Wear Characteristics of Dense Fine Particles Solid-Liquid Two-Phase Fluid Centrifugal Pump with Open Impellers

+e demand for a centrifugal pump with open impellers for conveying dense fine particles in solid-liquid two-phase flow has increased significantly in actual engineering. +e wear of dense fine particles on the centrifugal pump is also exceedingly prominent, which affects the engineering efficiency and economic benefits. +e two-phase flow in the open centrifugal pump is three-dimensional and unsteady; the movement of high-volume concentration particles in the centrifugal pump and its mutual influence on the two-phase flow, which results in the calculation of wear, are very intricate. To study the wear characteristics of the centrifugal pump with open impeller with high-volume concentration particles more accurately, numerical simulation and experimental comparison are carried out for the impeller wear of dense fine particles transported by the centrifugal pump with open impellers. Considering the relationship between particles and walls, we used the Fluent 18.0 built-in rebound function and wear model.+e RNG k-εmodel and the DDPMmodel were adopted in the numerical simulation, and the numerical solution for centrifugal pump wear was performed under flow rate (9.6m·h, 12.8m·h, 16m·h, and 19.2m·h), different particle sizes (0.048mm, 0.106mm, 0.15mm, 0.27mm, and 0.425mm), and different particle volume concentrations (10%, 15%, 20%, 25%, and 30%), respectively. By comparing the serious wear positions of the impeller, the experimental results correspond well with the numerical simulation, which can be used to predict and study the wear characteristics of the impeller. +e results show that the most serious area of blade wear is themiddle part of the pressure surface, followed by themiddle part of the upper part of the blade. +e wear of the impeller is greatly affected by relevant parameters, such as pump flow rate, particle diameter, and particle volume concentration. +ese results can provide some basis for the wear-resistant design of dense fine particle impeller.


Introduction
ere are complex flow problems in multiphase fluid transportation [1][2][3][4]. e solid-liquid two-phase centrifugal pump is an important piece of equipment for the hydraulic transportation of solid particles. In the process of conveying particles, due to the collision between the particles and the components in the pump (such as impeller and volute), the components in the pump are worn out [5]. e presence of particles will destroy the original flow field and the protective layer of the wall, resulting in performance degradation and wear damage [6][7][8][9][10], which further leads to frequent replacement or maintenance, and the corresponding conveying system needs to be stopped, thus leading to the significant increase of the conveying costs. e research of Wilson et al. [11] showed that the shutdown cost of a large mine is about 1 × 10 5 $/hour. erefore, the internal wear of centrifugal pumps is one of the important study directions of solid-liquid two-phase flow centrifugal pumps.
ere are many influencing factors for the wall wear problem of solid-liquid two-phase flow. e scholars have done a lot of research on the characteristics of solid-liquid two-phase flow. Gandhi et al. [12] studied the influence of particle diameter changes on wear and obtained the correlation between the wear and particle size. Ben-Ami et al. [13] established a wear model by studying the impact angle of particles and the wear law of surface materials on the wall. e volume concentration and sharpness of particles are also important factors for wall wear. e study of Nan et al. [14] showed that the flow rate affects the speed of the particles and then affects the wear performance. Within a certain range, the sharpness of the particles has a greater impact on the wall wear performance. Regarding the effect of particle volume concentration on the wear of solid-liquid two-phase flow, the study of Lai et al. [15] showed that the change of volume concentration will affect the position of impeller wear. Zhang's simulation and analysis of two-phase flow showed that the abrasion on the pressure side of the impeller of a centrifugal pump is higher than other parts when conveying high-volume concentration particles [16]. Adamczyk et al. [17] used the combination of DDPM and Euler-Euler to calculate the flow of circulating particles in the fluidized bed and, compared with the experiment, obtained a particle motion model suitable for the fluidized bed. Ou et al. [18] used the DDPM and KTGF models to carry out the corresponding numerical simulations on the wear of the elbow pipe under high-volume concentration coal conveying. e results showed that for the movement of particles under the resistance of centrifugal force and secondary flow, when they pass the elbow, partial reunion occurs, and the larger particles are susceptible to impact the curved back, which has a more obvious impact on erosion and wear. Jain et al. [19] studied the influence of different particle properties on the flow characteristics of fluidized beds through radioactive particle tracking technology and DDPM, and the results showed that DDPM can effectively predict the average particle velocity.
To make better use of solid-liquid two-phase centrifugal pump wear simulation to predict its experimental results, the relationship between particles and the wall (including wall rebound function and wall wear function) should be considered. Many scholars have proposed wall rebound functions that are more in line with the experiment according to different research directions. Sommerfeld and Huber [20] obtained the parameters of the wall rebound model (such as the coefficient of restitution and friction coefficient) based on the experimental data. e modified wall rebound function can predict the experiment well. Forder et al. [21] proposed the corresponding wear models through experiments and proposed a corresponding particle rebound model in combination with particle angles and wall materials to better study the wear mechanism of control valves. Based on the wear data of flat specimens in water or airflow and 90°s tandard elbows in airflow, E/CRC [5] obtained a new erosion equation and combined CFD with simulating and predicting the experiment. e wear rate and experimental results are in good consistency. Regarding the wear in the process of conveying solid particles in a fluidized bed, Bitter [22,23] proposed a wall wear function based on the movement properties of the particles, the hardness of the material, and the elastic parameters and explained the wear phenomenon of the fluidized bed in the experiment. By studying the wear characteristics of the particle shape, velocity, shooting angle, and different material properties on the wall surface, Neilson and Gilchrist [24] proposed the corresponding wear function to explain the wear phenomenon in the experiment. By studying particle properties and wall material properties (hardness and load relaxation), Oka [25,26] proposed wear functions for different materials. Huang [27] established a wear function including particle collision speed, angle, and particle size and wall material properties for the particle-wall wear characteristics during the jet process, which were in good agreement with the wear experiment of Finn [28]. Regarding the wear caused by the inhalation of solid particles by the turbine, G & T [29] proposed related particle rebound model and wall wear models based on the hydrodynamic resistance of the solid particles, the particle's rebound on the wall, and the wall wear, which were used to predict the relevant parts of the turbine, wear location, etc. However, the calculation of the three-dimensional nonconstant value of wear of centrifugal pumps that transport high-volume concentration solidliquid two-phase flow is still very small. In this work, to predict the overall wear performance of the centrifugal pump with open impeller under the condition of the highvolume concentration of solid-liquid two-phase flow, the method of three-dimensional indeterminate constant value analysis and the DDPM model are used and the influence of relevant parameters (flow rate, particle diameter, and volume concentration) on the wear characteristics of centrifugal pump flow components is studied. e results of this study are helpful to develop high-volume concentration solid-liquid two-phase flow centrifugal pumps, such as applying hard material [30] to wear-prone areas, avoiding unnecessary downtime, and reducing operating costs.

Mathematical Model
To predict the wear performance of the centrifugal pump, the numerical calculation includes the following conditions: basic assumptions, the establishment of solid-liquid twophase flow control equation, the analysis of particle forces, and the selection of particle-wall collision function and wear function.

Basic Assumption.
e solid-liquid two-phase flow inside the model pump is extremely complicated. To simplify the calculation and improve the accuracy of the numerical simulation results, the following assumptions are adopted: (1) e continuous phase (water) is an incompressible fluid, and the physical properties of each phase are constant (2) e particles are spherical glass beads with uniform particle size, regardless of the change in particle shape (3) e influence of temperature on the two-phase flow field is not considered (4) e collision between the particles and the wall is an elastic collision (5) e liquid phase and the solid phase adopt two-way coupling, and so on 2 Shock and Vibration

Solid-Liquid Two-Phase Governing Equation.
e twophase flow in the solid-liquid two-phase centrifugal pump is a turbulent flow. Considering the mixed movement and interaction of liquid and particles and the high-volume concentration of solid particles (C ≥ 10%), the Euler-Lagrange equation is used in this article to describe the liquid and solid phases in continuous media. Based on the principle of mass exchange and momentum conservation of incompressible two-phase flow, a basic solid-liquid two-phase governing equation, which is adopted by the Fluent 18.0 theory guide, is established: e momentum equation that is adopted by the Fluent 18.0 theory guide is as follows: where i � 1, 2 indicates the liquid and solid phase; ρ i is the density of i phase; n is the number of phases; p is the mixedphase pressure; α i is the volume fraction of i phase; v i is the relative velocity of i phase; _ m ij ( _ m ji ) indicates the mass transfer from i phase to j phase; μ i is the viscosity of i phase; u ij (u ji ) represent the phase velocity of i(j) phase and j(i) phase, if _ m ij > 0 (the mass of the i phase is transferred to the j phase), then u ij � u i and if _ m ij < 0 (the mass of the j phase is transferred to the i phase), then u ij � u j ; (the same, if _ m ji > 0, then u ji � u j ; if _ m ji < 0, then u ji � u i ); S DE represents the explicit part of the momentum exchange phase (provided by DPM); u s represents the average velocity of discrete phase particles; K DS represents the momentum exchange coefficient between the average phases of particles; k ji � k ij the exchange coefficient between phases.
F V represents the virtual mass force, which accelerates the fluid surrounding the particles. When the particle density is greater than the fluid density, this force cannot be ignored. e corresponding equation is as follows: In the formula, when the particles are spherical, the virtual quality coefficient C vm is 0.5 [31]; u p � dx/dt, u represents fluid velocity, u p represents particle velocity, and ρ p represents particle density. F S represents the Saffman force, which means that when the flow field has a large velocity gradient (such as near the wall), the velocity of the particle surface is different; that is, the pressure on the surface is different, which results in a difference between the particle and the fluid. For the force at the vertical velocity, the corresponding governing equation is as follows: Regarding the Saffman force under high Reynolds, the literature [32] proposed the following amendments: where Re p is the particle instantaneous Reynolds number.

Shock and Vibration 3
F L represents the lift force of the particle in the liquid, and the lift force of the secondary phase i in the main phase j can be expressed as follows: In the above formula, C l represents the lift coefficient, and its value is 0 for spherical particles [31]; ρ j represents the density of the main phase; α i represents the volume concentration of the secondary phase; u j represents the velocity of the main phase; u i represents the velocity of the secondary phase.

Solid Phase Control Model.
e mixture movement and interaction of liquid and particles make the movement of particles complex and difficult to predict. Since this study is about the wear of high-volume concentration particles on the pump, the Lagrange method is used to describe the particle movement. e particle trajectory equation in the Lagrange method can be written as follows: where u p � dx/dt, u represents fluid velocity, u p represents particle velocity, ρ p represents particle density, ρ represents liquid density, (u − u p )/τ r represents the resistance per unit particle mass, and τ r represents particle relaxation time and can be written as follows: In the formula, d p represents particle diameter, μ represents fluid viscosity, C d represents the resistance coefficient, and C d can be expressed by the following formula: In the above formula, α 1 , α 2 , and α 3 are constants provided by Morsi and Alexander [33].

Selection of Particle-Wall Rebound Function and Wear
Function. Many scholars [5,[16][17][18][19][20][21][22][23][24][25] put forward particlewall rebound functions and wear functions that are more suitable for their experiments according to different experimental conditions and explain the wear phenomenon under different conditions. According to its theoretical analysis, it is concluded that they are more suitable for wear under low-volume concentration conditions (C < 10%). For the high-volume concentration in this article, that is, the number of particles is too large, and to save the corresponding computing resources, the Fluent 18.0 built-in particle-wall rebound model and wear model are used. For specific models, refer to literature, which is adopted by Fluent 18.0 theory guide.

Pump Model and Mesh Generation.
e 1PN/4-3 KW single-stage centrifugal pump with open impeller is selected as the calculation and experimental model. e basic design parameters are shown in Table 1. To reduce the influence of the liquid in and out of the centrifugal pump on the inside of the centrifugal pump, a 0.2 m pipe is added upstream of the impeller (4 times the diameter of the impeller inlet). A 0.12 m pipe is added at the outlet of the volute (4 times the diameter of the impeller outlet). NX12.0 software is used to build the corresponding model in Figure 1(a), and the computational grid uses ICEM to build a grid for the computational domain. e overall grid of the model is 4120245, the number of nodes is 757118, and the corresponding calculation domain and grid are shown in Figure 1 Figure 2. e curve error of the numerical simulation results and experimental results in the figure is less than 8%. Considering the influence of factors such as valves and processing in the actual process, the external characteristic error of the model can be considered reasonable.

Calculation Model and Boundary Conditions.
According to experience, the inlet of the centrifugal pump is set as a speed inlet, and the outlet is a pressure outlet. e velocities at the inlet and outlet of the continuous phase and the discrete phase are uniform, and the initial velocity of the discrete phase is equal to that of the continuous phase. In the calculation domain, the speed of the impeller remains constant, and the inlet pipe, outlet pipes, and volute remain stationary. e discrete phase and continuous phase adopt bidirectional coupling. DDPM model and turbulence model RNG k − ε are used to calculate the wear of discrete phase on a centrifugal pump.

Results and Discussion
Numerical simulation is performed with the design conditions of the centrifugal pump with an open impeller (refer to Table 1) and the particle density of 2450 kg/m 3 . e effects of flow rate and particle properties (particle size and volume concentration) on the wear characteristics of the centrifugal pump with open impeller are studied, respectively, and the wear law of the whole centrifugal pump is predicted, and the experimental results are compared ( Table 2 is the numerical simulation working condition). e average wear rate and maximum wear rate of different parts of the centrifugal pump are calculated and compared. e pressure surface in this article is divided into the main working part of the blade, namely, the main pressure surface and the secondary pressure surface on the back blade. e suction surface is divided into the main working part of the blade, namely, the main suction surface and the secondary suction surface on the back blade. e graph shown in this article is a wear

Influence of Flow Rate on Centrifugal Pump Wear.
Under the premise of volume concentration C � 20% and particle size d � 0.106 mm, the influence of flow rate on the wear of the centrifugal pump with open impellers is studied. For cases 1-4 listed in Table 2 Figure 3 shows that the increase of flow rate changes the wear position and wear amount of the whole impeller. Figures 4 and 5 reveal the wear cloud diagram of the pressure surface and suction surface of the blade. e increase of flow rate makes the wear of the pressure surface gradually increase and the wear location is concentrated in the middle of the pressure surface; moreover, the wear location of the suction surface moves from the foremost to the middle. Figure 6 indicates the effect of flow rate on the wear of the volute. e increase in flow rate makes the wear position of the volute change, but the main wear area is around the volute diaphragm. e change of flow rate makes the movement of the solid-liquid two-phase flow at the volute tongue change. e wear area near the volute tongue shows an expanding trend as a whole; the wear area of the volute tongue under design conditions is relatively small compared to others. Figure 7 shows the relationship between the wear rate and flow rate of different parts of the solid-liquid two-phase centrifugal pump. e main trend of the average rate of wall wear is increased. e maximum wear rate of the main suction surface decreases first and then increases with the increase of the flow rate, the maximum wear rate of volute increases, decreases, and then increases, and the others keep increasing. e wear rate of the main parts of the centrifugal pump with open impeller (such as the main pressure surface, the main suction surface, and the volute) increases with the increase of the flow; the maximum wear rate of the main suction surface first increases and then decreases. e smallest value is under the design flow rate and the value of the maximum wear rate is the smallest, indicating that the maximum wear rate of the suction surface has a certain improvement under the design conditions.

e Influence of Particle Size on Centrifugal Pump Wear.
Based on the design flow Q � 16 m 3 ·h −1 and the high-volume concentration C � 20%, the effect of particle size on the wear of the centrifugal pump with an open impeller is studied. For cases 5-9 listed in Table 2, the particle sizes include d � 0.048 mm, 0.106 mm, 0.15 mm, 0.27 mm, and 0.425 mm, corresponding to the wear clouds in Figures 8-11. e change of particle size makes the particle more constrained by gravity and its own momentum changes.
at is, the change of particle size makes the wear position of different parts of centrifugal pump with open impellers change.
e particle size has a great influence on the wear position of the impeller (see Figure 8). e larger the particle size, the more severe the wear of the front end of the impeller. Figures 9 and 10 show the influence of the particle size on the wear of the pressure surface and suction surface, respectively. e increase of particle size causes the wear position of the pressure surface to move from the front end to the middle, and the wear of the front end of the suction surface is worse. e wear position of the pressure surface moves downward with the increase of gravity (i.e., the increase in particle size). e main wear of the front end of the suction surface becomes more serious. Different from the impeller, the increase of the particle size first increases the wear range around the volute tongue and then decreases to a certain extent. e average wear rate of the volute and the secondary suction surface decreases with the increase of the particle size, and in the other position, the average wear rate increases (Figure 12(a)). e increase of the particle size reduces its followability, which reduces the collision probability of particles with the wall of the volute, so its average wear rate gradually decreases. e increase in particle size makes the maximum wear rate of the volute wall increase gradually. e maximum wear rate of the secondary suction surface decreases with the increase of the particle size, and the wear rate of the volute and suction surface is the largest among all parts (Figure 12(b)). It is because that the increase of particle size reduces the probability of particles colliding with the secondary suction surface. Hence, both the average wear rate and the maximum wear rate of the secondary suction surface decrease.

e Influence of Particle Volume Concentration on Centrifugal Pump
Wear. Under the premise of design flow Q � 16 m 3 ·h −1 and particle size d � 0.106 mm, the influence of volume concentration on the wear of the centrifugal pump with open impeller is studied. For cases 10-14 listed in Table 2, the volume concentration includes C � 10%, 15%, 20%, 25 %, and 30 % and the corresponding wear clouds are in Figures 13-16. e probability of particles hitting the centrifugal pump changes with the change of particle volume concentration, which has a great effect on the wear rate and wear location of the wall.

Shock and Vibration
With the increase in particle volume concentration, the wear of the impeller gradually increases (as shown in Figure 13). e area of the pressure surface wear spreads to the entire pressure surface and the amount of wear increases related to the particle size volume concentration increases ( Figure 14). When the volume concentration is lower (C < 10%), the wear area of the suction surface is mainly concentrated in the front end, and when the volume concentration is higher (C ≥ 20%), it is mainly concentrated in the middle (Figure 15).
In Figure 16, with the increase in volume concentration, the main wear area of the volute extends from the tongue to the surrounding. e average wear rate of the secondary suction surface decreases and the other parts increases. e average wear rate of the main pressure surface shows an upward trend with the increase of the particle volume     concentration and maintains the maximum average rate of all parts. e average wear rate of the secondary suction surface is varying from 20% to 25% in all parts, which is the largest in Figure 17(a). e increase of particle volume concentration causes the maximum wear rate of the main suction surface to first decrease and then increase, the secondary suction surface maintains a consistent downward trend, and the other parts maintain an upward trend (Figure 17(b)). e increase of volume concentration makes the main wear area of the pressure surface extend from the front end to the tail. e average wear rate and maximum wear rate of the main pressure surface increase and the average wear rate of the secondary pressure surface increases, but the maximum wear rate of the secondary pressure surface decreases first and then increases with the increase of volume concentration. e average wear rate and maximum wear rate of the main suction surface increase. e particles with highvolume concentration will aggregate; as the volume concentration increases, more particles are located in the flow channel of the impeller, which makes the average wear and maximum wear of the secondary suction surface show a downward trend. e degree of wear around the volute tongue increases with the increase of particle volume concentration, the average wear rate gradually increases, and the maximum wear rate first decreases and then increases. Figure 18(a) is the painted impeller before the impeller wear test. Figures 18(b), and 18(c) are the wear test results of a centrifugal pump with the open impeller at the condition of volume concentration C � 20%, particle diameter d � 0.106 mm, and flow rate Q � 16 m 3 ·h −1 and centrifugal pump running 48 hours. It can be seen intuitively that the main wear positions of the impeller appear in the middle of the blade and the front end of the blade. By comparing the wear map of the impeller experiment (Figures 18(b), and 18(c)) with the wear cloud map in the simulation (Figures 3(c) and 4(c)), it is found that the wear position of the impeller appears at the middle and the leading edge of the blade, which is almost similar to that of the numerical simulation. When using this type of centrifugal pump to convey high-volume concentration particles, the wear resistance of the middle part of the impeller blade and the leading edge of the blade should be considered.

Conclusion
e wear of the centrifugal pumps with open impellers that convey high-volume concentrations of particles is mainly caused by particle movement. In this study, the three-dimensional unsteady and two-phase coupling Euler-Lagrange method is used to simulate the wear of the centrifugal pump with an open impeller.
rough the analysis of the wear cloud diagram, it is concluded that when the centrifugal pump delivers high-volume concentration solid-liquid twophase flow, the main wear part appears on the pressure surface of the impeller. Compared with other parts, the average wear rate of the main pressure surface is the largest. e second is the part of the volute tongue. According to the numerical simulation of the change of the wear cloud image of the volute tongue, it is concluded that the two-phase flow is extremely active around it, and the probability of particles colliding with the surrounding wall is greatly increased, which increases the wear rate. Parameters such as flow rate, particle size, and particle volume concentration mainly have a significant impact on the wear of the leading edge, the middle of the blade, and the volute tongue of the centrifugal pump with an open impeller.

Data Availability
All data included in this study are available upon request by contact with the corresponding author.

Conflicts of Interest
e authors declare no conflicts of interest.