# Dynamic Instability Analysis of a Double-Blade Centrifugal Pump
## 2 Computational Modeling and Experimental Test
### Experimental Setup  
The pump is directly driven by a Siemens motor and the speed is controlled by an ABB frequency converter. Figure 4 presents the pump test rig. It includes: 1-inlet tank, 2-flow meter, 3-inlet pipe with pressure detecting port, 4-outlet pipe with pressure detecting port, 5-test pump, 6-outlet tank, 7-inlet pressure transducer, and 8-outlet pressure transducer. To ensure a stable water flow at the pump inlet, the inlet tank was equipped with a flow straightener for stabilizing the flow. The error of the measuring devices is as follows: (1) the pressure error is \(\pm 0.2\%\); (2) the flow rate error is \(\pm 0.2\%\); (3) the speed error is \(\pm 1\) rpm; (4) the power error is \(\pm 1.5\%\). In addition, the repeatability of test fills the ISO 9906-2012 Grade 1 requirement.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Turbulence Model** & **\(\mathbf{H}\) (m)** & \(\mathbf{\Delta H}=1\mathbf{H_{\text{CFD}}}-\mathbf{H_{\text{EXP}}}\) 1/\(\mathbf{H_{\text{EXP}}}\) (\%) \\ \hline Standard \(k\)-\(\epsilon\) & 16.21 & 1.64 \\ RNG \(k\)-\(\epsilon\) & 16.14 & 2.06 \\ EARSM \(k\)-\(\epsilon\) & 16.30 & 1.09 \\ Standard \(k\)-\(\omega\) & 16.95 & 2.85 \\ BSL \(k\)-\(\omega\) & 16.76 & 1.69 \\ SST \(k\)-\(\omega\) & 16.74 & 1.57 \\ Exp. & 16.48 & - \\ \hline \hline \end{tabular}
\end{table}
Table 2: Turbulence model independence verification (\(Q=1.0Q_{\text{d}}\)).  
Figure 3: Grid independence analysis.  
Figure 2: Computational grid of pump model.  
Additionally, a piezoelectric vibration acceleration sensor and a signal acquisition and analysis system were used to measure the vibration levels of the pump. According to the requirements of ISO 10816 [25], 5 vibration acceleration monitoring points were arranged in the vibration sensitive area of the pump unit to obtain sufficient vibration information, see in Figure 5. No. 1 measuring sensor is located on top of pump housing (Z direction), No. 2 measuring sensor is located on side wall of pump housing (Y direction), No. 3 measuring sensor is located on foot of pump housing (Z direction), No. 4 measuring sensor is located on bearing housing (Z direction), No. 5 measuring sensor is located on bearing housing (Y direction). The technical information of acceleration sensors was described in Table 3. However, the special design feature of the pump volute is that it was covered by chamber, so it is difficult to mount the dynamic pressure sensors in the pump volute to measure the dynamic pressure pulsations. Therefore, the vibration data were measured as a limited experimental dataset to explain the dynamic instability of the pump.  
Figure 4: Test rig for the pump: (1) inlet tank; (2) flow meter; (3) inlet pipe with pressure detecting port; (4) outlet pipe with pressure detecting port; (5) test pump; (6) outlet tank; (7) inlet pressure transducer; (8) outlet pressure transducer.  
Figure 5: Arrangement of vibration acceleration sensors: 1# indicates the No. 1 measuring sensor; 2# indicates the No. 2 measuring sensor; 3# indicates the No. 3 measuring sensor; 4# indicates the No. 4 measuring sensor; 5# indicates the No. 5 measuring sensor.