# Effect of Flow on the Energy Conversion Characteristics of Multiphase Pumps Based on Energy Transport Theory

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Energy Transport Theory

## 3. Research Target

## 4. Mesh Division and Boundary Condition Setting

^{3}/h. From Table 2, it can be seen that as the number of meshes increases, the relative head and relative efficiency change within 1%. Considering the efficiency and accuracy of the computational resources, the third set of mesh numbers is selected for the computational study.

^{−5}, the rotational speed is set to 3000 rpm, the wall is set to be fixed without slip, and the “Scalable Function” is used in the near-wall region.

## 5. Experimental Procedure

^{3}/h) and gas–liquid two-phase condition (GVF = 5%), while the experimental results were summarized with the numerical simulation results and the external characteristic curve was drawn, as shown in Figure 5 and Figure 6. Figure simulation and tests of the head and efficiency were performed, and the output power error was less than 5%, which is unavoidable, so this verifies that the numerical simulation calculation method selected in this paper is reliable.

## 6. Analysis of Results

#### 6.1. Effect of Flow on the Pressure Propulsion Power within a Pressurization Unit

#### 6.2. Effect of Flow on the Lamb Vector Dispersion with a Pressurization Unit

#### 6.3. Effect of Flow on the Vortex Enstrophy Dissipation in the Pressurization Unit

## 7. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Vysotskii, V.; Dmitrievskii, A. Global Oil and Gas Resources and Their Development. Russ. J. Gen. Chem.
**2009**, 79, 2477–2485. [Google Scholar] [CrossRef] - Tong, X.; Zhang, G.; Wang, Z.; Wen, Z.; Tian, Z.; Wang, H.; Ma, F.; Wu, Y. Distribution and Potential of Global Oil and Gas Resources. Pet. Explor. Dev.
**2018**, 45, 779–789. [Google Scholar] [CrossRef] - Li, L.; Gu, Z.; Xu, W.; Tan, Y.; Fan, X.; Tan, D. Mixing Mass Transfer Mechanism and Dynamic Control of Gas-Liquid-Solid Multiphase Flow Based on VOF-DEM Coupling. Energy
**2023**, 272, 127015. [Google Scholar] [CrossRef] - Xu, Y.; Cao, S.; Sano, T.; Wakai, T.; Reclari, M. Experimental Investigation on Transient Pressure Characteristics in a Helico-Axial Multiphase Pump. Energies
**2019**, 12, 461. [Google Scholar] [CrossRef] - Xiao, W.; Tan, L. Design Method of Controllable Velocity Moment and Optimization of Pressure Fluctuation Suppression for a Multiphase Pump. Ocean Eng.
**2021**, 220, 108402. [Google Scholar] [CrossRef] - Li, C.; Luo, X.; Feng, J.; Zhu, G.; Xue, Y. Effects of Gas-Volume Fractions on the External Characteristics and Pressure Fluctuation of a Multistage Mixed-Transport Pump. Appl. Sci.
**2020**, 10, 582. [Google Scholar] [CrossRef] - Asfora, L.; dos Santos, A.; Duarte, L. Modeling Multiphase Jet Pumps for Gas Compression. J. Pet. Sci. Eng.
**2019**, 173, 844–852. [Google Scholar] [CrossRef] - Zhang, W.; Zhu, B.; Zi, D.; Ma, Z.; Wang, F. Transportability Improvement of a Gas-Liquid Rotodynamic Pump Using the Two-Step Multi-Objective Optimization Strategy. Front. Energy Res.
**2022**, 10, 900182. [Google Scholar] [CrossRef] - Shi, J.; Tao, S.; Shi, G.; Song, W. Effect of Gas Volume Fraction on the Energy Loss Characteristics of Multiphase Pumps at Each Cavitation Stage. Water
**2021**, 13, 2293. [Google Scholar] [CrossRef] - Liu, M.; Tan, L.; Cao, S. Influence of Viscosity on Energy Performance and Flow Field of a Multiphase Pump. Renew. Energy
**2020**, 162, 1151–1160. [Google Scholar] [CrossRef] - Quan, H.; Li, R.; Su, Q.; Han, W.; Wang, P. Analysis on Energy Conversion of Screw Centrifugal Pump in Impeller Domain Based on Profile Lines. Adv. Mech. Eng.
**2013**, 5, 512523. [Google Scholar] [CrossRef] - Zhang, X.L.; Hu, S.; Shen, Z.; Wu, S.; Li, K. Research on Energy Conversion Mechanism of Rotodynamic Pump and Design of Non-Overload Centrifugal Pump. IOP Conf. Ser. Mater. Sci. Eng.
**2016**, 129, 012003. [Google Scholar] [CrossRef] - Liu, Y.; Tan, L. Method of C Groove on Vortex Suppression and Energy Performance Improvement for a NACA0009 Hydrofoil with Tip Clearance in Tidal Energy. Energy
**2018**, 155, 448–461. [Google Scholar] [CrossRef] - Miao, S.; Yang, J.; Shi, F.; Wang, X.; Shia, G. Research on Energy Conversion Characteristic of Pump as Turbine. Adv. Mech. Eng.
**2018**, 10, 1687814018770836. [Google Scholar] [CrossRef] - Miao, S.; Zhang, H.; Shi, F.; Wang, X.; Ma, X. Study on Energy Conversion Characteristics in Volute of Pump as Turbine. Fluid Dyn. Mater. Process.
**2021**, 17, 201–214. [Google Scholar] [CrossRef] - Miao, S.; Zhang, H.; Zhang, J.; Wang, X.; Shi, F. Unsteady Flow Characteristics of Energy Conversion in Impeller of Centrifugal Pump as Turbine. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci.
**2022**, 236, 1502–1511. [Google Scholar] [CrossRef] - Zhang, J.; Tan, L. Energy Performance and Pressure Fluctuation of a Multiphase Pump with Different Gas Volume Fractions. Energies
**2018**, 11, 1216. [Google Scholar] [CrossRef] - Zhang, J.; Fan, H.; Zhang, W.; Xie, Z. Energy Performance and Flow Characteristics of a Multiphase Pump with Different Tip Clearance Sizes. Adv. Mech. Eng.
**2019**, 11, 1687814018823356. [Google Scholar] [CrossRef] - Shi, G.; Wang, S.; Xiao, Y.; Liu, Z.; Li, H.; Liu, X. Effect of Cavitation on Energy Conversion Characteristics of a Multiphase Pump. Renew. Energy
**2021**, 177, 1308–1320. [Google Scholar] [CrossRef] - Shi, G.; Liu, Z.; Xiao, Y.; Wang, Z.; Luo, Y.; Luo, K. Energy Conversion Characteristics of Multiphase Pump Impeller Analyzed Based on Blade Load Spectra. Renew. Energy
**2020**, 157, 9–23. [Google Scholar] [CrossRef] - Ji, L.; Li, W.; Shi, W.; Chang, H.; Yang, Z. Energy Characteristics of Mixed-Flow Pump under Different Tip Clearances Based on Entropy Production Analysis. Energy
**2020**, 199, 117447. [Google Scholar] [CrossRef] - Jin, Y.; Zhang, D.; Song, W.; Shen, X.; Shi, L.; Lu, J. Numerical Study on Energy Conversion Characteristics of Molten Salt Pump Based on Energy Transport Theory. Energy
**2022**, 244, 122674. [Google Scholar] [CrossRef] - Zhao, Z.; Song, W.; Jin, Y.; He, L. Numerical Study on Flow Stall and Kinetic Energy Conversion of Low-Specific-Speed Centrifugal Pump. Phys. Fluids
**2023**, 35, 044104. [Google Scholar] [CrossRef] - Liu, Y.; Tan, L.; Hao, Y.; Xu, Y. Energy Performance and Flow Patterns of a Mixed-Flow Pump with Different Tip Clearance Sizes. Energies
**2017**, 10, 191. [Google Scholar] [CrossRef] - Wang, L.; Lu, J.; Liao, W.; Guo, P.; Feng, J.; Luo, X.; Wang, W. Numerical Investigation of the Effect of T-Shaped Blade on the Energy Performance Improvement of a Semi-Open Centrifugal Pump. J. Hydrodyn.
**2021**, 33, 736–746. [Google Scholar] [CrossRef] - Ye, D.; Lai, X.; Chen, J.; Zhai, F.; Wu, J.; Gou, Q. Fluid Energy Conversion Analysis in Hydraulic Channels of Reactor Coolant under Flow Coastdown Transient. Energy Rep.
**2022**, 8, 9232–9241. [Google Scholar] [CrossRef]

**Figure 4.**Experimental system diagram of multiphase pump. 1—Water tank; 2—regulation valve; 3—booster pump; 4—flowmeter; 5—gas–liquid mixing tank; 6—pressure transducer; 7—multiphase pump; 8—torquemeter; 9—motor; 10—gas flowmeter; 11—regulation valve; 12—barometer; 13—air compressor.

**Figure 6.**Comparison of experimental and numerical simulation under gas–liquid two-phase conditions.

**Figure 7.**0.8Q (

**a**), 1.0Q (

**b**), 1.2Q (

**c**). Pressure propulsion power distribution in impeller under different flow conditions.

**Figure 8.**0.8Q (

**a**), 1.0Q (

**b**), 1.2Q (

**c**). Distribution of pressure propulsion power in the pressurization unit with different flow conditions.

**Figure 9.**0.8Q (

**a**), 1.0Q (

**b**), 1.2Q (

**c**). Distribution of Lamb vector dispersion in impeller with different flow conditions.

**Figure 10.**0.8Q (

**a**), 1.0Q (

**b**), 1.2Q (

**c**). Distribution of Lamb vector dispersion in the pressurization unit with different flow conditions.

**Figure 11.**0.8Q (

**a**), 1.0Q (

**b**), 1.2Q (

**c**). Distribution of the vortex enstrophy dissipation in the impeller with different flow conditions.

**Figure 12.**0.8Q (

**a**), 1.0Q (

**b**), 1.2Q (

**c**). Distribution of the vortex enstrophy dissipation in the pressurization unit with different flow conditions.

Geometric Parameter | Work Unit | Numerical Value | |
---|---|---|---|

Design flow | Q | m^{3}/h | 100 |

Design speed | N | rpm | 3600 |

Number of impeller blades | Z_{1} | (-) | 3 |

Number of diffuser blades | Z_{2} | (-) | 11 |

External diameter | D | mm | 161 |

Impeller inlet angle | α_{h}/α_{s} | ° | 9.05/6 |

Impeller outlet angle | β_{h}/β_{s} | ° | 27.05/24 |

Inlet angle of diffuser | α_{h}/α_{s} | ° | 0 |

Outlet angle of diffuser | β_{h}/β_{s} | ° | 35 |

Parameters | Mesh 1 | Mesh 2 | Mesh 3 | Mesh 4 |
---|---|---|---|---|

Mesh number | 2,246,540 | 2,627,229 | 3,093,387 | 4,054,644 |

Relative head | 1 | 0.9986 | 1.0023 | 1.0104 |

Relative efficiency | 1 | 1.0052 | 1.0021 | 0.9976 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Tang, M.; Shi, G.; Lv, W.; Peng, X.; Huang, Z.
Effect of Flow on the Energy Conversion Characteristics of Multiphase Pumps Based on Energy Transport Theory. *Water* **2023**, *15*, 4188.
https://doi.org/10.3390/w15234188

**AMA Style**

Tang M, Shi G, Lv W, Peng X, Huang Z.
Effect of Flow on the Energy Conversion Characteristics of Multiphase Pumps Based on Energy Transport Theory. *Water*. 2023; 15(23):4188.
https://doi.org/10.3390/w15234188

**Chicago/Turabian Style**

Tang, Manqi, Guangtai Shi, Wenjuan Lv, Xiaodong Peng, and Zongliu Huang.
2023. "Effect of Flow on the Energy Conversion Characteristics of Multiphase Pumps Based on Energy Transport Theory" *Water* 15, no. 23: 4188.
https://doi.org/10.3390/w15234188