## 1 Introduction  
Under the trend of global warming, countries are striving to achieve the target carbon peak [1]. The energy consumption of the shipping industry is huge, and ship energy saving and emission reduction have become hot issues. A large amount of low-grade waste heat is generated during a voyage, such as waste heat from the jacket water and exhaust gas of the main engine. The rational utilization of waste heat could effectively improve the energy efficiency of ships and reduce carbon emissions. Due to its advantages in energy saving and emission reduction [2], the steam ejector is widely used in low-grade energy utilization systems, such as low-temperature multieffect distillation [3] and waste heat refrigeration [4]. Therefore, it is of great significance to investigate steam ejectors driven by ship waste heat. The primary flow pressure (\(P_{m}\)) or primary flow temperature (\(T_{m}\)) have an important effect on the performance of the steam ejector. [PERSON] et al. [5] studied the influence of the \(T_{m}\) on the performance of a steam ejector in a refrigeration system. The results showed that the entrainment ratio increased first and then decreased when the temperature rose. Additionally, there was an optimal \(T_{m}\). [PERSON] et al. [6] found that the critical back pressure of the steam ejector increased with an increase in the \(T_{m}\). [PERSON] et al. [7,8] found that steam ejectors could be driven with heat sources at temperatures lower than 80 \({}^{\circ}\)C in a refrigeration system and a single-effect thermal vapor compression desalination system. The entrainment ratio of the steam ejector could be increased effectively by decreasing the \(P_{m}\) and increasing the secondary flow pressure (\(P_{e}\)). There are complex flow phenomena in steam ejectors, such as the shock wave and choked flow. The numerical simulation method can be used to deeply analyze the complex flow characteristics inside steam ejectors, which would be of great value in improving their performance [9]. [PERSON] et al. [10] adopted the ideal gas model to carry out numerical simulations on a steam ejector. They found that a series of diamond-shaped shock waves formed at the nozzle exit. [PERSON] et al. [11] studied the influence of the \(P_{m}\) on the shock wave train and the choking effect. It was found that the length of the shock wave train increased, the position of the shock choke moved downstream and the choking effect increased with the increase in the \(P_{m}\). [PERSON] et al. [12] found that the \(P_{m}\) would not affect the nozzle efficiency and entrainment ratio when the steam ejector was in a critical state. [PERSON] et al. [13] found that the width of the shock wave train increased when the \(P_{m}\) increased. This reduced the flow area of the secondary flow and, thus, reduced the entrainment ratio. [PERSON] et al. [14] found that the change in the \(P_{m}\) resulted in three states of fluid at the nozzle exit: underexpansion, complete expansion and overexpression. When the state of the fluid changed from underexpansion to overexpression, the entropy generation inside the ejector increased. The physical properties and phase change of working fluid have a significant influence on simulation results. [PERSON] et al. [15] considered the condensation inside a steam ejector for a simulation. They found that the critical back pressure calculated with the wet steam model was slightly lower than that calculated with the ideal gas model. [PERSON] [16] and [PERSON] [17] proposed that the critical back pressure and entrainment ratio predicted with the wet steam model were both higher than those predicted with the ideal gas model. [PERSON] et al. [18] compared the entrainment ratio calculated with the wet steam model and the ideal gas model with the experimental results. The comparison results showed that the results calculated with the wet steam model were closer to the experimental results. [PERSON] et al.