## 3 Results and Discussion
### Effect of the Shock Wave Structure on the Pumping Performance  
Under the condition of the secondary fluid, pressure is 2330 Pa and the back pressure is 3500 Pa, the pumping performance of the steam ejector with changing of the primary fluid pressure is analysed. The contour of Mach number above 1 under different primary fluid pressure is shown in Figure 6. The structure and characteristics of the shock wave can be clearly observed. An oblique-shock region consisting of a normal shock wave and a series of bifurcated shock waves represented in the dashed box. The velocity of the mixed fluid suddenly drops from supersonic to subsonic due to the existence of the normal shock wave. To accurately capture the shock wave position, only fluids above 1 Mach number are displayed and the subsonic part would not appear. It can be seen that the higher the primary fluid pressure is, the closer the normal shock wave is to the outlet of the ejector. While the length of the oblique-shock in the subsonic diffuser section increases with the increasing of the primary fluid pressure. The flow region in the throat section where the fluid velocity is higher than 1 Mach number expands. The length of the pseudo-shock strain is elongated with the increase of the primary fluid pressure when the primary fluid pressure is less than 0.34 MPa. When the pressure is more than 0.34 MPa, the length of the pseudo-shock region maintains constant. It shows that the energy and momentum of the primary fluid mixing with the secondary fluid continuously increases when the primary fluid pressure is less than 0.34 MPa. However, the increase of the oblique shock region consumes a part of the energy and momentum of the mixed fluid causing the energy of the mixed fluid to be reduced when it flows through this region. The shock wave structure changes significantly from the inviscid normal shock to the bifurcation oblique shock with the primary fluid pressure increasing. When the primary fluid pressure is less than or equal to 0.34 MPa, the upstream Mach number values and the intensity of the shock wave decrease. At 0.34 MPa, the velocity at the center of the shock wave is the highest. When the primary fluid pressure is more than 0.34 MPa, the upstream Mach number values of the shock wave rises significantly, and the normal shock changes to be a bifurcated oblique shock. Figure 7 shows the Mach number distribution curve at the axis of the ejector to illustrate the influence of the oblique-shock region. The Mach number values of the fluid in the mixing chamber section is significantly higher than that in the subsonic diffuser section. When the Mach number in  
Figure 6: The influence of primary fluid pressure on the shock structure. the subsonic diffuser section reaches 4.26, a shock train is generated. When the Mach number value is less than 1.53, a series of oblique shock waves are formed and accompanied by the transonic flow behaviour. As long as there is a normal shock wave in the subsonic diffuser section, the ejector is in the double-choked flow mode [55] with a better pumping performance. When the normal shock wave enters the throat section, the double-choked flow mode would be destroyed by the downstream back-pressure disturbance. The pumping performance of the ejector continuously decreases until it loses its function completely. It shows that the normal shock wave is of great significance in maintaining the pumping performance and the operational stability of the ejector. The variation of the entrainment ratio under different primary fluid pressure is shown in Figure 8. The experimental and simulation values of the entrainment ratio are in a good agreement. The entrainment ratio reaches the optimum value at 0.34 MPa. The entrainment ratio is more than 0.8 when the primary fluid pressure is at between 0.32 MPa and 0.36 MPa, while it is less than 0.8 when the primary pressure is outside of this range.