# Development of Hybrid Airlift-Jet Pump with Its Performance Analysis
## 5 Results and Discussion
### Pressure and Velocity Distributions inside Hybrid Pump  
Case No. 3 is chosen to illustrate the characteristics of the two-phase flow field inside the hybrid pump by investigating the detailed distributions of static gauge pressure and fluid velocity. As shown in Figure 12a, the air pressure decreases rapidly when it arrives at the air nozzle part. Just outside of the air nozzle (ejector), a negative pressure area forms. In Figure 12b, the maximal axial velocity is observed in the exit of the air nozzle, although the flow path is enlarged. This is due to the decrease in pressure that causes the air to obtain a significant expansion.  
The static gauge pressures and the Mach numbers of the air along the center line of the air nozzle and the primary exit pipe are shown in Figure 13, where Cases No. 1-4 are chosen to illustrate the relationship between these variables and the air inlet total pressure. It is noteworthy that the remaining cases share the similar trend. In each case, the negative gauge pressure is formed at the air nozzle exit due to the expansion of air. When the static pressure difference between the inlet and the outlet of pipe flow increases, the air flow is accelerated along the converging nozzle, and a choked flow is formed, in which the Mach number is maintained to be one in the nozzle. However, if the pressure difference continues to increase, the Mach number at the nozzle is maintained at 1, but the downstream flow is more accelerated to be supersonic in the diffusion region [27]. Note that the increase of the static pressure and the decrease of Mach number near the exit of main pipe are due to the diverging diffuser, as shown in Figure 12.  
Figure 12: Cross-sectional static pressure and velocity distributions: (**a**) static pressure; (**b**) axial velocity.  
Table 3 shows the inlet static pressures and the maximum Mach numbers along the center line of the air nozzle and the primary exit pipe. The static pressure at the air inlet increases and the minimum value decreases as a higher total pressure boundary condition is set at the air inlet. Meanwhile, a negative gauge pressure in the mixing section appears to be more obvious with a higher inlet total pressure, causing the pressure in the diffuser to recover more quickly. As shown in Figure 13b, despite the different inlet pressure distributions, the velocity in the air nozzle is almost the same at the inlet as that at the middle section of the air nozzle. At the air nozzle exit, air with a higher inlet pressure boundary condition increases significantly in velocity; the velocity difference persists until the air reaches the outlet of the diffuser.  
To compare the cases with different suction heights and volume fractions that are affected by the operation of the airlift part, distributions of static pressure and the Mach number in the cases with the same air inlet total pressure of 300 kPa are shown in Figure 14. In the static pressure distribution, compared with Case No. 3, the other cases have a smaller negative pressure at the air nozzle exit but a larger negative pressure in the primary exit pipe of the mixing section. A more obvious difference can be found in the Mach number plot, as the case with a shorter suction height and a lower volume fraction of water has a higher Mach number at the mixing section. Case No. 13 shows the highest Mach number distribution owing to the superposition of the two effects.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Case No.** & **Static Pressure at Air Inlet (kPa)** & **Maximum Mach Number** \\ \hline No. 1 & 41.8 & 0.70 \\ No. 2 & 104.0 & 1.00 \\ No. 3 & 168.1 & 1.24 \\ No. 4 & 233.7 & 1.43 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Static pressure and velocity at an air inlet.  
Figure 13: Static gauge pressure and Mach number along the center line of air nozzle: (**a**) static pressure distribution; (**b**) Mach number distribution (red: nozzle; blue: mixing section).