# Development of Hybrid Airlift-Jet Pump with Its Performance Analysis
## 4 Models of Target Pump
### Mesh and Boundary Conditions  
To evaluate the independence of numerical solutions to the mesh used, a grid refinement study is carried out. The boundary conditions of Case No. 7 in Table 2 are applied. Figure 5 shows the result in terms of the water mass flow rate at the outlet and the number of grids used. Based on this result, a mesh of 1.5 million tetrahedron elements, as shown in Figure 6a, is used in the computation domain in all of following computations. The mesh geometries at the air inlet and the air nozzle exit are densified to obtain a more precise simulation of the local detailed flow characteristics, as shown in Figure 6b,c. \begin{table}
\begin{tabular}{c c} \hline \hline Air nozzle inlet diameter & 6.5 \\ Air nozzle diameter & 24 \\ Air nozzle exit diameter & 8 \\ Water nozzle diameter & 50 \\ Distance between an air nozzle exit and a mixing section & 25 \\ Mixing section diameter & 24 \\ Diffuser outlet diameter & 34 \\ Mixing section and diffuser length & 200 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Geometry dimensions of a hybrid airlift-jet pump (units: mm). Figure 4: Schematics of a hybrid airlift-jet pump (units: mm; red-colored numbers and symbols present dimensions of a nozzle). The mesh size is set to be around 0.25 mm for the air inlet and the air nozzle, and 2.5 mm for the other parts. The maximum y-plus (y\({}^{+}\)) values are around 500 in the nozzle and 800 in the diffuser. The total pressure boundary conditions were applied at the inlet section of the air nozzle and the vertical pipe. The range of total pressure at the air inlet is determined according to the capacity of air compressor used in the validation experiment shown in Figure 7. The total pressure at the water inlet is determined by including the effects of suction pipe length submerged in water; the total pressures of 1 kPa and 6 kPa correspond to the submerged suction pipe height \(h_{s}\) (shown in Figure 7g) of 0.1 m and 0.6 m, respectively. However, the volume fraction of water at the water inlet, which depends on the capacity of air compressor, the generated cavitation types and the water flow velocity (water mass flow rate) are relatively difficult to determine. Therefore, the range of water volume fraction at the water inlet is set to investigate the effects of airlift pump on the overall performance of hybrid pump in its wide operation range. Altogether, eighteen cases are investigated including the operating conditions of only the jet part, and both the airlift and jet parts. For the jet-pump-only operation, the total pressure at the air inlet is varied along with specifying the volume fraction of air as one. At the water inlet, the volume fraction of air is specified as zero. In the hybrid mode, for simplicity, the volume fraction of air, as well as the total pressure at the water inlet, is varied to simulate the effects of the airlift pump and the submerged suction pipe height. The total pressure equation can be written as:  
\[p_{T}=p_{s}\bigg{(}1+\frac{\gamma-1}{2}M^{2}\bigg{)}^{\gamma/(\gamma-1)} \tag{10}\]  
where \(p_{T}\) is the total pressure, \(p_{S}\) is the static pressure, \(M\) is the Mach number and \(\gamma\) is the ratio of specific heats. The boundary conditions of each case are listed in Table 2. The total pressure boundary conditions are set at the air and water inlets. At the outlet, the static pressure condition is applied and set as zero gauge pressure. The total pressure range at the air inlet is varied from 100 kPa to 400 kPa. The cases denoted by No. 1-8 are set to simulate the influence of the air inlet pressure for different water inlet pressures, which are determined to represent different suction lengths (interpreted as the water suction pipe being buried into water or reducing the length of the suction pipe). Cases No. 9-12 are set