## 3 Numerical Analysis of Flow Behaviour inside the Steam Ejector  
The coefficient of performance (\(COP\)) is evaluated as the ratio of the refrigeration effect to the energy input of the system as given in Equation (1) [30]:  
\[COP=\frac{Q_{e}}{Q_{g}+W_{p}} \tag{1}\]  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Geometrical Parameters** & **Value** \\ \hline Diameter of the nozzle inlet & 12 mm \\ Diameter of the nozzle outlet & 11 mm \\ Diameter of the nozzle throat & 2.5 mm \\ Expand the angle of the nozzle & 10\({}^{\circ}\) \\ Nozzle exit position & 10 mm \\ Diameter of mixing chamber inlet & 70 mm \\ Diameter of throat & 28 mm \\ Length of mixing chamber & 122.2 mm \\ Length of throat & 90 mm \\ Length of diffuser & 210 mm \\ \hline \hline \end{tabular}
\end{table}
Table 1: Geometrical parameters of the steam ejector.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Boundary Conditions** & **Value** \\ \hline Primary fluid temperature & 134 \({}^{\circ}\)C–146 \({}^{\circ}\)C \\ Secondary fluid temperature & 5 \({}^{\circ}\)C–20 \({}^{\circ}\)C \\ Back pressure & 3000 Pa–5000 Pa \\ \hline \hline \end{tabular}
\end{table}
Table 2: Flow conditions of the steam ejector.  
Figure 1: The experimental steam ejector refrigeration system.  
The _COP_ can be rewritten after a series of calculations by neglecting pump work using Equation (2) [31]:  
\[COP=\frac{\dot{m_{p}}}{\dot{m_{a}}}\times\frac{\Delta h_{e}}{\Delta\dot{h_{b}}}=E_ {m}\times\frac{\Delta h_{e}}{\Delta\dot{h_{b}}} \tag{2}\]  
Therefore, it is obvious that the _COP_ of the whole system depends entirely on the entrainment ratio, and the value of _COP_ will be closer to the value of the entrainment ratio. Entrainment ratio (\(E_{m}\)) is a common index for evaluating the pumping performance and reflects the working capability of the steam ejector which is defined as the mass flow rate ratio of the secondary fluid to the primary fluid's mass flow rate [32]. Based on the existing experimental data, [PERSON] [18] established a 1-D model of the ejector with R113 and R141b as the primary fluid:  
\[E_{m}=\left(\frac{P_{2}}{P_{1}}\right)\cdot\frac{1}{\left(\frac{T_{2}}{T_{1}} \right)^{1/2}}\cdot K_{p}\cdot K_{f}\cdot K_{s}\cdot\varphi \tag{3}\]  
\(K_{p}\) is correlative with the structure of the nozzle, \(K_{f}\) is correlative with the effective area in the ejector, \(K_{s}\) is correlative with the aspect ratio and the exit Mach number of the primary nozzle, \(\varphi\) is a specific correction factor when the geometry structure of the ejector operating system is fixed. When the geometry dimensions of the nozzle are constant, the operating parameters \(K_{p}\), \(K_{s}\) of the primary fluid are invariant, the entrainment ratio of the ejector is varied with the primary fluid pressure and secondary fluid pressure. The maximum \(E_{m}\) of the ejector will be obtained when the ejector only operated at the double-choked flow mode under certain operating conditions [33; 34]. Previous researches have shown that the shock-mixing layer [35], effective area [36], shock train [37] and the choking flow [38] in the throat section of the ejector are key factors in dominating the pumping efficiency of the ejector [39; 40]. However, the research of the complex flow characteristics inside the ejector is limited by the present existing research methods.