# Numerical and Experimental Investigation on Radiated Noise Characteristics of the Multistage Centrifugal Pump

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## Abstract

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_{d}, which corresponds to the maximum efficiency working conditions. Furthermore, the experiment detects that the sound pressure level of the radiated noise in the multistage pump rises linearly with the increase of the rotational speed. Finally, an example of a low noise pump design is processed based on the obtained noise characteristics.

## 1. Introduction

## 2. Method and Basic Theory

#### 2.1. Theory of the Acoustic Simulation

_{ij}is the viscous stress tensor, and the last Lighthill function is expressed as:

_{ij}is the stress tensor, and ${T}_{ij}=\rho {u}_{i}{u}_{j}-{e}_{ij}+{\delta}_{ij}[(p-{p}_{0})-{c}_{0}{}^{2}(\rho -{\rho}_{0})]$; δ

_{ij}is the Kronecker function, ρ is the fluid density, ρ

_{0}is the undisturbed density, c

_{0}is the sound velocity, t is the time, x is the space coordinates, while the i, j represent the direction of the coordinate axis.

_{0}, v

_{0}and p

_{0}respectively represent the static density, static velocity, and static sound pressure. And ρ′, v′, p′, and q′, respectively represent the increment of the density, velocity, sound pressure, and the mass. With some mathematical treatment, the acoustic wave equation is expressed as:

#### 2.2. DES Method

_{v1}is a dimensionless function defined as:

_{v2}and f

_{v3}express dimensionless functions, which is respectively expressed as:

_{w}is expressed as:

_{w}as:

_{DES}= 0.6.

#### 2.3. Simulation Procedure

## 3. Numerical Method

#### 3.1. Study Object

^{3}/h. The single-stage head of the pump is 10 m and the total head is a superposition of the stages. The detailed hydraulic parameters of each stage are presented in Table 1. In order to simplify the model, this study only takes the three-stages hydraulic part of the pump and makes a prototype as shown in Figure 2b for the simulation and experimental test.

#### 3.2. Fluid Field Simulation

#### 3.2.1. Computational Domain

#### 3.2.2. Mesh Generation and Boundary Conditions

^{−4}s.

#### 3.2.3. Flow Field Results

_{d}. This might be related to subsequent acoustic characterization.

_{d}condition, the velocity distribution in the impeller is not uniform and the separation is detected at the inlet of the diffuser. With the increase of the flow rate, the flow field becomes better distributed while the diffusers are impugned by the high-velocity flow. The wake flow induced by the impingement can generate higher pressure pulsations. As pointed out by Gülish [36], the wake flow and the separation in the centrifugal pump gives rise to the pressure pulsations and the subsequent radiated noise.

_{d,}the number of separations is the fewest. This might indicate that minor noise would produce at this flow condition.

_{p}* as shown in Formula (20) is used for further data reduction.

_{2}is the circumferential velocity at the impeller outlet. Afterward, standard deviation C

_{PS}was used to characterize the pressure pulsation intensity of each monitoring point, and fast Fourier transform processing was used to obtain the frequency spectrum of the flow pressure fluctuation.

^{−4}s, the sampling frequency is 5600 Hz. According to the Nyquist sampling theorem, the maximum frequency that can be analyzed is 2800 Hz.

_{d}and 0.8Q

_{d}, there are many low-frequency pulsations smaller than the blade passing frequency for all monitoring points. It means the periodic pressure pulsation caused by the rotor-stator interaction between impeller and positive guide vane is the major source of the pump unstable operation. The 0.8Q

_{d}has the lowest amplitude of the frequency spectrum, which corresponds to the phenomenon that this flowrate present the highest efficiency.

#### 3.3. Radiated Noise Analysis

#### 3.3.1. Computational Domain

#### 3.3.2. Mesh Generation and Boundary Condition

#### 3.3.3. Acoustic Field Results

_{d}, and increases afterward. In addition, there is a slight increase in the SPL around 1500 Hz, which is assumed to be linked with the vibration mode of the pump system.

_{d}, while the sound pressure level reaches the highest near the vane diffuser of the first stage. This is due to the fact that the intensity of the pressure fluctuation at the first stage is highest and the structural strength is relatively lower around the first stage.

## 4. Experimental Verification

#### 4.1. Radiated Noise at the Different Flow Rate

^{3}/h–11.6 m

^{3}/h (0.375Q

_{d}–1.45Q

_{d}). Five positions set for the microphones followed the Chinese standard GB/T 29529-2013 [37], as shown in Figure 16a, consistent with the position of the monitoring point set in the numerical simulation. Figure 16b shows the setup with enclosures. Figure 17 shows the radiated noise of the model pump at different flowrates concerning the above two conditions and the comparison with the numerical simulation results. In order to analyze the variation of the total sound pressure level of the radiated noise of the multi-stage centrifugal pump, the average total sound pressure level ${\overline{L}}_{P}$ is expressed as follows. Where N represents the number of sound monitoring points and L

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

_{d}where the efficiency is the highest. As pointed out by Gülish [24], the sound pressure level of the induced noise is in the inverse relationship with the efficiency. The differences between the simulation and experiment are within the order of 10 dB because the background noise inside the anechoic chamber still provides some disturbance. Although we used sound elimination materials on the pipe system, the motor still emits a strong radiated noise even when we used an enclosure.

#### 4.2. Radiated Noise at the Different Rotational Speed

#### 4.3. Directivity of Radiated Noise at Different Flowrates

_{d}is vertical, which explains that the directivity varies with the change of the flowrate.

## 5. Hydraulic Optimization Design

_{d}, and the highest efficiency zone is widened.

## 6. Conclusions

- (1)
- The sound pressure level in the multi-stage pump increases first and decreases afterward with the increment of the flowrate. The sound pressure level reaches its lowest value at 0.8Q
_{d}, which corresponds to maximum efficiency working conditions. The sound pressure level of the radiated noise in the multistage pump rises linearly with the increase of the rotational speed. - (2)
- The radiated noise of the multi-stage pump is characterized by dipoles. Furthermore, the main frequency of the radiated noise is the blade passing frequency (327 Hz). This fact proves that the rotor-stator interaction between impeller and diffuser is still the main hydraulic exciting force and sound source. In addition, the directivity of the sound source changes with the variation of the flowrate.
- (3)
- Flow-induced radiated noise of the multi-stage centrifugal pump was calculated by the combined CFD(DES)/CA(FEM) method based on the Lighthill acoustic analogy theory. Comparisons of numerical predictions with the measured/analytical results reveal that the model can yield good results on the noise and the flow field. The most important aspect of the hydraulic design of a low-noise multi-stage centrifugal pump is to select the appropriate number of impeller blades and its matched guide vane.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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Geometry | Values | Geometry | Values |
---|---|---|---|

Impeller inlet diameter, D_{j} | 45/mm | Blade outlet angle, β_{2} | 37/° |

Impeller outlet diameter, D_{2} | 103/mm | Impeller blades number, Z_{a} | 7 |

Impeller outlet width, b_{2} | 10/mm | Diffuser vane number, Z_{d} | 12 |

Diffuser inlet diameter, D_{3} | 104.5/mm | Specific speed, n_{s} | 86 |

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

ABS | 1040 | 200 | 0.394 |

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**MDPI and ACS Style**

Si, Q.; Wang, B.; Yuan, J.; Huang, K.; Lin, G.; Wang, C.
Numerical and Experimental Investigation on Radiated Noise Characteristics of the Multistage Centrifugal Pump. *Processes* **2019**, *7*, 793.
https://doi.org/10.3390/pr7110793

**AMA Style**

Si Q, Wang B, Yuan J, Huang K, Lin G, Wang C.
Numerical and Experimental Investigation on Radiated Noise Characteristics of the Multistage Centrifugal Pump. *Processes*. 2019; 7(11):793.
https://doi.org/10.3390/pr7110793

**Chicago/Turabian Style**

Si, Qiaorui, Biaobiao Wang, Jianping Yuan, Kaile Huang, Gang Lin, and Chuan Wang.
2019. "Numerical and Experimental Investigation on Radiated Noise Characteristics of the Multistage Centrifugal Pump" *Processes* 7, no. 11: 793.
https://doi.org/10.3390/pr7110793