# Numerical Simulation of Solid Particle Erosion in Aluminum Alloy Spool Valve

Authors: Jin-gang Liu; Gao-sheng Wang; Tian-heng Peng; Sheng-qiang Jiang
Journal: Mathematical Problems in Engineering
 (2019)

---

## Abstract

Aluminum alloy spool valve body material is prone to severe wear on the wall under the condition of oil contamination. Aiming at this problem, combined with the theory of liquid-solid two-phase flow and erosion wear, the wear prediction model of aluminum alloy sliding valve wall is established based on computational fluid dynamics, and the effects of turbulence and wall materials, particle size distribution, and particle shape on particle motion are discussed. The calculation of the wear prediction model is done with Fluent software. This study predicts the wear of the wall under actual working conditions and calculates the influence of particle size, particle shape, and pressure difference on the wall wear of the aluminum alloy sliding valve. The research results have certain significance for the maintenance and upkeep of aluminum alloy sliding valve wall, improved design, and life prediction.


---

## Body

## 1. Introduction

With the gradual expansion of market demand and advances in material processing and manufacturing technology, the overall structure can reduce the size and weight of the automatic transmission electrohydraulic module [1]. The material of the valve body and the valve core are, respectively, aluminum alloy and alloy steel; the main valve core which plays an important role is directly assembled in the valve hole in the aluminum alloy valve body; and the steel valve sleeve in the conventional electrohydraulic module is no longer needed. However, the oil in the electrohydraulic module is easily contaminated, and the pollution adaptability of the integral electrohydraulic module is worse than that of the conventional electrohydraulic module, which may cause serious local wear on the valve wall surface, resulting in an increase in leakage. Degradation of the operating characteristic parameters leads to a decrease in control quality and even an impact on reliability [2, 3]. Excessive local wear of the valve body not only limits the volume of the electrohydraulic control module and further reduces its weight but also greatly reduces the service life of the electrohydraulic control module. Therefore, it is necessary to estimate the wear of the integral electrohydraulic module and perform maintenance work in advance.Previously, many scholars have studied the erosion wear of the hydraulic slide valve wall. Nøkleberg and Søntvedt [4, 5] used the CFD simulation method to predict the wear rate distribution of the wall position of the throttle valve. Kun Zhang et al. [6] established a performance characteristic degradation model and a life prediction method for the problem of servo valve failure due to the wear of contaminated particles. Forsberg and Jacobson [7] used the exhaust valve as the object to study the damage mechanism of the particles of different components mixed in hot air to the surface of the exhaust valve under different working conditions. Yaobao et al. [8] established a numerical simulation model of the two-dimensional flow field of the servo valve and predicted that the wall material removal rate at the valve port is the highest. And the evolution of the wear profile here and the effects of various parameters on the evolution of the wear profile are analyzed.In recent years, domestic and foreign scholars have carried out some research on the wall wear of steel hydraulic reversing valves and electrohydraulic servo valves under actual working conditions. The main shortcomings and problems existing in the current research are as follows: (1) The scope of the research object is not extensive enough, and the wall wear prediction method is not accurate enough. Most of today’s wear prediction methods simplify and ignore related factors, such as the shape of the particles and the distribution of particle size, resulting in more accurate prediction results [9]. (2) Most of the research only focused on the wear law of the electrohydraulic servo valve in the small opening. The position of the wear analysis is concentrated on the valve core and the valve sleeve sharp edge near the valve port, and the wear of other wall surfaces is not analyzed. Therefore, the guidance of practice has certain limitations.In this paper, the shifting slide valve in the integral electrohydraulic module is taken as the research object. For the problem that the wall surface is subjected to the particle impact wear, the wear prediction of the aluminum alloy sliding valve wall and the influence of the pollution condition parameters on the wall wear of the aluminum alloy sliding valve are studied. Calculate the velocity, pressure distribution, and particle trajectory of the oil flow inside the aluminum alloy slide valve, predict the distribution area of the wall wear and the corresponding wear rate, and find out influence of particle size, particle shape, and pressure on the wear of aluminum alloy sliding valve wall.


## 2. Liquid-Solid Two-Phase Flow Model

### 2.1. Fluid Motion Equation

The fluid motion equation includes a continuity equation and a Navier–Stokes equation, and the two equations are jointly solved to obtain the pressure and velocity of the fluid. The continuity equation is(1)∂ρ∂t+∇ρu=0,where ρ is the density of the fluid, t is the time, ∇ represents the divergence, and u is the velocity of the fluid. The momentum equation combined with the continuity equation gives the N-S equation, and its vector form is(2)∂u∂t+u⋅∇u=f−1ρ∇P+v∇2u+u3∇∇⋅u,where P is the oil pressure, v is the kinematic viscosity of the fluid, and f is the mass force acting on the fluid micelles.The N-S equation for the internal flow field of an aluminum alloy spool valve under constant and incompressible conditions is(3)∂v∂t+u⋅∇u=f−1ρ∇P+υ∇2u.After calculation, the oil flow state of the oil in the aluminum alloy slide valve is turbulent by the size of the Reynolds number Re. Several researchers have studied the flow field of the valve [10–12] and combined with the quality of the calculation grid divided in this paper. The turbulence model adopts the standard k−ε model, and its governing equation [13] is(4)∂∂tρk+∂∂tρkui=∂∂xjμ+μtσk∂k∂xj+Gk+Gb−ρε+Sk,∂∂tρε+∂∂xiρεui=∂∂xjμ+μtσε∂ε∂xj+G1εεkGk+G3εGb−G2ερε2k+Sε,where μt is the turbulent viscosity and can be expressed by the following equation:(5)μt=ρCμk2ε,where Gk represents the enthalpy flow energy term produced by the average velocity gradient; Gb is the turbulent flow energy term due to buoyancy; Cμ, G1ε, and G2ε are the constants, and their values are 0.09, 1.44, and 1.92, respectively; and σk and σε are k and ε, respectively. The turbulent Prandtl number, which takes 1.0 and 1.3, respectively; Sk and Sε are user-defined source items.


### 2.2. Equation of Motion of Solid Particles

The motion of the solid particles is determined by the motion of the fluid. The relevant variables obtained by solving the fluid motion equation, such as oil pressure and velocity, determine the force of the particle and determine the trajectory of the particle.The particle motion equation calculates the motion trajectory of the particle by correlating it with the correlation variable obtained by solving the fluid motion equation. The solution of the particle motion equation is done in the Lagrangian reference coordinate system. The equation of motion for solid particles is expressed as(6)mPdUPdt=FD+FG+FP+FL+FVM,where mP is the particle mass, UP is the particle velocity, FD is the drag force, FG is the force caused by gravity, FP is the pressure gradient force, FL is the lift force, and FVM is the virtual mass force. Since the concentration of particles in the oil inside the aluminum alloy slide valve is very low, less than 10%, the behavior of the solid particles has little effect on the flow of the oil, and its force on the flow field should not be considered.The calculation formula of the drag force is proposed by Haider and Levenspiel [14], and the force of different shapes of the particles can be simulated by setting different shape coefficients. The virtual mass force FVM is only important for large particles (dP > 250 μm), while the average particle size of the contaminating particles in the automatic transmission electrohydraulic module is only 5 μm. Its lift is always very small and can be ignored. In addition, the thermophoretic force can also be ignored.In this paper, the discrete random walk model [15] is used to simulate the turbulent diffusion effect of the particles so that the particle motion equation is solved by the instantaneous velocity generated by the fluid velocity pulsation. The expression of instantaneous velocity is(7)uPf=u¯+u′,where u′ is the pulsation velocity of the fluid, and its expression is(8)u′=ξu′2¯,where ξ is a random number obeying a normal distribution and u′2¯ is the Reynolds stress at the location of the particle with respect to the pulsation velocity of the fluid.When the particles hit the surface of different materials, the amount of change in the speed of movement will be different, and the elastic recovery coefficient model applied will be different. Since the aluminum alloy spool valve sleeve is made of the aluminum alloy valve body finishing valve hole and the valve core is steel valve core, different elastic recovery coefficient models should be selected to characterize the interaction between the particle and the wall surface. The elastic recovery coefficient models of the valve plug and the valve sleeve use the Forder model [16] and the Grant model [17], respectively.(1)
Forder model:(9)en=uP;n′uP;n=1−0.4159α+0.5994α2−0.292α3,et=uP;t′uP;t=1−2.12α+3.0775α2−1.1α3.(2)
Grant model:(10)en=uP;n′uP;n=0.993−1.76α+1.56α2−0.49α3,et=uP;t′uP;t=0.998−1.66α+2.11α2−0.67α3,where en and et are the normal recovery coefficient and the tangential recovery coefficient, respectively; uP;n′ and uP;t′ are the normal component and the tangential component of the velocity behind the collision wall; uP;n and uP;t are the normal component and the tangential component of the velocity of the particle as it approaches the wall; and α is the impact angle.


### 2.3. Wear Calculation Equation

The Fluent simulation calculation program solves the information about the liquid-solid two-phase flow, such as the angle, velocity, number, and position of the particles hitting the wall. The wear rate calculation of all the walls is performed on the corresponding wall unit, and each wall unit can store and display the calculation result of the wear rate. The calculation equation for the particle erosion wear rate used in this paper is(11)Re=∑i=1NPm˙PERAf=∑i=1NPm˙PAFsVPnfαAf,where m˙P is the mass flow rate of the particles; ER is the wear rate (kg/kg); A is the wall material constant, which is related to the material Boolean hardness HB; Fs is the particle sharpness factor; n is the empirical constant determined by the test; VP is the impact velocity of the particle; fα is the impact angle function, which is(12)fα=aα2+bα,α≤α0,xcos2α⋅sinwα+ysin2α+z,α>α0,where α is the impact angle and α,a,b,w,x,y,andz are the empirical constants determined by the properties of the wall material and the relevant empirical constants for carbon steel and aluminum (Table 1).Table 1
The value of the relevant parameter of the wear calculation model.
Empirical constant
A
α
0
a
b
w
x
y
z
n
Carbon steel
9.25 × 10−8
15°
−38.4
22.7
1
3.147
0.3609
2.532
2.41
Aluminum
2.388 × 10−7
10°
−34.79
12.3
5.205
0.147
−0.745
1
2.41In order to facilitate the prediction of the wall wear rate of the aluminum alloy spool under realistic conditions, the wear rate is defined as the mass loss of the wall material per unit area due to particle collision divided by the mass of all particles in the internal flow field, which can be expressed by the following formula:(13)ERm=ReM˙P,where M˙P is the total mass flow rate of the particles at the inlet and outlet and the mass loss of the material of the spool wall is obtained by integrating Re over a 0.01 mm2 area of the wall. The significance of the wear rate ERm is that in order to predict the loss quality of the wall material, it is only necessary to detect and calculate the concentration and total mass of the contaminated particles in the oil.


## 2.1. Fluid Motion Equation

The fluid motion equation includes a continuity equation and a Navier–Stokes equation, and the two equations are jointly solved to obtain the pressure and velocity of the fluid. The continuity equation is(1)∂ρ∂t+∇ρu=0,where ρ is the density of the fluid, t is the time, ∇ represents the divergence, and u is the velocity of the fluid. The momentum equation combined with the continuity equation gives the N-S equation, and its vector form is(2)∂u∂t+u⋅∇u=f−1ρ∇P+v∇2u+u3∇∇⋅u,where P is the oil pressure, v is the kinematic viscosity of the fluid, and f is the mass force acting on the fluid micelles.The N-S equation for the internal flow field of an aluminum alloy spool valve under constant and incompressible conditions is(3)∂v∂t+u⋅∇u=f−1ρ∇P+υ∇2u.After calculation, the oil flow state of the oil in the aluminum alloy slide valve is turbulent by the size of the Reynolds number Re. Several researchers have studied the flow field of the valve [10–12] and combined with the quality of the calculation grid divided in this paper. The turbulence model adopts the standard k−ε model, and its governing equation [13] is(4)∂∂tρk+∂∂tρkui=∂∂xjμ+μtσk∂k∂xj+Gk+Gb−ρε+Sk,∂∂tρε+∂∂xiρεui=∂∂xjμ+μtσε∂ε∂xj+G1εεkGk+G3εGb−G2ερε2k+Sε,where μt is the turbulent viscosity and can be expressed by the following equation:(5)μt=ρCμk2ε,where Gk represents the enthalpy flow energy term produced by the average velocity gradient; Gb is the turbulent flow energy term due to buoyancy; Cμ, G1ε, and G2ε are the constants, and their values are 0.09, 1.44, and 1.92, respectively; and σk and σε are k and ε, respectively. The turbulent Prandtl number, which takes 1.0 and 1.3, respectively; Sk and Sε are user-defined source items.


## 2.2. Equation of Motion of Solid Particles

The motion of the solid particles is determined by the motion of the fluid. The relevant variables obtained by solving the fluid motion equation, such as oil pressure and velocity, determine the force of the particle and determine the trajectory of the particle.The particle motion equation calculates the motion trajectory of the particle by correlating it with the correlation variable obtained by solving the fluid motion equation. The solution of the particle motion equation is done in the Lagrangian reference coordinate system. The equation of motion for solid particles is expressed as(6)mPdUPdt=FD+FG+FP+FL+FVM,where mP is the particle mass, UP is the particle velocity, FD is the drag force, FG is the force caused by gravity, FP is the pressure gradient force, FL is the lift force, and FVM is the virtual mass force. Since the concentration of particles in the oil inside the aluminum alloy slide valve is very low, less than 10%, the behavior of the solid particles has little effect on the flow of the oil, and its force on the flow field should not be considered.The calculation formula of the drag force is proposed by Haider and Levenspiel [14], and the force of different shapes of the particles can be simulated by setting different shape coefficients. The virtual mass force FVM is only important for large particles (dP > 250 μm), while the average particle size of the contaminating particles in the automatic transmission electrohydraulic module is only 5 μm. Its lift is always very small and can be ignored. In addition, the thermophoretic force can also be ignored.In this paper, the discrete random walk model [15] is used to simulate the turbulent diffusion effect of the particles so that the particle motion equation is solved by the instantaneous velocity generated by the fluid velocity pulsation. The expression of instantaneous velocity is(7)uPf=u¯+u′,where u′ is the pulsation velocity of the fluid, and its expression is(8)u′=ξu′2¯,where ξ is a random number obeying a normal distribution and u′2¯ is the Reynolds stress at the location of the particle with respect to the pulsation velocity of the fluid.When the particles hit the surface of different materials, the amount of change in the speed of movement will be different, and the elastic recovery coefficient model applied will be different. Since the aluminum alloy spool valve sleeve is made of the aluminum alloy valve body finishing valve hole and the valve core is steel valve core, different elastic recovery coefficient models should be selected to characterize the interaction between the particle and the wall surface. The elastic recovery coefficient models of the valve plug and the valve sleeve use the Forder model [16] and the Grant model [17], respectively.(1)
Forder model:(9)en=uP;n′uP;n=1−0.4159α+0.5994α2−0.292α3,et=uP;t′uP;t=1−2.12α+3.0775α2−1.1α3.(2)
Grant model:(10)en=uP;n′uP;n=0.993−1.76α+1.56α2−0.49α3,et=uP;t′uP;t=0.998−1.66α+2.11α2−0.67α3,where en and et are the normal recovery coefficient and the tangential recovery coefficient, respectively; uP;n′ and uP;t′ are the normal component and the tangential component of the velocity behind the collision wall; uP;n and uP;t are the normal component and the tangential component of the velocity of the particle as it approaches the wall; and α is the impact angle.


## 2.3. Wear Calculation Equation

The Fluent simulation calculation program solves the information about the liquid-solid two-phase flow, such as the angle, velocity, number, and position of the particles hitting the wall. The wear rate calculation of all the walls is performed on the corresponding wall unit, and each wall unit can store and display the calculation result of the wear rate. The calculation equation for the particle erosion wear rate used in this paper is(11)Re=∑i=1NPm˙PERAf=∑i=1NPm˙PAFsVPnfαAf,where m˙P is the mass flow rate of the particles; ER is the wear rate (kg/kg); A is the wall material constant, which is related to the material Boolean hardness HB; Fs is the particle sharpness factor; n is the empirical constant determined by the test; VP is the impact velocity of the particle; fα is the impact angle function, which is(12)fα=aα2+bα,α≤α0,xcos2α⋅sinwα+ysin2α+z,α>α0,where α is the impact angle and α,a,b,w,x,y,andz are the empirical constants determined by the properties of the wall material and the relevant empirical constants for carbon steel and aluminum (Table 1).Table 1
The value of the relevant parameter of the wear calculation model.
Empirical constant
A
α
0
a
b
w
x
y
z
n
Carbon steel
9.25 × 10−8
15°
−38.4
22.7
1
3.147
0.3609
2.532
2.41
Aluminum
2.388 × 10−7
10°
−34.79
12.3
5.205
0.147
−0.745
1
2.41In order to facilitate the prediction of the wall wear rate of the aluminum alloy spool under realistic conditions, the wear rate is defined as the mass loss of the wall material per unit area due to particle collision divided by the mass of all particles in the internal flow field, which can be expressed by the following formula:(13)ERm=ReM˙P,where M˙P is the total mass flow rate of the particles at the inlet and outlet and the mass loss of the material of the spool wall is obtained by integrating Re over a 0.01 mm2 area of the wall. The significance of the wear rate ERm is that in order to predict the loss quality of the wall material, it is only necessary to detect and calculate the concentration and total mass of the contaminated particles in the oil.


## 3. Numerical Model

### 3.1. Flow Field Geometry Model Establishment and Mesh Division

The working principle of the shift valve is as follows: when one gear is supplied with oil, the oil supply port of the other gear will be closed, and the two-position cylinder will be prevented from supplying oil at the same time. This paper simulates the internal flow field geometry of the spool valve and its structural dimensions (Figure1). Use ICEM to divide and generate computational grids. Its 3D geometry model is built in the DesignModeler program (Figure 2.). The Cartesian coordinate system of the 3D model takes the intersection of the inlet port boundary as the coordinate origin; the positive direction of the X-axis is the axial direction of the valve core, and the positive direction of the Z-axis is the flow direction of the oil at the oil inlet. Considering the relative regularity of the flow field geometry inside the spool valve, the divided flow field grid is a hexahedral structured grid (Figure 3). The number of flow field grids generated by using the entire aluminum alloy spool valve is about 350,000.Figure 1
Flow field geometry diagram (mm).Figure 2
Three-dimensional geometric model of flow field inside the spool valve.Figure 3
Structured grid of the flow field.The hexahedral structured mesh quality metrics are mainly aspect ratio and quality. The aspect ratio value should be less than 40, and the closer to 1 indicates the higher the grid quality. The quality value should be greater than 0.25, and the closer to 1 indicates the higher the grid quality. When the index is evaluated by the aspect ratio (Figure4(a)), the minimum value is 1, and the maximum value is 3.19, indicating that the overall grid quality is very good. When the orthogonal mass is used as the grid evaluation index (Figure 4(b)), the minimum value is 0.697 and the maximum value is 0.999, indicating that the overall grid quality is good. Overall, the resulting mesh is of good quality.Figure 4
Grid evaluation. (a) Aspect ratio. (b) Orthogonal quality.
(a)
(b)The flow field calculation results of different grid numbers is shown in Figure5(a). The maximum wear rate of the wall varies with the number of grids (Figure 5(b)). Therefore, as long as the number of meshes reaches 350,000, continuing to encrypt the mesh will not affect the numerical results. Considering the requirements of computational efficiency, the number of flow field grids in this simulation calculation is about 350,000.Figure 5
Simulation results for different grid numbers. (a) Flow field velocity distribution. (b) Maximum wear rate.
(a)
(b)


### 3.2. Boundary Conditions

For inlet boundary conditions, outlet boundary conditions, and related physical properties of solid particles and oil, see Table2. The concentration of the contaminating particles at the inlet was set to 300 mg/L, which corresponds to a mass flow rate of contaminated particles of 3.24e − 04 kg/s in the simulation calculation. According to the case described in the literature [18], the results of oil sample contamination analysis under different lengths of the integrated transmission test are shown in Table 3, and the number of contaminated particles with particle size greater than 10 μm in the oil is negligible, and the main distribution range of particle size is from 4 μm to 10 μm, and the proportion of particles in the interval of 4 μm to 6 μm is the largest, and the average particle diameter of the particles in the oil sample is 5 μm.Table 2
Boundary conditions for simulation calculations.
Solid particles
Oil
Entrance boundary condition
Mass flow rate (kg/s)
3.24e − 04
Pressure inlet2 MPa
Particle size distribution
Refer Figure6
Particle shape
Ellipsoid
Export boundary conditions
Complete escape
Pressure outlet1.8 MPa
Wall boundary condition
Elastic recovery systemNumber model
Wall function method
Density (kg/m3)
7500
875
Dynamic viscosity (Pa·s)
[—]
0.036Table 3
Analysis results of oil sample contamination at different lengths of the integrated transmission test (particles/mL).
Running time (h)
>4μm
>4.6μm
>6μm
>9.8μm
>14μm
>21μm
>38μm
>68μm
2.5
170956.60
141231.90
46905.43
1052.33
84.10
13.57
2.33
0.50
5
35704.70
21318.93
8147.37
2485.70
1225.93
450.20
85.83
17.30
10
63432.63
37664.87
12535.80
3131.57
1362.30
432.97
76.63
17.30
12.5
145938.40
110928.20
28992.47
1480.73
309.37
55.70
7.17
1.50
⋮
⋮
⋮
⋮
⋮
⋮
⋮
⋮
⋮
195
52965.27
25759.87
6862.93
1724.70
748.67
238.60
45.07
8.77
205
40054.20
20321.50
6342.80
1687.10
734.83
233.13
36.07
7.17
210
52914.20
28021.07
8961.10
2542.27
1163.70
388.13
59.13
7.17Therefore, in the simulation program, the maximum particle size at the particle inlet is set to 10μm, the minimum particle size is 4 μm, the average particle size is 5 μm, the distribution parameter is 3.5, and the number of particle diameters is 10, and the particle size of the particles at the inlet is obtained. The distribution (Figure 6) is substantially consistent with the particle size distribution in the test oil sample. The shape of the particles is an ellipsoidal shape. For the solution of the flow motion in the near wall region, the wall function method is used.Figure 6
Particle size distribution at the inlet.


## 3.1. Flow Field Geometry Model Establishment and Mesh Division

The working principle of the shift valve is as follows: when one gear is supplied with oil, the oil supply port of the other gear will be closed, and the two-position cylinder will be prevented from supplying oil at the same time. This paper simulates the internal flow field geometry of the spool valve and its structural dimensions (Figure1). Use ICEM to divide and generate computational grids. Its 3D geometry model is built in the DesignModeler program (Figure 2.). The Cartesian coordinate system of the 3D model takes the intersection of the inlet port boundary as the coordinate origin; the positive direction of the X-axis is the axial direction of the valve core, and the positive direction of the Z-axis is the flow direction of the oil at the oil inlet. Considering the relative regularity of the flow field geometry inside the spool valve, the divided flow field grid is a hexahedral structured grid (Figure 3). The number of flow field grids generated by using the entire aluminum alloy spool valve is about 350,000.Figure 1
Flow field geometry diagram (mm).Figure 2
Three-dimensional geometric model of flow field inside the spool valve.Figure 3
Structured grid of the flow field.The hexahedral structured mesh quality metrics are mainly aspect ratio and quality. The aspect ratio value should be less than 40, and the closer to 1 indicates the higher the grid quality. The quality value should be greater than 0.25, and the closer to 1 indicates the higher the grid quality. When the index is evaluated by the aspect ratio (Figure4(a)), the minimum value is 1, and the maximum value is 3.19, indicating that the overall grid quality is very good. When the orthogonal mass is used as the grid evaluation index (Figure 4(b)), the minimum value is 0.697 and the maximum value is 0.999, indicating that the overall grid quality is good. Overall, the resulting mesh is of good quality.Figure 4
Grid evaluation. (a) Aspect ratio. (b) Orthogonal quality.
(a)
(b)The flow field calculation results of different grid numbers is shown in Figure5(a). The maximum wear rate of the wall varies with the number of grids (Figure 5(b)). Therefore, as long as the number of meshes reaches 350,000, continuing to encrypt the mesh will not affect the numerical results. Considering the requirements of computational efficiency, the number of flow field grids in this simulation calculation is about 350,000.Figure 5
Simulation results for different grid numbers. (a) Flow field velocity distribution. (b) Maximum wear rate.
(a)
(b)


## 3.2. Boundary Conditions

For inlet boundary conditions, outlet boundary conditions, and related physical properties of solid particles and oil, see Table2. The concentration of the contaminating particles at the inlet was set to 300 mg/L, which corresponds to a mass flow rate of contaminated particles of 3.24e − 04 kg/s in the simulation calculation. According to the case described in the literature [18], the results of oil sample contamination analysis under different lengths of the integrated transmission test are shown in Table 3, and the number of contaminated particles with particle size greater than 10 μm in the oil is negligible, and the main distribution range of particle size is from 4 μm to 10 μm, and the proportion of particles in the interval of 4 μm to 6 μm is the largest, and the average particle diameter of the particles in the oil sample is 5 μm.Table 2
Boundary conditions for simulation calculations.
Solid particles
Oil
Entrance boundary condition
Mass flow rate (kg/s)
3.24e − 04
Pressure inlet2 MPa
Particle size distribution
Refer Figure6
Particle shape
Ellipsoid
Export boundary conditions
Complete escape
Pressure outlet1.8 MPa
Wall boundary condition
Elastic recovery systemNumber model
Wall function method
Density (kg/m3)
7500
875
Dynamic viscosity (Pa·s)
[—]
0.036Table 3
Analysis results of oil sample contamination at different lengths of the integrated transmission test (particles/mL).
Running time (h)
>4μm
>4.6μm
>6μm
>9.8μm
>14μm
>21μm
>38μm
>68μm
2.5
170956.60
141231.90
46905.43
1052.33
84.10
13.57
2.33
0.50
5
35704.70
21318.93
8147.37
2485.70
1225.93
450.20
85.83
17.30
10
63432.63
37664.87
12535.80
3131.57
1362.30
432.97
76.63
17.30
12.5
145938.40
110928.20
28992.47
1480.73
309.37
55.70
7.17
1.50
⋮
⋮
⋮
⋮
⋮
⋮
⋮
⋮
⋮
195
52965.27
25759.87
6862.93
1724.70
748.67
238.60
45.07
8.77
205
40054.20
20321.50
6342.80
1687.10
734.83
233.13
36.07
7.17
210
52914.20
28021.07
8961.10
2542.27
1163.70
388.13
59.13
7.17Therefore, in the simulation program, the maximum particle size at the particle inlet is set to 10μm, the minimum particle size is 4 μm, the average particle size is 5 μm, the distribution parameter is 3.5, and the number of particle diameters is 10, and the particle size of the particles at the inlet is obtained. The distribution (Figure 6) is substantially consistent with the particle size distribution in the test oil sample. The shape of the particles is an ellipsoidal shape. For the solution of the flow motion in the near wall region, the wall function method is used.Figure 6
Particle size distribution at the inlet.


## 4. Calculation Results and Analysis

### 4.1. Wear Rate Analysis

Before analyzing the wall wear rate, it is necessary to analyze the flow field characteristics and the particle motion characteristics because the loss of the wall material is the result of the movement of the oil and particles in the valve cavity. A cross-sectional view of the pressure and velocity of the internal flow field when the valve opening of the aluminum alloy slide valve is 3 mm under normal working conditions is shown in Figures7 and 8, respectively. The flow area of the oil at the valve port changes, resulting in a jet phenomenon, the pressure and speed of which vary the most at the valve port. The flow rate of the oil in the near wall area is low, which hinders the particles that will hit the wall.Figure 7
Pressure cloud diagram for different sections.
(a)
(b)Figure 8
Velocity cloud map of different sections.
(a)
(b)In this paper, the Fluent simulation calculation program uses about 15930 particles to simulate the mass flow rate of 3.24 × 10−4 kg/s solid particles moving in the oil. For the convenience of observation, the movement trajectories of individual solid particles at different starting positions are displayed (Figure 9), and the color of the motion trajectory of the solid particles at different positions is determined by the speed of their motion. As can be seen from Figure 9, the trajectory of the particles within the spool is related to the position of the slide valve. The starting position of the movement of solid particles of different particle sizes is only at the right end of the oil inlet, the movement trajectory is not tortuous, and the oil movement can be followed relatively stably; when the starting position of the movement is at other positions of the oil inlet, the randomness is relatively large, the motion path is very tortuous, and multiple reflows may occur at different or the same position, thereby causing a secondary collision on the wall surface. After the collision of solid particles with the wall surface, the movement speed of the particles will be significantly reduced due to the loss of the momentum of the particles. However, a small amount of particles do not collide with the surface of the spool and flow directly from the oil outlet with the oil.Figure 9
Motion trajectory of particles.
(a)
(b)
(c)
(d)Because the surface properties of the friction pair of the sliding valve have a very important influence on its function and service life, this paper mainly analyzes the wear rate of the cylindrical wall surface of the valve core and the cylindrical wall surface of the valve sleeve and the schematic diagram of the two walls and the cylindrical surface. The position is represented by the coordinate axis (Figure10), the origin of the coordinate is at the leftmost end of the central axis of the spool, the axial position is represented by the X-axis coordinate, and the circumferential position is represented by the angle rotated counterclockwise in the 0° direction.Figure 10
Schematic diagram of the friction surface of the aluminum alloy slide valve.The wear rate of the friction pair surface is distributed in the axial direction (Figure11). The wear rate of the friction pair surface in different circumferential directions is different, but the distribution trend of the wear rate along the axial direction has a certain regularity. At the position closer to the valve port, the wall wear rate is the largest. The cylindrical wall of the valve core has a trend of increasing wear in different circumferential directions, and the maximum wear rate occurs at the rightmost end. The cylindrical wall of the valve sleeve is in different circumferential directions, and its wear rate fluctuates up and down. It fluctuates greatly in the first half and fluctuates less in the second half; the maximum wear rate in the circumferential direction does not occur on the sharp edge of the valve sleeve. The wear rate of the cylindrical wall surface of the valve sleeve is larger in the circumferential direction of 90°–270°, and the wear rate is the largest when the circumferential direction is 270°. The wear of the contaminated particles on the cylindrical wall of the valve sleeve is 10 orders of magnitude higher than that of the cylindrical wall of the valve core mainly because the wear resistance of the aluminum alloy is worse than that of the steel, and the contaminated particles will cause greater wear.Figure 11
Friction pair surface wear rate along the axial direction. (a) Spool. (b) Valve sleeve.
(a)
(b)


### 4.2. Effect of Particle Size

When the particle size of the contaminated particles changes, the cylindrical wall wear rate of the valve core changes (Figure12). The overall distribution trend of the wear rate caused by the particles of different particle sizes in the same circumferential direction does not change; that is, the wall wear rate tends to increase in the overall circumferential direction in different circumferential directions, and the phenomenon of up and down fluctuation may occur, and the maximum wear may occur. Most of the rates occur at the far right. The wall wear rate caused by the larger particle size of the particles in the same area is generally smaller than that of the smaller particle size because the larger particle size is less affected by the turbulent pulsation, so the number of impacts on the cylindrical wall of the valve core is relatively small. For example, particle motion with a particle size of 40 μm is also affected by turbulent eddy and turbulent fluctuations. Some of the particles have a trajectory of reflow and fluctuations, but only some of the particles can follow the movement of the oil well.Figure 12
Effect of particle size on the wear rate of the cylindrical wall of the valve plug. (a)θ=0°. (b) θ=90°. (c) θ=180°. (d) θ=270°.
(a)
(b)
(c)
(d)The effect of particle size on the cylindrical wall wear rate of the valve sleeve is shown in Figure13. When the circumferential direction is 0°, the wear rate is significantly smaller than that of the other circumferential directions, and no obvious consistency is observed in the wear rate distribution caused by particles of different particle sizes. The cylindrical wall of the valve sleeve is in the range of 90°–270° in the circumferential direction of the surface, and the wear rate of the cylindrical wall is “large at both ends and small in the middle”; that is, the wear rate at both ends has obvious peaks. The maximum wear rate occurs near the valve port.Figure 13
Effect of particle size on the wear rate of the cylindrical wall of the valve sleeve. (a)θ=0°. (b) θ=90°. (c) θ=180°. (d) θ=270°.
(a)
(b)
(c)
(d)Particles with larger particle sizes on the same area result in wall wear rates generally smaller than those of smaller size particles. The particles with larger particle size move here and are still less affected by turbulent pulsation so that the movement of the oil can be better followed, and the probability of hitting the wall is relatively small.


### 4.3. Effect of Particle Shape

Several typical particle shapes in the polluted oil are selected, namely, spherical, ellipsoidal, and tetrahedral, with specific values of shape factor [19] and sharpness factor [20] (Table 4). In the wear prediction calculation program of the aluminum alloy spool valve wall, the shape factor affects the motion trajectory of the particle, and the sharpness factor is related to the wear calculation equation.Table 4
Characteristics of particles of different shapes.
Particle shape
Shape factor
Sharpness factor
Spherical
1
0.2
Ellipsoid
0.91
0.53
Tetrahedron
0.67
1It can be seen from Figures14 and 15 that the change in the shape of the particles does not change the position of the wear change in the different circumferential directions and the position of the maximum wear rate. Different shapes of particles have a good uniformity in the axial direction due to the wear rate in the same circumferential direction.Figure 14
Effect of particle shape on the wear rate of the cylindrical wall of the valve plug. (a)θ=0°. (b) θ=90°. (c) θ=180°. (d) θ=270°.
(a)
(b)
(c)
(d)Figure 15
Effect of particle shape on the wear rate of cylindrical wall of valve sleeve. (a)θ=0°. (b) θ=90°. (c) θ=180°. (d) θ=270°.
(a)
(b)
(c)
(d)As the sharpness of the particle profile increases, the wear rate at the same position is greater; that is, the tetrahedral particles have the strongest erosion wearability, the ellipsoidal particles are the second, and the spherical particles are the weakest. From the wear calculation equation, it can be found that when the impact conditions are the same, the sharpness factor determines the wall wear rate. The multiple relationship between the particle sharpness factors of different shapes is also the multiple relationship between the wear rates. It can be seen from Figures14 and 15 that the wear rate at the same position does not match the multiple relationships between the sharpness factors. This is because the trajectories of the particles of different shapes are different, and the collision speed and the collision angle at the same position are different.


### 4.4. Influence of Differential Pressure

When the pressure difference is gradually increased, the wear rate of the friction pair surface changes in different circumferential directions (Figures16 and 17). It can be seen from Figure 16 that the increase of the pressure difference changes the trend of the wear rate of the cylindrical wall surface of the valve core in the circumferential direction. When the pressure difference reaches 0.3 MPa and 0.4 MPa, there is no obvious consistency in the variation of the wear rate of the cylindrical wall surface of the valve core in different circumferential directions, and the position of the maximum wear rate is difficult to predict. In the wall area with a circumferential direction of 90° to 270°, the greater the pressure difference, the greater the wear rate at the same position.Figure 16
Effect of differential pressure on the wear rate of the cylindrical wall of the valve plug. (a)θ=0°. (b) θ=90°. (c) θ=180°. (d) θ=270°.
(a)
(b)
(c)
(d)Figure 17
Effect of differential pressure on the wear rate of cylindrical wall of valve sleeve. (a)θ=0°. (b) θ=90°. (c) θ=180°. (d) θ=270°.
(a)
(b)
(c)
(d)By analyzing Figure17, it can be found that the pressure difference has a much smaller influence on the change trend of the wear rate of the cylindrical wall surface of the valve sleeve in different circumferential directions than the cylindrical wall surface of the valve core. Although the pressure difference is different, the trend of the wall wear rate in the circumferential direction of 90°, 180°, and 270° can be observed to be more consistent. The wear rate of the wall in different circumferential directions is “upward fluctuation” along the axial direction. The wear rate near the valve port fluctuates the most. However, in the vicinity of the wall surface with a circumferential direction of 0°, the movement of the particles is greatly affected by the pressure difference, and the change in the wear rate along the axial direction is not significantly uniform. The maximum wear rate of the wall in the circumferential direction of 0°, 90°, and 270° is large with the increase of the pressure difference, and the increment is very large, and the maximum wear rate of the wall with the circumferential direction of 180° is not affected by the pressure difference influences. Therefore, the increase of the pressure difference not only greatly enhances the erosion wearability of the contaminated particles but also enhances the randomness of the particle motion and deteriorates the predictability of the wall wear.In summary, (1) the larger the particle size, the smaller the wear distribution area of the cylindrical wall surface of the valve sleeve, and the wear rate of the cylindrical wall surface of the valve sleeve is 90°, 180°, and 270° in the circumferential direction. The wear rate of both ends is large and the middle is small. That is, the wear rates of both ends have obvious peaks.” The maximum wear rate occurs at a position closer to the valve port. (2) The sharper the outer contour of the particles, the larger the wear distribution area on the different wall surfaces. Different shapes of particles have a good uniformity in the axial direction due to the wear rate in the same circumferential direction. As the sharpness of the particle profile increases, the wear rate at the same position is greater; that is, the tetrahedral particles have the strongest erosion wearability, the ellipsoidal particles are the second, and the spherical particles are the weakest. (3) The increase in differential pressure has a great influence on the wear distribution and wear rate. When the pressure difference reaches 0.3 MPa and 0.4 MPa, the wear distribution area on different wall surfaces is greatly increased, and the maximum value of local wear is greatly increased, which reduces the service life of the aluminum alloy slide valve and accelerates its functional degradation.


## 4.1. Wear Rate Analysis

Before analyzing the wall wear rate, it is necessary to analyze the flow field characteristics and the particle motion characteristics because the loss of the wall material is the result of the movement of the oil and particles in the valve cavity. A cross-sectional view of the pressure and velocity of the internal flow field when the valve opening of the aluminum alloy slide valve is 3 mm under normal working conditions is shown in Figures7 and 8, respectively. The flow area of the oil at the valve port changes, resulting in a jet phenomenon, the pressure and speed of which vary the most at the valve port. The flow rate of the oil in the near wall area is low, which hinders the particles that will hit the wall.Figure 7
Pressure cloud diagram for different sections.
(a)
(b)Figure 8
Velocity cloud map of different sections.
(a)
(b)In this paper, the Fluent simulation calculation program uses about 15930 particles to simulate the mass flow rate of 3.24 × 10−4 kg/s solid particles moving in the oil. For the convenience of observation, the movement trajectories of individual solid particles at different starting positions are displayed (Figure 9), and the color of the motion trajectory of the solid particles at different positions is determined by the speed of their motion. As can be seen from Figure 9, the trajectory of the particles within the spool is related to the position of the slide valve. The starting position of the movement of solid particles of different particle sizes is only at the right end of the oil inlet, the movement trajectory is not tortuous, and the oil movement can be followed relatively stably; when the starting position of the movement is at other positions of the oil inlet, the randomness is relatively large, the motion path is very tortuous, and multiple reflows may occur at different or the same position, thereby causing a secondary collision on the wall surface. After the collision of solid particles with the wall surface, the movement speed of the particles will be significantly reduced due to the loss of the momentum of the particles. However, a small amount of particles do not collide with the surface of the spool and flow directly from the oil outlet with the oil.Figure 9
Motion trajectory of particles.
(a)
(b)
(c)
(d)Because the surface properties of the friction pair of the sliding valve have a very important influence on its function and service life, this paper mainly analyzes the wear rate of the cylindrical wall surface of the valve core and the cylindrical wall surface of the valve sleeve and the schematic diagram of the two walls and the cylindrical surface. The position is represented by the coordinate axis (Figure10), the origin of the coordinate is at the leftmost end of the central axis of the spool, the axial position is represented by the X-axis coordinate, and the circumferential position is represented by the angle rotated counterclockwise in the 0° direction.Figure 10
Schematic diagram of the friction surface of the aluminum alloy slide valve.The wear rate of the friction pair surface is distributed in the axial direction (Figure11). The wear rate of the friction pair surface in different circumferential directions is different, but the distribution trend of the wear rate along the axial direction has a certain regularity. At the position closer to the valve port, the wall wear rate is the largest. The cylindrical wall of the valve core has a trend of increasing wear in different circumferential directions, and the maximum wear rate occurs at the rightmost end. The cylindrical wall of the valve sleeve is in different circumferential directions, and its wear rate fluctuates up and down. It fluctuates greatly in the first half and fluctuates less in the second half; the maximum wear rate in the circumferential direction does not occur on the sharp edge of the valve sleeve. The wear rate of the cylindrical wall surface of the valve sleeve is larger in the circumferential direction of 90°–270°, and the wear rate is the largest when the circumferential direction is 270°. The wear of the contaminated particles on the cylindrical wall of the valve sleeve is 10 orders of magnitude higher than that of the cylindrical wall of the valve core mainly because the wear resistance of the aluminum alloy is worse than that of the steel, and the contaminated particles will cause greater wear.Figure 11
Friction pair surface wear rate along the axial direction. (a) Spool. (b) Valve sleeve.
(a)
(b)


## 4.2. Effect of Particle Size

When the particle size of the contaminated particles changes, the cylindrical wall wear rate of the valve core changes (Figure12). The overall distribution trend of the wear rate caused by the particles of different particle sizes in the same circumferential direction does not change; that is, the wall wear rate tends to increase in the overall circumferential direction in different circumferential directions, and the phenomenon of up and down fluctuation may occur, and the maximum wear may occur. Most of the rates occur at the far right. The wall wear rate caused by the larger particle size of the particles in the same area is generally smaller than that of the smaller particle size because the larger particle size is less affected by the turbulent pulsation, so the number of impacts on the cylindrical wall of the valve core is relatively small. For example, particle motion with a particle size of 40 μm is also affected by turbulent eddy and turbulent fluctuations. Some of the particles have a trajectory of reflow and fluctuations, but only some of the particles can follow the movement of the oil well.Figure 12
Effect of particle size on the wear rate of the cylindrical wall of the valve plug. (a)θ=0°. (b) θ=90°. (c) θ=180°. (d) θ=270°.
(a)
(b)
(c)
(d)The effect of particle size on the cylindrical wall wear rate of the valve sleeve is shown in Figure13. When the circumferential direction is 0°, the wear rate is significantly smaller than that of the other circumferential directions, and no obvious consistency is observed in the wear rate distribution caused by particles of different particle sizes. The cylindrical wall of the valve sleeve is in the range of 90°–270° in the circumferential direction of the surface, and the wear rate of the cylindrical wall is “large at both ends and small in the middle”; that is, the wear rate at both ends has obvious peaks. The maximum wear rate occurs near the valve port.Figure 13
Effect of particle size on the wear rate of the cylindrical wall of the valve sleeve. (a)θ=0°. (b) θ=90°. (c) θ=180°. (d) θ=270°.
(a)
(b)
(c)
(d)Particles with larger particle sizes on the same area result in wall wear rates generally smaller than those of smaller size particles. The particles with larger particle size move here and are still less affected by turbulent pulsation so that the movement of the oil can be better followed, and the probability of hitting the wall is relatively small.


## 4.3. Effect of Particle Shape

Several typical particle shapes in the polluted oil are selected, namely, spherical, ellipsoidal, and tetrahedral, with specific values of shape factor [19] and sharpness factor [20] (Table 4). In the wear prediction calculation program of the aluminum alloy spool valve wall, the shape factor affects the motion trajectory of the particle, and the sharpness factor is related to the wear calculation equation.Table 4
Characteristics of particles of different shapes.
Particle shape
Shape factor
Sharpness factor
Spherical
1
0.2
Ellipsoid
0.91
0.53
Tetrahedron
0.67
1It can be seen from Figures14 and 15 that the change in the shape of the particles does not change the position of the wear change in the different circumferential directions and the position of the maximum wear rate. Different shapes of particles have a good uniformity in the axial direction due to the wear rate in the same circumferential direction.Figure 14
Effect of particle shape on the wear rate of the cylindrical wall of the valve plug. (a)θ=0°. (b) θ=90°. (c) θ=180°. (d) θ=270°.
(a)
(b)
(c)
(d)Figure 15
Effect of particle shape on the wear rate of cylindrical wall of valve sleeve. (a)θ=0°. (b) θ=90°. (c) θ=180°. (d) θ=270°.
(a)
(b)
(c)
(d)As the sharpness of the particle profile increases, the wear rate at the same position is greater; that is, the tetrahedral particles have the strongest erosion wearability, the ellipsoidal particles are the second, and the spherical particles are the weakest. From the wear calculation equation, it can be found that when the impact conditions are the same, the sharpness factor determines the wall wear rate. The multiple relationship between the particle sharpness factors of different shapes is also the multiple relationship between the wear rates. It can be seen from Figures14 and 15 that the wear rate at the same position does not match the multiple relationships between the sharpness factors. This is because the trajectories of the particles of different shapes are different, and the collision speed and the collision angle at the same position are different.


## 4.4. Influence of Differential Pressure

When the pressure difference is gradually increased, the wear rate of the friction pair surface changes in different circumferential directions (Figures16 and 17). It can be seen from Figure 16 that the increase of the pressure difference changes the trend of the wear rate of the cylindrical wall surface of the valve core in the circumferential direction. When the pressure difference reaches 0.3 MPa and 0.4 MPa, there is no obvious consistency in the variation of the wear rate of the cylindrical wall surface of the valve core in different circumferential directions, and the position of the maximum wear rate is difficult to predict. In the wall area with a circumferential direction of 90° to 270°, the greater the pressure difference, the greater the wear rate at the same position.Figure 16
Effect of differential pressure on the wear rate of the cylindrical wall of the valve plug. (a)θ=0°. (b) θ=90°. (c) θ=180°. (d) θ=270°.
(a)
(b)
(c)
(d)Figure 17
Effect of differential pressure on the wear rate of cylindrical wall of valve sleeve. (a)θ=0°. (b) θ=90°. (c) θ=180°. (d) θ=270°.
(a)
(b)
(c)
(d)By analyzing Figure17, it can be found that the pressure difference has a much smaller influence on the change trend of the wear rate of the cylindrical wall surface of the valve sleeve in different circumferential directions than the cylindrical wall surface of the valve core. Although the pressure difference is different, the trend of the wall wear rate in the circumferential direction of 90°, 180°, and 270° can be observed to be more consistent. The wear rate of the wall in different circumferential directions is “upward fluctuation” along the axial direction. The wear rate near the valve port fluctuates the most. However, in the vicinity of the wall surface with a circumferential direction of 0°, the movement of the particles is greatly affected by the pressure difference, and the change in the wear rate along the axial direction is not significantly uniform. The maximum wear rate of the wall in the circumferential direction of 0°, 90°, and 270° is large with the increase of the pressure difference, and the increment is very large, and the maximum wear rate of the wall with the circumferential direction of 180° is not affected by the pressure difference influences. Therefore, the increase of the pressure difference not only greatly enhances the erosion wearability of the contaminated particles but also enhances the randomness of the particle motion and deteriorates the predictability of the wall wear.In summary, (1) the larger the particle size, the smaller the wear distribution area of the cylindrical wall surface of the valve sleeve, and the wear rate of the cylindrical wall surface of the valve sleeve is 90°, 180°, and 270° in the circumferential direction. The wear rate of both ends is large and the middle is small. That is, the wear rates of both ends have obvious peaks.” The maximum wear rate occurs at a position closer to the valve port. (2) The sharper the outer contour of the particles, the larger the wear distribution area on the different wall surfaces. Different shapes of particles have a good uniformity in the axial direction due to the wear rate in the same circumferential direction. As the sharpness of the particle profile increases, the wear rate at the same position is greater; that is, the tetrahedral particles have the strongest erosion wearability, the ellipsoidal particles are the second, and the spherical particles are the weakest. (3) The increase in differential pressure has a great influence on the wear distribution and wear rate. When the pressure difference reaches 0.3 MPa and 0.4 MPa, the wear distribution area on different wall surfaces is greatly increased, and the maximum value of local wear is greatly increased, which reduces the service life of the aluminum alloy slide valve and accelerates its functional degradation.


## 5. Conclusions

(1)
In order to accurately predict the wear of the aluminum alloy spool wall, this paper establishes a wall wear prediction model based on CFD. In the wear prediction model of the aluminum alloy spool valve wall, the flow field is solved by considering the turbulence effect and the flow field characteristics in the near wall region. The particle shape coefficient is added to the drag model, and the trajectories of particles of different shapes are simulated by setting different particle shape coefficients. The DRW model was used to characterize the effect of turbulent diffusion on particle motion. Because the composition of the valve core and the valve sleeve is different, the elastic recovery coefficient model uses the Forder model and the Grant model, respectively, and the wall wear calculation equation is applicable to steel and aluminum alloy, respectively. The wear prediction model of the aluminum alloy spool valve wall is considered comprehensive and the prediction effect is better.
(2)
The flow field characteristics, particle motion characteristics, and wall wear rate distribution are obtained from the calculation results. For the flow field characteristics, the change is greatest in the valve port area. For particle motion, particles hit the wall in the near wall area. The particle motion trajectory depends on the position of the incoming slide valve. For the wear rate, the area of the friction pair surface near the valve port has a large wear rate, and the area away from the valve port has a small wear rate.
(3)
The effects of particle size, particle shape, and pressure difference on the wear rate of the friction pair surface were investigated. Contaminated particles with larger particle size are less affected by turbulent pulsation so that they can follow the movement of oil better, and the probability of impacting the surface of the friction pair is relatively small. The larger the particle size, the lesser the erosion wear on the surface of the friction pair. The change in particle shape does not change the position of the wear change trend and the maximum wear rate in different circumferential directions. Different shapes of particles have a good uniformity in the axial direction due to the wear rate in the same circumferential direction. As the sharpness of the particle profile increases, the wear rate at the same position is greater; that is, the tetrahedral particles have the strongest erosion wearability, the ellipsoidal particles are the second, and the spherical particles are the weakest. The increase of pressure difference not only greatly enhances the erosion and wear resistance of the contaminated particles but also enhances the randomness of particle motion and deteriorates the predictability of wall wear.



---

*Source: 9465406-2019-12-05.xml*