# A Performance Test and Internal Flow Field Simulation of a Vortex Pump
## 3 Model Pump Performance  
The pump is directly connected to the motor, and the power of the pump shaft was measured by the electronic method. The no-load motor is in line with GB/T 12785-91 standards (Test Methods for Submersible Motor Pumps), the pump performance test was carried out according to GB/T 3216-2005 (Rotodynamic Pumps--Hydraulic Performance Acceptance Tests, Grades 1 and 2), and the frequency converter was used to adjust to the rated speed. Figure 2 is the scheme of the experimental test bench. The technical data for instrumentation are provided in Table 2.  
Pump experimental performance curves are shown in Figure 3 (\(\eta_{gr}\) is the unit efficiency). The optimal operating conditions of the pump are: discharge (\(q_{v}\)) is 9.00 m\({}^{3}\)/h, pump head (\(H\)) is 12.88 m, maximum efficiency (\(\eta_{max}\)) is 53.13%, and specific speed \(n_{s}\) is 76.5. The pump \(q_{v}\)-\(H\) curve is flat, higher than in the design condition. The \(q_{v}\)-\(P\) curve rises faster than other curves. The discharge-critical net positive suction head (\(q_{v}\)-\(NPSH_{c}\)) curve is parabolic-diminishing and shows the opposite trend compared with the centrifugal pump's \(q_{v}\)-\(NPSH_{c}\) curve. The critical \(NPSH\) of small flow is larger, but the critical \(NPSH_{c}\) decreases with the increased discharge.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Design Parameters** & \multicolumn{4}{c}{**Hydroraulic and Geometric Parameters**} \\ \hline Discharge/\(q_{v}\) (m\({}^{3}\)/h) & 9 & Specific speed/\(n_{s}\) & 80.67 & \begin{tabular}{c} Diameters of \\ impeller/\(D_{2}\) (mm) \\ \end{tabular} & 94 \\ \hline Head/\(H\) (m) & 12 & \begin{tabular}{c} Chamber \\ diameter/\(D_{V}\) (mm) \\ \end{tabular} & 140 & \begin{tabular}{c} Chamber throat \\ area/\(F_{thr}\) (mm\({}^{2}\)) \\ \end{tabular} & 504 \\ \hline Rotational speed/\(n\) (r/min) & 2850 & \begin{tabular}{c} Width of \\ blade/\(b_{2}\) (mm) \\ \end{tabular} & 20 & \begin{tabular}{c} Width of \\ chamber (mm) \\ \end{tabular} & 25 \\ \hline Pump efficiency/\(\eta\) (\%) & 50 & \begin{tabular}{c} Volute chamber lines \\ \end{tabular} & ring-shaped & \begin{tabular}{c} Base circle diameter of \\ chamber/\(D_{3}\) (mm) \\ \end{tabular} & 100 \\ \hline Shaft power/\(P\) (\(kW\)) & 0.55 & \begin{tabular}{c} Number of \\ blades/\(Z\) (piece) \\ \end{tabular} & 8 & \
\begin{tabular}{c} Diameter of \\ volute/\(D_{i}\) (mm) \\ \end{tabular} & 32 \\ \hline Net positive suction & 4 &
\begin{tabular}{c} Blade \\ thickness/\(\delta\) (mm) \\ \end{tabular} & 1.5 & Blade airfoil lines & radialized \\ \hline \hline \end{tabular}
\end{table}
Table 1: Vortex pump design and hydraulic parameters.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameter** & **Instrument** & **Precision** & **Parameter** & **Parameter** & **Precision** \\ \hline Pump head/\(H\) & pressure gauge & 0.4 & \
\begin{tabular}{c} Current/\(A\) \\ Voltage/\(V\) \\ \end{tabular} &
\begin{tabular}{c} ammeter \\ voltmeter \\ \end{tabular} & 0.5 \\ \hline Discharge/\(q_{v}\) & electromagnetic flow meter & 0.5 & Shaft power/\(P\) & wattmeter & 0.5 \\ Rotation rate/\(n\) & digital tachometer & 0.5 & Resistance/\(R\) & digital resistance meter & 0.1 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The technical data for instrumentation.  
Figure 2: Scheme of the experimental test bench.  
\(\eta_{p}\): pump efficiency; \(\eta_{gr}\): unit efficiency; \(H\): pump head in m; \(P\): shaft power in W; \(\textit{NPSH}_{c}\): critical net positive suction head in m; \(q_{v}\): discharge in m\({}^{3}\)/h; \(q_{v}\)-\(H\): discharge-pump head; \(q_{v}\)-\(P\): discharge-pump shaft power in \(w\); \(q_{v}\)-\(\eta_{p}\): discharge-pump efficiency; \(q_{v}\)-\(\eta_{gr}\): discharge-unit efficiency; \(q_{v}\)-\(\textit{NPSH}_{c}\): discharge-critical net positive suction head.