Numerical and Experimental Study of Hydraulic Performance and Wear Characteristics of a Slurry Pump

: The slurry pump is widely used in ore mining, metal smelting, petrochemical, and other industries, mainly to transport ﬂuid media containing large solid particles. Importantly, it is easy to damage the impeller of a slurry pump in the operation process, which greatly affects the performance of the pump. In this paper, a 25 MZ slurry pump was selected as the research object, and the Euler– Euler multiphase ﬂow model was employed to analyze the internal ﬂow characteristics of the slurry pump under the conditions of clear water and solid–liquid two-phase ﬂow. Additionally, the ﬂow characteristics of each part under different ﬂow conditions were studied, and the effects of different particle volume concentrations, particle sizes, and pump speeds on the impeller’s wear characteristics and hydraulic performance were analyzed. In order to verify the reliability and accuracy of the numerical simulation results, clean water and solid–liquid two-phase ﬂow wear tests of the slurry pump were carried out, and the results showed that a high solid volume fraction and solid–phase slip velocity were generated at the junction of the blade leading edge and the rear cover plate, thus leading to easier wear of the blade. Therefore, enhancing the strength of the junction between the blade leading edge and the rear cover plate is beneﬁcial for improving service life and should be considered in the design of slurry pumps. of the solid-phase slip velocity of the impeller when the particle volume concentration was 15% and the particle diameters were 0.15, 0.3, and 0.6 mm. It can be seen from the ﬁgure that the solid slip velocity of the pressure surface gradually increased from the leading edge to the trailing edge. Additionally, with the increase in the particle diameter, the solid slip velocity at the trailing edge of the pressure surface gradually increased. This phenomenon is attributed to the increasing radial velocity and circumferential velocity of solid particles after they entered the impeller, which led to an increase in solid-phase slip velocity. Therefore, the solid phase slip velocity on the blade surface increased with the increase in solid particle diameter.


Introduction
As an important piece of energy conversion equipment, the slurry pump has been widely used in mining, electric power, metallurgy, coal, and other industries. Both the complexity of the solid-liquid two-phase flow in the slurry pump and the limitations of twophase flow field measurement technology have made it very difficult to obtain flow field information of an entire flow channel. Therefore, capturing the flow field characteristics of slurry pumps is the fundamental objective of their optimized design and wear investigation. In recent years, there has been much research on the motion of the solid-liquid two-phase flow. Wang et al. [1] used a CFD-DEM coupling algorithm to study the spatial distribution and motion characteristics of particles with different sizes, and the effects of particle diameter on the intensity and scale of the vortex in a guide vane were investigated; it was concluded that the existence of particles had a limited effect on the hydraulic performance of the pump in low-concentration fluids. In a numerical study of the internal flow field of the solid-liquid slurry pump, Shi et al. [2] analyzed the wear mechanism of the volute wall of a slurry pump and proposed an effective wear equation for estimating the wear strength and wear area of the slurry pump volute. Peng et al. [3] analyzed slurry flow under different particle concentrations and volume flows by using the Euler-Euler method, and the effects of particle concentration on flow resistance, reflux, and wall wear were assessed.

3D Modeling
In order to study the internal flow field of the slurry pump, the fluid domain was simplified into four parts: inlet, impeller, volute, and outlet. Based on the three-dimensional modeling software UG, the solid modeling of each fluid domain was built, and the threedimensional model of the main components is shown in Figure 1.

3D Modeling
In order to study the internal flow field of the slurry pump, the fluid domain was simplified into four parts: inlet, impeller, volute, and outlet. Based on the three-dimensional modeling software UG, the solid modeling of each fluid domain was built, and the three-dimensional model of the main components is shown in Figure 1.

Grids
In this paper, ICEM was employed to mesh the fluid domains. Considering that the quality of the grid has a great influence on the convergence and reliability of calculation results, the calculation domain was divided into a hexahedral structured grid to better improve the accuracy of the numerical simulation. The structural grids of the main components are shown in Figure 2.  Meanwhile, the greater the number and the higher the quality of grids that are generated, the more accurate the calculation results that can be obtained. However, too many grids consume many computing resources. Therefore, to ensure the accuracy of numerical simulation results and the rational use of computer resources, the grid independence of the calculation domain was conducted [15][16][17][18][19][20]. For this section, the calculation of slurry pump models with different grids was carried out, and a reasonable number of grids were obtained by comparing the fluctuation of head and efficiency. As shown in Figure 3, with the increase in grid number, the fluctuation value of the head efficiency gradually decreased. Additionally, when the grid number was 2.7 million, the fluctuation value of the external characteristic was less than 1.0%, which met the requirements of numerical simulations. Therefore, a grid number of 2.7 million was selected for the investigation.

Grids
In this paper, ICEM was employed to mesh the fluid domains. Considering that the quality of the grid has a great influence on the convergence and reliability of calculation results, the calculation domain was divided into a hexahedral structured grid to better improve the accuracy of the numerical simulation. The structural grids of the main components are shown in Figure 2.

3D Modeling
In order to study the internal flow field of the slurry pump, the fluid domain was simplified into four parts: inlet, impeller, volute, and outlet. Based on the three-dimensional modeling software UG, the solid modeling of each fluid domain was built, and the three-dimensional model of the main components is shown in Figure 1.

Grids
In this paper, ICEM was employed to mesh the fluid domains. Considering that the quality of the grid has a great influence on the convergence and reliability of calculation results, the calculation domain was divided into a hexahedral structured grid to better improve the accuracy of the numerical simulation. The structural grids of the main components are shown in Figure 2.  Meanwhile, the greater the number and the higher the quality of grids that are generated, the more accurate the calculation results that can be obtained. However, too many grids consume many computing resources. Therefore, to ensure the accuracy of numerical simulation results and the rational use of computer resources, the grid independence of the calculation domain was conducted [15][16][17][18][19][20]. For this section, the calculation of slurry pump models with different grids was carried out, and a reasonable number of grids were obtained by comparing the fluctuation of head and efficiency. As shown in Figure 3, with the increase in grid number, the fluctuation value of the head efficiency gradually decreased. Additionally, when the grid number was 2.7 million, the fluctuation value of the external characteristic was less than 1.0%, which met the requirements of numerical simulations. Therefore, a grid number of 2.7 million was selected for the investigation. Meanwhile, the greater the number and the higher the quality of grids that are generated, the more accurate the calculation results that can be obtained. However, too many grids consume many computing resources. Therefore, to ensure the accuracy of numerical simulation results and the rational use of computer resources, the grid independence of the calculation domain was conducted [15][16][17][18][19][20]. For this section, the calculation of slurry pump models with different grids was carried out, and a reasonable number of grids were obtained by comparing the fluctuation of head and efficiency. As shown in Figure 3, with the increase in grid number, the fluctuation value of the head efficiency gradually decreased. Additionally, when the grid number was 2.7 million, the fluctuation value of the external characteristic was less than 1.0%, which met the requirements of numerical simulations. Therefore, a grid number of 2.7 million was selected for the investigation.  ANSYS CFX was employed the calculation of the water, which was selected as the fluid medium, and the medium temperature was 298 K. Total pressure inflow (1 atm) and mass flow outflow were adopted, and the standard k-ε turbulence model was selected as the turbulence model. Meanwhile, the fluid domain of the impeller was set as the rotating part; the inlet section, the outlet section, and the volute were set as the stationary parts; the frozen rotor method was adopted for the interface; and the convergence accuracy was set to 1.0 × 10 −5 . In this paper, the continuity equation of incompressible fluid and the Navier-Stokes equation were employed to describe the three-dimensional turbulence in a centrifugal pump.
The continuity equation is as follows: The Navier-Stokes equation for incompressible fluid is as follows: In the formula, ρ: fluid density; t: time; Fi: the volume force component of a fluid per unit mass; P: pressure; ui and uj (i, j = 1, 2, 3): the velocity component of the fluid; xi and xj (i, j = 1, 2, 3): coordinate components; μ: molecular viscosity coefficient; and Sij: the fluid deformation rate tensor.
For the calculation of solid-liquid two-phase flow, the heterogeneous flow model of the particle in the Euler-Euler method was adopted. The flow conditions of 0.6 QBEP, 1.0 QBEP, and 1.5 QBEP were selected to carry out the calculations, and particle volume concentrations of 5%, 10%, 15%, 20%, and 25% were chosen. Meanwhile, the density of solid particles was set to 2900 kg/m 3 , and the particle diameters were 0.15, 0.3, and 0.6 mm. The Gidaspow model was selected for the drag force, the Favre-averaged drag force model was selected for the turbulent dissipative force, and the dissipation coefficient was 1.0. In this paper, the effects of lift, virtual mass force, and wall lubrication force on the flow field were not considered. The inlet of the two-phase flow adopted the mass flow inlet, and the outlet adopted the average static pressure outlet. Considering the liquid without the slip velocity on the wall, the liquid phase adopted the non-slip wall. However, the wear effect of particles on the wall was considered, the solid phase adopted a free slip wall, and the SIMPLE algorithm was used to solve the pressure-velocity coupling. ANSYS CFX was employed the calculation of the water, which was selected as the fluid medium, and the medium temperature was 298 K. Total pressure inflow (1 atm) and mass flow outflow were adopted, and the standard k-ε turbulence model was selected as the turbulence model. Meanwhile, the fluid domain of the impeller was set as the rotating part; the inlet section, the outlet section, and the volute were set as the stationary parts; the frozen rotor method was adopted for the interface; and the convergence accuracy was set to 1.0 × 10 −5 . In this paper, the continuity equation of incompressible fluid and the Navier-Stokes equation were employed to describe the three-dimensional turbulence in a centrifugal pump.
The continuity equation is as follows: The Navier-Stokes equation for incompressible fluid is as follows: In the formula, ρ: fluid density; t: time; F i : the volume force component of a fluid per unit mass; P: pressure; u i and u j (i, j = 1, 2, 3): the velocity component of the fluid; x i and x j (i, j = 1, 2, 3): coordinate components; µ: molecular viscosity coefficient; and S ij : the fluid deformation rate tensor.
For the calculation of solid-liquid two-phase flow, the heterogeneous flow model of the particle in the Euler-Euler method was adopted. The flow conditions of 0.6 Q BEP , 1.0 Q BEP , and 1.5 Q BEP were selected to carry out the calculations, and particle volume concentrations of 5%, 10%, 15%, 20%, and 25% were chosen. Meanwhile, the density of solid particles was set to 2900 kg/m 3 , and the particle diameters were 0.15, 0.3, and 0.6 mm. The Gidaspow model was selected for the drag force, the Favre-averaged drag force model was selected for the turbulent dissipative force, and the dissipation coefficient was 1.0. In this paper, the effects of lift, virtual mass force, and wall lubrication force on the flow field were not considered. The inlet of the two-phase flow adopted the mass flow inlet, and the outlet adopted the average static pressure outlet. Considering the liquid without the slip velocity on the wall, the liquid phase adopted the non-slip wall. However, the wear effect of particles on the wall was considered, the solid phase adopted a free slip wall, and the SIMPLE algorithm was used to solve the pressure-velocity coupling.
Due to the different densities of solid particles and water, the density of the transport medium of the slurry pump changed after the solid particles were added to the clear water, and the calculation formula is as follows: In the formula, ρ is the density of solid-liquid two-phase flow, ρ 1 is the density of solid particles, ρ 2 is the density of water, and C v is the volume concentration of particles. The calculation results of fluid density in the centrifugal pump under different solid phase volume concentrations are shown in Table 2.

Flow Field Analysis of Inlet
Figures 4 and 5 show the streamline distribution of the inlet section when using clean water and when using a medium containing 15% solid particles with a diameter of 0.6 mm under 0.6 Q BEP , 1.0 Q BEP , and 1.5 Q BEP . It can be seen from Figure 4 that the fluid in the inlet section had a slight pre-rotation, and the pre-rotation direction was consistent with the rotation direction of the impeller under 0.6 Q BEP . Under the effect of the rotation impeller, the fluid direction changed from axial flow to radial flow. Meanwhile, with the increase in the flow rate, the velocity at the impeller inlet gradually increased, and the ability of the impeller to rotate the fluid near the inlet was weakened. When the solid particles were added to the fluid, the kinematic viscosity and flow resistance of the medium were increased, and the ability of the pre-rotation was weaker than that of clean water, as shown in Figure 5. A slight pre-rotation could be observed at the impeller inlet under 1.0 Q BEP , and due to the solid particles being carried in the fluid, a certain degree of wear was generated at the leading edge of the blade. Furthermore, the ability of the pre-rotation continuously decreased with the increase in flow rate. When the flow rate reached 1.5 Q BEP , the fluid movement at the inlet section was relatively stable. Due to the different densities of solid particles and water, the density of the transport medium of the slurry pump changed after the solid particles were added to the clear water, and the calculation formula is as follows: In the formula, ρ′ is the density of solid-liquid two-phase flow, ρ1 is the density of solid particles, ρ2 is the density of water, and Cv is the volume concentration of particles. The calculation results of fluid density in the centrifugal pump under different solid phase volume concentrations are shown in Table 2.

Flow Field Analysis of Inlet
Figures 4 and 5 show the streamline distribution of the inlet section when using clean water and when using a medium containing 15% solid particles with a diameter of 0.6 mm under 0.6 QBEP, 1.0 QBEP, and 1.5 QBEP. It can be seen from Figure 4 that the fluid in the inlet section had a slight pre-rotation, and the pre-rotation direction was consistent with the rotation direction of the impeller under 0.6 QBEP. Under the effect of the rotation impeller, the fluid direction changed from axial flow to radial flow. Meanwhile, with the increase in the flow rate, the velocity at the impeller inlet gradually increased, and the ability of the impeller to rotate the fluid near the inlet was weakened. When the solid particles were added to the fluid, the kinematic viscosity and flow resistance of the medium were increased, and the ability of the pre-rotation was weaker than that of clean water, as shown in Figure 5. A slight pre-rotation could be observed at the impeller inlet under 1.0 QBEP, and due to the solid particles being carried in the fluid, a certain degree of wear was generated at the leading edge of the blade. Furthermore, the ability of the prerotation continuously decreased with the increase in flow rate. When the flow rate reached 1.5 QBEP, the fluid movement at the inlet section was relatively stable.

Flow Field Analysis of Impeller
The solid volume fraction and slip velocity had obvious influence on the wall wear, and the collision frequency of particles against the wall were enhanced with the increase in solid volume fraction. Additionally, the increase in solid particle slip velocity improved the impaction of a single particle on the wall. However, according to a previous investigation [3], solid-phase slip velocity has a great influence on wall wear. Figure 6 shows the solid volume fraction distribution on the impeller wall under different flow conditions; the solid volume concentration was 15% and the particle size was 0.6 mm. It can be seen from the figure that the solid volume fraction of the blade pressure surface gradually moved from the leading edge to the trailing edge with the increase in flow rate. Under the 0.6 QBEP condition, the velocity of the liquid and the centrifugal force on the solid particles was low, which made the solid particles accumulate at the impeller inlet. When the flow rate increased to 1.5 QBEP, the solid particles moved to the rear cover plate under the effect of inertia force, which resulted in a large solid volume fraction at the interface between the impeller and the rear cover plate.

Flow Field Analysis of Volute
Figures 7 and 8 present the solid volume fraction distributions of the volute wall under the flow conditions of 0.6 QBEP, 1.0 QBEP, and 1.5 QBEP; the solid volume concentration was 15% and the particle diameter was 0.6 mm. Under the 0.6 QBEP condition, the larger solid volume fraction was mainly distributed between the sixth and eighth sections, and the solid volume fraction at the tongue was lower.

Flow Field Analysis of Impeller
The solid volume fraction and slip velocity had obvious influence on the wall wear, and the collision frequency of particles against the wall were enhanced with the increase in solid volume fraction. Additionally, the increase in solid particle slip velocity improved the impaction of a single particle on the wall. However, according to a previous investigation [3], solid-phase slip velocity has a great influence on wall wear. Figure 6 shows the solid volume fraction distribution on the impeller wall under different flow conditions; the solid volume concentration was 15% and the particle size was 0.6 mm. It can be seen from the figure that the solid volume fraction of the blade pressure surface gradually moved from the leading edge to the trailing edge with the increase in flow rate. Under the 0.6 Q BEP condition, the velocity of the liquid and the centrifugal force on the solid particles was low, which made the solid particles accumulate at the impeller inlet. When the flow rate increased to 1.5 Q BEP , the solid particles moved to the rear cover plate under the effect of inertia force, which resulted in a large solid volume fraction at the interface between the impeller and the rear cover plate.

Flow Field Analysis of Impeller
The solid volume fraction and slip velocity had obvious influence on the wall wear, and the collision frequency of particles against the wall were enhanced with the increase in solid volume fraction. Additionally, the increase in solid particle slip velocity improved the impaction of a single particle on the wall. However, according to a previous investigation [3], solid-phase slip velocity has a great influence on wall wear. Figure 6 shows the solid volume fraction distribution on the impeller wall under different flow conditions; the solid volume concentration was 15% and the particle size was 0.6 mm. It can be seen from the figure that the solid volume fraction of the blade pressure surface gradually moved from the leading edge to the trailing edge with the increase in flow rate. Under the 0.6 QBEP condition, the velocity of the liquid and the centrifugal force on the solid particles was low, which made the solid particles accumulate at the impeller inlet. When the flow rate increased to 1.5 QBEP, the solid particles moved to the rear cover plate under the effect of inertia force, which resulted in a large solid volume fraction at the interface between the impeller and the rear cover plate.

Flow Field Analysis of Volute
Figures 7 and 8 present the solid volume fraction distributions of the volute wall under the flow conditions of 0.6 QBEP, 1.0 QBEP, and 1.5 QBEP; the solid volume concentration was 15% and the particle diameter was 0.6 mm. Under the 0.6 QBEP condition, the larger solid volume fraction was mainly distributed between the sixth and eighth sections, and the solid volume fraction at the tongue was lower.  With the increase in flow rate, the region with a large solid volume fraction on the volute wall gradually moved from the front cover to the rear cover. When the fluid entered the volute from the impeller under the effect of centrifugal force, the volume fraction of solid particles near the rear cover plate was larger, resulting in the wear on the rear cover plate being higher than that on the front cover.

Effect of Particle Parameters on Wear Characteristic
In this section, the effects of particle volume concentration and particle diameter on impeller wear are discussed, and the effects of the solid volume fraction and solid slip velocity on the blade are analyzed. Abscissa indicates the relative distance in the direction of the blade streamline (streamwise); a relative distance of the blade streamline of 0 represents the leading edge of the blade, a relative distance of the streamline of 1 indicates the trailing edge of the blade, and an ordinate represents the solid phase volume fraction (solid volume fraction) and the solid phase slip velocity (solid velocity). With the increase in flow rate, the region with a large solid volume fraction on the volute wall gradually moved from the front cover to the rear cover. When the fluid entered the volute from the impeller under the effect of centrifugal force, the volume fraction of solid particles near the rear cover plate was larger, resulting in the wear on the rear cover plate being higher than that on the front cover.

Effect of Particle Parameters on Wear Characteristic
In this section, the effects of particle volume concentration and particle diameter on impeller wear are discussed, and the effects of the solid volume fraction and solid slip velocity on the blade are analyzed. Abscissa indicates the relative distance in the direction of the blade streamline (streamwise); a relative distance of the blade streamline of 0 represents the leading edge of the blade, a relative distance of the streamline of 1 indicates the trailing edge of the blade, and an ordinate represents the solid phase volume fraction (solid volume fraction) and the solid phase slip velocity (solid velocity). With the increase in flow rate, the region with a large solid volume fraction on the volute wall gradually moved from the front cover to the rear cover. When the fluid entered the volute from the impeller under the effect of centrifugal force, the volume fraction of solid particles near the rear cover plate was larger, resulting in the wear on the rear cover plate being higher than that on the front cover.

Effect of Particle Parameters on Wear Characteristic
In this section, the effects of particle volume concentration and particle diameter on impeller wear are discussed, and the effects of the solid volume fraction and solid slip velocity on the blade are analyzed. Abscissa indicates the relative distance in the direction of the blade streamline (streamwise); a relative distance of the blade streamline of 0 represents the leading edge of the blade, a relative distance of the streamline of 1 indicates the trailing edge of the blade, and an ordinate represents the solid phase volume fraction (solid volume fraction) and the solid phase slip velocity (solid velocity).  Figure 9 shows the hydraulic performance curves of different concentrations under optimal flow conditions. Here, 0 indicates that the medium is clear water. It can be seen from the figure that with the increase in concentration, the head gradually and continuously decreased. With the increase in the concentration, the viscosity of the solid-liquid twophase flow increased and the friction force and energy loss between the internal fluids gradually increased, which resulted in a decrease in the head. At the same time, with the increase in solid particle volume concentration, the enhancement of the centrifugal pump impeller torque led to the increase in motor power consumption and the decrease in centrifugal pump efficiency. When the concentration was 5%, the head decreased by 0.33% and the efficiency decreased by 1.60%. When the concentration was 25%, the head decreased by 8.9% and the efficiency decreased by 8.09%. Therefore, the head and efficiency of the pump decreased with the increases in particle volume concentration.  Figure 9 shows the hydraulic performance curves of different concentrations under optimal flow conditions. Here, 0 indicates that the medium is clear water. It can be seen from the figure that with the increase in concentration, the head gradually and continuously decreased. With the increase in the concentration, the viscosity of the solid-liquid two-phase flow increased and the friction force and energy loss between the internal fluids gradually increased, which resulted in a decrease in the head. At the same time, with the increase in solid particle volume concentration, the enhancement of the centrifugal pump impeller torque led to the increase in motor power consumption and the decrease in centrifugal pump efficiency. When the concentration was 5%, the head decreased by 0.33% and the efficiency decreased by 1.60%. When the concentration was 25%, the head decreased by 8.9% and the efficiency decreased by 8.09%. Therefore, the head and efficiency of the pump decreased with the increases in particle volume concentration.  Figure 10 shows the solid phase slip velocity distribution of the impeller when the particle size was 0.6 mm and the particle volume concentrations were 5%, 15%, and 25%. It was found that the solid phase slip velocity at the leading edge of the pressure surface was the smallest-when the particles entered the impeller, the particles flowed from the axial direction to the radial direction under the effect of centrifugal force, which decreased the slip velocity. With the increase in concentration, the slip velocity of solid particles on the pressure surface gradually increased. There was no great change in the slip velocity on the suction surface, though a sudden change in the slip velocity of the solid particles was found at the trailing edge of the blade which resulted from the flow separation near the trailing edge of the suction surface. Additionally, the slip velocity of solid particles on the pressure surface was generally larger than that on the suction surface.  Figure 10 shows the solid phase slip velocity distribution of the impeller when the particle size was 0.6 mm and the particle volume concentrations were 5%, 15%, and 25%. It was found that the solid phase slip velocity at the leading edge of the pressure surface was the smallest-when the particles entered the impeller, the particles flowed from the axial direction to the radial direction under the effect of centrifugal force, which decreased the slip velocity. With the increase in concentration, the slip velocity of solid particles on the pressure surface gradually increased. There was no great change in the slip velocity on the suction surface, though a sudden change in the slip velocity of the solid particles was found at the trailing edge of the blade which resulted from the flow separation near the trailing edge of the suction surface. Additionally, the slip velocity of solid particles on the pressure surface was generally larger than that on the suction surface.   Figure 11 shows the solid volume fraction distribution of the impeller when the particle size was 0.6 mm and the particle volume concentrations were 5%, 15%, and 25%. It can be seen from the figure that the solid volume on the blade pressure surface gradually decreased from the leading edge to the trailing edge, with less and less accumulation of solid particles due to the work of the blade. Meanwhile, there were almost no solid particles on the suction surface of the blade, so the solid volume fraction on the pressure surface of the blade was larger than the suction surface. With the increase in the concentration, the solid particles and solid volume fraction gradually increased.   Figure 12 shows the comparison of the hydraulic performance curves of different particle diameters under design flow conditions, where a particle size of 0 mm indicates that the used medium was clear water. With the increase in the particle diameter, the energy driving the solid particles was greater and the head gradually decreased. At the same time, with the increase in solid particle diameter, the friction loss between particles and impeller increased, which led to the increases in impeller torque and motor power consumption. Therefore, as the particle diameter increased from 0.15 to 0.6 mm, the pump head decreased from 12 to 11.42 m and the efficiency decreased from 71.25% to 67.35%.  Figure 11 shows the solid volume fraction distribution of the impeller when the particle size was 0.6 mm and the particle volume concentrations were 5%, 15%, and 25%. It can be seen from the figure that the solid volume on the blade pressure surface gradually decreased from the leading edge to the trailing edge, with less and less accumulation of solid particles due to the work of the blade. Meanwhile, there were almost no solid particles on the suction surface of the blade, so the solid volume fraction on the pressure surface of the blade was larger than the suction surface. With the increase in the concentration, the solid particles and solid volume fraction gradually increased.   Figure 11 shows the solid volume fraction distribution of the impeller when the particle size was 0.6 mm and the particle volume concentrations were 5%, 15%, and 25%. It can be seen from the figure that the solid volume on the blade pressure surface gradually decreased from the leading edge to the trailing edge, with less and less accumulation of solid particles due to the work of the blade. Meanwhile, there were almost no solid particles on the suction surface of the blade, so the solid volume fraction on the pressure surface of the blade was larger than the suction surface. With the increase in the concentration, the solid particles and solid volume fraction gradually increased.   Figure 12 shows the comparison of the hydraulic performance curves of different particle diameters under design flow conditions, where a particle size of 0 mm indicates that the used medium was clear water. With the increase in the particle diameter, the energy driving the solid particles was greater and the head gradually decreased. At the same time, with the increase in solid particle diameter, the friction loss between particles and impeller increased, which led to the increases in impeller torque and motor power consumption. Therefore, as the particle diameter increased from 0.15 to 0.6 mm, the pump head decreased from 12 to 11.42 m and the efficiency decreased from 71.25% to 67.35%.  Figure 12 shows the comparison of the hydraulic performance curves of different particle diameters under design flow conditions, where a particle size of 0 mm indicates that the used medium was clear water. With the increase in the particle diameter, the energy driving the solid particles was greater and the head gradually decreased. At the same time, with the increase in solid particle diameter, the friction loss between particles and impeller increased, which led to the increases in impeller torque and motor power consumption. Therefore, as the particle diameter increased from 0.15 to 0.6 mm, the pump head decreased from 12 to 11.42 m and the efficiency decreased from 71.25% to 67.35%.

Effect of Particle Size on Wear Characteristic
Machines 2021, 9, x FOR PEER REVIEW Figure 12. Characteristic curve under different particle sizes. Figure 13 shows the distribution of the solid-phase slip velocity of the impell the particle volume concentration was 15% and the particle diameters were 0.15, 0.6 mm. It can be seen from the figure that the solid slip velocity of the pressure gradually increased from the leading edge to the trailing edge. Additionally, wit crease in the particle diameter, the solid slip velocity at the trailing edge of the surface gradually increased. This phenomenon is attributed to the increasing radi ity and circumferential velocity of solid particles after they entered the impelle led to an increase in solid-phase slip velocity. Therefore, the solid phase slip vel the blade surface increased with the increase in solid particle diameter.   Figure 14 shows the solid volume fraction distribution of the impeller when ticle volume concentration was 15% and the particle diameters were 0.15, 0.3, and It was found that with the increase in solid particle diameter, the region of the lar volume fraction moved from the suction surface to the pressure surface. When  Figure 13 shows the distribution of the solid-phase slip velocity of the impeller when the particle volume concentration was 15% and the particle diameters were 0.15, 0.3, and 0.6 mm. It can be seen from the figure that the solid slip velocity of the pressure surface gradually increased from the leading edge to the trailing edge. Additionally, with the increase in the particle diameter, the solid slip velocity at the trailing edge of the pressure surface gradually increased. This phenomenon is attributed to the increasing radial velocity and circumferential velocity of solid particles after they entered the impeller, which led to an increase in solid-phase slip velocity. Therefore, the solid phase slip velocity on the blade surface increased with the increase in solid particle diameter.  Figure 13 shows the distribution of the solid-phase slip velocity of the impeller when the particle volume concentration was 15% and the particle diameters were 0.15, 0.3, and 0.6 mm. It can be seen from the figure that the solid slip velocity of the pressure surface gradually increased from the leading edge to the trailing edge. Additionally, with the increase in the particle diameter, the solid slip velocity at the trailing edge of the pressure surface gradually increased. This phenomenon is attributed to the increasing radial velocity and circumferential velocity of solid particles after they entered the impeller, which led to an increase in solid-phase slip velocity. Therefore, the solid phase slip velocity on the blade surface increased with the increase in solid particle diameter.   Figure 14 shows the solid volume fraction distribution of the impeller when the particle volume concentration was 15% and the particle diameters were 0.15, 0.3, and 0.6 mm. It was found that with the increase in solid particle diameter, the region of the larger solid volume fraction moved from the suction surface to the pressure surface. When the solid particles entered the impeller, the effects of the particle's inertia and the extrusion of the blade resulted in a larger solid volume fraction at the leading edge. At the same time, with  Figure 14 shows the solid volume fraction distribution of the impeller when the particle volume concentration was 15% and the particle diameters were 0.15, 0.3, and 0.6 mm. It was found that with the increase in solid particle diameter, the region of the larger solid volume fraction moved from the suction surface to the pressure surface. When the solid particles entered the impeller, the effects of the particle's inertia and the extrusion of the blade resulted in a larger solid volume fraction at the leading edge. At the same time, with the increase in the particle diameter, the influence of the fluid centrifugal force on the solid particles was enhanced, which made the solid particles move from the suction surface to the pressure surface. Moreover, the maximum solid volume fraction was generated at the leading edge of the blade on the pressure surface, while the maximum solid volume fraction was generated at the trailing edge of the suction surface.

Effect of Pump Speed on External Performance
In the previous analysis of solid-liquid two-phase flow, it can be seen that increases in solid volume concentration led to decreases in the head and efficiency of the slurry pump. With the increase in the solid volume concentration, the viscosity between the solid-liquid two-phase flow increased and the friction force and energy loss between the internal fluids was increased, which resulted in the decline of the head. More importantly, the slurry pump could not reach the corresponding working condition, which may be another reasons for the wear of the impeller. Therefore, in this paper, the influence of speed on hydraulic performance was studied. Under the rated flow condition, solid-liquid two-phase flow simulation calculations were carried out at the rotational speeds of 1480, 1490, 1500, 1510, 1520, and 1530 r/min and media with solid-phase volume concentrations of 0, 5%, 10%, 15%, 20%, and 25%. Then, the head value data obtained by the simulation were plotted into a three-dimensional scatter diagram, as shown in Figure 15.

Effect of Pump Speed on External Performance
In the previous analysis of solid-liquid two-phase flow, it can be seen that increases in solid volume concentration led to decreases in the head and efficiency of the slurry pump. With the increase in the solid volume concentration, the viscosity between the solid-liquid two-phase flow increased and the friction force and energy loss between the internal fluids was increased, which resulted in the decline of the head. More importantly, the slurry pump could not reach the corresponding working condition, which may be another reasons for the wear of the impeller. Therefore, in this paper, the influence of speed on hydraulic performance was studied. Under the rated flow condition, solid-liquid two-phase flow simulation calculations were carried out at the rotational speeds of 1480, 1490, 1500, 1510, 1520, and 1530 r/min and media with solid-phase volume concentrations of 0, 5%, 10%, 15%, 20%, and 25%. Then, the head value data obtained by the simulation were plotted into a three-dimensional scatter diagram, as shown in Figure 15.
According to the head scatter diagram, the relationship between the rotational speed and solid volume concentration on the head was evaluated. The head reached its minimum value at C v = 25% and n = 1480 r/min, and it reached its maximum value at C v = 0% and n = 1530 r/min. At the same solid volume concentration, the head of the pump increased with the increase in rotational speed. At the same speed, the head of the pump decreased with the increase in solid volume concentration.
another reasons for the wear of the impeller. Therefore, in this paper, the inf speed on hydraulic performance was studied. Under the rated flow condition, uid two-phase flow simulation calculations were carried out at the rotational s 1480, 1490, 1500, 1510, 1520, and 1530 r/min and media with solid-phase volum trations of 0, 5%, 10%, 15%, 20%, and 25%. Then, the head value data obtaine simulation were plotted into a three-dimensional scatter diagram, as shown in F Figure 15. Three-dimensional fitting surface of different solid volume concentrations and According to the head scatter diagram, the relationship between the rotation and solid volume concentration on the head was evaluated. The head reached mum value at Cv = 25% and n = 1480 r/min, and it reached its maximum value a In order to better analyze the influence of rotational speed and solid volume concentration on the head, a three-dimensional fitting surface was built, and the relationship between the rotational speed, solid volume concentration, and the head was evaluated. In the figure, the head value of the thickened equipotential line is 12 m.
At the same speed, with the increase in solid volume concentration, the head first slowly decreased and then rapidly decreased. The surface fitting diagram showed that the fitting effect of C v = 10% was the best and the head value of C v = 20% was generally lower than the fitting value. On the whole, the fitting effect was able to meet the investigation requirements. From low rotational speed and high solid volume concentration to high rotational speed and low solid volume concentration, the distribution of head contours was uniform and gradually increased.
A three-dimensional fitting surface diagram was projected onto an XY plane, and solid volume concentration, rotational speed, and head diagram values were obtained, as shown in Figure 16. It can be seen from the figure that under the condition of equal head, the pump speed slowly improved with the increase in solid volume concentration. In the figure, the head value of the thickened equipotential line is 12 m. While the solid phase volume concentration increased, the pump head value could reach the corresponding required value via adjustments of the rotational speed of the pump, which ensured the pump operates at the rated flow condition and reduced the fluctuation of the shaft power. For other operating conditions or head values, the head equipotential curve could be obtained with the same method, and then the corresponding operating conditions could be reached by adjusting the pump speed. Therefore, the head first slowly decreased and then rapidly decreased with the increase in solid volume concentration, and it continuously increased with the increases in rotational speed. quired value via adjustments of the rotational speed of the pump, which ensured the pump operates at the rated flow condition and reduced the fluctuation of the shaft power. For other operating conditions or head values, the head equipotential curve could be obtained with the same method, and then the corresponding operating conditions could be reached by adjusting the pump speed. Therefore, the head first slowly decreased and then rapidly decreased with the increase in solid volume concentration, and it continuously increased with the increases in rotational speed.

Hydraulic Performance Test
The test of the slurry pump was divided into two parts: the clear water performance test and wear performance test. The clear water performance test mainly investigated the external characteristic performance of the pump by measuring its flow rate, pressure, rotational speed, and torque, which were compared with the numerical simulation results. Meanwhile, the wear test was carried out on the slurry pump wear test bench, and the amount of wear was calculated by the impeller weight-loss method.
In order to compare the hydraulic performance between the experiment and simulation, the head and efficiency were selected as evaluation indexes and the clear water hydraulic performance under different flow conditions was assessed, as shown in Figure 17. The expressions of the head and efficiency are, respectively, as follows: In the equations, p 1 , v 1 , and z 1 are the pump inlet parameters; p 2 , v 2 , and z 2 are the pump outlet parameters; η is the pump efficiency; and P s is the output power of the motor. During the test, a turbine flow meter (accuracy ± 0.1%) was used to measure the flow rate, and a pressure sensor (accuracy ± 0.1%) was used to measure the inlet and outlet pressure of the pump. A torque sensor (accuracy ± 0.5%) and a speed sensor (accuracy ± 0.1%) were used to measure torque and speed, respectively.
1 Figure 17. Hydraulic performance test bench. Figure 18 shows the hydraulic performance results of the simulation and experiment. The leakage loss, disk friction loss, and friction loss between the bearing and sealing device were not taken into account in the numerical simulation, which resulted in the numerical simulation results being larger than the experimental data and the trend of the simulation head and efficiency curve being the same as that of the test. The maximum deviation of the head under 8 m 3 /h was 4.32%, which was due to the instability of the internal flow field of the pump operation except for optimal flow conditions. However, when the flow rate was 26 m 3 /h, the minimum deviation between the simulation head and the test head was 2.52% and the efficiency deviation was less than 2.56%. The calculation deviation in the full flow range was less than 5%. Therefore, the calculation model could accurately predict the performance of the pump.

Wear Performance Test
The wear test bench was mainly composed of the slurry pump, pressure gauge, pipeline, valve, motor, and test system. The test system included strong electric parts, such as the step-down starting cabinet, system distribution cabinet, and test conversion protection cabinet, and weak current parts, such as intelligent display instrument, signal conversion device, and various signal sensors. Figure 19 shows the wear test bench.
In the wear test, the wear condition of the impeller was studied by means of equal flow control and impeller weight loss measurements. The inlet and outlet of the pump were equipped with pressure gauges. The wear test was divided into the following two stages.

Wear Performance Test
The wear test bench was mainly composed of the slurry pump, pressure gauge, pipe line, valve, motor, and test system. The test system included strong electric parts, such a the step-down starting cabinet, system distribution cabinet, and test conversion protectio cabinet, and weak current parts, such as intelligent display instrument, signal conversio device, and various signal sensors. Figure 19 shows the wear test bench. In the wear test, the wear condition of the impeller was studied by means of equa flow control and impeller weight loss measurements. The inlet and outlet of the pum were equipped with pressure gauges. The wear test was divided into the following tw stages.

The first stage
The total duration of the first-stage test was 24 h. The test was carried out under th

Wear Performance Test
The wear test bench was mainly composed of the slurry pump, pressure gau line, valve, motor, and test system. The test system included strong electric parts the step-down starting cabinet, system distribution cabinet, and test conversion p cabinet, and weak current parts, such as intelligent display instrument, signal co device, and various signal sensors. Figure 19 shows the wear test bench. In the wear test, the wear condition of the impeller was studied by means flow control and impeller weight loss measurements. The inlet and outlet of th were equipped with pressure gauges. The wear test was divided into the follow stages.

The first stage
The total duration of the first-stage test was 24 h. The test was carried out u condition of equal flow rate, and the running speed of the pump was 1500 r/mi while, the solid particles were brown corundum, the density was 2900 kg/m 3 , the 1.
The first stage The total duration of the first-stage test was 24 h. The test was carried out under the condition of equal flow rate, and the running speed of the pump was 1500 r/min. Meanwhile, the solid particles were brown corundum, the density was 2900 kg/m 3 , the particle size was 0.6 mm, and the solid volume was 15%. The mass of the impeller before the test was 2070 g. When the pump was running for 4 h, it was found that there was obvious wear at the intersection between the suction surface and the front cover plate, and slight wear was generated at the entrance of the blade. When the pump was running for 24 h, the weight of the impeller was 1960 g and the weight loss rate was 5.31%. Meanwhile, it was found that the blade was seriously worn at the entrance, and about 1-2 mm oval pits were created on the rear cover plate near the suction surface of the hub. Additionally, the wear of the blade suction surface and the front cover plate joint was more serious; there was an approximately 3 mm long groove on the blade, as shown in Figures 20 and 21. Machines 2021, 9, x FOR PEER REVIEW 15 of 19 size was 0.6 mm, and the solid volume was 15%. The mass of the impeller before the test was 2070 g. When the pump was running for 4 h, it was found that there was obvious wear at the intersection between the suction surface and the front cover plate, and slight wear was generated at the entrance of the blade. When the pump was running for 24 h, the weight of the impeller was 1960 g and the weight loss rate was 5.31%. Meanwhile, it was found that the blade was seriously worn at the entrance, and about 1-2 mm oval pits were created on the rear cover plate near the suction surface of the hub. Additionally, the wear of the blade suction surface and the front cover plate joint was more serious; there was an approximately 3 mm long groove on the blade, as shown in Figures 20 and 21.

The second stage
The total duration of the second stage was 24 h. The test was carried out under the condition of equal flow rate, the solid particles were brown corundum, the density was 2900 kg/m 3 , the particle size was 0.6 mm, the solid volume concentration increased to 25%, and the weight of the impeller before the test was 1960 g. When the pump was running for 24 h, the mass of the impeller was 1560 g and the weight loss rate was 20.41%. After the second-stage wear test, there was serious wear at the junction of the blade pressure surface and the front cover plate that extended from the blade leading edge to the trailing edge. At the same time, serious wear was generated at the junction of the impeller outlet and the rear cover plate, as shown in Figures 22 and 23. size was 0.6 mm, and the solid volume was 15%. The mass of the impeller before the test was 2070 g. When the pump was running for 4 h, it was found that there was obvious wear at the intersection between the suction surface and the front cover plate, and slight wear was generated at the entrance of the blade. When the pump was running for 24 h, the weight of the impeller was 1960 g and the weight loss rate was 5.31%. Meanwhile, it was found that the blade was seriously worn at the entrance, and about 1-2 mm oval pits were created on the rear cover plate near the suction surface of the hub. Additionally, the wear of the blade suction surface and the front cover plate joint was more serious; there was an approximately 3 mm long groove on the blade, as shown in Figures 20 and 21.

The second stage
The total duration of the second stage was 24 h. The test was carried out under the condition of equal flow rate, the solid particles were brown corundum, the density was 2900 kg/m 3 , the particle size was 0.6 mm, the solid volume concentration increased to 25%, and the weight of the impeller before the test was 1960 g. When the pump was running for 24 h, the mass of the impeller was 1560 g and the weight loss rate was 20.41%. After the second-stage wear test, there was serious wear at the junction of the blade pressure surface and the front cover plate that extended from the blade leading edge to the trailing edge. At the same time, serious wear was generated at the junction of the impeller outlet and the rear cover plate, as shown in Figures 22 and 23.

2.
The second stage The total duration of the second stage was 24 h. The test was carried out under the condition of equal flow rate, the solid particles were brown corundum, the density was 2900 kg/m 3 , the particle size was 0.6 mm, the solid volume concentration increased to 25%, and the weight of the impeller before the test was 1960 g. When the pump was running for 24 h, the mass of the impeller was 1560 g and the weight loss rate was 20.41%. After the second-stage wear test, there was serious wear at the junction of the blade pressure surface and the front cover plate that extended from the blade leading edge to the trailing edge. At the same time, serious wear was generated at the junction of the impeller outlet and the rear cover plate, as shown in Figures 22 and 23.

Analysis of Wear Distribution Characteristic
In this section, to analyze the wear distribution characteristic under the des condition, the calculation and experimental results with a solid volume concent 25% are discussed. Figure 24 shows a contrast diagram of the inlet wear of the The calculation results show that the high solid volume fraction was generated at tion of the blade inlet and the rear cover plate. The experiment results showed th wear was created at the entrance of the front cover, and the rear cover was worn o the previous analysis of blade wear, it could be seen that the high solid-phase slip was generated at the entrance of the front cover plate and the solid phase slip v the leading edge of the blade was larger, which resulted in the rear cover plate bei to wear out. Figure 25 shows the contrast diagram of impeller outlet wear. The n simulation results showed that the solid phase slip velocity at the junction bet blade and the rear cover plate was larger and the slip velocity gradually declined trailing edge to the leading edge. At the same time, the numerical simulation res in good agreement with the experimental results. Therefore, enhancing the streng junction between the blade leading edge and the rear cover plate was beneficia

Analysis of Wear Distribution Characteristic
In this section, to analyze the wear distribution characteristic under the des condition, the calculation and experimental results with a solid volume concent 25% are discussed. Figure 24 shows a contrast diagram of the inlet wear of the The calculation results show that the high solid volume fraction was generated at tion of the blade inlet and the rear cover plate. The experiment results showed th wear was created at the entrance of the front cover, and the rear cover was worn o the previous analysis of blade wear, it could be seen that the high solid-phase slip was generated at the entrance of the front cover plate and the solid phase slip ve the leading edge of the blade was larger, which resulted in the rear cover plate bei to wear out. Figure 25 shows the contrast diagram of impeller outlet wear. The n simulation results showed that the solid phase slip velocity at the junction betw blade and the rear cover plate was larger and the slip velocity gradually declined trailing edge to the leading edge. At the same time, the numerical simulation resu in good agreement with the experimental results. Therefore, enhancing the streng

Analysis of Wear Distribution Characteristic
In this section, to analyze the wear distribution characteristic under the design flow condition, the calculation and experimental results with a solid volume concentration of 25% are discussed. Figure 24 shows a contrast diagram of the inlet wear of the impeller. The calculation results show that the high solid volume fraction was generated at the junction of the blade inlet and the rear cover plate. The experiment results showed that slight wear was created at the entrance of the front cover, and the rear cover was worn out. From the previous analysis of blade wear, it could be seen that the high solid-phase slip velocity was generated at the entrance of the front cover plate and the solid phase slip velocity at the leading edge of the blade was larger, which resulted in the rear cover plate being easier to wear out. Figure 25 shows the contrast diagram of impeller outlet wear. The numerical simulation results showed that the solid phase slip velocity at the junction between the blade and the rear cover plate was larger and the slip velocity gradually declined from the trailing edge to the leading edge. At the same time, the numerical simulation results were in good agreement with the experimental results. Therefore, enhancing the strength of the junction between the blade leading edge and the rear cover plate was beneficial for improving the service life of the slurry pump.

Conclusions
In this paper, a 25 MZ slurry pump was selected as the research object, and the Euler-Euler multiphase flow model was employed to analyze the internal flow characteristic of the slurry pump under the conditions of clear water and solid-liquid two-phase flow. The following conclusions were obtained: (1) Pre-rotation was generated at the inlet section, and the pre-rotation direction was consistent with the rotation direction of the impeller under part-load conditions.

Conclusions
In this paper, a 25 MZ slurry pump was selected as the research object, and the Euler-Euler multiphase flow model was employed to analyze the internal flow characteristic of the slurry pump under the conditions of clear water and solid-liquid two-phase flow. The following conclusions were obtained: (1) Pre-rotation was generated at the inlet section, and the pre-rotation direction was

Conclusions
In this paper, a 25 MZ slurry pump was selected as the research object, and the Euler-Euler multiphase flow model was employed to analyze the internal flow characteristic of the slurry pump under the conditions of clear water and solid-liquid two-phase flow. The following conclusions were obtained: (1) Pre-rotation was generated at the inlet section, and the pre-rotation direction was consistent with the rotation direction of the impeller under part-load conditions. Meanwhile, the ability of the pre-rotation continuously decreased with the increase in flow rate. When the flow rate reached 1.5 Q BEP , the flow at the inlet section was relatively stable. Furthermore, the solid volume fraction of the blade pressure surface gradually moved from the leading edge to the trailing edge with the increase in flow rate. When the flow rate increased to 1.5 Q BEP , the solid particles moved to the rear cover plate under the effect of inertia force, which resulted in a large solid volume fraction at the interface between the impeller and the rear cover plate. (2) With the increase in the particle volume concentration, the viscosity of the solidliquid two-phase flow increased and the friction force and energy loss between the internal fluids gradually increased, which resulted in a decrease in the head. When the concentration was 5%, the head decreased by 0.33% and the efficiency decreased by 1.60%. When the concentration was 25%, the head decreased by 8.9% and the efficiency decreased by 8.09%. Therefore, the head and efficiency of the pump decreased with increases in particle volume concentration. (3) When the particle diameter gradually increased, the energy driving the solid particles was greater and the head gradually decreased. At the same time, with the increase in solid particle diameter, the friction loss between particles and impeller increased, which led to the increases in impeller torque and motor power consumption. Therefore, when the particle diameter increased from 0.15 to 0.6 mm, the pump head decreased from 12 to 11.42 m and the efficiency decreased from 71.25% to 67.35%. (4) Finally, clean water and solid-liquid two-phase flow wear tests of the slurry pump were carried out. The calculation deviation in the full flow range was less than 5%, so the calculation model could accurately predict the performance of the pump. By comparing the wear distribution of numerical and experiment, it was found that high solid volume fraction and solid-phase slip velocity were generated at the junction of the blade leading edge and the rear cover plate, which made the latter easier to wear out. Therefore, enhancing the strength of the junction between the blade leading edge and the rear cover plate would be beneficial for improving the service life of a slurry pump.
In this paper, in order to simplify the analysis model, a uniformly spherical particle was employed in the calculation process. However, particles in a slurry pump have a lot of different shapes during actual operation. Therefore, the influence of particle shapes on the hydraulic performance and wear characteristics of slurry pumps will be investigated in the future.