# Numerical and Experimental Study on the Flow-Induced Noise Characteristics of High-Speed Centrifugal Pumps

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{0}and the multiple) at the low-frequency region, but also to the frequency of the structural mode (3000–6000 Hz region). Rotor-stator interaction of the pump flow field between the impeller and volute is the main reason of flow-induced noise; unstable flow also contributes to the broadband components in the noise spectrum.

## 1. Introduction

## 2. Research Object and Methods

#### 2.1. Pump Model

_{r}= 10.2 m

^{3}/h, head H

_{r}= 14 m. The pump impeller has 6 blades, with a diameter of 0.063 m.

#### 2.2. Theory of the Proposed CFD/CFA

_{0}denotes density at rest, v is velocity, p is pressure, T denotes the Lighthill’s tensor, c

_{0}is the speed of sound at rest, and τ is the viscous stress tensor. In practice, an acoustic analogy uses a two-step procedure. In the first step, an unsteady flow analysis is used to compute hydrodynamics sources. The second step consists in computing the propagation and radiation of the fluid noise sources. The implementation of the second step can be achieved by using frequency-domain formulation. Harmonic perturbations are considered in such a way that any perturbed quantity p can be written as

_{0}, correspond to acoustic density fluctuations ρ

_{c}. Then, Lighthill’s equation can be rewritten using the frequency domain transform.

_{0}denotes the acoustic wavenumber. Equivalently, Lighthill’s analogy in a frequency domain computation requires the Fourier transform of T in the source term, which means every frequency component of T is a function of all frequency components of v. The weak variational statement as follows.

#### 2.3. Experimental Support

^{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 NI6343 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).

_{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; ρ denotes the fluid density; g denotes the standard acceleration of gravity; P

_{e}is the shaft power calculated by the input power and motor 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].

_{P}is expressed as Equation (3) in order to analyze the variation of the radiated noise levels. N represents the number of sound monitoring points, and L

_{pi}is the total sound pressure level of each sound monitoring point. P

_{ref}is the reference sound pressure, which is equal to 2×10

^{-5}Pa.

#### 2.4. Numerical Setups

#### 2.4.1. Computation Domain and Mesh Generation of the Flow Field

#### 2.4.2. Boundary Conditions and Turbulence Model of the CFD

_{t}, predicted by the RANS model is larger than the local mesh spacing. The actual formulation for a two-equation model is

^{-4}. An appropriate time step is important to perform unsteady flow field calculations. Courant number is always used as a criterion to judge if the time step satisfies the periodic numerical simulation, which is defined by Equation (11) [27]. The time step for the unsteady simulation is set to the value equivalent impeller rotational step of 3. Data from 10 full rotations are stored after the calculation convergence and used as the sound source starting information file.

^{−5}s. Then, the calculated maximum C

_{o}is 6.17, which satisfies the time-step independence.

#### 2.4.3. Computation setup of the acoustic field

_{max}—maximum mesh size for acoustic calculation, c—speed of sound, f

_{max}—maximum frequency identified by acoustic calculation. The maximum frequency covered by the unsteady flow field calculation is 6750 Hz, which identifies the maximum frequency of acoustic calculation to 6750 Hz. The speed of sound in the air is 346 m/s when the temperature reaches 25 °C, and in the water, it is 1497 m/s. Then, the grid size of the acoustic propagation region should be less than 8.54 mm in the air domain and 36.96 mm in the water domain. The maximum grid size of the computational domain used in this paper is 0.0014 m, which can meet the requirements of grid size in the acoustic finite element calculation.

## 3. Experimental Results

#### 3.1. Overall Pump Performances

_{2}—outlet diameter of the impeller, b

_{2}—outlet width of the impeller, u

_{2}—exit circumferential velocity of the impeller. The dimensionless pump performance curves at different rotational speeds are shown in Figure 8. φ

_{r}represents the flow rate coefficient at Q

_{r}. It can be seen that the dimensionless head and efficiency performance curves at different rotational speeds have high similarity, which means the internal flow in the pump also follows a similar law. However, the dimensionless head curve decreases faster at a large flow rate with the increase of rotating speed. These trends can be easily explained by the 1D Euler theory and the general knowledge of the flow phenomena taking place in the impeller under off-design operating conditions. The fluid inside the pump flows faster at higher rotating speed, which leads to more head loss. The high-efficiency area of the efficiency curve moves towards the direction of small flow, and the maximum value of efficiency decreases continuously with the decrease of rotational speed. This is because the operating point of the pump is also determined by the resistance of the circulation system, and the operation condition of the pump at low rotational speed offset to small flowrate (relative to the condition with maximum efficiency). Pumps produce more flow disturbances in the flow field under non-designed conditions. The internal flow is similar and that volume loss is less when the pump is working at a high rotational speed.

#### 3.2. Analysis of Radiation Noise Characteristic

#### 3.2.1. Sound Pressure Level at Different Flow Rates

_{d}. As can be seen from Figure 9, the sound pressure level curve increases slightly with the increase of the flow rate, then increases sharply after a small drop of the amplitude. Associated with the efficiency characteristic curves, the flow rate point that presents the minimum value of the sound pressure level corresponds to the highest efficiency area (0.7 Q

_{r}). In general, the rotor–stator interaction, especially close to the volute tongue, may be considered a very significant energy dissipation mechanism and also the main fluid-borne noise source. When the pump is operating at a low flow rate, there is a clear wake-jet flow structure at the impeller outlet area. The greater extent in the velocity field fluctuation inside the blade channels would result in bigger fluid-borne noise. Increasing efficiency has a certain effect on reducing noise under this condition. When the flow rate exceeds the optimal working condition, the sound pressure level is increased greatly. On the one hand, this is due to the higher velocity level of the fluid in the pump at high flow rates, which causes a stronger rotor-stator interaction effect. Moreover, the coupling effect between the fluid and the structure is enhanced and the fluid load is also increasing, which could cause higher mechanical noise.

#### 3.2.2. Acoustic Directivity at Different Flow Rates

_{r}, the quadrupole shape of the characteristics becomes not so obvious, and the distribution of sound pressure level tends to be uniform at each measuring point. When the flow rate reaches Q

_{r}, the polarity of 45°and 135° measuring points disappears, and the directivity curve shows the characteristics of dipoles. In view of the flow-induced noise mechanism, the backflow at the inlet and outlet of impeller and flow separation from the turbulence inside the flow-path can be regarded as a quadrupole sound source under a small flow rate. The increase of flow rate makes the flow field more uniform, which leads to the decrease of the contribution of the quadrupole sound source to the whole sound field. When the flow rate reaches the design operation point, the interaction between the moving fluid and the solid boundary is enhanced and the contribution of dipole sound source to the radiation noise increases, which becomes the main noise source. At 45° oblique direction, the directivity characteristics of radiation noise are not obvious, which indicates that the directivity characteristics of radiation noise are closely related to the spatial distribution.

#### 3.2.3. Frequency Domain Characteristics of the Radiate Noise

_{r}under 6750 r/min. Another two tests under 5875 and 5000 r/min rotational speed without changing the system resistance characteristics are also processed. Signals from microphone 3, located directly above the pipeline, are used to carry out frequency characteristics analysis. The cutoff frequency of the analysis is 6400 Hz. f

_{0}represents the fundamental frequency, which corresponds to the shaft rotation speed. As can be seen from Figure 11, the energy of the noise of all three rotational speed is mainly concentrated in the low-frequency region. At frequencies higher than 20f

_{0}, the pressure level amplitudes decay rapidly. The noise spectral component shows obvious discreteness; its frequency is the shaft rotation frequency and its multiples. The SPL amplitude is the highest at the blade passing frequency (six times the shaft rotation frequency) because of the rotor–stator interaction influence. The discrete characteristics of the dimensionless frequency spectrum at three pump rotational speed demonstrate the same, so the next numerical simulation can only focus on the situation of 6750 r/min.

## 4. Numerical Results Analysis

#### 4.1. Flow Field Results Analysis

_{r}is equivalent to the flow rate coefficient C

_{q}= 0.0715. Seen from the figure, the simulated and experimental values of both the head coefficient and efficiency are almost the same at Q

_{r}. The maximum error between the test value and the simulated value of the head coefficient is below 5.5% for the full flow rate. From the simulated efficiency curve, the operation point with the highest efficiency is near 0.7Q

_{r}. At the small flow rate condition, the test value of efficiency is close to the simulated ones. The maximum error is not higher than 4.3% for the full flow rate. Therefore, the selected calculation model used in the simulation can be considered to accurately predict the performance of the pump and could be used to translate pump internal flow information for further analysis.

_{r}), the number of vortices gradually increased, and the size continued to expand, which severely affected the impeller operation and caused noise problems. In addition to 0.7Q

_{r}, flow separation near the volute tongue also occurred, which also became a source of flow-induced noise. The special structure of the exit with a 90° corner also caused a vortex, which resulted in a significant hydraulic problem.

_{r}. Due to insufficient flow, large areas of backflow and secondary flow exist in the impeller flow channel at a low flow rate (0.5Q

_{r}), showing relatively high vorticity and asymmetric distribution. Under large flow conditions, the vortex diffuses into the impeller flow channel, which is related to the high-speed area at the leading edge of impeller blade. In addition, a small amount of high-energy vortex mass also appears at the exit of the volute. When the vorticity moves in the same direction of the mean flow inside the rotational impeller, the energy dissipation rate on the blade surface will be reduced. On the contrary, it is not conducive to the fluid energy conversion between the impeller and the volute, which explains the head and efficiency dropping at large flow rates. To be fair, the hydraulic design of this model pump is not excellent due to space constraints, resulting in lower hydraulic efficiency and vibration and noise problems.

#### 4.2. Unsteady Flow Characteristic Analysis

_{p}is introduced to characterize the pressure pulsation intensity at each monitoring point [29]. C

_{p}is defined by Equation (15), with p denoting the static pressure and p standing for the averaged static pressure.

_{p}in the time domain, the frequency domain amplitude coefficients C

_{p}

^{*}of the pressure pulsation at every monitoring point are obtained. The trusted sampling frequency is 6756 Hz based on DES unsteady calculation, which could cover the analysis frequency range of flow-induced noise from the experiment information. The location and spectrum of the monitoring points are shown in Figure 15. As seen from it, the spectrum curves present discrete characteristics; the main frequency of mostly monitoring points is blade passing frequency (6f

_{0}= 675 Hz) and its multiple due to the rotor–stator interaction between the impeller and the volute. The characteristic frequency is concentrated in the low-frequency region; the pulsation peak decreases after increasing above the threshold of 30f

_{0}. C

_{p}

^{*}appears largest at the impeller exit area, especially around the volute tongue (P6, P7, P8). Affected by unstable flow phenomena such as flow separation and stall in the impeller, pulsations also obviously exist below 6f

_{0}. The main frequency of P11 located at the inlet of the impeller blade is 2f

_{0}, which may be due to the stall phenomenon in the flow channel. The main frequencies of P9 and P10 are also 6f

_{0}, which indicates that the pump’s outlet pressure wave propagation is characterized by rotor–stator interaction as dipole characteristics.

_{0}presents the moment that one blade passes the volute tongue. T means 1/(6f

_{0}). The shape and size of the flow vortex in each of the six flow-paths are different and there is relative motion with the direction of impeller rotation. The flow field does not change much from the volute tongue to the pump outlet during a blade passing time. Many flow pulsations occur with a period higher than one blade passage time, which is reflected by the low-frequency characteristic of the pressure pulsation for each monitoring point. Low-speed vortices areas are generated, developed, and disappear in the impeller flow path and, mostly, at the impeller outlet. The velocity varies greatly at the impeller blade inlet, which corresponds to the peak value of pressure pulsation amplitude at P11. The main reason for the change of the flow field is still the unsteady flow of the impeller and rotor–stator interaction between the blade and the volute tongue.

#### 4.3. Modal Analysis

#### 4.4. Acoustic Field Results Analysis

#### 4.4.1. Fluid-Borne Noise

_{r}. The coupling effect of the pump shell is considered in the simulation. Distribution map of sound pressure level and the spectrum curve of field point located at the pump outlet are shown in Figure 18. It can be seen from the figure that the sound pressure level is steadily decreasing from volute inlet to volute outlet. The regions with the highest sound pressure level are distributed at the impeller outlet, especially the volute tongue area. That might be because of the rotor-stator interaction between the rotating impeller and stationary volute. Flow-path space of the spiral volute start from the first cross-section is increased and eventually becomes big enough for the passing fluid, which results in weakening of sound source intensity. The frequency spectrum of predicted noise is dominated by discrete frequencies. The sound pressure level in the low-frequency area is relatively high overall; f

_{0}and 6f

_{0}(675Hz) are the main frequencies, which are consistent with the aforementioned noise test and flow field simulation results. There are relatively large peaks between 3000–6000 Hz, which might be due to the coupling of the pump shell and the vibro-acoustic interaction.

#### 4.4.2. Fluid-Induced Radiated Noise

## 5. Conclusions

_{0}) at the low-frequency region, but also to the natural vibration frequency of the structural mode (3000–6000 Hz region).

_{0}), which further causes the radiated noise to show dipole characteristics. Therefore, rotor–stator interaction between the rotating impeller and stationary volute of the pump flow field is the main cause of flow-induced noise. The unstable flow such as the stall vortex in the pump impeller and the flow separation in the tongue area lead to the broadband characteristics of pressure pulsation concentrated at the low-frequency region, which also present in the noise spectrum.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Gülich, J.F. Centrifugal Pumps, 3rd ed.; Springer: Berlin/Heidelberg, Germany, 2014. [Google Scholar]
- Guo, C.; Gao, M.; He, S.Y. A review of the flow-induced noise study for centrifugal pumps. Appl. Sci.
**2020**, 10, 1022. [Google Scholar] [CrossRef] [Green Version] - Wu, Y.L.; Li, S.C.; Liu, S.H.; Dou, H.S.; Qian, Z.D. Vibration of Hydraulic Machinery; Springer: Dordrecht, The Netherlands, 2013. [Google Scholar]
- Zhong, S.Y.; Huang, X. A review of aero acoustics and flow-induced noise: For beginners. Acta Aero Dyn. Sin.
**2018**, 36, 363–371. [Google Scholar] - Lighthill, M. On sound generated aerodynamically: I. general theory. Proc. R. Soc. Lond.
**1954**, 222, 1–32. [Google Scholar] - Si, Q.R.; Ali, A.; Yuan, J.P.; Fall, I.; Muhammad, F.Y. Flow-induced noises in a centrifugal pump: A review. Sci. Adv. Mater.
**2019**, 11, 909–924. [Google Scholar] [CrossRef] - Simpson, H.C.; Macaskill, R.; Clark, T.A. Generation of hydraulic noise in centrifugal pumps. Proc. Instn. Mech. Engrs.
**1966**, 181, 84–108. [Google Scholar] - Chu, S.M.; Dong, R.Y.; Katz, J. Relationship between unsteady flow pressure fluctuations and noise in a centrifugal pump. Part A: Effects of blade-tongue interactions. J. Fluid Eng.-T ASME
**1995**, 117, 24–29. [Google Scholar] [CrossRef] - Chu, S.M.; Dong, R.Y.; Katz, J. Relationship between unsteady flow pressure fluctuations and noise in a centrifugal pump. Part B: Effects of blade-tongue interactions. J. Fluid Eng.-T ASME
**1995**, 117, 30–35. [Google Scholar] [CrossRef] - Choi, J.S.; Mclaughlin, D.K.; Thompson, D.E. Experiments on the unsteady flow field and noise generation in a centrifugal pump impeller. J. Sound Vib.
**2003**, 263, 493–514. [Google Scholar] [CrossRef] - Černetič, J. The use of noise and vibration signals for detecting cavitation in kinetic pumps. Proc. Inst. Mech. Eng. C
**2009**, 223, 1645–1655. [Google Scholar] [CrossRef] - Langthjem, M.A.; Olhoff, N. A numerical study of flow-induced noise in a two-dimensional centrifugal pump, Part II. Hydroacoustics. J. Fluid Struct.
**2004**, 19, 369–386. [Google Scholar] [CrossRef] - Parrondo, J.; Pérez, J.; Barrio, R.; Gonzales, J. A simple acoustic model to characterize the internal low frequency sound field in centrifugal pumps. Appl. Acoust.
**2011**, 72, 59–64. [Google Scholar] [CrossRef] - Keller, J.; Barrio, R.; Parrondo, J.; Barrio, R.; Fernandez, J.; Blanco, E. Effects of the pump-circuit acoustic coupling on the blade-passing frequency perturbations. Appl. Acoust.
**2014**, 76, 150–156. [Google Scholar] [CrossRef] - Mao, X.L.; Pavesi, G.; Chen, D.Y. Flow induced noise characterization of pump turbine in continuous and intermittent load rejection processes. Renew. Energy
**2019**, 139, 1029–1039. [Google Scholar] [CrossRef] - Jiang, Y.Y.; Yoshimura, S.; Imai, R.; Katsura, H.; Yoshida, T.; Kato, C. Quantitative evaluation of flow-induced structural vibration and noise in turbomachinery by full-scale weakly coupled simulation. J. Fluid Struct.
**2007**, 23, 531–544. [Google Scholar] [CrossRef] - Si, Q.R.; Shen, C.H.; Ali, A.; Cao, R.; Yuan, J.P.; Wang, C. Experimental and numerical study on gas-liquid two-phase flow behavior and flow induced noise characteristics of radial blade pumps. Process
**2019**, 7, 920. [Google Scholar] [CrossRef] [Green Version] - Si, Q.R.; Wang, B.B.; Yuan, J.P.; Huang, K.L.; Lin, G.; Wang, C. Numerical and experimental investigation on radiated noise characteristics of the multistage centrifugal pump. Processes
**2019**, 7, 793. [Google Scholar] [CrossRef] [Green Version] - Kapellos, C.S.; Papoutsis-Kiachagias, EM.; Giannakoglou, K.C.; Hartmann, M. The unsteady continuous adjoint method for minimizing flow-induced sound radiation. J. Comput. Phys.
**2019**, 392, 368–384. [Google Scholar] [CrossRef] [Green Version] - Velarde, S.; Tajadura, R. Numerical simulation of the aerodynamic tonal noise generation in a backward-curved blades centrifugal fan. J. Sound Vib.
**2006**, 295, 781–786. [Google Scholar] - Cravero, C.; Marsano, D. Numerical Prediction of Tonal Noise in Centrifugal Blowers. In Proceedings of the Turbo Expo 2018: Turbomachinery Technical Conference & Exposition, Oslo, Norway, 11–15 June 2018. [Google Scholar]
- Caro, S.; Ploumhans, P.; Gallez, X. Implementation of Lighthill’s Acoustic Analogy in a Finite/Infinite Elements Framework. In Proceedings of the 10th AIAA/CEAS Aeroacoustics Conference, Manchester, UK, 10–12 May 2004. [Google Scholar]
- International Organization for Standardization (ISO). ISO 9906: 2012 Rotodynamic Pumps-Hydraulic Performance Acceptance Tests—Grades 1, 2 and 3; ISO: Geneva, Switzerland, 2012. [Google Scholar]
- Si, Q.R.; Lu, R.; Shen, C.H.; Xia, S.J.; Sheng, G.C.; Yuan, J.P. An intelligent CFD-based optimization system for fluid machinery: Automotive electronic pump case application. Appl. Sci.
**2020**, 10, 366. [Google Scholar] [CrossRef] [Green Version] - Huang, K.; Yuan, J.; Si, Q.; Lin, G. Numerical simulation on pressure pulsation in multistage centrifugal pump under several working conditions. J. Drain. Irrig. Mach. Eng.
**2019**, 37, 387–392. [Google Scholar] - Strelets, M. Detached Eddy Simulation of Massively Separated Flows. In Proceedings of the 39th Aerospace Sciences Meeting and Exhibit, Reno, NV, USA, 8–11 January 2001. [Google Scholar]
- Si, Q.; Bois, G.; Liao, M.; Zhang, H.; Cui, Q.; Yuan, S. A comparative study on centrifugal pump designs and two-phase flow characteristic under inlet gas entrainment conditions. Energies
**2020**, 13, 65. [Google Scholar] [CrossRef] [Green Version] - Free Field Technologies Co. MSC Actran14.1 User’s Guide; Free Field Technologies, Co.: Mont-Saint-Guibert, Belgium, 2012. [Google Scholar]
- Yang, J.; Xie, T.; Liu, X.H.; Si, Q.R.; Liu, J. Study of unforced unsteadiness in centrifugal pump at partial flow rates. J. Therm Sci.
**2019**. [Google Scholar] [CrossRef]

**Figure 6.**The sound field calculation: (

**a**) water flow domain; (

**b**) pump casing structure; (

**c**) air radiation sound fields.

**Figure 8.**Pump performance curves at different rotational speed: (

**a**) dimensionless head curve; (

**b**) pump efficiency curves.

**Figure 10.**Half directivity characteristics curves of radiated noise at different operating conditions: (

**a**) vertical direction; (

**b**) skew 45 °direction.

**Figure 13.**Velocity streamline line of model pump: (

**a**) 0.5 Q

_{r}, (

**b**) 0.7 Q

_{r}, (

**c**) 1.0 Q

_{r}, (

**d**) 1.2Q

_{r}.

**Figure 14.**Vortex distribution of model pump: (

**a**) 0.5 Q

_{r}, (

**b**) 0.7 Q

_{r}, (

**c**) 1.0 Q

_{r}, (

**d**) 1.2 Q

_{r}.

**Figure 15.**Spectrum of pressure fluctuation in the cooling pump at Q

_{r}: (

**a**) monitoring points location; (

**b**) pressure spectrum of P1–P4; (

**c**) pressure spectrum of P5–P8; (

**d**) pressure spectrum of P9–P11.

**Figure 16.**Velocity vortex distribution under Q

_{r}: (

**a**) t = t

_{0}; (

**b**) t = t

_{0}+ 1/2T; (

**c**) t = t

_{0}+ T; (

**d**) t = t

_{0}+ 3T; (

**e**) t = t

_{0}+ 5.5T.

**Figure 18.**Fluid-borne noise characteristics at Q

_{r}: (

**a**) the L

_{p}contour at 6f

_{0}with unit dB; (

**b**) spectrum curve.

**Figure 19.**Radiated noise characteristics under 6f

_{0}: (

**a**) cloud map; (

**b**) directivity and radiated noise level curve.

Material | Density/(kg/m^{3}) | Young’s Modulus/GPa | Poisson Ratio |
---|---|---|---|

PPS | 1500 | 11.95 | 0.4 |

ADC | 2700 | 71 | 0.33 |

Mode | Natural Frequency/Hz | Mode | Natural Frequency/Hz |
---|---|---|---|

1st mode | 928.29 | 6th mode | 3702.2 |

2nd mode | 1095.7 | 7th mode | 3840.5 |

3rd mode | 2045.2 | 8th mode | 4767.8 |

4th mode | 2932.3 | 9th mode | 5089 |

5th mode | 3670.6 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Si, Q.; Shen, C.; He, X.; Li, H.; Huang, K.; Yuan, J.
Numerical and Experimental Study on the Flow-Induced Noise Characteristics of High-Speed Centrifugal Pumps. *Appl. Sci.* **2020**, *10*, 3105.
https://doi.org/10.3390/app10093105

**AMA Style**

Si Q, Shen C, He X, Li H, Huang K, Yuan J.
Numerical and Experimental Study on the Flow-Induced Noise Characteristics of High-Speed Centrifugal Pumps. *Applied Sciences*. 2020; 10(9):3105.
https://doi.org/10.3390/app10093105

**Chicago/Turabian Style**

Si, Qiaorui, Chunhao Shen, Xiaoke He, Hao Li, Kaile Huang, and Jianping Yuan.
2020. "Numerical and Experimental Study on the Flow-Induced Noise Characteristics of High-Speed Centrifugal Pumps" *Applied Sciences* 10, no. 9: 3105.
https://doi.org/10.3390/app10093105