mass fraction, we incorporated the mass flux per unit cross-sectional area (density multiplied by the velocity) into the FLUENT user-defined function (UDF) and it is shown in Figure 8. The value of the secondary fluid mass flux lying in the same position gradually reduced with an increase in \(Y_{1}\). The value of the primary fluid mass flux in the red region of Figure 8 was slightly elevated when \(Y_{1}\) increased from 0 to 0.5. Therefore, air leaking into the primary fluid reduces the entrainment ratio of the ejector.  
Figure 8: Isolines of the secondary flow mass flux with different \(Y_{1}\) values.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(Y_{1}\) & **Steam** & **Velocity** & **Density** & **Sound** & **Er** \\  & & **U (m/s)** & \(P\) (kg/m3) & _a (m/s)_ & & \\ \hline
0.0 & Pri & 1048.5 & 0.0318 & 279.20 & 0.398 \\  & Sec & 185.37 & 0.0085 & 405.49 & \\
0.1 & Pri & 1026.10 & 0.0339 & 272.03 & 0.386 \\  & Sec & 187.17 & 0.00847 & 405.37 & \\
0.3 & Pri & 979.61 & 0.0373 & 256.96 & 0.37 \\  & Sec & 188.93 & 0.00845 & 405.25 & \\
0.5 & Pri & 930.40 & 0.0414 & 240.77 & 0.357 \\  & Sec & 190.55 & 0.0084 & 405.13 & \\ \hline \hline \end{tabular}
\end{table}
Table 5: Physical parameters with different \(Y_{1}\) values.