# Influence of Channel-Diffuser Blades on Energy Performance of a Three-Stage Centrifugal Pump

^{1}

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## Abstract

**:**

^{3}/h, the head of the pump is 138.67 m and the efficiency of pump is 69.48%.

## 1. Introduction

## 2. Research Model and Numerical Methods

#### 2.1. Research Model

^{3}/h, the overall head is 131 m, and the rotation speed is 1480 r/min. The inducer is the equal-pitch inducer of which the blade number is four. The impeller is the backward inclined type of closed impeller. The key geometric parameters of the impeller and the channel-diffusers are as following. The impeller inlet diameter D

_{1}is 260 mm, the impeller outlet diameter D

_{2}is 420 mm, the impeller outlet width b

_{2}is 48.2 mm, the blade wrap angle of impeller φ

_{1}is 134°, blade number of first-stage impeller is 5, blade number of second-stage impeller and third-stage impeller are 6, the base circle diameter of channel-diffuser D

_{3}is 425 mm, inlet width of channel-diffuser b

_{3}is 52 mm, and the blade wrap angle of channel-diffuser φ

_{2}= 160°, blade number of channel-diffuser is 10, which includes 5 long blades and 5 short blades. Hydraulic structures and 3D models of inducer, impeller and channel-diffuser are shown in Figure 1, Figure 2 and Figure 3. The structure and three-dimensional model of the three-stage centrifugal pump are shown in Figure 4.

#### 2.2. Grid Generation

#### 2.3. Turbulence Model and Boundary Conditions

^{−4}.

## 3. Numerical Calculation Results and Internal Flow Losses Analysis

^{3}/h, 850 m

^{3}/h and 1050 m

^{3}/h are shown in Table 3.

^{3}/h. As can be seen from Figure 6, the velocity distribution in the first-stage impeller is uniform and stable. However, a vortex appeared at the connection of impeller outlet and diffuser inlet. The vortex generated at the connection and was distributed along the inner streamline. Then the vortex developed towards the interior of the channel-diffuser and eventually the entire vortex formed in the inlet of the channel-diffuser, which nearly extended to the transition section of the channel-diffuser blade. There was no visible vortex on the outer streamline. There were still some vortices existing in the connection between second-stage impeller and channel-diffuser, and there were two vortices in the impeller and the channel-diffuser. The distribution of vortices in the second-stage channel-diffuser was similar to that in the first-stage channel-diffuser, but the vortices in the second-stage channel-diffuser were larger, which extended to the outer streamline. The vortex inside the impeller was generated close to the inner streamline of the impeller, which corresponded to that inside the channel-diffuser. The flow pattern in the connection of the third-stage impeller and channel-diffuser was the same as that in the previous stage. The difference is that the generation of the vortex was more serious and the area was larger. At the connection between the channel-diffuser and the next-stage impeller, the vortex and the separation flow generated on outer streamline in the inlet of the impeller.

^{3}/h). As can be seen from Table 4, flow loss in the three-stage impeller increases from the first-stage impeller to the final-stage impeller gradually. The flow loss in first-stage diffuser casing is minimal and the flow loss in third-stage diffuser casing is maximal. The reason is that there are some defects in the design of channel-diffuser, the diffuser could not eliminate the rotational component of the liquid effectively, which then leads to the disorder of the flow regime in the next-stage of the flow passage component and increase flow losses.

## 4. Influence of Channel-Diffuser Blades on Energy Performance of the Pump

#### 4.1. Influence of Channel-Diffuser Blades Inlet Angle on Energy Performance of the Pump

^{3}/h numerically. The calculation results are shown in Table 5.

#### 4.2. Influence of Channel-Diffuser Blades Outlet Angle on Energy Performance of the Pump

^{3}/h. The simulation results are shown in Table 6.

#### 4.3. Influence of Blades Wrap Angle on Energy Performance of the Pump

#### 4.4. Influence of Channel-Diffuser Blades Inlet Shape on Energy Performance of the Pump

^{3}/h) are shown in Table 8. From Table 8, efficiency and head of the pump with diffusion inlet model is higher than twisted inlet model. That is to say that when the flow regime of junction area between impeller outlet and diffuser inlet is improved, the vortices in diffuser will be decreased. In the meantime, the efficiency and head of the pump will be increased.

#### 4.5. Influence of Channel-Diffuser Blades Outer Edge Camber Lines on Energy Performance of the Pump

^{3}/h. The head and efficiency of all the pumps with the non-uniform transition are not as good as that of pumps with uniform transition, which also objectively proved the flow regime in the diffuser with uniform transition outer edge camber lines being better.

#### 4.6. Comparison of Performance between Original and Final Designs

^{3}/h, 850 m

^{3}/h and 1050 m

^{3}/h. The numerical calculation results are compared with the original scheme, as shown in Table 10.

^{3}/h, 850 m

^{3}/h and 1050 m

^{3}/h) are larger than the original channel-diffuser. And efficiency of pump under the flow rate of 850 m

^{3}/h increases from 66.30% to 71.49%, which improved by 5.19 percent.

#### 4.7. Experiment Verification

^{3}/h, head of the pump is 197.08 m. When the flow rate is 850 m

^{3}/h, head of the pump is 136.67 m and efficiency of the pump is 69.48%. When the flow rate is 1050 m

^{3}/h, head of the pump is 116.85 m and efficiency of the pump is 69.89%.

## 5. Conclusions

^{3}/h, the head of pump is 136.67 m and the efficiency of pump is 69.48%.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 5.**Grid of flow passage components: (

**a**) grid of inducer model; (

**b**) grid of first-stage impeller; (

**c**) grid of first-stage diffuser casing.

**Figure 8.**Pressure distributions on the first-stage channel-diffuser blade pressure surface with different inlet angles: (

**a**) 10°; (

**b**) 12°; (

**c**) 15°; (

**d**) 17°; (

**e**) 20°.

**Figure 9.**Pressure distributions on the first-stage channel-diffuser blade pressure surface with different outlet angles: (

**a**) 80°; (

**b**) 85°; (

**c**) 90°.

**Figure 10.**Pressure distributions on the first-stage channel-diffuser blade pressure surface with different wrap angles: (

**a**) 120°; (

**b**) 130°; (

**c**) 140°; (

**d**) 150°; (

**e**) 160°; (

**f**) 170°.

**Figure 12.**Flow in first-stage impeller and first-stage channel-diffuser: (

**a**) twisted inlet; (

**b**) diffusion inlet.

**Figure 13.**Pressure distributions on the first-stage channel-diffuser blade surface with different blades inlet shape: (

**a**) twisted inlet; (

**b**) diffusion inlet.

**Figure 14.**Two different blade outer edge camber lines: (

**a**) non-uniform transition; (

**b**) uniform transition.

**Figure 15.**Flow in first-stage channel-diffuser: (

**a**) non-uniform transition; (

**b**) uniform transition.

**Figure 16.**Pressure distributions on the first-stage channel-diffuser blade surface with different outer edge camber lines: (

**a**) non-uniform transition; (

**b**) uniform transition.

No. | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

Mesh numbers | 4,316,569 | 6,544,729 | 8,569,243 | 9,986,897 | 11,750,827 |

Head/m | 130.99 | 133.26 | 135.02 | 135.87 | 135.75 |

Efficiency/% | 65.42 | 65.89 | 66.30 | 66.32 | 66.31 |

Inlet Section | Inducer | First-Stage Impeller | First-Stage Diffuser Casing | ||
---|---|---|---|---|---|

Mesh numbers | 2,422,142 | 563,153 | 513,670 | 1,150,410 | |

Second-stage impeller | Second-stage diffuser casing | Third-stage impeller | Third-stage diffuser casing | Outlet section | |

Mesh numbers | 509,484 | 1,143,147 | 501,830 | 1,200,924 | 564,483 |

Flow Rate/m^{3}·h^{−1} | 50 | 850 | 1050 |
---|---|---|---|

Head/m | 182.15 | 135.02 | 101.92 |

Efficiency/% | 4.45 | 66.30 | 68.38 |

First-Stage | Second-Stage | Third-Stage | |
---|---|---|---|

Diffuser | 12.46 | 15.76 | 16.38 |

Impeller | 3.42 | 11.10 | 12.22 |

Inducer | 2.71 |

Blade Inlet Angle/° | 10 | 12 | 15 | 17 | 20 |
---|---|---|---|---|---|

Efficiency/% | 67.07 | 68.13 | 67.22 | 66.30 | 63.50 |

Head/m | 135.92 | 136.74 | 136.14 | 135.02 | 134.06 |

Blade Outlet Angle/° | 80 | 85 | 90 |
---|---|---|---|

Efficiency/% | 67.49 | 67.75 | 68.13 |

Head/m | 135.37 | 135.89 | 136.74 |

Blade Wrap Angle/° | 120 | 130 | 140 | 150 | 160 | 170 |
---|---|---|---|---|---|---|

Efficiency/% | 68.09 | 68.63 | 68.28 | 68.67 | 68.13 | 68.34 |

Head/m | 137.59 | 138.16 | 137.74 | 138.02 | 136.74 | 137.55 |

Blade Inlet Shape | Twisted Inlet | Diffusion Inlet |
---|---|---|

Efficiency/% | 68.67 | 71.21 |

Head/m | 138.02 | 139.00 |

Blade Outer Edge Camber Lines | Non-Uniform Transition | Uniform Transition |
---|---|---|

Efficiency/% | 71.21 | 71.49 |

Head/m | 139.00 | 140.30 |

Q = 50 m^{3}/h | Q = 850 m^{3}/h | Q = 1050 m^{3}/h | ||||
---|---|---|---|---|---|---|

Head/m | Efficiency/% | Head/m | Efficiency/% | Head/m | Efficiency/% | |

Original | 182.15 | 4.45 | 135.02 | 66.30 | 101.92 | 68.38 |

Final | 187.56 | 4.93 | 140.30 | 71.49 | 120.41 | 70.28 |

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**MDPI and ACS Style**

Zhao, W.; Hu, J.; Wang, K.
Influence of Channel-Diffuser Blades on Energy Performance of a Three-Stage Centrifugal Pump. *Symmetry* **2021**, *13*, 277.
https://doi.org/10.3390/sym13020277

**AMA Style**

Zhao W, Hu J, Wang K.
Influence of Channel-Diffuser Blades on Energy Performance of a Three-Stage Centrifugal Pump. *Symmetry*. 2021; 13(2):277.
https://doi.org/10.3390/sym13020277

**Chicago/Turabian Style**

Zhao, Wenbin, Jianbin Hu, and Kai Wang.
2021. "Influence of Channel-Diffuser Blades on Energy Performance of a Three-Stage Centrifugal Pump" *Symmetry* 13, no. 2: 277.
https://doi.org/10.3390/sym13020277