Analysis of Internal Flow and Wear Characteristics of Binary Mixture Particles in Centrifugal Pump Based on CFD-DEM

Abstract

Solid-liquid two-phase flow centrifugal pumps are widely used in many fields closely related to economic development, such as energy exploitation, and the petrochemical industry. Many scholars have studied the influence of solid particles with different parameters on the transportation performance of centrifugal pumps but have mainly focused on the study of low-concentration single-component particles, and the research on the transportation of high-concentration binary mixture particles in centrifugal pumps is insufficient. In this paper, two kinds of glass beads (0.4 mm and 2 mm) were mixed as a solid phase medium, representing small particles and large particles, respectively. The effects of a high concentration (C_v = 10%) of binary mixture particles on the transport and wear characteristics of a solid-liquid centrifugal pump were analyzed by simulation and experiment. Computational Fluid Dynamics-Discrete Element Method (CFD-DEM) and Archard wear model were used for simulation, realized by Fluent software and EDEM software. The results show that the large particles have a greater effect on the performance decline than the small particles, and the increase of the proportion of large particles has a greater effect on the efficiency decline than the head decline. The wear degree of the flow channel in the pump changes obviously with the particle ratio, and the overall wear is small when the particle ratio is 1:2.

1. Introduction

Solid-liquid two-phase flow centrifugal pump is an important solid-liquid mixture conveying machinery, widely used in energy exploitation, petrochemical, water conservancy engineering, sewage treatment and many other fields closely related to economic development. In the practical application process, the solid particles collide with the components of the centrifugal pump with high impact energy and extremely frequent, which not only reduces the operating efficiency and increases the energy consumption, but also makes the components wear seriously and need to be frequently stopped for replacement. At present, in order to improve the performance of solid-liquid centrifugal pump, many scholars have carried out studies on its internal flow characteristics and wear characteristics under different particle transport conditions.

1.1. Research on Flow Characteristics in Solid-Liquid Two-Phase Centrifugal Pump

Figure 1 shows the schematic diagram of centrifugal pump, under the rotation of the impeller, the kinetic energy of the solid-liquid mixture in the pump increases and is discharged to the volute. Part of the kinetic energy of the mixture in the volute is converted into pressure energy and then pushed out of the pump to a certain height. The external characteristics of pump, such as efficiency and head, and the internal characteristics of flow field pressure and eddy are the main concerns of scholars. Cheng et al. [1] applied the CFD-DEM method to simulate solid-liquid flow in a single-channel pump, and the results showed that the velocity distribution range and velocity peak value of small particles were large. The hub and front plate are subjected to small contact forces, but the blade and volute wall are subjected to considerable contact force. Peng et al. [2] studied the slurry flow of heavy slurry pump. The results show that the pump flow is very unstable at low flow rates, and the flow resistance increases and reflux increases with the increase of particle concentration. Zhao et al. [3] simulated the solid-liquid flow in a centrifugal pump and their results showed that, with the increase of particle concentration, the external characteristics and turbulent kinetic energy of the pump would be more and more affected. Zhang et al. [4] studied the transient characteristics of solid-liquid centrifugal pump during startup, and the results showed that, compared with the clean water condition, the solid-liquid two-phase flow would lead to higher shaft power and pressure fluctuation. Liu et al. [5] simulated the solid-liquid two-phase flow in the chemical process pump and found that the particle concentration near the back of the blade was higher. With the increase of particle diameter, the particles tended to move towards the back of the blade. Wang et al. [6] simulated the solid-liquid flow in the slurry pump of deep-sea mining, and the results showed that with the increase of particle diameter, the strength and size of vortex in the guide vane increased significantly, and the flow rate changed more obviously. In addition to the use of numerical simulation, scholars also used the experimental way to study the centrifugal pump. Gao et al. [7] and Durmuş et al. [8] used experimental method to analyze the rotating flow at the entrance, it was found that inlet vortices caused the rotation of particles. Li et al. [9] through numerical simulation and experimental study, found that at low flow rate, solid-phase characteristics had basically no influence on the performance of centrifugal pumps. With the increase of particle size and volume fraction, the optimal efficiency of centrifugal pump decreased and the optimal efficiency point tends to the direction of a low flow rate. Cheng et al. [10] studied the flow characteristics of salt particles transported by molten salt pump and found through experiments that, the pump with more blades had a better performance except under the condition with large solid particles. Wang et al. [11] conducted numerical simulation of the internal flow field of mud pump and compared it with the experimental results of external characteristics. They pointed out that with the increase of particle concentration, the eddy current in the impeller passage became stronger, and the impeller obstruction became larger, leading to the reduction of working capacity and the increase of shaft power. Through simulation and experiments, Tarodiya et al. [12,13] found that the head and efficiency of centrifugal pump decreased with the increase of particle size and concentration, and the change of particle size distribution significantly affected the particle flow in the impeller passage and particle pressure intensity. Li et al. [14] simulated the deep-sea lifting motor pump under different speed conditions through CFD-DEM model and found that the simulation of CFD-DEM is more accurate than CFD through experimental verification.

1.2. Research on Wear of Solid-Liquid Two-Phase Centrifugal Pump

In the solid-liquid two-phase transportation of centrifugal pump, in addition to the transport efficiency, head and other flow characteristics, the wear of particles on the wall is also the focus of attention. The study of particle wear mechanism on the wall is also to improve the operating life of centrifugal pump components. Yan et al. [15] simulated results of solid-liquid centrifugal pump showed that blade wear was mainly concentrated at the end part and inlet part, and with the increase of clearance, the maximum wear value of impeller first increased and then decreased. Huang et al. [16] predicted the wear in the centrifugal pump through the Archard wear model, and the results showed that the wear of volute is about 70% of the total wear of the pump, and the wear area of the impeller was mainly on the leading edge of the blade, the junction between the hub and the back of the pressure side of the blade, and the junction between the wear plate and the back of the suction side of the blade. Shen et al. [17] used the DPM model to simulate the transportation of large particles by spiral centrifugal pump, and the results showed that small particles had a long track and more collisions with the flow channel, and the erosion part was relatively uniform. The collision angle of large particles with the impeller and volute surface is larger, and the wear area is more concentrated. Wu et al. [18] studied the influence of unstable flow characteristics on pump performance and found that relatively high-speed particles would accelerate blade tail wear. Shi et al. [19] studied the internal flow field in a solid-liquid centrifugal pump and proposed the wear equation to predict the volute wear caused by solid-liquid two-phase flow. The experimental results showed that the predicted area of high erosion intensity showed good consistency with the experimental area of erosion. Peng et al. [20] found that the relative wear rate on impeller blade and guide blade increases with the increase of sediment concentration, and the maximum wear part on impeller blade is in the open area. Adnan et al. [21] predicted the wear of lime slurry on slurry pump and found that the cochlear tongue and abdomen of the volute were the most severely worn areas, and the wear rate was proportional to the particle impact rate, particle concentration and particle size. Hong et al. [22] proposed a numerical simulation model of a particle motion balance equation based on the particle deposition movement of the pump and found that when the particle movement trajectory in the pump was similar to the blade profile, the particle wear on the blade was very low. Numerical simulation cannot completely predict wear, so some scholars also conducted wear experiments in order to obtain more realistic wear data. Li et al. [23] conducted wear experiments on large particles transported by centrifugal pumps and found by measuring the thickness of impeller that the wear rate increased with the increase of particle mass concentration, but the increase rate of wear rate decreased due to the movement of particles towards the inner wall of the volute to form a particle layer. Sunil et al. [24] conducted an experimental study on erosion wear of pump bodies made of bronze and mild steel materials, and the weight loss analysis showed that the wear had a great relationship with the size of solid particles. Arabnejad et al. [25] carried out experiments and analyses through particle erosion, introduced the expression of sharp particles at an erosion Angle of zero into the motion equation, and deduced the corresponding empirical formula of wear and erosion. Khalid et al. [26] designed a wear device to test the weight, diameter, thickness, and height loss of the impeller, and found that the weight loss of the impeller was due to the wear of the material removed from the blade. The loss of impeller diameter is caused by the impact of solid particles on the impeller surface area.

The above studies mainly focus on the concentration range of single component particles and dilute phase, while there are few studies on the concentration of multi-component mixed particles and dense phase (C_v ≥ 10%), but in practical engineering applications, such as mining with centrifugal pump, the mineral medium size is not uniform, along with the increase in particle composition, the flow situation in the centrifugal pump is more complicated. Therefore, the flow characteristics and wear characteristics of centrifugal pump under the condition of transporting high-concentration binary mixture particles are studied in this paper, which can provide theoretical reference for the transportation of high-concentration two-component medium and the design optimization of centrifugal pump. Experimental research can obtain the external characteristics of the pump during operation, but it lacks the details of the internal flow of the centrifugal pump. Therefore, numerical simulation is the main research method in this paper, and experiments play an auxiliary role in verification.

2. Models and Methods

2.1. Solid-Liquid Two-Phase Coupling Method

In this paper, solid-liquid two-phase flow was solved based on CFD-DEM coupling method which is a Euler–Lagrange method. CFD solves flow field by Fluent software under ANSYS 19.2 and DEM calculates particle movement by EDEM 2020.2. The data transmission between Fluent software and EDEM software through the application programming interface (API). The overall process can be seen from Figure 2. In the solving process, Fluent software firstly calculates the flow field information in a set time step. After the flow field calculation iteration reaches the convergence standard, the flow field parameter information is imported into the drag calculation model to calculate the flow field force on particles, and the data is transmitted to EDEM software. Then, EDEM software applied the force of the flow field to the particles under the time step. Based on the flow field data, the particle-particle collision, particle-wall collision and the interaction force between the particles and the fluid within the time step were calculated, and the trajectory of the particles was simulated according to the calculated force. Finally, the particle calculation results of EDEM software are returned to Fluent software again in the form of momentum, and the iterative calculation of the next time step is carried out, which is repeated until the coupling calculation reaches the set total time step number.

2.2. Governing Equations

The fluid governing equation is shown below:

$$\frac{\partial }{\partial t}({\alpha }_f{\rho }_f)+\frac{\partial }{\partial x_j}({\alpha }_f{\rho }_f{u}_j)=0$$

(1)

$$\frac{\partial }{\partial t}({\alpha }_f{\rho }_f{u}_i)+\frac{\partial }{\partial x_j}({\alpha }_f{\rho }_f{u}_i{u}_j)=-\frac{\partial p}{\partial x_i}+\frac{\partial }{\partial x_i}\left[{\alpha }_f{\mu }_{eff}(\frac{\partial u_i}{\partial x_j}+\frac{\partial u_j}{\partial x_i})\right]+{\alpha }_f{\rho }_{f}g+F_s$$

(2)

where ρ_f is the fluid density, u is the fluid velocity, p is the pressure of the fluid, μ_eff is the effective viscosity, g is the gravitational acceleration, F_s is the interaction force between the fluid and the particle, ${\alpha }_f$ is the porosity around the particle, which can be calculated as follows:

$${\alpha }_f=1-{\displaystyle \sum _{i=1}^n{V}_{p,i}}/V_{cell}$$

(3)

where V_p,i is the particle volume, n is the number of particles in the cell, and V_cell is the volume of the mesh cell.

Based on Newton’s second law of motion and assuming that particles have translation and rotation in space, the equation for solving relevant solid particles is expressed as follows:

$$m_p\frac{d{v}_p}{dt}=m_{p}g+{\displaystyle \sum F_C}+F_{drag}+F_{basset}$$

(4)

$$I_p\frac{d{\omega }_p}{dt}={\displaystyle \sum (T_C+M_p)}+T_f$$

(5)

where m_p is the particle mass, v_p is the particle velocity, F_C represents collision contact force between particles and between particles and wall surface, F_drag is the drag force exerted by fluid on particles calculated by Gidaspow [27] drag model, F_basset is the Basset force, ω_p is the angular velocity of particles, and I_p is the moment of inertia of particles, T_C is the contact torque of particles, M_p is the rolling friction torque of the particles, T_f is the torque generated by fluid force on particles.

In the process of studying the wear characteristics of particles in centrifugal pump, it is very important to choose the appropriate wear model for the accuracy of later wear analysis. Li et al. [28] conducted wear experiments on elbow and compared with wear results predicted by Archard model, it was pointed out that the model has better applicability in predicting wear rate in solid-liquid two-phase flow. The wear prediction model adopted in this paper is the Archard wear model, which is derived by Archard [29] by studying the contact mechanics between particles and wall surface and belongs to the semi-empirical wear model considering the parameters of material hardness, contact point load and so on. The specific calculation method is as follows:

$$Q=\frac{K}{H}P{d}_s$$

(6)

where Q is the wear volume (mm³), d_s is the sliding distance (mm), P is the applied load, H is the hardness of contact material surface, and K is the dimensionless wear constant associated with the material itself.

2.3. Meshing and Boundary Conditions

The main design parameters of centrifugal pump are shown in

Table 1. Main design parameters of centrifugal pump.

Design Flow Rate (m3/h)	Design Head (m)	Rotating Speed (r/min)	Inlet Diameter (mm)	Outlet Diameter (mm)	Number of Blades
16	12	1450	50	40	5

. Figure 3a show the geometry and mesh, the main components of centrifugal pump included: semi-open impeller, volute, front and rear cover plate. In order to eliminate the influence of the difference in the number of grids on the numerical simulation results, a total of 7 sets of grids were drawn, and the number of grids gradually increased from 1 million to 2.7 million. After the numerical simulation under clean water condition, it can be seen from Figure 3b that when the number of grids increases to the fourth set, the head almost remains unchanged. In order to ensure the credibility of simulation and improve the computational efficiency, the fifth set of grids was selected as the grid for the later numerical simulation research, that is, the number of grids was 2,191,997.

The numerical simulation calculation of fluid phase was completed by Fluent software, which was mainly set as follows: The pump design flow is 16 m³/h, so the pump inlet was defined as 2.26 m/s velocity-inlet, and the outlet was set as outflow. The RNG k-ε turbulence model was used because of the strong eddy current and swirling flow in the fluid movement in the pump. SIMPLEC algorithm was selected to couple velocity and pressure in flow field. The time step of the fluid phase calculation is 1.15 × 10⁻⁴ s, during which the impeller rotates about 1°. The total number of time steps was set as 3600, and the total simulation time is 0.414 s, that is, the impeller rotates 10 times.

The particle phase was calculated by EDEM software. The setting parameters of wall surface and particles are shown in

Table 2. Material parameters.

Material	Poisson’s Ratio	Shear Modulus (MPa)	Density (kg · m−3)
Wall	0.3	70	7700
Particle	0.4	20	2450

. Due to the high-speed rotation of the impeller and considering the rolling friction generated by model particles at the contact point, the contact model selected in the simulation is Hertz–Mindlin (no slip) with RVD rolling friction. Each friction coefficient is shown in

Table 3. Collision parameters.

Collision Coefficient	Restitution	Static Friction	Rolling Friction
Particle-Particle	0.5	0.15	0.01
Particle-Wall	0.45	0.3	0.01

. The binary mixture particles were made by mixing round glass beads (2450 kg/m³) with diameters of 0.4 mm and 2 mm, the mixing ratio of particles is 1:0, 2:1, 1:1, 1:2 and 0:1, where 1:0 and 0:1 represent the single component particle condition, and the total particle volume concentration is 10%. Since it is necessary to simulate binary mixture particles, two particle factories were set. The large particle factory was set at the entrance, while the small particle factory was set at a distance from the entrance, so as to ensure the stable generation of large and small particles, as shown in Figure 4. The particle incidence was adjusted according to different particle ratio and concentration, and an initial velocity of 1 m/s was given. The time step in EDEM should be smaller than the time step in Fluent and divisible, and the Rayleigh timesStep in EDEM should be 10~30%. Therefore, the time step in EDEM was set as 1.15 × 10⁻⁶ s with a ratio of 100:1.

3. Experimental Verification

In order to ensure the reliability of the internal flow characteristics of the binary mixture particles transported by the centrifugal pump, a solid-liquid two-phase flow test bench of the centrifugal pump was built, as shown in the Figure 5. The model of centrifugal pump used in the experiment was 2/1.5B-AH (Make: Hebei ShiShui (Shijiazhuang, China)), and the main parameters are listed in Table 1. The pump is driven by three-phase asynchronous motor (YTL2-112M-4, 4.0 kW, 380 V, 8.8 A, 1450 rpm, Make: Hebei Teli (Shijiazhuang, China)). The flow meter (LDG-SUP, 2.26 m³/h~22.6 m³/h, ±0.5%, make: Hangzhou Mei Instrument (Hangzhou, China)) was arranged on the pump outlet pipe to monitor the flow, and the flow was controlled by adjusting the inlet valve. The pressure gauges (SCYG310, −150 kPa~150 kPa, ±0.5%, Make: Wuxi SaiEnNuo (Wuxi, China)) were set at 4d₁ from the centrifugal pump inlet (d₁ is the inlet tube diameter, d₁ = 50 mm) and 5d₂ from the pump outlet (d₂ is the outlet tube diameter, d₂ = 40 mm) to measure the pressure. The torque meter (DYN-210, 0~20 N · M, ±0.1%, Make: Bengbu DaYang (Bengbu, China)) was installed between the centrifugal pump and the motor to monitor the torque. The measurement uncertainties of the head, input power, and efficiency are estimated as ±1.27%, ±0.42%, and ±1.34% respectively. The particles used in the experiment were round glass beads with a density of 2450 kg/m³, with mean diameters of 0.4 mm (±0.05 mm) and 2 mm (±0.1 mm) respectively, as shown in the Figure 6. The particles and water are mixed in different proportions according to the set conditions and put into the tank. And through the stirrer constantly stirring to ensure that the solid suspended fully inside the tank. The experiment was carried out at room temperature, and the temperature change has little influence on the experiment. The performance curve of the centrifugal pump could be obtained by processing the measured data.

According to the results of the binary mixture particles external characteristics test and corresponding numerical simulation of centrifugal pump with 1:1 ratio and C_v = 10% at different flow rates, the numerical calculation and experimental results are compared and analyzed, and the results are shown in Figure 7. The overall trend of the two results is basically the same, the head decreases with the increase of flow, and the efficiency increases with the increase of flow, which is similar to the trend of performance curve in literature [2,10]. The numerical simulation results are slightly larger than the experimental results, because many factors are ignored in numerical simulation, while various energy losses (such as pipe loss, valve loss, friction loss and other factors) may occur in the experimental system in the actual process. Considering the influence of various losses, it can be considered that the CFD-DEM numerical method can be used to simulate the solid-liquid two-phase flow of binary mixture particles transported by centrifugal pump, and the set calculation parameters are reasonable.

4. Results

4.1. Flow Characteristic of Centrifugal Pump with Different Particle Ratios

Figure 8 shows performance curves of centrifugal pumps with different particle ratios. It can be found that the experimental results are generally close to the simulation results, the efficiency curve is closer than the head curve, and the experimental results are still slightly smaller than the simulation results. With the increase of the proportion of large particles, the head and efficiency of centrifugal pump tend to decrease, and the efficiency decreased more, which is consistent with the conclusion of literature [13]. When the particle ratio was from 1:0 to 2:1, the decrease of simulated head was the largest. From the particle ratio of 2:1, with the increase of the proportion of large particles, the simulated head decreases less and less, and the experimental head oscillation remained at about 10.70 m. The decreasing amplitude of efficiency is stable with the change of particle ratio, which is about 3%, and the efficiency of 1:1 and 1:2 ratio is relatively close.

Figure 9 shows the total pressure distribution in the centrifugal pump at different particle ratios. It can be seen that the total pressure distribution trend is similar under different ratios, and the low pressure at the impeller entrance is slowly pressurized by the work of the impeller. The high-pressure area is mainly in the transition area between impeller and volute, and the pressure near the outlet is higher. After leaving this area, the total pressure drops slightly and then maintains this pressure to the pump outlet. With the increase of the proportion of large particles, the range of high-pressure zone first increased and then decreased. When the particle ratio is 2:1 (Figure 9b), the range of high-pressure zone is the widest and its value is high; when the particle ratio is 0:1 (Figure 9e), the range of high-pressure zone was the smallest and its value is also slightly lower.

Figure 10 shows the velocity–streamline distribution of centrifugal pump in the horizontal cross section under different particle ratios. The velocity distribution is mainly divided into three regions, from the low-speed zone at the impeller entrance to the high-speed zone in the middle of the impeller runner, and then to the medium-speed zone in the volute region. There is a region with the highest velocity in the impeller passage (Refer to Area 1 in Figure 10a), which has a wider range and higher value in the binary mixture particles particle condition (Figure 10b–d). Vortices appear in both the impeller passage and the volute passage, and the volute passage has more vortices and a larger range than the impeller passage. The vortices on the upside of the volute are smaller than those on the downside, this is because the particles on the downside of the volute are closer to the wall under the action of gravity.

4.2. Particle Distribution in Centrifugal Pump with Different Particle Ratios

Figure 11 shows the distribution of particles in the centrifugal pump at different particle ratios. Particles will accumulate at the entrance of the impeller, and then begin to accelerate under the force of the impeller. In the middle and back of the impeller, the speed of small particles is higher, and then in the volute flow channel, the particle speed drops slightly. Most particles move to the volute region along the pressure surface and hub wall in the impeller runner, and then spiral up in the volute passage to the pump outlet, this is similar to the particle movement route in literature [7,30]. The spiral range formed by small particle groups is larger and more concentrated, while the spiral range formed by large particle groups is more dispersed. Among them, small particles have better followability, leading to some particles deviating from the pressure surface to the suction surface, and even some small particles rotate to the blade tip with the flow field and then detach and enter the next impeller passage. With the increase of the proportion of large particles, the number of small particles moving on the blade tip decreased as a whole. When the particle ratio is 1:1 (Figure 11b), the number of small particles at the blade tip is less than that when the particle ratio is 1:2 (Figure 11d), and small particles gather in the latter part of the impeller passage to form a cluster.

4.3. Wear of Centrifugal Pump with Different Particle Ratios

Figure 12 shows the distribution of volute wear under different particle ratios. It can be seen that in the condition with small particles (Figure 12a–d), wear is mainly in the volute flow channel near the inlet side (Refer to Area 1 in Figure 10a), it is similar to volute wear in literature [16,31]. With the increase of the proportion of large particles, wear tends to reduce, and the wear degree is the minimum when the particle ratio is 1:2 (Figure 12d), which may be because the movement track of small particles is disrupted by large particles. However, when the particle ratio is 0:1 (Figure 12e), the wear degree of the volute is the most serious compared with other working conditions, with higher wear in the area near the inlet side and the back plate (Refer to Area 2 and Area 3 in Figure 12e), but the wear distribution in the middle of the volute is relatively uniform, which is because the movement of large particles in the volute is scattered.

Figure 13 shows the wear distribution of the impeller with different particle ratios. It can be seen that the most serious wear parts of the impeller occur in the pressure surface of the impeller, the head of the impeller and the hub close to the pressure surface, which is greatly related to the movement trajectory of particles, the parts with severe wear are consistent with the paint wear test conducted by Li et al. [23]. The wear degree is the least when the particle ratio is 1:2 (Figure 13d), which is because the particle contact frequency with the wall surface is small. When the particle ratio is 1:0 (Figure 13a), the wear is more concentrated and regular, while when the particle ratio is 0:1 (Figure 13e), the wear part is more disorderly, because small particles are more likely to gather on a track, while the movement of large particles is more dispersed.

Figure 14 can be obtained by expanding and comparing the pressure surface wear cloud images of the impellers with different particle ratios. As can be seen from the figure, except for the condition of particle ratio 0:1 (Figure 14e), the wear distribution of different blades on the pressure surface of the same impeller is basically the same, but the wear distribution of the pressure surface under different ratio is quite different. When the particle ratio is 1:0 (Figure 14a), the wear is a thin strip along the pressure surface, because the movement of small particles is closer to the hub wall. When the particle ratio is 0:1, the wear behavior is mainly long and thick strip in front of pressure and disorderly spots in the end of pressure surface, which is because the poor following performance of large particles leads to dispersion of motion. However, in the binary mixture particles condition (Figure 14b–d), the wear shows a semi-elliptic shape in the front segment and a circular shape in the back segment, indicating that the large particles and small particles influence each other to change their respective motion trajectory. In Figure 14c, the wear at the end of the pressure surface is serious, and combined with the particle distribution in Figure 11, it can be considered that the wear degree at the end of the pressure surface is mainly related to small particles.

Figure 15 shows the average wear rate and maximum wear rate curves of centrifugal pump components with different particle ratios. It can be seen that the wear rate of pressure surface, hub and volute is much higher than that of blade tip and suction surface. The average wear rate of the pressure surface is the lowest when the particle ratio is 1:2, and close to and larger when the particle ratios are 1:0, 1:1 and 0:1. The average wear rate of the hub is smaller under the binary mixture particles condition (the particle ratios are 2:1, 1:1 and 1:2). The average wear rate of the volute first decreased slightly and then increased greatly with the increase of the proportion of large particles. The average wear rate of the volute was the lowest when the particle ratio was 1:2, and the maximum when the particle ratio was 0:1. The average wear rate of blade tip oscillates with the change of particle ratio, and the change trend is just opposite to the change trend of pressure surface. The blade tip wear rate is the lowest when the particle ratio is 1:1, because there are few particles moving on the blade tip surface under this condition (Refer to Figure 11c). The average wear rate of the suction surface increases as the proportion of large particles increases, indicating that the movement of large particles has a great influence on the wear of the suction surface. In terms of the maximum wear rate, the value of volute is the largest, and on the whole, it decreases with the increase of the proportion of large particles, because the force of large particles on the wall is dispersed. The maximum wear rate of pressure surface and hub is relatively close, in which the maximum wear rate of pressure surface is the minimum when the particle ratio is 1:2, and the maximum wear rate of the wheel hub is the minimum when the particle ratio is 1:1.

5. Conclusions

In this paper, the centrifugal pump conveying binary mixture particles is taken as the research object, and the internal flow characteristics and wear characteristics are analyzed by using CFD-DEM coupling model and Archard wear model. The main conclusions of this paper are as follows:

(1)

The CFD-DEM coupling model is reliable for simulating solid-liquid two-phase flow in centrifugal pump.

(2)

Large particles have a greater impact on performance decline of centrifugal pump than small particles, especially on efficiency. The static pressure high pressure region in the pump is mainly in the interface region between impeller and volute, and the range and value decrease with the increase of the proportion of large particles. The vortexes of the flow field mainly appear in the impeller outlet area and volute passage.

(3)

The particles mainly move along the pressure surface and the hub in the impeller passage. In the volute passage, the particles will form spiral trajectory and rise to the pump outlet. Small particles have more concentrated trajectories, while large particles are more dispersed. The change of the ratio of particles will affect the trajectory of small particles.

(4)

There is a great relationship between wear distribution and particle motion distribution. The aggregation effect of small particles leads to a higher maximum wear rate, while the wear caused by large particles is more dispersed, the average wear rate is higher. The wear is mainly serious in volute, impeller pressure surface and hub. The wear of single component particles, especially large particles, is more serious than that of binary mixture particles. When the particle ratio is 1:2, the wear of these parts is the least. Due to less contact with particles, the wear degree of suction surface and blade tip is low, which is the lowest when the particle ratio is 1:1.