# Numerical Simulation Prediction of Erosion Characteristics in a Double-Suction Centrifugal Pump

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Research Object

_{d}= 3.083 m

^{3}/s, rated head H = 50 m, rated efficiency η

_{r}= 86%, rotation speed n = 490 r/min, number of blades z

_{b}= 16, impeller diameter D = 1275 mm, as shown in Figure 1. Figure 2 shows the name of the impeller components, ω is rotational angular velocity.

#### 2.2. Basic Equation of Particle Motion

_{p}is particle mass, u

_{p}is particle velocity, F

_{D}is resistance, F

_{B}is basset force, F

_{G}is gravity, F

_{V}is virtual mass force, F

_{P}is pressure gradient force, F

_{X}is the sum of other external forces considered.

_{s}is the slip velocity between particles and liquid, C

_{D}is the drag coefficient related to Reynolds number, ρ

_{f}is the liquid density, ρ

_{p}is the particle density, D

_{p}is the particle diameter, and x

_{pi}is the spatial coordinate position of particles. It can be seen from the formula that when the particle moves in the liquid, the particle trajectory is related to the particle diameter and density.

#### 2.3. Erosion Model

_{p}is the particle impact velocity. V

_{1}, V

_{2}, and V

_{3}are the parameters of particle impact velocity. γ is the impact angle in radians between the approaching particle track and the wall, γ

_{0}being the angle of maximum erosion. k

_{1}, k

_{12}, and γ

_{0}are model constants and depend on the particle/wall material combination.

#### 2.4. Calculation Method for Solution

^{−5}.

## 3. Discussion of Calculation Results

#### 3.1. Verification of Calculation Scheme and Reliability

_{d}= 0.771 m

^{3}/s, Q

_{d}= 3.083 m

^{3}/s and 1.27Q

_{d}= 3.91 m

^{3}/s, as shown in Table 1.

^{3}and the particle size is 0.025 mm. In engineering, pump erosion is due to long-term damage caused by different factors. However, numerical simulation is an ideal method to calculate the erosion prediction under a specific condition, and there are inevitably some errors in the predicted erosion results. On the whole, the erosion position and erosion morphology of the front cover plate wall and the blade outlet pressure surface predicted by the numerical simulation were consistent with the erosion characteristics of the pump impeller in the project site. The calculation results of external characteristics and erosion show that the numerical simulation method is reliable.

#### 3.2. Analysis of Flow and Erosion in Double-Suction Pumps under Different Flow Conditions

#### 3.2.1. Influence of Flow Rate on Particle Movement

^{3}. Under the condition of small flow rate, the flow pattern in the impeller was the worst, and there were different degrees of vortex and secondary flow caused by flow separation in many locations, as shown in Figure 8a. The multi-scale vortex flow in the blade channel blocks the blade channel, and the junction between the vortex boundary and the blade was the high-speed region. There were frequent frictions between the particles carried by the vortex and the wall. With the increase in flow rate, the uniformity of flow pattern in the impeller was obviously improved. The flow velocity in the pump under the rated flow condition Q

_{d}is relatively small compared with that under the large flow rate condition 1.27Q

_{d}and due to the existence of the outlet tongue, so a small-scale vortex appears near the tongue, as shown in Figure 8b. Under the two flow conditions of 1.27Q

_{d}, the flow was smooth in the blade channel, and there was no vortex, as shown in Figure 8c.

^{3}. Under the condition of small flow, the particle distribution in the impeller was uneven, as shown in Figure 9a. With the increase in flow, the uniformity of particle distribution in the impeller increased. However, the number of particles and the relative velocity of particles varied greatly in different blade channels. At the impeller inlet, the particle concentration distribution was the largest, and the number of particles in contact with the impeller inlet was also the largest. The relative velocity of the particles at the tail edge of impeller outlet was the largest under the non-rated condition (1.27Q

_{d}), as shown in Figure 9c. The distribution patterns of the particle in the impeller were consistent with the changes in the flow states under different flow conditions, which indicates that the flow rate has a great influence on the characteristics of the particle movements.

#### 3.2.2. Effect of Flow Rate on Surface Erosion

_{s}the area erosion rate, kg·m

^{−2}·s

^{−}

^{1}, W is the erosion wight, kg, S is the erosion area, m

^{2}, T is the erosion time, s.

_{T}is the erosion rate within a certain period of time, kg·s

^{−1}, W is the erosion wight, kg, m

^{2}, T is the erosion time, s.

^{3}. The results show that the erosion distribution and erosion mass loss of blades and hub on both sides of double-suction centrifugal pump are asymmetric. The erosion positions under different flow conditions were obviously different, which was directly related to the distribution position and motion trajectory of particles, indicating that the flow condition directly affected the erosion positions in the impeller. Under the condition of small flow rate, the internal erosion of double-suction centrifugal pump mainly included inflow impact erosion, blade channel friction erosion, vortex erosion, and blade head impact erosion, as shown in Figure 10a and Figure 11a.

_{d}to Q

_{d}and increases from Q

_{d}to 1.27Q

_{d}. The variation of the erosion rate of the hub wall with the flow condition also shows that the erosion amount on both sides of the double-suction centrifugal pump is also different.

#### 3.2.3. Local Erosion Caused by Vortex in Impeller

#### 3.3. Effect of Particle Concentration on Erosion Characteristics

_{d}are analyzed to explore the influence of particle concentration on erosion characteristics.

#### 3.3.1. Influence of Particle Concentration on Particle Tracks

^{3}, the particle distribution in the impeller is very uniform, and there is a strip of particle aggregation distribution at the impeller inlet, as shown in Figure 17a. With the increase in particle concentration, particles gather in the outlet direction of the suction surface of the blade passage, and the impact frequency of particles on the blade surface increases. The larger the particle concentration is, the more uneven the particle distribution is in the impeller, and the more serious the particle aggregation is on the suction surface and pressure surface of the blade, as shown in Figure 17b–d. Due to the backflow near the tongue of the impeller, the concentration of particles near the tongue increases.

#### 3.3.2. Effect of Particle Concentration on Erosion Characteristics

## 4. Conclusions

_{d}, Q

_{d}, and 1.27Q

_{d}, and different particle concentrations, 1 kg/m

^{3}, 7 kg/m

^{3}, 11 kg/m

^{3}, and 15 kg/m

^{3}. The conclusions are as follows:

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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Parameter | Scheme Number | |||||
---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | |

Flow rate (m^{3}/s) | 0.25Q_{d} | Q_{d} | 1.27Q_{d} | Q_{d} | Q_{d} | Q_{d} |

particle concentration (kg/m^{3}) | 15 | 15 | 15 | 11 | 7 | 1 |

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**MDPI and ACS Style**

Song, X.; Qi, D.; Xu, L.; Shen, Y.; Wang, W.; Wang, Z.; Liu, Y.
Numerical Simulation Prediction of Erosion Characteristics in a Double-Suction Centrifugal Pump. *Processes* **2021**, *9*, 1483.
https://doi.org/10.3390/pr9091483

**AMA Style**

Song X, Qi D, Xu L, Shen Y, Wang W, Wang Z, Liu Y.
Numerical Simulation Prediction of Erosion Characteristics in a Double-Suction Centrifugal Pump. *Processes*. 2021; 9(9):1483.
https://doi.org/10.3390/pr9091483

**Chicago/Turabian Style**

Song, Xijie, Dunzhe Qi, Lijuan Xu, Yubin Shen, Wei Wang, Zhengwei Wang, and Yan Liu.
2021. "Numerical Simulation Prediction of Erosion Characteristics in a Double-Suction Centrifugal Pump" *Processes* 9, no. 9: 1483.
https://doi.org/10.3390/pr9091483