# Study on the Effect Mechanism of Inlet Pre-Swirl on Pressure Pulsation within a Mixed-Flow Centrifugal Pump

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## Abstract

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## 1. Introduction

## 2. Geometry and Parameters

_{des}= 200 m

^{3}/h. The rated design speed of this mixed-flow centrifugal pump is n

_{des}= 2900 r/min, and the rated design head is H

_{des}= 22.5 m. Therefore, the design specific speed of this mixed-flow centrifugal pump is

## 3. Numerical Modeling

#### 3.1. Model Building

#### 3.2. Governing Equations and Boundary Conditions

_{t}is given by the following equation:

_{1}and F

_{2}are calculated as

_{1}= 0.31, σ

_{k}= 0.85, σ

_{ω}= 0.5, β = 0.075, β* = 0.09.

^{−4}s. The roughness of the solid wall surface in the calculation domain is set to 10 μm, as appropriate for this case. In addition, the isothermal condition is chosen for the heat transfer model, with the residual target set to 10

^{−5}and the discrete format set to second order. It is worth noting that ω-based low Reynolds number turbulence models usually require a very high quality boundary layer mesh at walls (y

^{+}< 2). Taking into account the reasonable allocation of computational resources and the need for accuracy in capturing the boundary layer flow for this numerical calculation, the automatic wall function is enabled to handle the boundary layer flow.

#### 3.3. Grid and Irrelevance Analysis

^{+}of the mesh was controlled to be between 50 and 200, in line with the basic requirements for automatic wall function processing. The meshes of the inlet/outlet sections and the chamber are generated by ANSYS ICEM software. This paper also examines how the accuracy of numerical results is affected by the grid number, which is achieved by controlling the global maximum grid size. This process takes the head and efficiency of the mixed-flow centrifugal pump as the dependent variables and observes the change pattern of the dependent variables by adjusting the global maximum grid size, as shown in Table 2. Observably, when the global maximum grid size is equal to or less than 1.8 mm, the numerical predictions exhibit fluctuations of less than 0.3% for both head and efficiency. As a result, a global maximum grid size of 1.8 mm is adopted for the research.

#### 3.4. Monitoring Points Arrangement

## 4. Results and Discussion

#### 4.1. Pump Performance Validation

_{p}= ±0.5%. The electromagnetic flow meter model is DN200, with a range of 0–400 m

^{3}/h and a permissible error in measurement of D

_{Q}= ±0.5%. The torque meter can measure a maximum torque value of 300 N·m, with a permissible error of D

_{M}= ±0.2% in its torque measurement and a permissible error of D

_{N}= ±0.1% in its rotational speed measurement.

_{des}), the numerical predictions of head and efficiency are slightly higher than the experimental results due to an increase in pump head and internal pressure, leading to an increase in volume losses during the test. However, the change could not be detected by the numerical simulation, resulting in higher numerical results than experimental results. At high flow conditions (1.4 Q

_{des}), the numerical predictions of head and efficiency are significantly lower than the test results due to the strong fluctuation state of the pump head when the flow rate deviates from the rated flow condition. The instantaneous data obtained from the test are located just near the extreme value of the fluctuation state, indicating that the mixed-flow pump exhibits more obvious transient characteristics at this time. In summary, both the numerical results and the experimental results have errors within 4% under full flow conditions (0.6 Q

_{des}~1.4 Q

_{des}), and both keep the same trend with the change of flow rate. Therefore, the numerical methods adopted in this paper have a relatively high accuracy.

#### 4.2. Flow Field Pattern within Impeller and Chamber

#### 4.3. Comparative Analysis of Pressure Pulsation

_{p}, which was calculated as follows.

_{2}is the impeller outlet circumferential velocity, m/s; ρ is the density of liquid medium, kg/m

^{3}.

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

Symbols | |

Q | flow rate, m^{3}/h |

n | rotational speed, r/min |

H | head, m |

n_{s} | specific speed |

Z_{1} | number of impeller blade |

Z_{2} | number of diffuser vane |

D_{in} | diameter of inlet, mm |

D_{Shr} | diameter of shroud, mm |

D_{Hub} | diameter of hub, mm |

D_{Out} | diameter of outlet, mm |

D_{out1} | diameter of outlet outer, mm |

D_{Out2} | diameter of outlet inner, mm |

b_{Out} | width of outlet, mm |

k | turbulent kinetic energy, m^{2}/s^{2} |

ω | turbulent eddy frequency, s^{−1} |

ε | turbulent dissipation rate, m^{2}/s^{3} |

v_{t} | turbulent viscosity, m^{2}/s |

F_{1}, F_{2} | blending function |

S | vorticity, s^{−1} |

y | near-wall distance, m |

y^{+} | dimensionless wall distance |

D_{H} | error in head measurement |

D_{T} | error in shaft power measurement |

D_{Q} | error in flow measurement |

D_{S} | total systematic error |

p | transient pressure, Pa |

$\overline{p}$ | average pressure during impeller rotation circle, Pa |

u_{2} | impeller outlet circumferential velocity, m/s |

ρ | density of liquid medium, kg/m^{3} |

Abbreviations | |

SST | shear stress transport |

GGI | general grid interface |

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**Figure 7.**Circumferential velocity at min-span of impeller with different inlet pre-swirl angle. Tips: The inlet pre-swirl angles from left to right clouds are 0, 10, 20, and 30. (

**a**) 0.6Q

_{des}; (

**b**) Q

_{des}; (

**c**) 1.4Q

_{des}

_{.}

**Figure 8.**Pressure distribution on min-span of the chamber with different inlet pre-swirl angle. Tips: The inlet pre-swirl angles from left to right clouds are 0, 10, 20, and 30. (

**a**) 0.6Q

_{des}; (

**b**) Q

_{des}; (

**c**) 1.4Q

_{des}

_{.}

Impeller | Diffuser | ||
---|---|---|---|

Number of blades Z_{1} | 6 | Number of vanes Z_{2} | 7 |

Diameter of shroud D_{Shr} (mm) | 120 | Diameter of inlet D_{in} (mm) | 187.2 |

Diameter of hub D_{Hub} (mm) | 45.6 | Diameter of outlet outer D_{out1} (mm) | 120 |

Diameter of outlet D_{Out} (mm) | 162 | Diameter of outlet inner D_{Out2} (mm) | 66 |

Width of outlet b_{Out} (mm) | 36 |

Maximum Grid Size (mm) | 2.4 | 2.2 | 2 | 1.8 | 1.6 |

Number of Grids (×10^{6}) | 2.9 | 4.8 | 5.7 | 7.0 | 9.1 |

Predicting Head (m) | 22.68 | 22.55 | 22.39 | 22.36 | 22.37 |

Predicting Efficiency (%) | 84.52 | 83.94 | 83.50 | 83.27 | 83.24 |

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**MDPI and ACS Style**

Ma, X.; Bian, M.; Yang, Y.; Dai, T.; Tang, L.; Wang, J.
Study on the Effect Mechanism of Inlet Pre-Swirl on Pressure Pulsation within a Mixed-Flow Centrifugal Pump. *Water* **2023**, *15*, 1223.
https://doi.org/10.3390/w15061223

**AMA Style**

Ma X, Bian M, Yang Y, Dai T, Tang L, Wang J.
Study on the Effect Mechanism of Inlet Pre-Swirl on Pressure Pulsation within a Mixed-Flow Centrifugal Pump. *Water*. 2023; 15(6):1223.
https://doi.org/10.3390/w15061223

**Chicago/Turabian Style**

Ma, Xiaogang, Mengying Bian, Yang Yang, Tingting Dai, Lei Tang, and Jun Wang.
2023. "Study on the Effect Mechanism of Inlet Pre-Swirl on Pressure Pulsation within a Mixed-Flow Centrifugal Pump" *Water* 15, no. 6: 1223.
https://doi.org/10.3390/w15061223