# Numerical Study of the Unsteady Flow Characteristics of a Jet Centrifugal Pump under Multiple Conditions

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## Abstract

**:**

## 1. Introduction

## 2. Research Method and Model

#### 2.1. The Model Pump

_{d}= 2.5 m

^{3}/h, rated water head H

_{d}= 23 m, rated efficiency η

_{d}= 20%, rotational speed n = 2850 r/min, shaft-passing frequency SPF = 47.5 Hz, blade-passing frequency of impeller BPF

_{I}= 285 Hz, and blade-passing frequency of guide vane BPF

_{G}= 237.5 Hz. The main geometric parameters of the impeller and guide vane are listed in Table 1. Two- and three-dimensional structure diagrams of the model pump are shown in Figure 1.

#### 2.2. Numerical Method

^{-5}.The simulation was completed on a workstation with 20 cores and 128 GB of memory. For a model, it takes 90 min to complete 2000 steps of steady calculation, and about 1000 min to complete the transient calculation of 13 impeller cycles.

#### 2.3. Numerical Validation

## 3. Analysis of the Velocity Vector and Streamline

_{d}, 0.6 Q

_{d}, 1.4 Q

_{d}represent conditions at which the pump provides 20%, 60%, and 140% of the rated flow, respectively. It can be seen that there are obvious eddies in the lower half of the pump chamber near the inlet side under each condition; the flow velocity in this area is slow, and the flow passage is seriously blocked, which affects the normal flow in the upstream and downstream flow passage components and leads to obvious recirculation at the border of the impeller and ejector. Under the conditions of small flow rates, there are eddies near the outlet in the upper half of the pump chamber, and the smaller the flow rate, the more obvious the eddies. The eddies in the upper and lower sides of the pump chamber cause a blockage of the outlet channels in both sides of the ejector tube, where the flow is relatively more symmetrical. With the increasing flow rate, the eddies in the upper side of the pump chamber gradually weaken, while the eddies in the lower side gradually strengthen, and the flow in the ejector tube shows a tendency of upward deviation. There is obvious circulation movement in the pump chamber, and the flow patterns of the left and right sides are also not balanced; this is related to the asymmetry of the guide vane blades, of which there are five. There is a counter-clockwise eddy along the circumferential direction near the right-hand side of the outlet pipeline in the pump chamber, and the greater the flow rate, the greater the eddy. The area with the fastest velocity in the pump chamber is located in the circle near the ejector tube, and the flow in this area is very complicated.

## 4. Analysis of Unsteady Flow Field Characteristics Based on a Statistical Method

_{0}are grid nodes, the number of samples in an impeller rotating period, and the starting time of the rotation cycle, respectively.

_{2}means the circumferential speed at the impeller outlet.

#### 4.1. Time-Averaged Distribution Characteristics of the Flow Field

#### 4.2. Distribution Characteristics of the Fluctuation Intensity of the Flow Field

## 5. Analysis of Spatial–Temporal Evolution of Vortices in the Rotor–Stator Cascades

## 6. Pressure Fluctuation Characteristics of the Main Flow Passage Components

#### 6.1. Impeller

#### 6.1.1. Monitoring Points Stationary Relative to the Fixed Coordinate System

_{I}, and it has obvious amplitudes at other low-order frequency multiplications of BPF

_{I}. Along the direction of radius increase, the pressure fluctuation curves rise overall, but the fluctuation amplitude does not change much.

#### 6.1.2. Monitoring Points Stationary Relative to the Rotating Coordinate System

_{G}, and obvious amplitudes appear at low-order frequency multiplications of the dominant frequency. As the monitoring point gets closer to the impeller outlet, the rotor and stator interference becomes more and more violent, so the fluctuation amplitude at each characteristic frequency becomes larger and larger. In addition, relatively small fluctuation amplitudes are also shown at the shaft-passing frequency and its multiplication frequency, which reflects the influence of the impeller operating parameters (pump rotation speed) on the unsteady flow field of the JCP.

_{G}, and there are obvious amplitudes at low-order frequency multiplications of BPF

_{G}. At the dominant frequency, the fluctuation amplitude in the middle region of the flow channel is larger, while that at the points near the pressure or suction surface is relatively small.

#### 6.2. Guide Vane

_{I}, and there are obvious amplitudes at low-order frequency multiplications of BPF

_{I}.

_{I}, and there are amplitudes at other frequency multiplications of BPF

_{I}. As the radius increases, the influence of the impeller on the guide vane gradually weakens, so the amplitude, in turn, decreases at characteristic frequencies, but it rises slightly at the outlet of the positive guide vane, where the flow is complex.

_{I}and its low-order frequency multiplications, among which the dominant frequency is BPF

_{I}along the outlet direction. The amplitude of pressure fluctuation at the dominant frequency and other characteristic frequencies decreases monotonically, which is due to the influence of rotor–stator interaction becoming weaker and weaker as the monitoring point is farther away from the impeller.

#### 6.3. Pump Chamber and Ejector

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

Q_{d} | Rated volume flow m^{3}/h |

H_{d} | Rated water head m |

η_{d} | Rated efficiency % |

n | Rotational speed r/min |

SPF | Shaft passing frequency Hz |

BPF_{I} | Blade passing frequency of impeller Hz |

BPF_{G} | Blade passing frequency of guide vane Hz |

D_{j} | Inlet diameter of impeller mm |

D_{2} | Outlet diameter of impeller mm |

Z_{1} | Blade number of impeller |

φ_{1} | Blade wrap angle of impeller ° |

b_{2} | Blade outlet width of impeller mm |

D_{3} | Base diameter of guide vane mm |

D_{4} | Outlet diameter of guide vane mm |

Z_{2} | Blade number of guide vane |

GGI | General grid interface |

$\overline{\varphi}$ | Time-averaged components |

$\tilde{\varphi}$ | Periodic components |

n | Grid nodes |

N | Number of samples in an impeller rotating period |

t | Total time |

t_{0} | Starting time of the rotation cycle |

${C}_{P}^{\ast}$ | Non-dimensional pressure fluctuation intensity |

${C}_{U}^{\ast}$ | Non-dimensional velocity fluctuation intensity |

${C}_{T}^{\ast}$ | Non-dimensional turbulence energy fluctuation intensity |

$\tilde{P}$ | Pressure fluctuation intensity |

$\tilde{U}$ | Velocity fluctuation intensity |

$\tilde{T}$ | Turbulence energy fluctuation intensity |

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**Figure 1.**Structural diagrams of the model pump. (

**a**) Two-dimensional structure diagram; (

**b**) Three-dimensional structure diagram. 1: Ejector nozzle; 2: Ejector; 3: Pump chamber; 4: Ejector tube; 5: Guide vane; 6: Impeller; 7: Pump cover.

**Figure 2.**Grid diagrams of the impeller, guide vane, and jet. (

**a**) Impeller; (

**b**) Guide vane; (

**c**) Ejector nozzle and tube.

**Figure 3.**Experimental system and result. (

**a**) Experimental system; (

**b**) A comparison of hydraulic performance between the experiment and the numerical simulation. 1: Valve at pump outlet; 2: Flowmeter; 3: Pressure sensor at pump outlet; 4: The model pump; 5: Electric motor; 6: Pressure sensor at pump inlet; 7: Tachometer; 8: Valve at pump inlet; 9: Computer; 10: Measuring instrument of electric power.

**Figure 6.**Time-averaged distribution contours of absolute velocity on two planes under four conditions.

**Figure 7.**Time-averaged distribution contours of turbulent kinetic energy on two planes under four conditions.

**Figure 8.**Fluctuation intensity distribution contours of pressure on two planes under four conditions.

**Figure 9.**Fluctuation intensity distribution contours of velocity on two planes under four conditions.

**Figure 10.**Fluctuation intensity distribution contours of velocity on two planes under four conditions.

**Figure 11.**Evolution processes of the vortices in the stator and rotor cascade during a 1/6 period of impeller rotation under condition 0.2 Q

_{d}.

**Figure 12.**Evolution processes of the vortices in the stator and rotor cascade during a 1/6 period of impeller rotation under condition 0.6 Q

_{d}.

**Figure 13.**Evolution processes of the vortices in the stator and rotor cascade during a 1/6 period of impeller rotation under condition 1.0 Q

_{d}.

**Figure 14.**Evolution processes of the vortices in the stator and rotor cascade during a 1/6 period of impeller rotation under condition 1.4 Q

_{d}.

**Figure 16.**The time and frequency domain diagrams of pressure fluctuation for the monitoring points at the middle streamline of a single impeller channel when the monitoring points are stationary relative to the fixed coordinate system.

**Figure 17.**The time and frequency domain diagrams of pressure fluctuation at monitoring points on the middle streamline of a single impeller channel when the monitoring points are stationary relative to the rotational coordinate system.

**Figure 18.**The time and frequency domain diagrams of pressure fluctuation for the monitoring points at the outlet edge of a single impeller channel.

**Figure 19.**The time and frequency domain diagrams of pressure fluctuation for monitoring points at the inlet edge of a guide vane channel.

**Figure 20.**The time and frequency domain diagrams of pressure fluctuation for monitoring points at the middle streamline of a guide vane channel.

**Figure 21.**The time and frequency domain diagrams of pressure fluctuation for monitoring points at the middle streamline of a return guide vane channel.

**Figure 22.**The time and frequency domain diagrams of pressure fluctuation for monitoring points in the pump chamber.

Parameter | Value | |
---|---|---|

Impeller | Inlet Diameter D_{j} (mm) | 40 |

Outlet Diameter D_{2} (mm) | 123 | |

Blade Number Z_{1} | 6 | |

Blade Wrap Angle φ (°) | 76 | |

Blade Outlet Width b_{2} (mm) | 5.3 | |

Guide Vane | Base Diameter (mm) | 125 |

Outlet Diameter D_{3} (mm) | 64 | |

Blade Number Z_{2} | 5 |

Schemes | Scheme 1 | Scheme 2 | Scheme 3 | Scheme 4 | Scheme 5 | Scheme 6 |
---|---|---|---|---|---|---|

Number of the grid | 1,483,718 | 1,975,598 | 2,526,764 | 3,030,389 | 3,494,674 | 4,046,652 |

Head (m) | 23.97 | 24.22 | 25.43 | 26.15 | 26.17 | 26.16 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Guo, R.; Li, R.; Zhang, R.; Han, W.
Numerical Study of the Unsteady Flow Characteristics of a Jet Centrifugal Pump under Multiple Conditions. *Processes* **2019**, *7*, 786.
https://doi.org/10.3390/pr7110786

**AMA Style**

Guo R, Li R, Zhang R, Han W.
Numerical Study of the Unsteady Flow Characteristics of a Jet Centrifugal Pump under Multiple Conditions. *Processes*. 2019; 7(11):786.
https://doi.org/10.3390/pr7110786

**Chicago/Turabian Style**

Guo, Rong, Rennian Li, Renhui Zhang, and Wei Han.
2019. "Numerical Study of the Unsteady Flow Characteristics of a Jet Centrifugal Pump under Multiple Conditions" *Processes* 7, no. 11: 786.
https://doi.org/10.3390/pr7110786