# Numerical Simulation of Drilling Fluid Flow in Centrifugal Pumps

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## Abstract

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## 1. Introduction

## 2. Mathematical Models

#### 2.1. Non-Newtonian Fluid Models

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#### 2.2. Turbulent Models

## 3. Model Description

#### 3.1. Computational Domain and Meshing

#### 3.2. Grid Independence Tests and Model Validation

^{3}/h). Furthermore, the power of shaft is calculated as:

## 4. Results and Discussion

#### 4.1. Pump Performance

#### 4.2. Pressure Distributions

#### 4.3. Turbulent Kinetic Energy and Velocity Distributions

_{d}, large vortex clusters formed within the impeller, and, therefore, the energy loss was high. As the flow rate increased, areas of high turbulent energy at small volute casing cross-sections and vortex clusters formed between the blades. In the case of the drilling fluid, as shown in Figure 13b, when the flow rate was low, a high turbulent energy region formed near the blades, away from the inlet, which was a result of the effect of the viscosity. As the flow rate increased, the vortex clusters became concentrated between the impellers close to the inlet. The region of high entropy (present within the impeller) was primarily located near the outlet of the impeller. The energy loss in this region was caused by the shear effects generated between the outlet fluid of the impeller and the fluid in the volute region. These observations may also be attributed to the dynamic and static interference effects.

## 5. Conclusions

- The blades consumed mechanical energy through friction with the fluid contact during the operation of the centrifugal pump. The viscosity of the drilling fluid was higher than that of the water. Therefore, the head and efficiency of the drilling fluid were lesser than those of the water at the same flow rate. However, stronger torque and lager power were generated for the drilling-fluid cases. In practice, when transporting high-viscosity non-Newtonian fluids, attention should be paid to the reasonable use of larger rotating speeds in centrifugal pumps as a means of achieving greater efficiency.
- For the drilling-fluid cases, irregular variations in pressure distribution were observed, which could be attributed to the effects of viscous forces causing the fluid to cling to the volute wall. The pressure did not change with changes in the mode of impeller rotation. This could be attributed to the blocking effect of the volute. This affected the flow conditions under different viscosity conditions and potentially contributed to the differences in the radial or axial velocity at the different cross-sections. It was also observed that the nature of the fluid flow in the small cross-sections of the volute was highly sensitive to the rotation of the rotor.
- When the pump drew the power-law fluid, as the flow rate increased and after it flowed into the stationary front chamber, its velocity gradually decreased. This resulted in flow detachment at the back of the blades. At the same time, the non-Newtonian fluid became less detached from the flow at the blade, and swirls were generated at the impeller inlet. The effects of shear collision exerted on the outlet fluid of the impeller and the fluid in the snail casing area, as well as the dynamic and static interferences, made the non-Newtonian power-law fluid consume more mechanical energy than the water.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 5.**Simulation results of the centrifugal pump external characteristics and a comparison with the experiments.

**Figure 6.**Comparison of the efficiency, head, and power of the water and drilling fluid at different flow rates.

**Figure 7.**Pressure contours in the centrifugal pump. (

**a**) Cases with water; (

**b**) cases with drilling fluid.

**Figure 9.**Pressure coefficients at the different points within volute (P1–P8). (

**a**) Water case; (

**b**) drilling-fluid case.

**Figure 10.**Pressure coefficients at the different points on blade surface (B1–B6). (

**a**) Water case; (

**b**) drilling-fluid case.

**Figure 11.**Pressure coefficients at the different points on the volute spacer tongue (C1–C3). (

**a**) Water case; (

**b**) drilling-fluid case.

**Figure 13.**Turbulent kinetic energy contours in the centrifugal pump. (

**a**) Cases with water; (

**b**) cases with drilling fluid.

**Figure 14.**Velocity contours in the centrifugal pump. (

**a**) Cases with water; (

**b**) cases with drilling fluid.

Parameters | Value | |
---|---|---|

Design flow rate | ${Q}_{d}$ | 45 m^{3}/h |

Design head | ${H}_{d}$ | 31.8 m |

Design efficiency | ${\eta}_{d}$ | 66.85% |

Rated speed | ${n}_{d}$ | 2900 rpm |

Specific speed | ${n}_{s}$ | 90 |

Number of blades | Z | 6 |

Volute inlet diameter | ${D}_{1}$ | 86 mm |

Volute outlet diameter | ${D}_{2}$ | 161 mm |

Volute base circle diameter | ${D}_{3}$ | 173 mm |

Pump inlet diameter | ${D}_{s}$ | 80 mm |

Pump outlet diameter | ${D}_{d}$ | 50 mm |

Mesh | Impeller | Volute | Front Chamber | After Chamber | In-Pipe | Out-Pipe | Total |
---|---|---|---|---|---|---|---|

1 | 449,862 | 53,480 | 145,495 | 307,532 | 147,355 | 412,901 | 1,516,625 |

2 | 872,733 | 600,705 | 297,415 | 307,532 | 83,289 | 108,078 | 2,267,952 |

3 | 1,333,972 | 1,251,006 | 297,415 | 307,532 | 83,289 | 108,078 | 3,381,292 |

4 | 1,333,972 | 1,251,006 | 500,475 | 500,873 | 195,580 | 235,695 | 4,017,601 |

5 | 1,676,438 | 1,965,268 | 500,475 | 500,873 | 195,580 | 235,695 | 5,074,329 |

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**MDPI and ACS Style**

Hu, J.; Li, K.; Su, W.; Zhao, X. Numerical Simulation of Drilling Fluid Flow in Centrifugal Pumps. *Water* **2023**, *15*, 992.
https://doi.org/10.3390/w15050992

**AMA Style**

Hu J, Li K, Su W, Zhao X. Numerical Simulation of Drilling Fluid Flow in Centrifugal Pumps. *Water*. 2023; 15(5):992.
https://doi.org/10.3390/w15050992

**Chicago/Turabian Style**

Hu, Jianxin, Ke Li, Wenfeng Su, and Xinyi Zhao. 2023. "Numerical Simulation of Drilling Fluid Flow in Centrifugal Pumps" *Water* 15, no. 5: 992.
https://doi.org/10.3390/w15050992