## 2 Microbubble Pump with a Novel 'S-Shape' Impeller  
The conventional microbubble pump has an open channel impeller due to the simple impeller structure and lower manufacturing cost. There are a few drawbacks to an open channel impeller, mostly related to the aerodynamic performance of the pump such as cavitation, early flow separation, corrosion, and rusting of the edges and tips.  
The main reason for this problem is the discontinuity of pressure fluctuations due to the high-pressure recirculating flow between the impeller blades of the microbubble pump when operating at high pressure of 5 bar or more, as shown in Figure 1.  
The conventional open channel impeller has a weakness in structural strength with its cantilever structure, in which only the blade hub is fixed, as shown in Figure 2. In the present study, to improve the structural strength of the impeller blades and the pump performance, an impeller with so-called \"S-shape\" blades was connected in series, as shown in Figure 2, and was developed with an optimal design method [4].  
The optimally designed microbubble pump was manufactured, as shown in Figure 3, to analyze flow field characteristics in the design and off-design flow conditions. Its rotational diameter is 72.6 mm, and it has 30 'S' turns. Table 1 summarizes all of the important details about the designed impeller.  
Flow coefficient (\(\phi\)) and pressure coefficient (\(\psi\)) of the pump are defined as:  
\[\phi=\frac{Q}{AU_{t}} \tag{1}\]  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Variable** & **Value** \\ \hline Flow coefficient (\(\phi\)) & 0.39 \\ Pressure coefficient (\(\psi\)) & 2.0 \\ Designed rotational speed (RPM) & 3550 \\ Impeller tip diameter (mm) & 72.6 \\ Blade height (mm) & 6 \\ Specific speed & 89 \\ Specific diameter & 5.2 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Design characteristics of the S-shape pump impeller.  
Figure 1: Recirculating flow generated between impeller blades for conventional pump impeller.  
Figure 3: Microbubble pump manufactured with an (**a**) ‘S-shape’ impeller; (**b**) assembled pump.  
Figure 2: Microbubble pump impeller modeled in (**a**) conventional shape; (**b**) novel ‘S-shape’.  
\[\psi=\frac{2\Delta p}{\rho U_{t}{}^{2}} \tag{2}\]  
where \(Q\) is the volumetric flow rate of water, \(\Delta p\) is the pressure rise, \(U_{t}\) is the impeller tip speed, \(\rho\) is the density, and \(A\) is the cross-sectional area of the outlet duct of the pump.  
The pump efficiency (\(\eta\)) is defined as the work done by the pump impeller on the working fluid to raise its pressure divided by the power supplied to the pump. It is mathematically expressed as:  
\[\eta=\frac{Q\Delta p}{T\omega} \tag{3}\]  
where \(T\) and \(\omega\) are the torque and the rotational speed acting on the impeller, respectively.  
Similarly, specific speed (\(N_{s}\)) and specific diameter (\(D_{s}\)) are two dimensionless parameters related to the operational specifications of the pump and can be defined as follows, respectively:  
\[N_{s}=\frac{\omega\sqrt{Q}}{\left(gH\right)^{\frac{1}{4}}} \tag{4}\]  
\[D_{s}=\frac{D(gH)^{\frac{1}{4}}}{\left(Q\right)^{\frac{1}{2}}} \tag{5}\]  
where \(D\) is the tip diameter of the impeller, \(g\) is the gravitational acceleration constant, and \(H\) is the total head at the best efficiency point (BEP). The values of \(N_{s}\) and \(D_{s}\) along with other parameters of the pump are summarized in Table 1.