# Energy Characteristics and Internal Flow Field Analysis of Centrifugal Prefabricated Pumping Station with Two Pumps in Operation

^{1}

^{2}

^{*}

## Abstract

**:**

_{d}= 33.93 m

^{3}/h) is 63.96%, the head is 8.66 m, the head at the starting point of the saddle area is 10.50 m, which is 1.21 times of the designed head. The efficiency of the high-efficiency zone of the prefabricated pump station is 58.0~63.0%, and the corresponding flow range is 0.62Q

_{d}~1.41Q

_{d}(21.0~48.0 m

^{3}/h). The uniformity of the inlet flow rate of impeller of pump 1 is 74.70%, and that of pump 2 is 75.57%. The flow fields of water pumps on both sides are inconsistent. The results of the flow field indicate that there are severe back flow phenomena at the prefabricated bucket intake, more back flow in the bucket, and many eddies on the side wall. With the increase in flow rate, the eddy structure at the intake expands continuously and moves towards the center area, which has a negative impact on the flow field in the center area. The research results of this paper can provide a theoretical reference for the research and operation of the same type of prefabricated pumping stations.

## 1. Introduction

## 2. Three-Dimensional Modeling and Numerical Calculation Setup

#### 2.1. Calculation Model

#### 2.2. Meshing

_{d}= 33.93 m

^{3}/h) are selected for the numerical calculation of the centrifugal prefabricated pumping station, and the efficiency of the centrifugal prefabricated pumping station is used as the evaluation index. It can be seen from Figure 3 that when the number of grids is between 0.9 million and 3 million, the efficiency changes greatly and is unstable. When the number of grids reaches 3.2 million, the efficiency curve basically remains unchanged, indicating that the increase in the number of grids has little impact on the calculation results [19]. Considering the computer performance and the accuracy of the calculation results, this paper selects 3.2 million grids for numerical calculation.

#### 2.3. Boundary Conditions and Turbulence Model

^{−5}, and in principle, the smaller the residuals are, the better.

#### 2.4. Calculation Formula

#### 2.4.1. Control Equations

^{3}); x

_{i}and x

_{j}are spatial coordinates; u

_{i}and u

_{j}are the velocity components of the fluid parallel to the corresponding axes x

_{i}and x

_{j}, respectively, and F

_{i}is the volume force component in the i-direction; μ is the fluid dynamic viscosity coefficient; P is the pressure (Pa).

_{k}, G

_{ω}is the generating term of the equation; Y

_{k}, Y

_{ω}is the generating term of the diffusive action; S

_{k}, S

_{ω}is the user-defined source term; D

_{ω}is the term generated by the orthogonal divergence; k is the turbulent kinetic energy; ω is the turbulent special dissipation; μ

_{t}is turbulent dynamic viscosity coefficient.

#### 2.4.2. Hydraulic Performance Prediction

^{3}/s; H

_{1}, H

_{2}—prefabricated barrel inlet and outlet section elevation, m.

_{1}, s

_{2}—prefabricated barrel inlet and outlet section area; u

_{1}, u

_{2}—prefabricated barrel inlet and outlet flow velocity at each point, m/s; u

_{t}

_{1}, u

_{t}

_{2}—prefabricated barrel inlet and outlet section flow velocity normal component at each point, m/s.

_{1}, P

_{2}—prefabricated barrel inlet and outlet section at each point of the static pressure, Pa; g—gravitational acceleration, m/s

^{2}.

#### 2.4.3. Uniformity of Flow Velocity Distribution

_{zu}of the section at the impeller inlet reflects the water inlet quality of the impeller, and the closer V

_{zu}is to 100%, the more uniform the water inlet of the impeller is, and its calculation formula is as follows [30]:

_{zu}—uniformity of flow velocity distribution at impeller inlet, %; V

_{a}—arithmetic mean of axial flow velocity at impeller inlet; V

_{ai}—axial velocity of each calculation unit at impeller inlet, m/s; n—number of calculation units at impeller inlet.

## 3. Energy and Internal Flow Characteristics Analysis

^{3}/h (0.33Q

_{d}), 16.96 m

^{3}/h (0.50Q

_{d}), 22.62 m

^{3}/h (0.67Q

_{d}), 28.27 m

^{3}/h (0.83Q

_{d}), 33.93 m

^{3}/h (1.00Q

_{d}), 39.58 m

^{3}/h (1.17Q

_{d}), 45.24 m

^{3}/h (1.33Q

_{d}), 50.89 m

^{3}/h (1.50Q

_{d}), 56.55 m

^{3}/h (1.67Q

_{d}), 62.20 m

^{3}/h (1.83Q

_{d}), 67.86 m

^{3}/h (2.00Q

_{d}), 73.51 m

^{3}/h (2.17Q

_{d}), and 79.17 m

^{3}/h (2.33Q

_{d}); design flow working condition is Q

_{d}= 33.93 m

^{3}/h.

#### 3.1. Energy Characteristics Analysis

^{3}/h), and at the flow condition 0.33Q

_{d}(Q = 11.31 m

^{3}/h), the centrifugal prefabricated pumping station enters the flow instability condition (saddle zone effect area), and this phenomenon can be obviously found through the head, the head increases less from 0.50Q

_{d}to 0.33Q

_{d}, and the slope of growth here is close to 0 from the head curve and reaches the maximum value at the design condition (Q

_{d}= 33.93 m

^{3}/h) with the maximum efficiency value of 63.96% and the head is 8.66 m. The head at the starting point of the saddle area is 10.50 m, which is 1.21 times the design head, indicating that the operable head range for small flow is small and the operable head range for large flow is wide. Under the high flow rate condition (Q = 33.93~79.17 m

^{3}/h), the efficiency decreases gradually with the increase in flow rate. The slope of the efficiency curve change increases with increasing flow rate. When the flow rate is between 21.0~48.0 m

^{3}/h, the prefabricated pumping station is in the high-efficiency zone (the high-efficiency zone is defined as the range of flows where the efficiency of the optimal efficiency point decreases by 5%); at this time, the pumping station device efficiency is around 58.0~63.0%. The head curve of the prefabricated pumping station gradually decreases with the increase in flow, from 10.50 m to 0.57 m, and the efficiency curve is parabolic with the increase in flow; the head curve is approximately straight with a small change in slope.

_{d}(Q = 28.27 m

^{3}/h), the uniformity of flow velocity at the impeller inlet remains basically the same with the increase in flow rate. Overall, the uniformity of flow velocity at the impeller inlet of pump 2 is greater than that of pump 1; at the design working condition (Q

_{d}= 33.93 m

^{3}/h), the uniformity of flow velocity at the impeller inlet of pump 1 is 74.70%, and that of pump 2 is 75.57%, with a difference of 0.87%, which is caused by the different uniformity of flow velocity at the impellers of pump 1 and pump 2 due to bias flow. When the flow condition is less than 0.83Q

_{d}(Q = 28.27 m

^{3}/h), the uniformity of flow velocity at the impeller inlet decreases significantly, which indicates that the unevenness of the flow pattern inside the prefabricated barrel of the centrifugal prefabricated pumping station increases at this time and cannot provide a better impeller inlet water flow pattern.

#### 3.2. Analysis of Internal Flow Characteristics

_{d}, 0.67Q

_{d}, 1.00Q

_{d}, 1.33Q

_{d}, 1.67Q

_{d}, and 2.00Q

_{d}are selected for the analysis of the flow field inside the prefabricated pumping station, and in order to better depict the flow field inside the prefabricated pumping station, four characteristic sections as shown in Figure 6 are selected for analysis in this paper. The A1 section is the horizontal cross section at the impeller inlet of the submersible centrifugal pump, A2 is the cross section at the center of the precast barrel inlet, A3 is the horizontal cross section at the highest liquid level of the precast barrel, and A4 is the vertical cross section at the center of the precast barrel.

_{d}, 0.67Q

_{d}, 1.00Q

_{d}, 1.33Q

_{d}, 1.67Q

_{d}, and 2.00Q

_{d}flow conditions are shown below.

_{d}; only a small part of the high-pressure area exists on the upper side of the inlet and the upper side of the prefabricated barrel. Prefabricated pumping station prefabricated barrel outlet side pressure with the flow rate increases, the low-pressure area gradually decreases; until the maximum flow rate of 2.00Q

_{d}, the low-pressure area basically does not exist. In the centrifugal pump outlet connection pipeline, with the increase in flow, the low-pressure area becomes larger, mostly concentrated in the elbow of the double pump sink pipe. As the flow rate increases, the low-pressure area also appears on the waterward side of the centrifugal pump motor. Prefabricated barrel pressure distribution is not uniform, mainly in the inlet and outlet side is not consistent, along the inlet and outlet water axis, the symmetry of the left and right sides is slightly better, but also not completely symmetrical, can also be found in the phenomenon of partial flow.

## 4. Experiment Equipment, Test and Result Analysis

#### 4.1. Test Bench Introduction

^{3}/h, accuracy ±0.5%), and the flow pattern is captured by a high-speed camera (OLYMPUS i-SPEED 3, working range 2000 fps full resolution, accuracy ±1 μs).

_{d}= 33.93 m

^{3}/h) by controlling the pipeline pump 6, and then the high-speed camera was used to take pictures of the internal flow state of the integrated, prefabricated pumping station.

#### 4.2. Analysis of Experimental Results

_{d}= 33.93 m

^{3}/h), and a tracer red line is used to show the water flow to obtain pictures of the internal flow of the centrifugal prefabricated pumping station at different moments under different orientations.

## 5. Conclusions

_{d}= 33.93 m

^{3}/h); the maximum efficiency value is 63.96%; the head is 8.66 m; the head at the starting point of the saddle area is 10.50 m, which is 1.21 times of the design head; the operable head range for small flow is small; and the operable head range for large flow is wide. The efficiency of the prefabricated pumping station in the high-efficiency zone is 58.0~63.0%, corresponding to the flow range of 0.62Q

_{d}~1.41Q

_{d}(21.0~48.0 m

^{3}/h).

_{d}to 2.33Q

_{d}. The impeller inlet flow uniformity of pump 2 is greater than that of pump 1. At the design working condition (Q

_{d}= 33.93 m

^{3}/h), the impeller inlet flow uniformity of pump 1 is 74.70%, and that of pump 2 is 75.57%. The inlet flow fields of the pumps on both sides are not consistent. When the flow condition is less than 0.83Q

_{d}(Q = 28.27 m

^{3}/h), the uniformity of flow velocity at the impeller inlet increases significantly and cannot provide a better impeller inlet flow pattern.

## 6. Suggestions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**General assembly drawing of three-dimensional model of centrifugal prefabricated pumping station. 1. Inlet; 2. outlet; 3. round prefabricated barrels; 4. couplers; 5. submersible centrifugal pump 1; 6. submersible centrifugal pump 2.

**Figure 2.**Grid of each calculation domain. (

**a**) Prefabricated barrel grid; (

**b**) impeller grid; (

**c**) worm gear grid; (

**d**) outlet section grid.

**Figure 7.**Cross-section A1 flow velocity and streamline distribution. (

**a**) 0.33Q

_{d}, (

**b**) 0.67Q

_{d}, (

**c**) 1.00Q

_{d}, (

**d**) 1.33Q

_{d}, (

**e**) 1.67Q

_{d}, and (

**f**) 2.00Q

_{d}.

**Figure 8.**Cross-section A2 flow velocity and streamline distribution. (

**a**) 0.33Q

_{d}, (

**b**) 0.67Q

_{d}, (

**c**) 1.00Q

_{d}, (

**d**) 1.33Q

_{d}, (

**e**) 1.67Q

_{d}, and (

**f**) 2.00Q

_{d}.

**Figure 9.**Cross-section A3 velocity and streamline distribution. (

**a**) 0.33Q

_{d}, (

**b**) 0.67Q

_{d}, (

**c**) 1.00Q

_{d}, (

**d**) 1.33Q

_{d}, (

**e**) 1.67Q

_{d}, and (

**f**) 2.00Q

_{d}.

**Figure 10.**Cross-section A4 velocity and streamline distribution. (

**a**) 0.33Q

_{d}, (

**b**) 0.67Q

_{d}, (

**c**) 1.00Q

_{d}, (

**d**) 1.33Q

_{d}, (

**e**) 1.67Q

_{d}, and (

**f**) 2.00Q

_{d}.

**Figure 11.**Prefabricated pumping station wall pressure distribution diagram. (

**a**) 0.33Q

_{d}, (

**b**) 0.67Q

_{d}, (

**c**) 1.00Q

_{d}, (

**d**) 1.33Q

_{d}, (

**e**) 1.67Q

_{d}, and (

**f**) 2.00Q

_{d}.

**Figure 12.**Sketch of centrifugal prefabricated pumping station test bench. 1. PLC variable frequency control cabinet; 2. round prefabricated barrels; 3. submersible centrifugal pump; 4. couplers; 5. electromagnetic flowmeter; 6. pipe pump; 7. turbo butterfly valve; 8. backflow tank.

**Figure 15.**Flow pattern of prefabricated pumping station. (

**a**) Left side of prefabricated barrel; (

**b**) right side of prefabricated barrel; (

**c**) filming at the inlet of the prefabricated barrel.

Flow Rate Q (m^{3}/h) | Head H (m) | Efficiency η (%) |
---|---|---|

11.31 (0.33Q_{d}) | 10.50 | 45.05 |

16.96 (0.50Q_{d}) | 10.33 | 55.28 |

22.62 (0.67Q_{d}) | 9.91 | 59.77 |

28.27 (0.83Q_{d}) | 9.39 | 63.22 |

33.93 (1.00Q_{d}) | 8.66 | 63.96 |

39.58 (1.17Q_{d}) | 7.77 | 61.78 |

45.24 (1.33Q_{d}) | 6.84 | 60.36 |

50.89 (1.50Q_{d}) | 5.91 | 57.54 |

56.55 (1.67Q_{d}) | 4.93 | 53.17 |

62.20 (1.83Q_{d}) | 3.94 | 47.15 |

67.86 (2.00Q_{d}) | 2.92 | 39.18 |

73.51 (2.17Q_{d}) | 1.90 | 28.97 |

79.17 (2.33Q_{d}) | 0.57 | 9.98 |

Flow Rate Q (m^{3}/h) | Water Pump 1 Impeller Inlet Flow Rate Uniformity (%) | Water Pump 2 Impeller Inlet Flow Rate Uniformity (%) |
---|---|---|

11.31 (0.33Q_{d}) | 68.55 | 66.05 |

16.96 (0.50Q_{d}) | 70.55 | 73.03 |

22.62 (0.67Q_{d}) | 73.93 | 74.74 |

28.27 (0.83Q_{d}) | 74.59 | 75.40 |

33.93 (1.00Q_{d}) | 74.70 | 75.57 |

39.58 (1.17Q_{d}) | 74.61 | 75.52 |

45.24 (1.33Q_{d}) | 74.65 | 75.55 |

50.89 (1.50Q_{d}) | 74.70 | 75.61 |

56.55 (1.67Q_{d}) | 74.74 | 75.66 |

62.20 (1.83Q_{d}) | 74.77 | 75.70 |

67.86 (2.00Q_{d}) | 74.79 | 75.72 |

73.51 (2.17Q_{d}) | 74.79 | 75.70 |

79.17 (2.33Q_{d}) | 74.78 | 75.67 |

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## Share and Cite

**MDPI and ACS Style**

Xie, C.; Yuan, Z.; Feng, A.; Wang, Z.; Wu, L. Energy Characteristics and Internal Flow Field Analysis of Centrifugal Prefabricated Pumping Station with Two Pumps in Operation. *Water* **2022**, *14*, 2705.
https://doi.org/10.3390/w14172705

**AMA Style**

Xie C, Yuan Z, Feng A, Wang Z, Wu L. Energy Characteristics and Internal Flow Field Analysis of Centrifugal Prefabricated Pumping Station with Two Pumps in Operation. *Water*. 2022; 14(17):2705.
https://doi.org/10.3390/w14172705

**Chicago/Turabian Style**

Xie, Chuanliu, Zhenyang Yuan, Andong Feng, Zhaojun Wang, and Liming Wu. 2022. "Energy Characteristics and Internal Flow Field Analysis of Centrifugal Prefabricated Pumping Station with Two Pumps in Operation" *Water* 14, no. 17: 2705.
https://doi.org/10.3390/w14172705