# Study on the Effects of the Wear-Rings Clearance on the Solid-Liquid Two-Phase Flow Characteristics of Centrifugal Pumps

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Method

#### 2.1. Calculation Model

^{3}/h (Q means flow rate), H = 80 m (H means head), and n = 2900 r/min (n means Rotating speed). Figure 1a shows a schematic diagram of the pump body and parts of a single-stage single-suction centrifugal pump. Figure 1b is the clearance diagram of the straight orifice ring of the centrifugal pump, where L represents the clearance length and d represents the clearance size.

#### 2.2. Meshing and Boundary Conditions

^{−4}.

#### 2.3. Governing Equation

_{q}is the volume fraction of the phase q, u is the instantaneous velocity, F is the interphase force, g is the acceleration of gravity, ρ is the density, μ is the dynamic viscosity, and λ is the volume viscosity [28].

#### 2.4. Wear Model

_{P}is the particle shape coefficient. The solid phase is angular particles, and F

_{P}= 1 is taken. In addition, v

_{p}is the speed of the solid phase, m/s, φ is the solid-phase incident angle, rad, ER is the wear rate, q

_{m}is the solid phase mass flow rate, kg/s, and A

_{cell}is the area of the grid wall of the calculation unit. When the material of the centrifugal pump is unchanged, it can be seen from the formula that the wear rate is related to the incident collision velocity, incident collision angle, and mass flow rate of the solid phase.

#### 2.5. Verification of a Numerical Simulation Method

## 3. Results and Discussions

#### 3.1. Effects of Wear-Rings Clearance on External Characteristics of Centrifugal Pump

#### 3.2. Unsteady Clearance Flow Analysis

^{3}/h. Figure 8 shows the instantaneous static pressure distribution diagram of the centrifugal pump under different clearances under standard working conditions, and studies the pressure distribution in the centrifugal pump under a different clearance with sandy water. As can be seen from the pressure nephogram of the cross section of the centrifugal pump in Figure 6, the pressure distribution of each flow channel in the impeller is very regular and symmetrical in the center, except the flow channel near the tongue. There is a pressure accumulation near the septum tongue, and a small pressure drop occurs in the diffusion tube area connected to it. At the same time, the internal flow field distribution is basically the same while the clearance is different and the internal pressure of the centrifugal pump impeller increases with the radial gradient. This is because the centrifugal force generated by the rotation of the impeller does work for the fluid in the impeller passage. The larger the radius, the greater the centrifugal force suffered by the fluid, and the more work is done. The more kinetic energy is converted to pressure energy, the higher the static pressure value is. The pressure near the inlet of the impeller is the lowest and the pressure distribution is relatively uniform, while the pressure near the outlet of the impeller is higher. However, the pressure distribution is not uniform. This non-uniformity is mainly caused by the geometric asymmetry of the volute and the static interference. The pressure on the working surface of the blade is higher than that on the non-working surface, which is mainly caused by the inertial force and viscous force of the fluid in the flow passage. It can also be seen from the figure that the pressure gradient of the middle section of the impeller gradually decreases with the increase of the clearance. From the blade inlet to blade outlet, the clearance increases, the pressure in the area near the blade inlet increases, and the pressure in the area near the blade outlet decreases. Then the head tends to decrease, corresponding to the relationship between clearance and head in Figure 7.

#### 3.3. Wear Characteristics Analysis of the Impeller with a Different Clearance

^{3}under rated conditions. It can be seen from the solid phase volume distribution of the blade in the figure that the solid phase is more distributed in the blade head, upper edge, and tail of the blade suction surface. The solid distribution on the pressure surface is much smaller than that on the suction surface. This is related to the flow state inside the centrifugal pump. According to the velocity flow diagram of the middle section of the impeller, it can be seen that the solid phase flow velocity at the blade head is small, while the velocity increases along the radial direction, and the velocity at the blade tail reaches the maximum. As the area becomes larger after entering the diffusion tube, the solid phase velocity decreases. Where the solid phase volume fraction is small, there is a vortex in the impeller passage. It can be speculated that the vortex causes the solid particles to be affected by centrifugal force, resulting in the decrease of solid phase particle concentration. The distribution range of the solid phase volume fraction of the blade increases when the clearance of the wear-rings increases from 0.1 mm to 0.15 mm. When the gap of the wear-rings continues to increase to 0.2 mm, 0.3 mm, and 0.5 mm, it is clear that the distribution range of the solid phase significantly decreases.

^{3}. It can be seen that the wear on the suction surface of the blade is more serious than that on the pressure surface. The wear on the suction surface is mainly concentrated in the head, middle, and tail of the blade, while the wear on the pressure surface is mainly concentrated in the tail. The severe wear at the tail of the blade may be due to the greater absolute velocity of the fluid, and the mutual interference is more significant. The blade head is significantly worn because of the positive impact angle of solid particles accompanied by fluid flow. When the clearance of the wear-rings changes from 0.1 mm to 0.15 mm, the blade shows more wear. When it increases from 0.15 mm to 0.2 mm, 0.3 mm, and 0.5 mm, the wear degree tends to decrease. The maximum wear rate of the clearance from 0.4 mm to 1.2 mm is 4.16 × 10

^{−3}kg/(m

^{2}·s), 5.67 × 10

^{−3}kg/(m

^{2}·s), 5.58 × 10

^{−3}kg/(m

^{2}·s), 5.34 × 10

^{−3}kg/(m

^{2}·s), and 3.55 × 10

^{−3}kg/(m

^{2}·s), respectively.

#### 3.4. Wear Characteristics’ Analysis of the Volute Wall under a Different Clearance

^{3}. The volute wall surface is basically free of wear when the clearance of the wear-rings is 0.1 mm and 0.15 mm with only a slight erosion at the tongue. When the clearance of the mouth ring is 0.20 mm, the wear of the volute wall becomes very clear. The wear rate is at a high level, and the wear damage is dense and significant. The areas with a higher wear rate are mainly three parts: areas I and II, which are symmetrically distributed on the volute wall surface, and the outer wall area III of the outlet flow section of the volute. In these areas, especially area III, there are a large number of turbulent states and high-pressure regions. The motion of particles shows a disordered and a random motion state. The collision between particles and the wall surface, the collision between particles and particles, and the interaction between particles and fluid make the wear more severe on the wall. As the clearance increases from 0.20 mm to 0.50 mm, the peak wear rate ranges from 2.03 × 10

^{−5}kg/(m

^{2}·s), 1.78 × 10

^{−5}kg/(m

^{2}·s), 1.40 × 10

^{−5}kg/(m

^{2}·s). In turn, the size of areas I, II, and III was significantly reduced, and the wear changes from sheet to a random pitting corrosion with a high wear rate.

#### 3.5. Wear Characteristics Analysis of Wear-Rings under Different Clearances

^{3}. When the clearance is 0.1 mm, the velocity distribution is relatively uniform. With the clearance of the wear-rings increasing, the velocity at the wear-rings increases gradually, and the velocity gradient near the front cavity is relatively fast. However, the velocity distribution in the front cavity is not uniform, which is caused by the asymmetry of the volute structure. It can be seen from Figure 10 that vortexes are likely to occur in the front cavity, and the vortexes decrease when the clearance increases. When the vortex decreases, the solid phase back-flow can be reduced, so that the mass flow through the clearance increases, and the velocity finally increases.

^{3}and under different clearance conditions of the wear-rings. It can be seen from the figure that, when the clearance is 0.1 mm, the area with severe wear is the wear-rings near the front cavity, which is linearly distributed. In the middle of the wear-rings, there is a point-like circumferential distribution with severe wear at the center of the point and uneven distribution. With the increase of the clearance, the wear area near the front cavity gradually widens and presents a zonal distribution, and the severe wear area in the middle of the wear-rings expands from a point-like circumferential distribution to a round-like circumferential distribution.

## 4. Conclusions

- (1)
- The wear of the centrifugal pump blade is mainly concentrated in the end and the inlet of the blade because the tip of the blade is moving at a higher speed and the solid particles at the front of the blade have a better positive impact angle. Under the influence of vortexes, the wear at the end of the blade suction surface is very severe, while, that at the front of blade, is more serious.
- (2)
- With the clearance changing, the maximum wear of the blade changes. When the clearance increases from 0.1 mm to 0.15 mm, the maximum wear in the impeller increases. When the clearance increases from 0.15 mm to 0.5 mm, the maximum wear in the impeller decreases because of the leakage of the wear-rings and energy loss.
- (3)
- It can be found through the analysis of the solid distribution and pressure distribution at the wear-rings that the solid distribution presents different distribution states with the change of the clearance. In general, the larger the clearance is, the higher the solid concentration is. The analysis of the impeller’s front cavity shows that the pressure of the front cavity is affected by the change of the clearance, which influences the flow of the fluid and the movement of solid particles in the front cavity.
- (4)
- As the clearance of the wear-rings increases, the wear of the centrifugal pump becomes more significant, and the severe wear area presents a point-like circumferential distribution.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 5.**Centrifugal pump test bench. 1-Water-sealed valve, 2-voltage stabilizer, 3-experimental pump, 4-torque meter, 5-motor, 6-flow meter, 7-Flow control valve, 8-water tank, 9-digital indicator, 10-pressure gauge, and 11-outlet valve.

**Figure 6.**Simulation of the external characteristics of the centrifugal pump-experimental value curve.

**Figure 8.**Instantaneous static pressure distribution of centrifugal pumps under a different clearance.

**Figure 11.**Distribution of liquid velocity on the axis of the front pump cavity under a different clearance.

**Figure 12.**Streamline of liquid velocity at y = 0 cross-section in the front cavity under a different clearance.

**Figure 14.**Distribution of solid volume and flow velocity in the middle section under a different clearance.

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

Impeller inlet diameter D_{1} | 80 mm |

Impeller outer diameter D_{2} | 250 mm |

Number of blades Z | 5 |

Angle of the tongue β | 24° |

Impeller outlet width b | 6.5 mm |

Base circle diameter D_{3} | 260 mm |

Outlet diameter D_{4} | 50 mm |

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**MDPI and ACS Style**

Yan, C.; Liu, J.; Zheng, S.; Huang, B.; Dai, J.
Study on the Effects of the Wear-Rings Clearance on the Solid-Liquid Two-Phase Flow Characteristics of Centrifugal Pumps. *Symmetry* **2020**, *12*, 2003.
https://doi.org/10.3390/sym12122003

**AMA Style**

Yan C, Liu J, Zheng S, Huang B, Dai J.
Study on the Effects of the Wear-Rings Clearance on the Solid-Liquid Two-Phase Flow Characteristics of Centrifugal Pumps. *Symmetry*. 2020; 12(12):2003.
https://doi.org/10.3390/sym12122003

**Chicago/Turabian Style**

Yan, Chaoshou, Jianfei Liu, Shuihua Zheng, Bin Huang, and Jiacheng Dai.
2020. "Study on the Effects of the Wear-Rings Clearance on the Solid-Liquid Two-Phase Flow Characteristics of Centrifugal Pumps" *Symmetry* 12, no. 12: 2003.
https://doi.org/10.3390/sym12122003