# Influence of Different Particle Parameters and Operating Conditions on Flow Characteristics and Performance of Deep-Sea Mining Pump

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Three-Dimensional Model and Numerical Calculation Strategy

#### 2.1. Three-Dimensional Model

_{d}= 420 m

^{3}/h, a single-stage head H

_{d}= 45 m, a rated efficiency η

_{d}= 52%, and a rated rotational speed n = 1450 r/min. The overall structure model is shown in Figure 1.

#### 2.2. Numerical Calculation Strategy

^{−4}was set for the numerical simulation. Convergence was judged when the monitored pressure and pump inlet and outlet mass flow rate change between adjacent iteration steps was not more than 0.001%.

^{2}), $\rho $ is the fluid density (kg/m

^{3}), ${\rho}_{p}$ is the particle density (kg/m

^{3}), ${d}_{p}$ is the particle diameter (mm), ${g}_{x}$ is the acceleration of gravity in the x-axis direction (m/s

^{2}), ${F}_{V}$ is additional mass force, ${F}_{P}$ is the additional force induced by pressure gradient in flow field, and ${F}_{X}$ is the force in the x-direction.

^{2}).

_{N}is the normal recovery coefficient, e

_{T}is the tangential recovery coefficient, and θ is the collision angle between the particle and the surface of the through-passage component.

#### 2.3. Boundary Condition Setting

## 3. Influence on Flow Characteristics and Performance

#### 3.1. Numerical Analysis Scheme

#### 3.2. Influence of Different Particle Parameters

#### 3.2.1. Different Particle Sizes

^{3}/h; the pump speed was 1450 rpm; and the particle sizes were 3, 6, 10, 14, 17, and 20 mm, respectively.

_{r}, and the efficiency variation coefficient, η

_{r}. can be introduced, as follows:

_{r}= H

_{m}/H

_{w}

_{r}= η

_{m}/η

_{w}

_{m}and H

_{w}are the pump head values when transporting solid-fluid two-phase flow and pure water (m), respectively; and η

_{m}and η

_{w}are the pump efficiencies when transporting solid-fluid two-phase flow and pure water (%), respectively.

^{3}); Q is the slurry pump inlet flow rate (m

^{3}/s); g is the gravitational acceleration (m/s

^{2}); and P is the shaft power (kW).

#### 3.2.2. Different Concentrations

_{v}, was set to 4, 7.5, and 11.5%, respectively, with a flow rate of 420 m

^{3}/h, a pump rotational speed of 1450 rpm, and a particle size of 6 mm.

_{v}is between 4 and 11.5%, the main flow passage components, including the impellers and guide vanes, are capable of normal energy conversion for the flow transported in the calculation domain. Under the action of the impellers, the fluid pressure gradually increases from the inlet to the outlet of the pump, the fluid velocity also increasing within the impellers. However, as the particle concentration increases, the low-speed zones in the space vane guide expand, suggesting that the increase in the number of particles causes the fluid flow pattern to deteriorate.

#### 3.2.3. Different Particle Densities

^{3}/h, while the particles transported had a particle size of 6 mm, a particle concentration of 7.5%, and particle densities of 1400, 1900, and 2800 kg/m

^{3}, respectively.

^{3}has the longest movement trajectory in the flow passage, followed by the particle of density 1900 kg/m

^{3}, and finally the particle of density 2800 kg/m

^{3}. Moreover, the respective collisions between the three particles and the space vane guide hub in the outlet section of the pump indicate that the densest particle has the largest angle of collision. Moreover, it also has the largest elastic recovery coefficient after collision with the flow passage component surface, thus the smallest flow loss owing to the collision. Additionally, the densest particle travels the longest radial distance after being energized by the first-stage impeller before being ejected from the impeller outlet owing to inertia and subsequently collides with the flow passage components in the impeller-vane guide transition section many times.

#### 3.3. Influences of Different Operating Conditions

#### 3.3.1. Different Flow Rates

_{d}, 1.0 Q

_{d}, and 1.33 Q

_{d}were used, respectively. The particle concentration was set to 7.5%, the pump rotational speed to 1450 rpm, and the particle size to 6 mm.

_{d}, the particle movement trajectories in the calculation domain are obviously more turbulent than those with the design or large flow rates, indicating flow instability. Since the inlet flow rate is less than the design flow rate, both the fluid and the particles enter the flow field with a relatively low velocity, the relatively large rotational speed of the impellers causing the formation of a large preswirl that worsens the structure of the flow field and increases the flow loss at the pump inlet.

_{d}, while the maximum RE is 28% when Q = 0.68 Q

_{d}. This indicates that with this particle size, an increase in inlet flow rate causes the head to decrease and the efficiency to increase when transporting solid-fluid two-phase flow. The small flow rate causes the internal flow structures of the pump to become turbulent more easily, leading to phenomena such as cavitation that signify instability, increasing the flow loss of the internal flow field, which in turn leads to low pump efficiency.

#### 3.3.2. Different Rotational Speeds

^{3}/h. The volume concentration of the solid-phase particles being transported was 7.5%, and the particle size was 6 mm.

_{h}, volumetric efficiency, η

_{v}, and mechanical efficiency, η

_{m}, in the fluid domain during operation. In particular, the friction loss of the disc that affects mechanical efficiency is directly related to the rotational speed. The power owing to friction loss of the pump disc can be calculated based on the empirical formula of Equation (21), as follows:

^{−6}); ρ is the fluid density (kg/m

^{3}); ${u}_{2}^{}$ is the circumferential velocity component at the impeller outlet (m/s); and ${D}_{2}$ is the outer diameter of the impeller (mm).

## 4. Hydraulic Performance Experiment

#### 4.1. Experiment Principle

^{−1}]; $n$ is the test speed of the pump [rpm]; ${P}_{0}$ and ${P}_{1}$ are respectively the measured no-load power and power under a load [kW]; ${I}_{1}$ is the measured current under a load [A]; and ${R}_{0}$ and ${R}_{1}$ are respectively the motor DC wire resistances after the no-load and load tests [Ω].

#### 4.2. Comparative Analysis of Results

_{d}= 420 m

^{3}/h, the test head is 94.86 m, and the simulated head is 96.51 m, a relative error of just 1.7%. The maximum relative error occurs when the flow is Q = 100 m

^{3}/h, the relative error being 4.3%, which is within a reasonable range. It can be seen from Figure 25b that the test efficiency and the numerically simulated efficiency are also in good agreement. At the rated flow point Q

_{d}= 420 m

^{3}/h, the relative error is 4.1%, while the maximum relative error occurring when the flow is Q = 100 m

^{3}/h is 7.3%, which is again within a reasonable range. Similarly, the overall trends of the tested shaft power and simulated shaft power are in good agreement. At the rated flow point Q

_{d}= 420 m

^{3}/h, the relative error is −2.3%. Over the entire flow range, the maximum relative error is −2.8%, the relative error being within a reasonable range.

## 5. Test Validation of Method and Model

#### 5.1. Testing Principle

_{d}= 20 m

^{3}/h, a single-stage head H

_{d}= 15 m, a rated efficiency η

_{d}= 64%, and a rated rotational speed n = 2860 r/min. The actual test pump is shown in Figure 26.

^{3}/h), rated flow (20 m

^{3}/h) and large flow (26 m

^{3}/h) conditions. Before the test, the same thickness of water-based paint was applied to the impeller runners. After the paint was completely dried, the test was carried out. We observed the impact of the particles on the runners after 2 h of unsteady flow in the runners, and then the numerical calculation results under the same boundary conditions were compared. The comparison diagrams of the impeller before and after applying water-based paint are shown in Figure 28.

^{3}/h, 20 m

^{3}/h, and 26 m

^{3}/h flow conditions, the site is shown in Figure 29.

#### 5.2. Comparative Analysis of the Results

#### 5.2.1. Low Flow Conditions

#### 5.2.2. Rated Flow Conditions

#### 5.2.3. Large Flow Conditions

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

C_{v} | particle volume concentration | p_{1} | inlet pressure of the pump |

d_{p} | particle diameter | p_{2} | outlet pressure of the pump |

e_{N} | normal recovery coefficient | Q | pump inlet flow rate |

e_{T} | tangential recovery coefficient | Q_{d} | rated flow rate |

f | AC frequency | R_{0} | the motor DC wire resistances after the no-load tests |

F_{P} | additional force induced by pressure gradient | R_{1} | the motor DC wire resistances after the load tests |

F_{V} | additional mass force | RH | reduced head |

F_{X} | force in the x-direction | Re | Reynolds number |

g | gravitational acceleration | RE | reduced efficiency |

g_{x} | acceleration of gravity in x-axis direction | u_{p} | particle velocity |

H | head for pump | v_{1} | inlet velocity of the pump |

H | single-stage head | v_{2} | outlet velocity of the pump |

H_{m} | head for transporting two-phase flow | β | comprehensive coefficient |

Hp | head values for the actual pump | η | efficiency for pump |

H_{r} | head variation coefficient | η_{m} | efficiency for transporting two-phase flow |

H_{w} | head for transporting pure water | η_{r} | efficiency variation coefficient |

I_{1} | the measured current under a load | η_{w} | efficiency for transporting pure water |

n | rotational speed | θ | collision angle |

n_{0} | synchronous speed of the motor | μ | dynamic viscosity |

n_{m} | shaft rotational speeds of model pump | ρ | fluid density |

n_{p} | shaft rotational speeds of actual pump | ρ_{p} | particle density |

P | shaft power | υ | dynamic viscosity of fluid |

P_{0} | the measured under no-load power | ||

P_{1} | the measured under load power |

## References

- Yu, H.Y.; Liu, S.J. Dynamics of vertical pipe in deep-ocean mining system. J. Cent. South Univ. Technol.
**2007**, 14, 552–556. [Google Scholar] [CrossRef] - Zou, W.S.; Li, Z.H.; Chen, A.L. Lifting motor pump in deep sea mining. J. Cent. South Univ. Nat. Sci. Ed.
**2011**, 42, 221–225. [Google Scholar] - Mortazavi, F.; Riasi, A.; Nourbakhsh, S.A. Numerical investigation of back vane design and its impact on pump performance. J. Fluids Eng.
**2017**, 139, 121104. [Google Scholar] [CrossRef] - Engin, T.; Gur, M.; Calli, I. Slurry and tip clearance effects on the performance of an open impeller centrifugal pump. Handb. Powder Technol.
**2001**, 10, 499–504. [Google Scholar] - Bai, L.; Zhou, L.; Han, C.; Zhu, Y.; Shi, W. Numerical study of pressure fluctuation and unsteady flow in a centrifugal pump. Processes
**2019**, 7, 354. [Google Scholar] [CrossRef][Green Version] - Huang, S.; Huang, J.; Mo, Y.; Zhang, Z. Study on wear properties of the flow parts in a centrifugal pump based in EDEM-Fluent coupling. J. Eng. Therm. Energy Power
**2019**, 7, 431. [Google Scholar] [CrossRef][Green Version] - Zhou, L.; Wang, W.; Hang, J.; Shi, W.; Yan, H.; Zhu, Y. Numerical investigation of a high-speed electrical submersible pump with different end clearances. Water
**2020**, 12, 1116. [Google Scholar] [CrossRef][Green Version] - Minemura, K.; Zhong, Y.; Uchiyama, T. Numerical Prediction of Erosion Wear on Pump Casing under Solid-Water Two-Phase Flow Conditions. Multiph. Flow
**1995**, 61, 2571–2578. [Google Scholar] [CrossRef][Green Version] - Wang, J.; Jiang, W.; Kong, F.; Qu, X.; Su, X. Numerical simulation of solid-liquid two-phase flow field in centrifugal pump based on particle model. J. Drainage Irrigat. Mach. Eng.
**2013**, 31, 846–850+878. [Google Scholar] - Gandhi, B.K.; Singh, S.N.; Seshadri, V. Prediction of performance characteristics of a centrifugal slurry pump handling clear liquid. Indian J. Eng. Mater. Sci.
**1998**, 5, 91–96. [Google Scholar] - Peng, G.J.; Fan, F.Y.; Zhou, L.; Huang, X.; Ma, J. Optimal hydraulic design to minimize erosive wear in a centrifugal slurry pump impeller. Eng. Fail. Analysis
**2021**, 120, 105105. [Google Scholar] [CrossRef] - Tarodiya, R.; Gandhi, B.K. Effect of particle size distribution on performance and particle kinetics in a centrifugal slurry pump handling multi-size particulate slurry. Adv. Powder Technol.
**2020**, 31, 4751–4767. [Google Scholar] [CrossRef] - Gandhi, B.K.; Singh, S.N.; Seshadri, V. Effect of speed on the performance characteristics of a centrifugal slurry pump. J. Hydraul. Eng.
**2002**, 182, 225–233. [Google Scholar] [CrossRef] - Zarya, A.N. The effect on the solid phase of a slurry on the head developed by a centrifugal pump. Fluid Mech. Sov. Res.
**1975**, 4, 144–154. [Google Scholar] - Wang, Z.; Qian, Z. Effects of concentration and size of silt particles on the performance of a double-suction centrifugal pump. Energy
**2017**, 123, 36–46. [Google Scholar] [CrossRef] - Gahlot, V.K.; Seshadri, V.; Malhotra, R.C. Effect of density, size distribution, and concentration of solid on the characteristics of centrifugal pumps. ASME J. Fluids Eng.
**1992**, 114, 386. [Google Scholar] [CrossRef] - Sellgren, A.; Addie, G.; Scott, S. The effect of sand-clay slurries on the performance of centrifugal pumps. Can. J. Chem. Eng.
**2000**, 78, 764–769. [Google Scholar] [CrossRef] - Li, Y.; Zhu, Z.; He, W.; He, Z. Numerical simulation and experimental research on the influence of solid-phase characteristics on centrifugal pump performance. Chin. J. Mech. Eng.
**2012**, 25, 1184–1189. [Google Scholar] [CrossRef] - Serrano, R.O.P.; Ferreira, A.G., Jr.; Castro, A.L.P.; Santos PA, B.V.; Menezes, M.V.; Martinez, C.B. Desgaste do rotor por abrasão: O efeito do bombeamento de água bruta com diferentes cargas de sedimento. In Proceedings of the XXVII Congreso Latinoamericano de Hidráulica, Lima, Peru, 26–30 September 2016; p. 9. [Google Scholar]
- Zhao, J. Experimental study on the effect of solid materials on the performance of centrifugal pumps. J. Tsinghua Univ. (Natl. Sci. Ed.)
**1986**, 1, 91–99. [Google Scholar] - Jeon, S.Y.; Kim, C.K.; Lee, S.M.; Yoon, J.-Y.; Jang, C.-M. Performance enhancement of a pump impeller using optimal design method. J. Therm. Sci.
**2017**, 26, 119–124. [Google Scholar] [CrossRef] - Tarodiya, R.; Gandhi, B.K. Numerical simulation of a centrifugal slurry pump handling solid-liquid mixture: Effect of solids on flow field and performance. Adv. Powder Technol.
**2019**, 30, 2225–2239. [Google Scholar] [CrossRef] - Tarodiya, R.; Gandhi, B.K. Hydraulic performance and erosive wear of centrifugal slurry pumps—A review. Powder Technol.
**2017**, 305, 27–38. [Google Scholar] [CrossRef] - Kadambi, J.R.; Charoenngam, P.; Subramanian, A.; Wernet, M.P.; Sankovic, J.M.; Addie, G.; Courtwright, R. investigations of particle velocities in a slurry pump using PIV: Part 1, the tongue and adjacent channel flow. J. Energy Res. Technol.
**2004**, 126, 271–278. [Google Scholar] [CrossRef] - Kumar, S.; Gandhi, B.K.; Mahapatra, S.K. Investigation on centrifugal slurry pump performance with variation of operating speed. Int. J. Mech. Mater. Eng.
**2013**, 8, 40–47. [Google Scholar] - Bai, L.; Zhou, L.; Jiang, X.; Pang, Q.; Ye, D. Vibration in a multistage centrifugal pump under varied conditions. Shock. Vib.
**2019**, 2019, 2057031. [Google Scholar] [CrossRef] - Dong, X.; Zhang, H.L.; Wang, X.Y. Finite element analysis of wear for centrifugal slurry pump. Procedia Earth Planet. Sci.
**2009**, 1, 1532–1538. [Google Scholar] - Noon, A.A.; Kim, M.H. Erosion wear on centrifugal pump casing due to slurry flow. Wear
**2016**, 364, 103–111. [Google Scholar] [CrossRef] - Shen, Z.J.; Chu, W.; Li, X.J.; Dong, W. Sediment erosion in the impeller of a double-suction centrifugal pump-A case study of the Jingtai Yellow River Irrigation Project. Wear
**2019**, 422, 269–279. [Google Scholar] [CrossRef] - Song, X.J.; Yao, R.; Shen, Y.B.; Bi, H.; Zhang, Y.; Du, L.; Wang, Z. Numerical Prediction of Erosion Based on the Solid-Liquid Two-Phase Flow in a Double-Suction Centrifugal Pump. J. Mar. Sci. Eng.
**2021**, 9, 836. [Google Scholar] [CrossRef]

**Figure 3.**Pressure distribution on first-stage impeller-guide vane B2B view: (

**a**) d

_{p}= 3 mm; (

**b**) d

_{p}= 6 mm; (

**c**) d

_{p}= 10 mm; (

**d**) d

_{p}= 14 mm; (

**e**) d

_{p}= 17 mm; (

**f**) d

_{p}= 20 mm.

**Figure 4.**Velocity distribution on first-stage impeller-guide vane B2B view: (

**a**) d

_{p}= 3 mm; (

**b**) d

_{p}= 6 mm; (

**c**) d

_{p}= 10 mm; (

**d**) d

_{p}= 14 mm; (

**e**) d

_{p}= 17 mm; (

**f**) d

_{p}= 20 mm.

**Figure 5.**Particle movement trajectories in the calculation domain: (

**a**) d

_{p}= 3 mm; (

**b**) d

_{p}= 6 mm; (

**c**) d

_{p}= 10 mm; (

**d**) d

_{p}= 14 mm; (

**e**) d

_{p}= 17 mm; (

**f**) d

_{p}= 20 mm.

**Figure 7.**Pressure distribution on first-stage impeller-guide vane B2B view: (

**a**) C

_{v}= 4%; (

**b**) C

_{v}= 7.5%; (

**c**) C

_{v}= 11.5%.

**Figure 8.**Velocity distribution on first-stage impeller-guide vane B2B view: (

**a**) C

_{v}= 4%; (

**b**) C

_{v}= 7.5%; (

**c**) C

_{v}= 11.5%.

**Figure 9.**Particle movement trajectories in the calculation domain; (

**a**) C

_{v}= 4%; (

**b**) C

_{v}= 7.5%; (

**c**) C

_{v}= 11.5%.

**Figure 11.**Pressure distribution on first-stage impeller-guide vane B2B view. (

**a**) 1400 kg/m

^{3}; (

**b**) 1900 kg/m

^{3}; (

**c**) 2800 kg/m

^{3}.

**Figure 12.**Velocity distribution on first-stage impeller-guide vane B2B view: (

**a**) 1400 kg/m

^{3}; (

**b**) 1900 kg/m

^{3}; (

**c**) 2800 kg/m

^{3}.

**Figure 13.**Single particle movement trajectory in the calculation domain: (

**a**) 1400 kg/m

^{3}; (

**b**) 1900 kg/m

^{3}; (

**c**) 2800 kg/m

^{3}.

**Figure 15.**Pressure distribution on first-stage impeller-guide vane B2B view: (

**a**) 0.68 Q

_{d}; (

**b**) 1.0 Q

_{d}

_{;}(

**c**) 1.33 Q

_{d}.

**Figure 16.**Velocity distribution on first-stage impeller-guide vane B2B view: (

**a**) 0.68 Q

_{d}; (

**b**) 1.0 Q

_{d}; (

**c**) 1.33 Q

_{d}.

**Figure 17.**Particle movement trajectories in the calculation domain: (

**a**) 0.68 Q

_{d}; (

**b**) 1.0 Q

_{d}

_{;}(

**c**) 1.33 Q

_{d}.

**Figure 19.**Pressure distribution on first-stage impeller-guide vane B2B view: (

**a**) n = 900 r/min; (

**b**) n = 1450 r/min; (

**c**) n = 1800 r/min.

**Figure 20.**Velocity distribution on first-stage impeller-guide vane B2B view: (

**a**) n = 900 r/min; (

**b**) n = 1450 r/min; (

**c**) n = 1800 r/min.

**Figure 21.**Particle movement trajectories in the calculation domain: (

**a**) n = 900 r/min; (

**b**) n = 1450 r/min; (

**c**) n = 1800 r/min.

**Figure 24.**Test site: (

**a**) mining pump test bench; (

**b**) measurement and control system; (

**c**) test particles.

**Figure 25.**Performance curves of the mining pump under thirteen flow conditions: (

**a**) flow-head curve; (

**b**) flow-efficiency curve; (

**c**) flow-shaft power curve.

**Figure 27.**Test system diagram: 1—test pump (including motor); 2—test pump support mechanism; 3—flow meter; 4—outlet pipe; 5—return pipe; 6-regulating valve; 7—return pipe support member; 8—cable terminal; 9—cable fixing component; 10—water tank; 11—anti-submersible pump swing component.

**Figure 28.**Comparison diagram of impeller runner before and after applying water-based paint: (

**a**) before painting; (

**b**) after painting.

**Figure 30.**Comparison of numerical calculation results and test results of the erosion area under low flow conditions: (

**a**) first stage impeller; (

**b**) secondary impeller.

**Figure 31.**Comparison of numerical calculation results and test results of the erosion area under rated flow conditions: (

**a**) first stage impeller; (

**b**) secondary impeller.

**Figure 32.**Comparison of numerical calculation results and test results of the erosion area under large flow conditions: (

**a**) first stage impeller; (

**b**) secondary impeller.

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

Impeller | Inlet diameter/mm | 216.8 |

Outlet diameter/mm | 440 | |

No. of blades | 3 | |

Blade wrap angle/° | 140 | |

Outlet placement angle/° | 28 | |

Outlet width/mm | 61 | |

Outlet inclination angle/° | 10 |

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

Particle diameter d_{p} | mm | 3, 6, 10, 14, 17, 20 |

Particle volume concentration C_{v} | % | 4, 7.5, 11.5 |

Particle density ρ | kg/m^{3} | 1400, 1900, 2800 |

Inlet flow rate Q/Q_{d} | / | 0.68, 1.0, 1.33 |

Rotational speeds n | rpm | 900, 1450, 1800 |

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## Share and Cite

**MDPI and ACS Style**

Hong, S.; Hu, X.
Influence of Different Particle Parameters and Operating Conditions on Flow Characteristics and Performance of Deep-Sea Mining Pump. *J. Mar. Sci. Eng.* **2022**, *10*, 363.
https://doi.org/10.3390/jmse10030363

**AMA Style**

Hong S, Hu X.
Influence of Different Particle Parameters and Operating Conditions on Flow Characteristics and Performance of Deep-Sea Mining Pump. *Journal of Marine Science and Engineering*. 2022; 10(3):363.
https://doi.org/10.3390/jmse10030363

**Chicago/Turabian Style**

Hong, Shunjun, and Xiaozhou Hu.
2022. "Influence of Different Particle Parameters and Operating Conditions on Flow Characteristics and Performance of Deep-Sea Mining Pump" *Journal of Marine Science and Engineering* 10, no. 3: 363.
https://doi.org/10.3390/jmse10030363