## 2 Research Object and Methods
### Experimental Support  
The experimental test rig of high-speed centrifugal pumps is built in a semi-anechoic room, as shown in Figure 3a. The open-type system is used to simulate the actual working condition of the cooling water pump. A tank, together with the valves, adjusts the resistance of the circulation system and the pump inlet pressure. In order to reduce the noise interference during the measurement, the experiment uses a motor to drive the pump instead of the engine drive. The pump base is welded on the thick iron plate, and the pump shaft is connected to a permanent magnet DC motor. In this pipeline system, all parts are wrapped with sound-absorbing cotton. The stabilized voltage supply and all the data collection equipment is put in the monitoring room to improve the accuracy of the measurement. The semi-anechoic room supplies a damping base to install the pump loop with 15 dB background noise and 50 Hz cut-off frequency measurement surroundings. The test system includes a pump performance measurement module and a noise data collection module. The flow rate is obtained by an LDCK-32 JM25 MY/TBS type electromagnetic flowmeter with a range of 0-45 m\({}^{3}\)/h. The head of the pump, defined by Equation (1), is measured by a CYG1204F type differential pressure transducer with a range of 0-300 kPa. The data acquisition system consists of an Nl6343 data acquisition card and the LabVIEW acquisition program. Typically, the main parameters used to evaluate pump performance are head and efficiency. The head represents the ability of the centrifugal pump to transport water, usually expressed as the height of the water \(H\). It can be expressed as the increase in the pressure energy, kinetic velocity energy, and potential energy of the fluid, defined by Equation (5). The efficiency of centrifugal pumps is the ratio of useful power to input power, defined in Equation (6). \[H=\frac{p_{2}-p_{1}}{\rho g}+\frac{{v_{2}}^{2}-{v_{1}}^{2}}{2g}+(z_{2}-z_{1}) \tag{5}\]  
\[\eta=\frac{\rho gQH}{P_{e}} \tag{6}\]  
where \(p_{1}\) and \(p_{2}\) imply the inlet pressure and outlet pressure, respectively; \(v_{1}\), \(v_{2}\) denote the average velocities of the inlet and outlet section, respectively; \(z_{1}\), \(z_{2}\) are the heights at the inlet and outlet center section of the model pump to the reference horizontal plane; \(\rho\) denotes the fluid density; \(g\) denotes the standard acceleration of gravity; \(P_{\rm e}\) is the shaft power calculated by the input power and motor  
Figure 2: The flow chart of the radiated noise analysis of the high-speed centrifugal pump. efficiency. The accuracy of the flow rate measurements is 0.5%; the rotational speed uncertainty is 1%. The estimated uncertainty of head measurement is below 0.32%, and efficiency uncertainty is no more than 0.72%, which meets the Grade 1 accuracy based on the ISO 9906.2012 standard [23]. The noise is measured with the PCB 14043 type microphone (PCB Piezotronics Inc., New York, USA) and processed based on the LMS Test Lab platform. The accuracy of the SPL of the radiated noise is \(\pm\)1 dB. The acquisition sampling frequency is set to 6400 Hz, and the resolution frequency is set to 1 Hz. Every test used 120 s for the signal acquisition and treated frequency resolution by the Hanning window in general. Five microphones set to evaluate noise level and sound source directivity followed the Chinese standard GB/T 29529-2013 [24]. The position of the microphone sensor is as shown in Figure 3b, all the microphone sensors are uniformly distributed as a semicircle with a distance of 1 m to the high-speed centrifugal pump. In order to accurately capture the intensity distribution of the radiated noise field, two sets of microphone sensors are arranged, respectively, in the direction perpendicular to the inlet tube and 45 \({}^{\circ}\)oblique to the inlet tube. The average total sound pressure level \(\overline{L}_{\text{P}}\) is expressed as Equation (3) in order to analyze the variation of the radiated noise levels.