## 2 The Generation Mechanism and Propagation Route of Flow-Induced Noise  
Flow-induced noise, which is related to various complex phenomena inside pumps, plays a crucial role in the noise level evaluation of centrifugal pumps with good structural design and stable installation [11]. Table 1 summarizes the different flow phenomena and noise generation mechanisms. To evaluate the noise level generated by the above phenomena, the most widely used standard is the sound pressure level (SPL) and total sound pressure level (TSPL). SPL and TSPL are defined as,  
\[SPL=20\lg\frac{P_{e}}{P_{ref}} \tag{1}\]  
\[TPSL=10\lg\sum_{i=1}^{n}10^{SPL_{i}/10}, \tag{2}\]  
where \(P_{ref}\) is the reference sound pressure (\(2\times 10^{-5}\) Pa in air, \(1\times 10^{-6}\) Pa in water), \(n\) is the number of frequencies, \(P_{e}\) is the effective sound pressure and it is defined as,  
\[P_{e}=\sqrt{\frac{1}{T}}\int_{0}^{T}p^{2}dt, \tag{3}\]  
where \(p^{\prime}\) is the instantaneous sound pressure, \(T\) represents several rotational periods. In addition, other parameters used for noise level evaluation, such as the sound power level and sound energy density [25], could be calculated from the SPL and TSPL, which are not discussed here. Figure 1: Paper publication information related directly to flow-induced noise of centrifugal pumps. Currently, analysis of the noise induced by rotor-stator interaction and cavitation accounts for the majority. (1) Rotor-stator interaction  
In the process of fluid motion, the physical quantities, such as pressure, velocity and vorticity, at a certain spatial point inside pumps fluctuate rapidly once as a blade passes. With blades continuously rotating, the physical quantities fluctuate periodically [26], that is, the rotor-stator interaction effect exists in whole pumps. As the main cause of flow-induced noise, the rotor-stator interaction could cause the frequency response characteristics of flow-induced noise at different monitoring points that are dominated by characteristic frequencies such as the blade-passing frequency (\(f_{b}\)) and its harmonic frequencies in a low frequency band. As shown in Figure 2, the SPL reaches to peak at 290 Hz (\(f_{b}\)) and its high order harmonics and also shows a trend of fluctuating downward. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Flow Phenomena** & **References** & **Noise Generation Mechanism** \\ \hline Rotor-stator interaction & [12; 13; 14] & Periodic interference occurs between blade and volute. The flow passage width changes periodically, which causes periodic pressure fluctuations and noise. \\ \hline Cavitation & [15; 16; 17] & The generated-bubbles due to cavitation implode in contact with solid surface in high pressure region, which induce pressure waves that result in the generation of noise. \\ \hline Turbulence & [18; 19] & Combined with the jet-wake effect at impeller outlet, the interaction between blade and high-speed fluid causes the blade acted by the unsteady load continuously and broadband noise is generated. \\ \hline Back flow & [20] & Pre-rotation occurs at impeller inlet, strong eddy and eddy strip are formed. Then pressure fluctuations with low frequency are generated and further induce the low frequency noise. \\ \hline Rotating stall & [21; 22] & Under low flow rate condition, stall vortex is formed in impeller, which blocks the flow passage and induces low frequency noise. \\ \hline Water hammer & [23; 24] & Rapid change of flow velocity occurs, which could induce intermittent noise. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Complex flow phenomena and flow-induced noise generation mechanism. Figure 2: Frequency response characteristics of noise induced by rotor-stator interaction at inlet and outlet pipes [27]. (2) Cavitation  
Different from the noise induced by rotor-stator interaction, the noise induced by cavitation is a kind of broadband noise and concentrates in a high frequency band [28]. During the cavitation inception stage, the noise level decreases slightly in the broadband band [29].