# Numerical Simulation of Flow-Induced Noise in Horizontal Axial Flow Pumps in Forward and Reverse Conditions

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## Abstract

**:**

## 1. Introduction

## 2. Numerical Simulation

#### 2.1. Governing Equations

#### 2.2. Calculation Model

^{3}/s; the design head is 2.5 m; the rated speed is 250 r/min, and the number of runner blades is four, that of the front guide vanes is five, and that of the active guide vanes is seven.

#### 2.3. Meshing

#### 2.4. Numerical Setup and Monitoring Points

^{−4}. The inlet and outlet boundary conditions are set as mass inlet and free outflow boundary conditions. When calculating the working conditions of the turbine in reverse, the inlet is the total pressure inlet, and the outlet is the static pressure outlet.

_{o}is 44.8, which satisfies the time-step independence.

#### 2.5. Sound Field Calculation

^{3}), ${\rho}_{0}$ is the average density (kg/m

^{3}), t is time (s), and ${c}_{0}$ is the speed of sound. ${X}_{i}$ and ${X}_{j}$ both represent spatial coordinates; ${T}_{ij}$ represents the Lighthill stress tensor; f represents the solid boundary function, and ∇ represents the Laplace operator. p represents the flow field pressure (Pa); ${p}_{0}$ represents the time-averaged pressure value (Pa), and ${\delta}_{ij}$ is the Kronecker function.

_{water}is 1500 m/s, and c

_{air}is 340 m/s. Because the time step set in the unsteady calculation is 0.002 s, f

_{max}is 500 Hz. Then, it can be obtained that L must be less than 113 mm. The maximum grid size is 60 mm, which provides a good calculation. The total number of grids is 1.2 million. The material selected for the blade part is ZG06Cr13Ni4Mo; the density is 7730 kg/m

^{3}; the pump water body is used as the inner sound field, and the external air is set as the outer sound field. The sound wave propagation speed in the inner sound field is 1500 m/s, and the sound wave propagation speed in the air is 340 m/s. The medium of the internal sound field is water, whose density is 1000 kg/m

^{3}, and the water temperature is 25 °C. The medium of the external sound field is air, whose density is 1.255 kg/m

^{3}.

## 3. Test Verification

#### 3.1. External Characteristic Test

#### 3.2. Pressure Pulsation Test

## 4. Results

#### 4.1. Comparison of Experiment and Simulation

^{3}).

#### 4.2. Flow Field Analysis

#### 4.3. Sound Field Analysis

## 5. Conclusions

- The axial flow pump’s external characteristic curve obtained from the numerical simulation slightly deviates from the test value at a low flow rate, and the rest is consistent with the test value. The error is within a reasonable range. The pressure pulsation is obtained from the simulation, and the test value is obtained from the measurement. The changes with time are similar, and the primary and secondary frequency distributions are the same, indicating that the results obtained from the numerical simulation can effectively verify the test results and have high reliability.
- The unit’s pressure pulsation during forward operation is much larger than during reverse operation, and the pressure pulsation at the runner’s inlet and outlet is significantly higher than the pressure pulsation in the bladeless area. When the unit is in the pump condition, the blade frequency is the primary pressure pulsation frequency at the runner’s inlet and outlet. On the monitoring surface far from the runner chamber, the primary pressure pulsation frequency is the rotation frequency. The primary frequency at the leaf outlet is the pilot frequency, indicating that static interference and dynamic interference primarily affect the pressure pulsation and have a specific relationship with the number of blades. With the increase in flow rate, the pressure pulsation amplitude decreases. The flow state is poor at a low flow rate, and spurious frequencies occur in the low-frequency band. Avoiding the operation of low flow conditions can effectively reduce the pressure pulsation and protect the unit.
- The flow-induced noise is distributed symmetrically at each blade frequency and has dipole characteristics. At the first-order blade frequency, the sound field’s radiation characteristics are the strongest, and the sound pressure amplitude is the largest. The sound pressure amplitude decreases, and the sound field radiation characteristics under the pump condition are significantly stronger than that of the turbine at the same flow rate. Consistent with the pressure pulsation change, the blade frequency primarily affects the flow-induced noise sound field distribution and the radiation characteristics. The same is true for the sound pressure distribution variation with flow rate.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Flow channel diagram. 1. Inlet channel. 2. Front guide vane. 3. Runner. 4. Guide vane. 5. Outlet channel.

**Figure 3.**Unstructured mesh in some regions of the axial flow pump in the flow field. (

**a**) Front guide vane area. (

**b**) Turbine blade region. (

**c**) Active guide vane region.

**Figure 7.**Experimental setup. (

**a**) Monitoring point layout. (

**b**) Pressure sensor. (

**c**) Measuring instrument.

**Figure 8.**Comparison of experimental and numerical simulation results. (

**a**) Time domain diagram of inlet pressure pulsation of preguide vanes. (

**b**) Time domain diagram of runner inlet pressure pulsation. (

**c**) The frequency domain diagram of the inlet pressure pulsation of the front guide vane. (

**d**) Frequency domain diagram of runner inlet pressure pulsation.

**Figure 10.**Frequency domain distribution of pressure pulsation in pump working conditions. (

**a**) Monitoring point a3 (

**b**) Monitoring point b3. (

**c**) Monitoring point c3.

**Figure 11.**The frequency domain distribution of pressure pulsation under turbine operating conditions. (

**a**) Monitoring point a3 (

**b**) Monitoring point b3. (

**c**) Monitoring point c3.

**Figure 12.**Amplitude distribution of sound pressure amplitude in pump conditions. (

**a**) 1.0 Q first-order leaf frequency sound pressure amplitude. (

**b**) 1.0 Q second-order leaf frequency sound pressure amplitude. (

**c**) 1.0 Q third-order leaf frequency sound pressure amplitude.

**Figure 13.**Amplitude distribution of sound pressure in turbine operating conditions. (

**a**) 1.0 Q first-order leaf frequency sound pressure amplitude. (

**b**) 1.0 Q second-order leaf frequency sound pressure amplitude. (

**c**) 1.0 Q third-order leaf frequency sound pressure amplitude.

**Figure 14.**Noise directivity distribution at the sound source. (

**a**) First-order. (

**b**) Second-order. (

**c**) Third-order.

Pump | 1700ZWSQ10-2.5 | Blade Placement Angle | –6° ~ + 4° |
---|---|---|---|

Diameter of impeller | 1.7 m | Impeller center elevation | 1 m |

Number of impeller blades | 4 | Design discharge | 10 m^{3}/s |

Number of front guide vanes | 5 | Design head | 2.5 m |

Number of guide vanes | 7 | Design speed | 250 r/min |

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**MDPI and ACS Style**

Wu, D.; Bai, Y.
Numerical Simulation of Flow-Induced Noise in Horizontal Axial Flow Pumps in Forward and Reverse Conditions. *Water* **2023**, *15*, 322.
https://doi.org/10.3390/w15020322

**AMA Style**

Wu D, Bai Y.
Numerical Simulation of Flow-Induced Noise in Horizontal Axial Flow Pumps in Forward and Reverse Conditions. *Water*. 2023; 15(2):322.
https://doi.org/10.3390/w15020322

**Chicago/Turabian Style**

Wu, Donglei, and Yalei Bai.
2023. "Numerical Simulation of Flow-Induced Noise in Horizontal Axial Flow Pumps in Forward and Reverse Conditions" *Water* 15, no. 2: 322.
https://doi.org/10.3390/w15020322