## 3 Numerical Analysis of Flow Behaviour inside the Steam Ejector
### Numerical Simulation Method  
The CFD simulation software ANSYS Fluent version 19.2 was employed in this numerical study. Previously, the research work studied by [PERSON] and [PERSON] [41] has already demonstrated that the simulation results by the two-dimensional axisymmetric model and three-dimensional model were almost identical. Therefore, a two-dimensional axisymmetric model can be made as an assumption to perform the analysis of this study. The segregated solver is applied in ANSYS Fluent and the pressure is modelled by pressure velocity coupling approaches, which is typical for a wide range heat fluid interaction problems [42; 43]. [PERSON] [44] divided the ejector operating mode into three parts. When the back pressure of the ejector was below the critical value, the ejector was in the double-choked flow mode and is operating normally. The ejector is in unchoked flow and reversed flow modes when it was greater than the critical value. In practice, the spontaneous condensation of water vapour exists inside the steam ejector. A few study results have pointed out that the ideal gas cannot truly reflect the flow characteristics of the ejector [45]. The wet steam model can better predict the actual flow conditions and the simulation results are closer to the experimental values [46; 47]. Nevertheless, the research of comparing the CFD simulation values with the experimental values studied by [PERSON] et al. [48], it was concluded that the simulated value of the ideal gas model is closer to the experimental value and can better reflect the fluid flow characteristics than the wet steam model in the double-choked flow mode. [PERSON] [38] pointed out that there was no significant difference between the ideal gas and the real gas in the linear axisymmetric supersonic ejector. The ideal gas can be used to replace the real gas in numerical analysis reflect the flow property inside the ejector. [PERSON] [49] also proved that the ideal gas model could provide similar simulation results to the real gas in a steam ejector with lower operating pressure. To save computational cost and to improve simulation efficiency, the ideal gas model is selected for simulation analysis for thermal fluidic flows [50; 51]. The fluid flow inside the steam ejector is governed by the compressible steady-state flow conservation equations includingthe mass conservation equation, the momentum conservation equation and the energy conservation equation, which can be written as follows:  
The continuity equation:  
\[\frac{\partial\rho}{\partial t}+\frac{\partial}{\partial x_{i}}(\rho u_{i})=0 \tag{4}\]  
The momentum equation:  
\[\frac{\partial}{\partial t}(\rho u_{i})+\frac{\partial}{\partial x_{j}}\Big{(} \rho u_{i}u_{j}\Big{)}=-\frac{\partial P}{\partial x_{i}}+\frac{\partial\tau _{ij}}{\partial x_{j}} \tag{5}\]  
The energy equation:  
\[\frac{\partial}{\partial t}(\rho E)+\frac{\partial}{\partial x_{i}}(u_{i}( \rho E+P))=\vec{\
abla}\left(\alpha_{eff}\frac{\partial T}{\partial x_{i}} \right)+\vec{\
abla}\left(u_{j}\Big{(}\tau_{ij}\Big{)}\right) \tag{6}\]  
where:  
\[\tau_{ij}=\mu_{eff}(\frac{\partial u_{i}}{\partial x_{j}}+\frac{\partial u_{ j}}{\partial x_{i}})-\frac{2}{3}\mu_{eff}\frac{\partial u_{k}}{\partial x_{k}} \delta_{ij} \tag{7}\]  
with:  
\[\rho=\frac{P}{RT} \tag{8}\]  
where \(\tau_{ij}\) is the stress tensor, \(E\) is the total energy, \(\alpha_{eff}\) is the effective thermal conductivity, and \(\mu_{eff}\) is the effective molecular dynamic viscosity. The density-based model is employed for the simulation. The turbulence model was a realizable k-\(\varepsilon\) model [52; 53] with which we can obtain higher accuracy of simulation results based on our previous research. The two inlets were set as pressure-inlets, and the outlet was set as a pressure-outlet. The wall-boundary was assumed to be a no-slip and adiabatic, using Enhanced Wall Treatment for near-wall treatment with y plus = 0.835 (<1) [54; 55]. The second-order upwind format was used to calculate all the convective terms.