## 4 The Study about the Distribution Characteristics of Flow-Induced Noise  
### Noise Source Identification and Comparison  
Actually, various flow phenomena exist in different flow passage components of centrifugal pump systems, which include impeller, volute, vane, leakage passage and so on [86; 87; 88]. The various flow phenomena are combined into a noise source for flow-induced noise calculation, which makes the noise source identification and comparison an important part of the distribution characteristics analysis of flow-induced noise. For centrifugal pumps with different structures, the unsteady flow fluctuations in different flow passage components have different contributions to overall noise. As the main flow passage components, the impeller and volute are widely considered. [PERSON] et al. [89] proposed that thenoise source could be identified qualitatively and quantitatively by calculating the standard deviation (STD) of the noise source. As shown in Figure 4, the maximum of STD in volute is located near the volute tongue and extends downstream slightly along the impeller rotation direction, which is much higher than that in other regions and is the main noise source region. [PERSON] et al. [90] also compared sound pressure intensity generated by impeller and volute dipole sources based on Lighthill acoustic analogy theory and found that the minimum of sound pressure intensity induced by the volute dipole source is about 26 dB higher than the maximum of sound pressure intensity induced by the impeller dipole source and the maximum is located near the volute tongue, which also shows that the volute dipole source is the main noise source. Besides the dipole source being obtained by unsteady flow fluctuations, the vibration of pump structures induced by flow could also induce noise, namely the flow-induced structure noise [72], which implies that the vibration is also a kind of noise source. To compare the vibration at different locations of the centrifugal pump system, [PERSON] et al. [80] measured the vibration intensity at different locations of the pump system by using an acceleration sensor, as shown in Figure 5. It is observed that the vibration intensity at the pump body is the largest, followed by pump foot and the vibration intensity at inlet and outlet flanges is the lowest, which means that the vibration of the pump body contributes more to overall noise. The analysis above only discusses the overall vibration intensity at different locations, while the analysis of the relationship between vibration and noise is not involved. Based on coherence analysis, [PERSON] et al. [83] analyzed the distribution characteristics of the vibration signal and noise signal in the frequency domain, as shown in Figure 6. The coherence coefficient between vibration and noise is close to 1 at characteristic frequencies, which further reveals the relationship between vibration and noise. Figure 4: The STD distribution characteristics of noise source [89]. Figure 5: The vibration intensity at different locations of pump system. (a1) inlet flange; (a2) outlet flange; (a3) pump body; (a4) pump foot [80]. Figure 6: _Cont._  
In addition, to further compare the effect of dipole source and vibration on flow-induced noise, [PERSON] et al. [72; 91] compared the internal flow noise and external radiation noise obtained by different noise sources, as shown in Figures 7 and 8. By comparing Figures 7 and 8, it is found that the noise source has different contributions to internal flow noise and external radiation noise. Specifically, the flow-induced noise obtained by a casing (volute, cover, inlet and outlet pipes) dipole source is the highest inside the pump, while the flow-induced structure noise obtained by the acoustic-vibration-coupling method is the highest outside the pump. The analysis reveals that the casing dipole source contributes most to internal flow noise, while the vibration excited by unsteady flow fluctuations makes the biggest contribution to external radiation noise.