Characterization of the Solid Particle Erosion of the Sealing Surface Materials of a Ball Valve

: The ball valve is an essential piece of equipment in an oil and gas pipeline. The sand particles transported through the pipeline can cause erosion and wear to the ball valve, thus causing it to fail, leading to serious safety hazards. In this paper, the self-designed erosion experiment method was combined with computational ﬂuid dynamics (CFD), while the Euler-Lagrange method was also introduced to optimize the Oka erosion model and Ford particle-wall rebound model. The erosion mechanism and characteristics of the ball valve sealing surface in gas-solid two-phase ﬂow were simulated, while the erosion condition of the specimen was analyzed and compared when exposed to different factors, such as different particle velocities, impact angle, particle size, and specimen materials. The experimental data conformed well to the CFD erosion simulation data, verifying the accuracy of the CFD simulation analysis. The results indicated that the worn surface was caused by various wear mechanisms, while a “stagnation zone” was identiﬁed at the center of the specimen. The maximum erosion area, which was U-shaped, was also located at the center. The erosion rate increased in conjunction with an increase in the particle velocity and size, both of which failed to affect the erosion pattern. The erosion rate initially increased, after which it decreased with the impact angle, reaching the maximum value at an impact angle of 30 ◦ . This paper summarizes the erosion failure mechanism and characteristics in gas–solid two-phase ﬂow and provides both technical support and a theoretical basis for the on-site maintenance of essential vulnerable parts in the pipeline, such as ball valves.


Introduction
The ball valve is responsible for cutting off, distributing, and changing the medium in oil and gas pipelines and is an essential regulating component presenting several advantages, such as low fluid resistance, convenient and rapid switching, an extended service life, and high reliability. However, during the operational process, there may be leakage or even failure of the ball valve, causing serious safety hazards due to the erosion and wear of the sealing surface of the ball valve by the sand and abrasive particles in the pipeline [1]. As a phenomenon of surface material loss caused by the repeated collision between the wall surface and the sand particles carried by the fluid, erosion wear occurs extensively in production, transmission, and processing equipment [2]. Therefore, erosion wear can directly lead to the failure, damage, and scrapping of equipment and its parts. According to a British scholar, Eyre [3], erosion wear accounts for 8% of the total wear and tear damage during industrial production. Therefore, it is necessary to study the erosion characteristics and mechanism of the sealing surface of the ball valve to reveal its specific erosion law, while improving its service life and ensuring the safe operation of oil and gas pipelines. experiments. However, not many researchers have provided a comprehensive comparative analysis involving theory, simulations, and experiments. Therefore, it is necessary to study the erosion mechanism of the ball valve core and the sealing surface in natural gas pipelines via simulations and experimental comparisons. Since a natural gas pipeline contains no liquid, this paper focuses on gas-solid erosion, while completely disregarding liquid-solid erosion.
This paper is mainly designed to analyze the erosion mechanism of the ball valve sealing surface and reveal its erosion characteristics. The scope of this work is to characterize the erosive behavior of the materials of the ball valve sealing through the well-established method of the direct impact test at the laboratory scale, as a preliminary step toward the analysis of a real ball valve geometry. The numerical erosion model is selected as a theoretical basis to simulate the cross-section of the ball valve in a natural gas pipeline using a plane specimen. The change in the erosion rate, the erosion characteristics, and the erosion mechanism when exposed to different conditions are clarified by assessing the impact of the sand-carrying gas on the specimen. The commonly used CFD software package (ANSYS Fluent 18.0) is employed to simulate and predict the erosion mode and study the flow field. The experimental data were highly consistent with the CFD simulation results and theoretical model, verifying the erosion failure process of the ball valve cross-section, presenting the erosion law, and providing theoretical guidance regarding the failure mechanism of the ball valve in natural gas pipelines.    The air compressor provided airflow, while the airspeed was regulated by a valve between the compressor and the nozzle. The sand slowly flowed into the nozzle via the sand conveyor, impacting the specimen from the nozzle outlet to generate material loss when reaching a certain airspeed. The cylindrically shaped specimen, φ30 mm × 4 mm in size, was installed on the base. The initial angle between the specimen and the centerline The air compressor provided airflow, while the airspeed was regulated by a valve between the compressor and the nozzle. The sand slowly flowed into the nozzle via the sand conveyor, impacting the specimen from the nozzle outlet to generate material loss when reaching a certain airspeed. The cylindrically shaped specimen, ϕ30 mm × 4 mm in size, was installed on the base. The initial angle between the specimen and the centerline of the nozzle was 90 • and could be adjusted by bending it. When changing the inclination angle of the specimen, the distance from its center point to the nozzle outlet was not adjusted but kept at a fixed value.

Experimental Materials
The materials used in this study included Q235 carbon steel, A304 stainless steel, and 6061 aluminum alloy materials, which are commonly used in the ball valve section of an oil and gas pipeline. The characteristics of these materials are shown in Table 1. Considering the influence of particle size on erosion, quartz sand with different particle sizes was selected to facilitate the experimental erosion process. The SEM equipment (FEI Quanta 200F, Waltham, MA, USA) was used to observe the surface morphology of three sand particle sizes. The mirror image is shown in Figure 3.
Considering the influence of particle size on erosion, quartz sand with different particle sizes was selected to facilitate the experimental erosion process. The SEM equipment (FEI Quanta 200F, Waltham, MA, USA) was used to observe the surface morphology of three sand particle sizes. The mirror image is shown in Figure 3.

Experimental Procedures
Before the experiments, all parts of the equipment were checked to ensure that the experimental conditions were met. At the same time, the specimen surface was polished before each experiment to avoid the surface roughness influencing the erosion results. Before and after the erosion process, the mass loss of the specimen was recorded several times using an electronic microgram analytical balance, and the average value was calculated. During each group of experiments, the comparative tests were carried out repeatedly by the particle sizes, specimen materials, inlet velocities, impact angles, and various other parameters. The three groups of comparative tests were performed as follows: (1) The Q235 carbon steel specimen and sand with a particle size of 300 μm were selected to be used at nozzle inlet velocities of 45 m/s, 55 m/s, and 60 m/s during the erosion process, while the angle between the nozzle and the specimen was changed to 20°, 30°, 45°, 60°, 75°, and 90°, respectively. The scanning electron microscopy (SEM) images of different particle sizes. (a) Quartz sand with a particle diameter of 100 µm. (b) Quartz sand with a particle diameter of 300 µm. (c) Quartz sand with a particle diameter of 500 µm.

Experimental Procedures
Before the experiments, all parts of the equipment were checked to ensure that the experimental conditions were met. At the same time, the specimen surface was polished before each experiment to avoid the surface roughness influencing the erosion results. Before and after the erosion process, the mass loss of the specimen was recorded several times using an electronic microgram analytical balance, and the average value was calculated. During each group of experiments, the comparative tests were carried out repeatedly by the particle sizes, specimen materials, inlet velocities, impact angles, and various other parameters. The three groups of comparative tests were performed as follows: (1) The Q235 carbon steel specimen and sand with a particle size of 300 µm were selected to be used at nozzle inlet velocities of 45 m/s, 55 m/s, and 60 m/s during the erosion process, while the angle between the nozzle and the specimen was changed to 20 • , 30 • , 45 • , 60 • , 75 • , and 90 • , respectively. (2) A constant angle of 90 • between the specimen and the nozzle, an air inlet velocity of 60 m/s, and average sand particle sizes of 100 µm, 200 µm, 300 µm, 400 µm, and 500 µm, respectively, were selected for the erosion process. (3) Test pieces, including Q235 carbon steel, A304 stainless steel, and 6061 aluminum alloy, as well as sand with a particle size of 300 µm, were selected to be used at a nozzle inlet velocity of 60 m/s for the erosion process, while the angle between nozzle and the specimen was changed to 20 • , 30 • , 45 • , 60 • , 75 • , and 90 • respectively.

SEM Image Results
SEM was used to analyze the micro image of the sample surfaces after erosion to study the erosion mechanism further. Figure 4 shows the SEM images the erosion of the A304 stainless steel specimen using sand particles of 300 µm in size at a speed of 55 m/s, and three respective impact angles of 30 • , 75 • , and 90 • . Figure 4 shows that when the impact angle was 30 • , the erosion characteristics included pits, wear debris, and scratches, while the erosion mechanism involved microcutting. As the impact time increased, the debris was transferred to the pit boundary, leaving the specimen surface as the subsequent particles made contact. When the impact angle was 75 • , the erosion characteristics included pits, scratches, and wear debris. The erosion mechanism involved both micro-cutting and impact extrusion deformation. When the angle was 90 • , the erosion characteristics presented mainly pits. The erosion mechanism involved impact extrusion deformation since the particles made vertical contact with the center of the specimen center that caused the formation of pits, while the repeated impact led to the presence of deformation debris on the specimen surface. Figure 5 shows the SEM images of the erosion involving sand particles of 300 µm and 500 µm in size at a speed of 45 m/s and an impact angle of 90 • . The sizes of pits on the specimen surface increased in conjunction with an increase in the particle sizes, indicating that the larger the particle size, the higher the erosion rate. μm, respectively, were selected for the erosion process.
(3) Test pieces, including Q235 carbon steel, A304 stainless steel, and 6061 aluminum alloy, as well as sand with a particle size of 300 μm, were selected to be used at a nozzle inlet velocity of 60 m/s for the erosion process, while the angle between nozzle and the specimen was changed to 20°, 30°, 45°, 60°, 75°, and 90° respectively.

SEM Image Results
SEM was used to analyze the micro image of the sample surfaces after erosion to study the erosion mechanism further. Figure 4 shows the SEM images the erosion of the A304 stainless steel specimen using sand particles of 300 μm in size at a speed of 55 m/s, and three respective impact angles of 30°, 75°, and 90°.  Figure 4 shows that when the impact angle was 30°, the erosion characteristics included pits, wear debris, and scratches, while the erosion mechanism involved micro-cutting. As the impact time increased, the debris was transferred to the pit boundary, leaving the specimen surface as the subsequent particles made contact. When the impact angle was 75°, the erosion characteristics included pits, scratches, and wear debris. The erosion mechanism involved both micro-cutting and impact extrusion deformation. When the angle was 90°, the erosion characteristics presented mainly pits. The erosion mechanism involved impact extrusion deformation since the particles made vertical contact with the center of the specimen center that caused the formation of pits, while the repeated impact led to the presence of deformation debris on the specimen surface. Figure 5 shows the SEM images of the erosion involving sand particles of 300 μm and 500 μm in size at a speed of 45 m/s and an impact angle of 90°. The sizes of pits on the specimen surface increased in conjunction with an increase in the particle sizes, indicating that the larger the particle size, the higher the erosion rate.  . SEM images of erosion specimen surface exposed to different particle sizes. (a) The appearance of 300 μm particle impact specimen (b) The appearance of 500 μm particle impact specimen.

CFD Simulation and Analysis
To fully verify the reliability of the test data, CFD was used to simulate similar erosion behavior and comparatively analyze the test results. The CFD simulation method assesses the flow field distribution law by introducing the basic conservation equation, as well as the initial and boundary conditions. In this paper, the ANSYS Fluent [25] software (Version 18.0, Ansys, Pittsburgh, PA, USA) was used to simulate the erosion behavior of the gas-solid two-phase flow impact specimen.
This study regarded gas as the continuous phase and solid particles as the discrete phase using the Euler-Lagrange method [26]. In the Euler coordinate system, considering a shear stress transfer (SST) k-ω turbulence model, the motion of the continuous phase is obtained [27]. In the Lagrange coordinate system, the discrete phase motion is tracked using the discrete particle model (DPM) and Newton's second law. Without considering the influence of particle motion on fluid motion, the unidirectional coupling method was used in this paper to obtain the flow field, velocity, and angle of particles impacting the Figure 5. SEM images of erosion specimen surface exposed to different particle sizes. (a) The appearance of 300 µm particle impact specimen (b) The appearance of 500 µm particle impact specimen.

CFD Simulation and Analysis
To fully verify the reliability of the test data, CFD was used to simulate similar erosion behavior and comparatively analyze the test results. The CFD simulation method assesses the flow field distribution law by introducing the basic conservation equation, as well as the initial and boundary conditions. In this paper, the ANSYS Fluent [25] software (Version 18.0, Ansys, Pittsburgh, PA, USA) was used to simulate the erosion behavior of the gas-solid two-phase flow impact specimen.
This study regarded gas as the continuous phase and solid particles as the discrete phase using the Euler-Lagrange method [26]. In the Euler coordinate system, considering a shear stress transfer (SST) k-ω turbulence model, the motion of the continuous phase is obtained [27]. In the Lagrange coordinate system, the discrete phase motion is tracked using the discrete particle model (DPM) and Newton's second law. Without considering the influence of particle motion on fluid motion, the unidirectional coupling method was used in this paper to obtain the flow field, velocity, and angle of particles impacting the specimen plane via CFD and particle tracking. Then, the Oka erosion model and Forder et al. [28] particle-wall rebound model were used to predict the erosion wear of the specimen [29].

Numerical Model and Boundary Condition Settings
The numerical CFD simulation model corresponding to the follow-up experiments was established ( Figure 6) with the following parameters: the nozzle diameter was D = 7 mm with a pipe wall thickness of 2 mm and a length of L n . The distance from the nozzle to the specimen center line was H = 12.7 mm, with a specimen diameter of D S = 30 mm, and thickness of d s = 4 mm. The shape of the external computational fluid domain was cylindrical, in which the diameter of the external flow field was D t = 100 mm, and the length was d t = 60 mm. The specimen center was in the positive center of the external flow field, while the angle between the specimen plane and the nozzle centerline was about 30 • to 90 • , and H did not change in conjunction with θ. The detailed geometry features, numerical schemes, and boundary conditions in the CFD simulation are listed in Table 2. To avoid the influence of the number of particles on the final erosion result, this paper refines the nozzle entrance grid size to increase the number of particles incident from the nozzle, and sets the entrance grid size to 0.06 mm, making the number of entrance grids reach 12,520. Table 2. Geometry features, numerical schemes, and boundary conditions in computational fluid dynamics (CFD).

Project Description
Geometry parameters  The detailed geometry features, numerical schemes, and boundary conditions in the CFD simulation are listed in Table 2. To avoid the influence of the number of particles on the final erosion result, this paper refines the nozzle entrance grid size to increase the number of particles incident from the nozzle, and sets the entrance grid size to 0.06 mm, making the number of entrance grids reach 12,520.

Grid Independence Test
To ensure that the fluid formed a steady flow at the nozzle outlet and did not affect the analysis results under the boundary outlet conditions while reaching the maximum calculation accuracy, it was necessary to determine the optimal nozzle length.
At an inlet fluid velocity of 60 m/s, a particle velocity of 19 m/s, a particle mass flow rate of 5e × 10 −5 kg/s, and a particle size of 300 µm, the velocity distribution of the flow field at the H/3 position of the XOY plane in different working conditions was compared at nozzle lengths of 14 D, 18 D, and 22 D, and grid densities of 1 mm and 2 mm, respectively. From Figure 7, it is evident that the maximum velocity occurred within 5 mm around the center of the specimen. In addition, the maximum velocity was located at a point 1.5 times that of the nozzle radius from the specimen center. Furthermore, the velocity at the point directly opposite to the specimen center was relatively small, mainly because a high-pressure zone in this location led to the maximum velocity at a certain distance away from itself. Therefore, the overall velocity curve at H/3 on the specimen surface presented a W shape. Based on the result, the average variation of the velocity achieved by the 1 mm and 2 mm grid was about 4.9 pct. For the 0.5 mm and 1 mm gird, their axial velocity variation was about 0.6 pct. Therefore, the simulation model was not sensitive to the gird number, using the 0.5 mm and 1 mm grid. The computational time required by the 0.5 grid was 2.3 times than by the 1 mm grid. Furthermore, computational time required by the nozzle lengths of 22 D was 1.13 times than that of 14 D. This paper analyzed the 1 mm grid size and the 14 D nozzle length. point directly opposite to the specimen center was relatively small, mainly because a highpressure zone in this location led to the maximum velocity at a certain distance away from itself. Therefore, the overall velocity curve at H/3 on the specimen surface presented a W shape. Based on the result, the average variation of the velocity achieved by the 1 mm and 2 mm grid was about 4.9 pct. For the 0.5 mm and 1 mm gird, their axial velocity variation was about 0.6 pct. Therefore, the simulation model was not sensitive to the gird number, using the 0.5 mm and 1 mm grid. The computational time required by the 0.5 grid was 2.3 times than by the 1 mm grid. Furthermore, computational time required by the nozzle lengths of 22 D was 1.13 times than that of 14 D. This paper analyzed the 1 mm grid size and the 14 D nozzle length.  Figure 8 shows the impact simulation results obtained using CFD at a 60 m/s gas velocity at the nozzle inlet, as well as a particle velocity of 19 m/s, and a particle size of 300 μm, while illustrating the velocity nephogram, the particle trajectory map, the pres-   Figure 8 shows the impact simulation results obtained using CFD at a 60 m/s gas velocity at the nozzle inlet, as well as a particle velocity of 19 m/s, and a particle size of 300 µm, while illustrating the velocity nephogram, the particle trajectory map, the pressure nephogram, and the erosion nephogram.  Figure 8a indicates that the maximum velocity in the flow field was located at the centerline of the nozzle. When the gas-solid mixture reached the specimen center (i.e., the stagnation zone), the velocity decreased to 0 m/s, and the diameter of the stagnation zone was approximately the same as that of the nozzle. Additionally, Figure 8b shows that the particles ejected from the nozzle rebounded after directly impacting the specimen surface. The gas-solid two-phase flow exhibited a larger Stokes number, and the momentum transfer between the gas and sand particles was lower. Moreover, the particles continued to move according to the original trajectory when exposed to the action of inertial force until they impacted the specimen surface, forming a circular erosion zone. The particles that collide with the specimen surface might be involved in a secondary collision at a higher speed, rebounding into the outer fluid domain. Figure 8c shows the formation of a static pressure zone at the specimen center, while the gas velocity near the center of the specimen decreased continuously. The maximum velocity region on the surface of the specimen was located at a nozzle radius of 2-2.5 times from the specimen center and decreased in a radial direction. According to Figure 8d, the diameter of the erosion area was basically the same as that of the nozzle, while the maximum erosion position was located in the center of the specimen center, indicating that the erosion rate became lower further away from the specimen center. Furthermore, it was evident that the interface was Ushaped due to erosion.  Figure 8a indicates that the maximum velocity in the flow field was located at the centerline of the nozzle. When the gas-solid mixture reached the specimen center (i.e., the stagnation zone), the velocity decreased to 0 m/s, and the diameter of the stagnation zone was approximately the same as that of the nozzle. Additionally, Figure 8b shows that the particles ejected from the nozzle rebounded after directly impacting the specimen surface. The gas-solid two-phase flow exhibited a larger Stokes number, and the momentum transfer between the gas and sand particles was lower. Moreover, the particles continued to move according to the original trajectory when exposed to the action of inertial force until they impacted the specimen surface, forming a circular erosion zone. The particles that collide with the specimen surface might be involved in a secondary collision at a higher speed, rebounding into the outer fluid domain. Figure 8c shows the formation of a static pressure zone at the specimen center, while the gas velocity near the center of the specimen decreased continuously. The maximum velocity region on the surface of the specimen was located at a nozzle radius of 2-2.5 times from the specimen center and decreased in a radial direction. According to Figure 8d, the diameter of the erosion area was basically the same as that of the nozzle, while the maximum erosion position was located in the center of the specimen center, indicating that the erosion rate became lower further away from the specimen center. Furthermore, it was evident that the interface was U-shaped due to erosion.

Comparative Analysis of the Different Parameters
In an experiment, Vieira [12] measured the particle velocity using particle image velocimetry (PIV) and found the presence of a slip velocity between the particles and the gas at the nozzle outlet. The particle velocity was 0.317 times lower than the gas velocity. When the gas velocity was 45 m/s, 55 m/s, and 60 m/s, the particle velocity was 14 m/s, 17 m/s, and 19 m/s.

Simulation Analysis at Different Impact Angles
A Q235 carbon steel specimen and sand particles of 300 µm in size were selected for the experiment. The air velocity at the nozzle inlet was altered to 45 m/s, 55 m/s, and 60 m/s, while the impact angle between nozzle and specimen was adjusted to 20 • , 30 • , 45 • , 60 • , 75 • , and 90 • , respectively. Considering a nozzle inlet velocity of 60 m/s as an example, the velocity nephogram of the XOY plane at different angles is shown in Figure 9, the particle trajectory is shown in Figure 10, and the erosion nephogram is shown in Figure 11. particle trajectory is shown in Figure 10, and the erosion nephogram is shown in Figure  11.   According to Figure 9, when the impact angle is below 90 • , the fluid flows from the nozzle and to the side at a larger angle. Furthermore, "retention zones" are evident on the specimen surface at different angles. However, when the angle between the specimen and the nozzle decreases, the location of the retention zone gradually moves from the center of the specimen to its upper side.
As shown in Figure 10, when the angle between the specimen and the nozzle is lower than 90 • , the particles collide with the specimen surface and rebound to the side at a larger angle between the specimen and the nozzle, while the air does not affect the particle movement.
According to Figure 11, the maximum erosion positions at different impact angles are located in the central area of the specimen. When the angle is 20 • and 30 • , the erosion area is elliptical. Increasing the angle between the specimen and the nozzle causes the erosion area to gradually change from elliptical to circular. The length of the cloud image in the direction perpendicular to the screen is basically the same, while the length along the surface direction of the specimen on the XOY section increases and a decrease in the erosion position occurs at the center of the specimen at different angles. When the inclination angles of the specimens are 20 • , 30 • , 45 • , 60 • , 75 • , and 90 • , the lengths of the angle decrease. According to Figure 9, when the impact angle is below 90°, the fluid flows from the nozzle and to the side at a larger angle. Furthermore, "retention zones" are evident on the specimen surface at different angles. However, when the angle between the specimen and the nozzle decreases, the location of the retention zone gradually moves from the center of the specimen to its upper side.
As shown in Figure 10, when the angle between the specimen and the nozzle is lower than 90°, the particles collide with the specimen surface and rebound to the side at a larger angle between the specimen and the nozzle, while the air does not affect the particle movement.
According to Figure 11, the maximum erosion positions at different impact angles are located in the central area of the specimen. When the angle is 20° and 30°, the erosion area is elliptical. Increasing the angle between the specimen and the nozzle causes the erosion area to gradually change from elliptical to circular. The length of the cloud image in the direction perpendicular to the screen is basically the same, while the length along the surface direction of the specimen on the XOY section increases and a decrease in the erosion position occurs at the center of the specimen at different angles. When the incli- In engineering practices, the failure of equipment is mainly related to erosion depth. The greater the erosion depth, the higher the failure risk. Figure 12 shows the variations in erosion depth on the intersecting line formed by the XOY plane and the right surface of the specimen. The abscissa denotes the distance from the upper point to the lower point of the intersecting line formed by the XOY plane and the inner surface of the specimen, while the ordinate is the erosion depth. Therefore, the maximum erosion areas are 17 mm, 15 mm, 12.5 mm, 10 mm, 8.5 mm, and 8 mm, respectively, while the maximum erosion area is located in the center of the specimen at different impact angles.
in erosion depth on the intersecting line formed by the XOY plane and the right surface of the specimen. The abscissa denotes the distance from the upper point to the lower point of the intersecting line formed by the XOY plane and the inner surface of the specimen, while the ordinate is the erosion depth. Therefore, the maximum erosion areas are 17 mm, 15 mm, 12.5 mm, 10 mm, 8.5 mm, and 8 mm, respectively, while the maximum erosion area is located in the center of the specimen at different impact angles.  Figure 13a,b compares the effect of gas velocity and particle size on erosion depth at the intersecting line between the XOY plane and the specimen surface. The erosion area was within 4 mm from the specimen center, while the maximum erosion area was located in the center of the specimen surface. When the Q235 carbon steel specimen with a particle size of 300 μm was selected with a consistently maintained 90° angle between the specimen and the nozzle, and respective gas velocities set at 45 m/s, 55 m/s, and 60 m/s, the corresponding erosion depths were 102.9 μm, 175.5 μm, and 264.5 μm, respectively. When the angle between the specimen and the nozzle was kept at 90°, with an air velocity of 60 m/s, and particle sizes of 100 μm, 200 μm, 300 μm, 400 μm, and 500 μm, the corresponding erosion depths were 204.2 μm, 231.4 μm, 263.5 μm, 368.1 μm, and 418.4 μm, respectively. Therefore, it is evident that the erosion depth increases with an increase in the gas velocity and particle size. These results indicated that the gas velocity and particle size might be related to higher kinetic energy, leading to an increase in the material removal rate. In addition, the change in gas velocity and particle size did not affect the erosion mode.  Figure 13a,b compares the effect of gas velocity and particle size on erosion depth at the intersecting line between the XOY plane and the specimen surface. The erosion area was within 4 mm from the specimen center, while the maximum erosion area was located in the center of the specimen surface. When the Q235 carbon steel specimen with a particle size of 300 µm was selected with a consistently maintained 90 • angle between the specimen and the nozzle, and respective gas velocities set at 45 m/s, 55 m/s, and 60 m/s, the corresponding erosion depths were 102.9 µm, 175.5 µm, and 264.5 µm, respectively. When the angle between the specimen and the nozzle was kept at 90 • , with an air velocity of 60 m/s, and particle sizes of 100 µm, 200 µm, 300 µm, 400 µm, and 500 µm, the corresponding erosion depths were 204.2 µm, 231.4 µm, 263.5 µm, 368.1 µm, and 418.4 µm, respectively. Therefore, it is evident that the erosion depth increases with an increase in the gas velocity and particle size. These results indicated that the gas velocity and particle size might be related to higher kinetic energy, leading to an increase in the material removal rate. In addition, the change in gas velocity and particle size did not affect the erosion mode.

Analysis of the Erosion Law at Different Velocities and Specimen Angles
At a particle size of 300 µm, as well as adjusted impact angles (20 • , 30 • , 45 • , 60 • , 75 • , and 90 • ) and gas velocities (45 m/s, 55 m/s, and 60 m/s), the comparison diagrams denoting the CFD simulation results and erosion model results of the different specimen materials (Q235 carbon steel, A304 stainless steel, and 6061 aluminum alloy) are shown in Figures 14-16: (a) dp = 300 μm (b) vg = 60 m/s Figure 13. A comparison of the erosion depth at different velocities and particle sizes (θ = 90°). (a) Depth erosion at different air velocities (dp= 300 μm). (b) Erosion depth at different particle diameters (vg = 60m/s).

Analysis of the Erosion Law at Different Velocities and Specimen Angles
At a particle size of 300 μm, as well as adjusted impact angles (20°, 30°, 45°, 60°, 75°, and 90°) and gas velocities (45 m/s, 55 m/s, and 60 m/s), the comparison diagrams denoting the CFD simulation results and erosion model results of the different specimen materials (Q235 carbon steel, A304 stainless steel, and 6061 aluminum alloy) are shown in Figures 14-16:   Figure 14. A comparison between the simulation and erosion models of the Q235 carbon steel specimen (vg = ~45-60 m/s, vp = ~14-19 m/s, dp = 300 μm, and θ = ~20°-90°).  According to these images, the simulation results of the different materials at different angles, gas velocities, and particle velocities were close to the theoretical predictions. Due to the difference in hardness between the three specimens, the erosion rate of the Q235 carbon steel was slightly higher than that of the A304 stainless steel, while the erosion rates of both these materials were about 2.5 times that of the 6061 aluminum alloy. In  According to these images, the simulation results of the different materials at different angles, gas velocities, and particle velocities were close to the theoretical predictions. Due to the difference in hardness between the three specimens, the erosion rate of the Q235 carbon steel was slightly higher than that of the A304 stainless steel, while the ero- According to these images, the simulation results of the different materials at different angles, gas velocities, and particle velocities were close to the theoretical predictions. Due to the difference in hardness between the three specimens, the erosion rate of the Q235 carbon steel was slightly higher than that of the A304 stainless steel, while the erosion rates of both these materials were about 2.5 times that of the 6061 aluminum alloy. In addition, the erosion rate could be used to characterize the mass-loss rate. Given that the material density of the 6061 aluminum alloy was approximately one third of Q235 carbon steel and A304 stainless steel, it can be stated that the volume loss of these three materials was similar.

A Comparison of the Erosion Results at Different Angles and Particle Sizes
When the same material (Q235 carbon steel) specimen was selected, with adjusted impact angles of 20 • , 30 • , 45 • , 60 • , 75 • , and 90 • , and particle sizes of 100 µm, 300 µm, and 500 µm, respectively, the contrast diagram denoting the CFD erosion simulation results and erosion model is represented by Figure 17. According to the image, the simulation results were generally similar to the theoret ical prediction. The erosion rate increased in conjunction with an increase in the particl size, but the erosion effect caused by the particle velocity exceeded that of the particl diameter. Figure 18 shows the comparison diagram denoting the erosion rates of the simulation and experimental data of the Q235 carbon steel specimen at different gas velocities and impact angles, indicating that the erosion rate of the simulation and test increases at higher velocity. In addition, the maximum error between the simulation data and the ex perimental data was about 15.6%, which can be ascribed to two reasons. First, the particl size cannot be accurate and uniform during the experimental process, and some particle form a circle, resulting in more severe erosion. Second, the interaction between the parti cles and the rebound particles is ignored during the CFD simulation process.  According to the image, the simulation results were generally similar to the theoretical prediction. The erosion rate increased in conjunction with an increase in the particle size, but the erosion effect caused by the particle velocity exceeded that of the particle diameter. Figure 18 shows the comparison diagram denoting the erosion rates of the simulation and experimental data of the Q235 carbon steel specimen at different gas velocities and impact angles, indicating that the erosion rate of the simulation and test increases at a higher velocity. In addition, the maximum error between the simulation data and the experimental data was about 15.6%, which can be ascribed to two reasons. First, the particle size cannot be accurate and uniform during the experimental process, and some particles form a circle, resulting in more severe erosion. Second, the interaction between the particles and the rebound particles is ignored during the CFD simulation process. Figure 19 shows the comparison diagram denoting the erosion rates of the simulation and experimental data of three different materials (Q235 carbon steel, A304 stainless steel, and 6061 aluminum alloy) at different impact angles. and experimental data of the Q235 carbon steel specimen at different gas velocities an impact angles, indicating that the erosion rate of the simulation and test increases at higher velocity. In addition, the maximum error between the simulation data and the e perimental data was about 15.6%, which can be ascribed to two reasons. First, the partic size cannot be accurate and uniform during the experimental process, and some particl form a circle, resulting in more severe erosion. Second, the interaction between the par cles and the rebound particles is ignored during the CFD simulation process. Figure 18. The comparison diagram denoting the erosion rates of the CFD simulation and experimental data at different particle velocities (Q235 carbon steel and particle size dp = 300 μm). Impact angle θ/°E rosion rate /(kg/kg) v g =60m/s v p =19m/s(CFD result) v g =60m/s v p =19m/s(Experiment data) v g =55m/s v p =17m/s(CFD result) v g =55m/s v p =17m/s(Experiment data) v g =45m/s v p =14m/s(CFD result) v g =45m/s v p =14m/s(Experiment data) Figure 18. The comparison diagram denoting the erosion rates of the CFD simulation and experimental data at different particle velocities (Q235 carbon steel and particle size d p = 300 µm).  Figure 19 shows the comparison diagram denoting the erosion rates of the simulati and experimental data of three different materials (Q235 carbon steel, A304 stainless ste and 6061 aluminum alloy) at different impact angles. Figure 19. The comparison diagram denoting the erosion rates of the CFD simulation and experimental data of different materials (gas velocity vg = 60 m/s and particle size dp = 300 μm).

The Comparative Analysis of Different Materials at Different Impact Angles
The maximum error between the simulation data and experimental data was abo 21.7%, which is within a reasonable error range. In addition, the erosion rate of the Q2 carbon steel was slightly higher than that of the A304 stainless steel, both of which e ceeded that of the 6061 aluminum alloy, verifying the accuracy of the CFD simulation a erosion models.

Conclusions
This paper employs experimental and CFD simulation methods to simulate the se ing surface of the ball valve in natural gas pipelines using a specimen. Based on the stead state model [30], the erosion wear law of the specimens exposed to various influenci factors is studied, and the erosion wear mechanism is verified. The study results are follows: 1. A set of jet erosion experimental devices is developed based on gas-solid two-pha flow. In the same conditions as those of the simulation, the erosion experiment ve fication study is completed by changing the influencing factors, such as gas veloci particle size, impact angle, and specimen material. By observing the surface morph ogy mechanism of the specimen with SEM, the erosion mechanism and character tics at different impact angles and different particle sizes are proposed, including m cro-cutting, impact extrusion deformation and pits, craters, scratches, and wear d bris. 2. The simulation results show that the erosion rate increases with an increase in par cle size and erosion velocity. Furthermore, it is concluded that the maximum erosi area is located in the center of the specimen surface and presents a U shape und Impact angle θ/°E rosion rate /(kg/kg) Q235 carbon steel(CFD result) Q235 carbon steel(Experiment data) A304 carbon steel(CFD result) A304 carbon steel(Experiment data) 6061 aluminum alloy(CFD result) 6061 aluminum alloy(Experiment data) Figure 19. The comparison diagram denoting the erosion rates of the CFD simulation and experimental data of different materials (gas velocity v g = 60 m/s and particle size d p = 300 µm).
The maximum error between the simulation data and experimental data was about 21.7%, which is within a reasonable error range. In addition, the erosion rate of the Q235 carbon steel was slightly higher than that of the A304 stainless steel, both of which exceeded that of the 6061 aluminum alloy, verifying the accuracy of the CFD simulation and erosion models.

Conclusions
This paper employs experimental and CFD simulation methods to simulate the sealing surface of the ball valve in natural gas pipelines using a specimen. Based on the steady-state model [30], the erosion wear law of the specimens exposed to various influencing factors is studied, and the erosion wear mechanism is verified. The study results are as follows:

1.
A set of jet erosion experimental devices is developed based on gas-solid two-phase flow. In the same conditions as those of the simulation, the erosion experiment verification study is completed by changing the influencing factors, such as gas velocity, particle size, impact angle, and specimen material. By observing the surface morphology mechanism of the specimen with SEM, the erosion mechanism and characteristics at different impact angles and different particle sizes are proposed, including micro-cutting, impact extrusion deformation and pits, craters, scratches, and wear debris.

2.
The simulation results show that the erosion rate increases with an increase in particle size and erosion velocity. Furthermore, it is concluded that the maximum erosion area is located in the center of the specimen surface and presents a U shape under different conditions. At the same time, the surface pits of the eroded specimen increase with an increase in the particle size and velocity, while the service life of the specimen is reduced. In addition, when the impact angle is 30 • , the erosion rate reaches the peak value, exhibiting a prominent "stagnation area" at different impact angles. 3.
The difference between the CFD simulation and erosion model and the experimental data are compared, and the accuracy of the Euler-Lagrange method is verified. Furthermore, the applicability and accuracy of the SST k-ω turbulence model and Oka erosion prediction model are verified and found to be in good agreement with the experimental data. Institutional Review Board Statement: Not applicable.

Informed Consent Statement: Not applicable.
Data Availability Statement: Data available on request due to restrictions, as the research is ongoing.