## 1 Introduction  
The steam ejector is a simple energy conversion device that is widely used in many industrial fields, such as power generation [1], refrigeration [2], the desalination of seawater [3], fuel cell applications [4], and steam generation systems [5]. As depicted in Figure 1, the steam ejector can convert a higher-pressure primary fluid and a lower-pressure secondary fluid into a mixed fluid of higher-pressure energy and then realize the vacuum effect in the mixing chamber. The nozzle of the steam ejector plays a key role in the above-mentioned process. Its function is to convert the higher-pressure energy of the primary fluid into greater kinetic energy, thereby providing a source of power for the operation of the entire steam ejector system. Therefore, the nozzle directly affects the efficiency of the entire steam ejector system. The nozzle's geometric structure has a great influence on the performance of the steam ejector and this has been confirmed by many researchers. Six nozzles with different throat diameters were used in a 1 kW steam ejector cooling capacity experimental system that was constructed by [PERSON] et al. [6, 7] and it was found that the geometries of the primary nozzle had strong effects on the steam ejector's performance. [PERSON] et al. [8] investigated the effects of nozzles with conical, oval, square, rectangular, and cross-shaped exit sections on a steam ejector's performance by using the CFD method. They discovered that the steam eject with the nozzle that had a cross-shaped exit section could achieve the largest entrainment ratio. [PERSON] et al. [9] numerically investigated the effects of the primary nozzle's outlet diameter on the performance of steam ejectors, the CFD results illustrated that the entrainment ratio initially increased sharply with the growth of the nozzle's outlet diameter and then it would reduce when the diameter exceeded a certain value. The influence of the throat area ratio between the nozzle and the ejector on the efficiencies in the MED-TVC desalination system was also investigated by [PERSON] et al. [3] and they noted that the mixing efficiency between the primary and secondary fluids and the entrainment ratio of the steam ejector could be improved by adjusting the throat area ratio between the nozzle and the ejector. Other key geometric parameters such as the nozzle's exit position and the nozzle's outlet diameter were optimized by [PERSON] et al. [10] by using the CFD method. This research revealed that the nozzle outlet diameter was the most sensitive influencing factor for the performance of the steam ejector. Apart from the nozzle's geometric structure, the spontaneous condensation behavior of the steam that is in the nozzle also affects the performance of the steam ejector and this is a variable which attracts the attention of many researchers. [PERSON] et al. [11] measured the pressure distribution within the nozzle's condensation zone by conducting a wet-steam tunnel experiment as early as 1973. Subsequently, [PERSON] and [PERSON] [12] documented the homogeneous nucleation and growth of steam droplets using static pressure and laser light scattering methods. [PERSON] [13] experimentally studied the nucleation characteristics of high-pressure saturated steam and determined the Wilson lines and the droplet size and number count that are present in Laval nozzles. Meanwhile, the influence of the Wilson point position was first theoretically explained in [PERSON]'s early experiments [14]. [PERSON] and [PERSON] [15] derived a set of numerical algorithms to be used for solving two-dimensional steam two-phase flows in a nozzle. The fundamental equations of gas-droplet multiphase flows were proposed by [PERSON] for the calculation of the non-equilibrium condensation of wet steam in nozzles and turbine cascades [16; 17; 18]. With the help of a CFD simulation, [PERSON] et al.