Study on Fiber Clogging Mechanism in Sewage Pump Based on CFD–DEM Simulation

: A large number of solid particles and ﬁbrous impurities are always entrained in the ﬂuid transported by a sewage pump, which can easily lead to the blockage of the sewage pump. In view of this, CFD–DEM simulations were conducted in this paper to reveal the ﬁber clogging mechanism in the sewage pump. A CFD–DEM coupling method with a ﬁber model was established and veriﬁed by an experimental benchmark, i.e., the rectangular ﬂow channel. The method was then applied to a model sewage pump to, after mesh independence tests, analyze the effects of ﬂow rate and ﬁber length on ﬁber motion and clogging. The results showed that the position of ﬁber retention coincides with the position of the vortex, mainly located at the inlet of the impeller, the head of the blade, the middle of the blade, and the tongue in the pump. In the case of a low ﬂow rate, the ﬁber was more likely to cause blockage in the head of the blade, and in the case of a large ﬂow rate, the ﬁber would wind around the tongue in the pump. At the same ﬂow rate, long ﬁber was more likely to stay on the blade’s suction surface.


Introduction
With the acceleration of urbanization in the world, sewage volume is also increasing continuously. At present, the total sewage discharge in the world has exceeded 400 billion cubic meters, which pollutes 5.5 trillion cubic meters of water, accounting for more than 14% of the total runoff in the world. In China, 55.465 billion cubic meters of sewage were discharged in 2019 alone. According to the National Energy Information Platform in 2022, the industry will actively practice carbon neutralization and peak carbon requirements in sewage treatment, sludge treatment and disposal, rural sewage treatment, etc. In this context, the rapid development of sewage treatment technology and equipment has also led to many new technologies and methods [1][2][3].
In sewage transport, sewage pumps have good self-priming ability, and they are widely used to transport all kinds of domestic sewage and industrial wastewater. However, the water quality in some special areas is complicated, such as eutrophication of water in some coastal areas leading to excessive growth of algae, and there is a large amount of sediment in the water in the seasonally frozen regions of the Loess Plateau [4,5]. The fluid the pumps transport is typically a solid-liquid two-phase flow containing solid suspensions.
Pumps running under such miscellaneous conditions are prone to blockage or wear of internal components of the pump; thus affecting the normal operation of the pump [6][7][8][9]. In response to this, researchers have made many improvements to the pump model in order to improve the anti-clogging performance of the sewage pump [10][11][12][13]. At the same time, researchers have also carried out a large number of studies on the solid-liquid two-phase flow in the pump, aiming to provide a theoretical basis for improving the performance of the pump from the flow mechanism of multiphase flow.
where t is time, ρ is the fluid density, u is the fluid velocity, F is the external mass force, and τ is the viscous stress tensor, which is expressed as where p is the fluid pressure, δ ij is the unit tensor, λ = −2/3µ, and µ is the dynamic viscosity. In this study, the turbulence was described by the RANS k-ε model.

Discrete Element and Contact Model
The discrete element method (DEM), constructed by Cundall and Strack [26] as an extension of the Lagrange model method, is used to model the granular fluid, e.g., sand, powder, and slurry, which is characterized by a high particle density and significant interaction between particles. The major feature of the DEM is that the interaction between particles based on the Hertz contact theory is included in the motion equation [27]. The following Hertz-Mindlin contact model is a variation of the nonlinear spring-damper contact model [28], as shown in Figure 1a, in which the contact forces are calculated using a spring-damper system: where K is spring stiffness, d is overlapping particles, N is damping, and v is relative velocity. In addition, the subscripts n and t denote normal components and tangential components, respectively. The particles are connected by massless bonds, as shown in Figure 1b. The bonds transfer force and momentum, as well as the bonding strength between particles. The forces and moments acting on the particles are calculated as follows: M i = M n n i +M s t i (6) where M is the moment acting on the contact surface; subscript s is the shear direction component. where M is the moment acting on the contact surface; subscript s is the shear direction component.

The Fiber Model
In this study, several nonslip soft sphere models were used to represent fibers for numerical simulation. The soft sphere model overcomes the limitation of the number of particles contacted by the hard sphere model, allowing multiple particles to contact at the same time, and can describe a series of action processes from particle contact to rebound separation. Therefore, the soft sphere model has great advantages in simulating quasistatic problems [29].
The software combining the discrete element method (DEM) with the CFD can connect the soft sphere model and simulate the fiber. The particle model can be expanded into more complex (flexible) shapes or structures by using the soft sphere model connection. In the simulation, the particle cluster model was used to create groups to change the particles into complex shapes. As shown in Figure 2, the fiber model for numerical simulation in this study adopted DEM fibers formed by connecting spherical DEM particles through particle bonds [25], and the force between particles constituting fibers adopted the spring-damper model mentioned above.

Method Verification
In order to verify the established method in terms of accuracy and reliability, the numerical simulation results were compared to the visual experiments of Imasaka et al. [25]. The cross-section size of the rectangular channel was 80  80 mm, and the height of the channel was 280 mm as depicted in Figure 3. Five cylindrical rods that imitated the impeller cascade were arranged at even intervals in the water passage, and the diameter of the rods was 8 mm. A sketch of the grid division is also presented in Figure 3. The inlet boundary condition was enforced on the top of the channel with a mass flow rate of 8.318 kg/s. The free outflow boundary condition was enforced on the bottom of the channel, and the other faces were regarded as nonslip walls. The inlet Reynolds number was 1.304 × 10 5 while that defined by the rod diameter was 1.304 × 10 4 . Thus, the flow was turbulent, and the RANS k-ε model was selected in this work. Details are listed in Table 1.

The Fiber Model
In this study, several nonslip soft sphere models were used to represent fibers for numerical simulation. The soft sphere model overcomes the limitation of the number of particles contacted by the hard sphere model, allowing multiple particles to contact at the same time, and can describe a series of action processes from particle contact to rebound separation. Therefore, the soft sphere model has great advantages in simulating quasi-static problems [29].
The software combining the discrete element method (DEM) with the CFD can connect the soft sphere model and simulate the fiber. The particle model can be expanded into more complex (flexible) shapes or structures by using the soft sphere model connection. In the simulation, the particle cluster model was used to create groups to change the particles into complex shapes. As shown in Figure 2, the fiber model for numerical simulation in this study adopted DEM fibers formed by connecting spherical DEM particles through particle bonds [25], and the force between particles constituting fibers adopted the spring-damper model mentioned above.
where M is the moment acting on the contact surface; subscript s is the shear direc component.

The Fiber Model
In this study, several nonslip soft sphere models were used to represent fiber numerical simulation. The soft sphere model overcomes the limitation of the numb particles contacted by the hard sphere model, allowing multiple particles to contact a same time, and can describe a series of action processes from particle contact to rebo separation. Therefore, the soft sphere model has great advantages in simulating qu static problems [29].
The software combining the discrete element method (DEM) with the CFD can nect the soft sphere model and simulate the fiber. The particle model can be expan into more complex (flexible) shapes or structures by using the soft sphere model con tion. In the simulation, the particle cluster model was used to create groups to change particles into complex shapes. As shown in Figure 2, the fiber model for numerical si lation in this study adopted DEM fibers formed by connecting spherical DEM part through particle bonds [25], and the force between particles constituting fibers ado the spring-damper model mentioned above.

Method Verification
In order to verify the established method in terms of accuracy and reliability numerical simulation results were compared to the visual experiments of Imasaka e [25]. The cross-section size of the rectangular channel was 80  80 mm, and the heig the channel was 280 mm as depicted in Figure 3. Five cylindrical rods that imitated impeller cascade were arranged at even intervals in the water passage, and the diam of the rods was 8 mm. A sketch of the grid division is also presented in Figure 3. The boundary condition was enforced on the top of the channel with a mass flow rate of 8 kg/s. The free outflow boundary condition was enforced on the bottom of the chan and the other faces were regarded as nonslip walls. The inlet Reynolds number was 1 × 10 5 while that defined by the rod diameter was 1.304 × 10 4 . Thus, the flow was turbu and the RANS k-ε model was selected in this work. Details are listed in Table 1.

Method Verification
In order to verify the established method in terms of accuracy and reliability, the numerical simulation results were compared to the visual experiments of Imasaka et al. [25]. The cross-section size of the rectangular channel was 80 × 80 mm, and the height of the channel was 280 mm as depicted in Figure 3. Five cylindrical rods that imitated the impeller cascade were arranged at even intervals in the water passage, and the diameter of the rods was 8 mm. A sketch of the grid division is also presented in Figure 3. The inlet boundary condition was enforced on the top of the channel with a mass flow rate of 8.318 kg/s. The free outflow boundary condition was enforced on the bottom of the channel, and the other faces were regarded as nonslip walls. The inlet Reynolds number was 1.304 × 10 5 while that defined by the rod diameter was 1.304 × 10 4 . Thus, the flow was turbulent, and the RANS k-ε model was selected in this work. Details are listed in Table 1. The fiber consisted of 50 DEM particles. The diameter of the particles was 1.2 m and the size of the overlapping region is depicted in Figure 4. The density of the fiber w 1100 kg/m 3 . The Hertz-Mindlin contact model was adopted between particles, a Young's modulus was 51.7 MPa [25].

Calculation Conditions
Selection solution mode unsteady turbulence model RANS k-ε inlet boundary condition mass flow 8.318 (kg/s) outlet boundary condition static pressure 0 (Pa) time-step 1.0 × 10 −4 (s) working fluid water Figure 5 is a diagram of the simulation and experimental results of string motion a straight pipe. The position of the string at different times after entering the straight tu was recorded and compared with the experimental photos at the same time. As can seen from the contrast picture, the string only inclined when it came into contact with t cylindrical tube. Comparing the string states in (a) and (b) at the same time, it can be se that the simulation diagram simulated the motion states in the experiment very we which shows that the above calculation method was accurate and effective.  The fiber consisted of 50 DEM particles. The diameter of the particles was 1.2 mm, and the size of the overlapping region is depicted in Figure 4. The density of the fiber was 1100 kg/m 3 . The Hertz-Mindlin contact model was adopted between particles, and Young's modulus was 51.7 MPa [25]. The fiber consisted of 50 DEM particles. The diameter of the particles was 1.2 m and the size of the overlapping region is depicted in Figure 4. The density of the fiber w 1100 kg/m 3 . The Hertz-Mindlin contact model was adopted between particles, a Young's modulus was 51.7 MPa [25].     Figure 5 is a diagram of the simulation and experimental results of string motion in a straight pipe. The position of the string at different times after entering the straight tube was recorded and compared with the experimental photos at the same time. As can be seen from the contrast picture, the string only inclined when it came into contact with the cylindrical tube. Comparing the string states in (a) and (b) at the same time, it can be seen that the simulation diagram simulated the motion states in the experiment very well, which shows that the above calculation method was accurate and effective. In order to further explain the rationality and accuracy of the calculation method, quantitative analysis was carried out for this example. The fiber was injected into the fluid domain from the square center position on the straight tube. In the experiment, the fiber trajectory was recorded by a high-definition camera, and the fiber trajectory was depicted in the model. As shown in Figure 6, Yamato Imasaka depicted the trajectory of the head, tail, and middle three particles of the fiber. In the simulation calculation, three monitoring points A, B, and C were set according to the experiment, and the displacement changes of the three points on both the X-axis and the Y-axis were monitored. In order to further explain the rationality and accuracy of the calculation method, quantitative analysis was carried out for this example. The fiber was injected into the fluid domain from the square center position on the straight tube. In the experiment, the fiber trajectory was recorded by a high-definition camera, and the fiber trajectory was depicted in the model. As shown in Figure 6, Yamato Imasaka depicted the trajectory of the head, tail, and middle three particles of the fiber. In the simulation calculation, three monitoring points A, B, and C were set according to the experiment, and the displacement changes of the three points on both the X-axis and the Y-axis were monitored. The final simulation results are shown in Figure 7 below. It can be seen from the figure that points A and B were both at X = 0 at the beginning, and point C was in the negative direction of the X-axis, which means that the lower end of the fiber entered the straight tube and began to tilt. The relative position fluctuated greatly at 0.06-0.08 s, because A, B, and C touched the cylindrical obstacle rod successively at this time. At the same time, under the influence of the Karman vortex of the second cylindrical rod, the fibers began to shift to the right, and finally the fibers moved to the bottom of the flow channel. Comparing the position curves of points A, B, and C in the figure, it was observed that the simulated value of the motion state of the fiber in the straight tube was consistent with the experimental value, and the error was within 5%, indicating that the calculation method used was accurate and effective.  The final simulation results are shown in Figure 7 below. It can be seen from the figure that points A and B were both at X = 0 at the beginning, and point C was in the negative direction of the X-axis, which means that the lower end of the fiber entered the straight tube and began to tilt. The relative position fluctuated greatly at 0.06-0.08 s, because A, B, and C touched the cylindrical obstacle rod successively at this time. At the same time, under the influence of the Karman vortex of the second cylindrical rod, the fibers began to shift to the right, and finally the fibers moved to the bottom of the flow channel. Comparing the position curves of points A, B, and C in the figure, it was observed that the simulated value of the motion state of the fiber in the straight tube was consistent with the experimental value, and the error was within 5%, indicating that the calculation method used was accurate and effective. The final simulation results are shown in Figure 7 below. It can be seen from the figure that points A and B were both at X = 0 at the beginning, and point C was in the negative direction of the X-axis, which means that the lower end of the fiber entered the straight tube and began to tilt. The relative position fluctuated greatly at 0.06-0.08 s, because A, B, and C touched the cylindrical obstacle rod successively at this time. At the same time, under the influence of the Karman vortex of the second cylindrical rod, the fibers began to shift to the right, and finally the fibers moved to the bottom of the flow channel. Comparing the position curves of points A, B, and C in the figure, it was observed that the simulated value of the motion state of the fiber in the straight tube was consistent with the experimental value, and the error was within 5%, indicating that the calculation method used was accurate and effective.   Table 2 lists the basic design parameters of the model pump. According to the data in Table 2, the Reynolds number at the pump inlet was calculated to be 1.909 × 10 4 .  Figure 8 shows the model pump and computational fluid domain. Table 2 lists the basic design parameters of the model pump. According to the data in Table 2, the Reynolds number at the pump inlet was calculated to be 1.909 × 10 4 .

Grid and Boundary Conditions
The computational fluid domain was meshed by polyhedral structured mesh. The requirement that the change of the calculated head value is less than 1% was taken as the standard for grid independence verification. The grid division scheme and verification results are shown in Table 3, and the number of selected grids was 2,208,488. Figure 9 is a schematic diagram of mesh division. The CFD-DEM coupling method and RANS k-ε turbulence model were used to analyze the flow field characteristics of fiber in a sewage pump and the movement characteristics of fiber in a pump. The inlet was a mass flow inlet, the outlet condition was set as free outflow, and all walls were without a slip boundary. In this study, the time-step of fiber motion simulation was set to 1 × 10 −5 s, the total calculation time was 2 s, and the particle diameter was 1 mm; considering the calculation cost and simulation accuracy, the number of fibers flowing into the pump per second was set to 20.

Grid and Boundary Conditions
The computational fluid domain was meshed by polyhedral structured mesh. The requirement that the change of the calculated head value is less than 1% was taken as the standard for grid independence verification. The grid division scheme and verification results are shown in Table 3, and the number of selected grids was 2,208,488. Figure 9 is a schematic diagram of mesh division. The CFD-DEM coupling method and RANS k-ε turbulence model were used to analyze the flow field characteristics of fiber in a sewage pump and the movement characteristics of fiber in a pump. The inlet was a mass flow inlet, the outlet condition was set as free outflow, and all walls were without a slip boundary. In this study, the time-step of fiber motion simulation was set to 1 × 10 −5 s, the total calculation time was 2 s, and the particle diameter was 1 mm; considering the calculation cost and simulation accuracy, the number of fibers flowing into the pump per second was set to 20.

External Characteristic Experiment
Because of the complexity of the internal details of the model pump, it was difficult to measure directly. In order to ensure the accuracy and reliability of the fluid domain model established above, it was necessary to carry out external characteristic tests to verify it. The external characteristic test device is shown in Figure 10. According to the above experimental and simulation settings, eight different flow conditions were selected to carry out external characteristic experiments and simulations on the model pump. The experimental values were compared with the simulation results, and the results are shown in Figure 11 below. By comparing the simulated data with the experimental data, it was seen that the numerical simulation results were basically consistent with the experimental results, and the errors were all within 3%, so the simulation results met the calculation requirements.

External Characteristic Experiment
Because of the complexity of the internal details of the model pump, it was difficult to measure directly. In order to ensure the accuracy and reliability of the fluid domain model established above, it was necessary to carry out external characteristic tests to verify it. The external characteristic test device is shown in Figure 10.

External Characteristic Experiment
Because of the complexity of the internal details of the model pump, it was difficult to measure directly. In order to ensure the accuracy and reliability of the fluid domain model established above, it was necessary to carry out external characteristic tests to verify it. The external characteristic test device is shown in Figure 10.  Figure 11 below. By comparing the simulated data with the experimental data, it was seen that the numerical simulation results were basically consistent with the experimental results, and the errors were all within 3%, so the simulation results met the calculation requirements.  According to the above experimental and simulation settings, eight different flow conditions were selected to carry out external characteristic experiments and simulations on the model pump. The experimental values were compared with the simulation results, and the results are shown in Figure 11 below. By comparing the simulated data with the experimental data, it was seen that the numerical simulation results were basically consistent with the experimental results, and the errors were all within 3%, so the simulation results met the calculation requirements.

External Characteristic Experiment
Because of the complexity of the internal details of the model pump, it was difficult to measure directly. In order to ensure the accuracy and reliability of the fluid domain model established above, it was necessary to carry out external characteristic tests to verify it. The external characteristic test device is shown in Figure 10.  Figure 11 below. By comparing the simulated data with the experimental data, it was seen that the numerical simulation results were basically consistent with the experimental results, and the errors were all within 3%, so the simulation results met the calculation requirements.

Fiber Motion Analysis
There are many factors that affect the blockage caused by fibers in sewage pumps, such as the structure of pumps, operating conditions, fiber shape, etc. However, due to the limited time and cost of research, only the influence of flow conditions and fiber length has been discussed. Different flow conditions will change the complexity of the internal flow field. The greater the flow rate, the more obviously the fiber is affected by the fluid, and the fiber will show different flow conditions. Fiber shape is also an important factor affecting blockage. It is generally recognized that long fibers are more likely to cause blockage in pumps, but the specific clogging mechanism is difficult to know. Based on the above facts, the clogging problem of sewage pumps was studied from different flow conditions (0.8Q, Q, and 1.2Q) and different fiber lengths (80, 120, and 160 mm). Figure 12 shows the fiber distribution in the pump at 1/4T, 1/2T, 3/4T, and T times in the same cycle under three working conditions. The fiber length was set to 80 mm, and the simulation set of fiber flow rate was 20/s.

Fiber Motion Analysis
There are many factors that affect the blockage caused by fibers in sewage pumps, such as the structure of pumps, operating conditions, fiber shape, etc. However, due to the limited time and cost of research, only the influence of flow conditions and fiber length has been discussed. Different flow conditions will change the complexity of the internal flow field. The greater the flow rate, the more obviously the fiber is affected by the fluid, and the fiber will show different flow conditions. Fiber shape is also an important factor affecting blockage. It is generally recognized that long fibers are more likely to cause blockage in pumps, but the specific clogging mechanism is difficult to know. Based on the above facts, the clogging problem of sewage pumps was studied from different flow conditions (0.8Q, Q, and 1.2Q) and different fiber lengths (80, 120, and 160 mm). Figure 12 shows the fiber distribution in the pump at 1/4T, 1/2T, 3/4T, and T times in the same cycle under three working conditions. The fiber length was set to 80mm, and the simulation set of fiber flow rate was 20/s. As can be seen from the figure, fibers easily remained at the inlet of the flow channel, such as A in the figure, which was very similar to the distribution of particles in the pump [30]; the B fibers moved smoothly to the tail of the blade; under the flow rate of 0.8Q and Q, the fibers easily remained in the impeller head, such as C in the figure; when the flow rate increased to 1.2Q, the fibers did not stay at the head of the blade, but they did stay at the tongue of the volute. The above analysis of different flow rates showed the influence of flow rates on the position of fiber blockage: under a small flow rate, fibers tended to stay at the blade head; under the condition of a large flow rate, the fibers were more likely to stay at the tongue of the volute. In the condition of rated flow rate, the fiber length was changed, and the fiber trajectory was analyzed again, and the fiber lengths were selected as 80, 120, and 160 mm. Figure 13a is the diagram of fiber motion tracking with different lengths under rated flow condition. It can be seen from the diagram that no matter how the fiber length changed, there were three typical fibers: A, B, and C. When the fiber length increased, the fiber not only caused blockage at the inlet and head of the impeller, but also adhered to As can be seen from the figure, fibers easily remained at the inlet of the flow channel, such as A in the figure, which was very similar to the distribution of particles in the pump [30]; the B fibers moved smoothly to the tail of the blade; under the flow rate of 0.8Q and Q, the fibers easily remained in the impeller head, such as C in the figure; when the flow rate increased to 1.2Q, the fibers did not stay at the head of the blade, but they did stay at the tongue of the volute. The above analysis of different flow rates showed the influence of flow rates on the position of fiber blockage: under a small flow rate, fibers tended to stay at the blade head; under the condition of a large flow rate, the fibers were more likely to stay at the tongue of the volute.

Trajectory Analysis
In the condition of rated flow rate, the fiber length was changed, and the fiber trajectory was analyzed again, and the fiber lengths were selected as 80, 120, and 160 mm. Figure 13a is the diagram of fiber motion tracking with different lengths under rated flow condition. It can be seen from the diagram that no matter how the fiber length changed, there were three typical fibers: A, B, and C. When the fiber length increased, the fiber not only caused blockage at the inlet and head of the impeller, but also adhered to the middle position of the suction surface of the blade, as shown with E in Figure 14b,c. This phenomenon was quite different from the movement of particles in the pump. For particles, regardless of the flow rate, most of them are distributed on the pressure surface of the blade rather than gathering on the suction surface [30]. Through observation, it was found that although 120 and 160 mm fibers were attached to the middle of the suction surface of the blade, the attachment positions of the two fibers were still obviously different: the 120 mm fibers were closer to the tail of the blade, and the 160 mm fibers were closer to the head of the blade. In addition, because the shorter 80 mm fibers would not adhere to the leaves, it can be inferred from the position of the binding E fibers that long fibers are more likely to stay on the leaves.

Position Analysis
In order to further study the motion mechanism of the three typical fibers A, B, and C, the movement changes of the three fibers were quantitatively analyzed under suitable working conditions. Because the three kinds of fibers under the 0.8 Q were relatively small from the force of fluid, and their moving speed was slow, which was easier to distinguish on the graph, the 0.8 Q flow rate was selected for analysis. Figure 14 is a three-dimensional coordinate system established with the impeller center as the origin, and the coordinate changes of fibers represent the position changes of the fibers in the process of movement, so as to obtain the position change law of fibers. Figure 15a shows the movement position change diagram of A-type fibers in the pump; that is, fibers wandering at the impeller inlet. It can be seen from the figure that after the A-type fiber entered from the inlet, the displacement in the Z-axis direction decreased first, which showed that the A-type fibers first moved towards the center of the impeller. When moving to 15 mm on the Z-axis, the fiber began to rebound, and the displacement along the Xand Y-axes also changed abruptly, which indicated that the fiber encountered a reflux vortex at this place. After 0.2 s, the displacement along the X-, Y-, and Z-axes tended to be stable, and the displacement positions were 7, 10, and 35 mm, respectively. Therefore, it could be judged that the reflux vortex at the inlet of the impeller in the pump appeared near this position. Figure 15b shows the movement position change of B-type fibers in the pump. After entering the flow channel, B-type fibers flowed normally and moved with the rotation of the impeller, finally flowing out from the outlet. In the direction of the Xand Y-axes, the fibers changed periodically in the early stage of movement. During this period, the fibers moved with the rotation of the impeller in the impeller passage, and the peak displacement in the direction of the Xand Y-axes gradually increased, which showed that the fibers moved to the periphery and finally flowed out from the outlet. While in the direction of the Z-axis, we can see that the fiber always moved around Z = 0 mm. The normal outflow time of the fibers was about 0.13 s. particles, regardless of the flow rate, most of them are distributed on the pressure surface of the blade rather than gathering on the suction surface [30]. Through observation, it was found that although 120 and 160 mm fibers were attached to the middle of the suction surface of the blade, the attachment positions of the two fibers were still obviously different: the 120 mm fibers were closer to the tail of the blade, and the 160 mm fibers were closer to the head of the blade. In addition, because the shorter 80 mm fibers would not adhere to the leaves, it can be inferred from the position of the binding E fibers that long fibers are more likely to stay on the leaves.

Position Analysis
In order to further study the motion mechanism of the three typical fibers A, B, and C, the movement changes of the three fibers were quantitatively analyzed under suitable working conditions. Because the three kinds of fibers under the 0.8 Q were relatively small from the force of fluid, and their moving speed was slow, which was easier to distinguish on the graph, the 0.8 Q flow rate was selected for analysis. Figure 14 is a three-dimensional coordinate system established with the impeller center as the origin, and the coordinate changes of fibers represent the position changes of the fibers in the process of movement, so as to obtain the position change law of fibers.

Position Analysis
In order to further study the motion mechanism of the three typical fibers A, B, C, the movement changes of the three fibers were quantitatively analyzed under suit working conditions. Because the three kinds of fibers under the 0.8 Q were relatively sm from the force of fluid, and their moving speed was slow, which was easier to distingu on the graph, the 0.8 Q flow rate was selected for analysis. Figure 14 is a three-dimensio coordinate system established with the impeller center as the origin, and the coordin changes of fibers represent the position changes of the fibers in the process of movem so as to obtain the position change law of fibers.  Figure 15a shows the movement position change diagram of A-type fibers in pump; that is, fibers wandering at the impeller inlet. It can be seen from the figure creased, finally stabilizing at about Z = 0 mm. C-type fibers tended to move in the Z-axis neutral position after entering the flow channel, which was caused by the fast flow velocity; as can be seen from the displacement changes in the X-and Y-axes, the fibers moved to the blade head after entering the impeller, and it can be seen from the peak movement that the retention position was 34 mm away from the center point. Analysis of the diagram showed that once the fibers were caught at the blade head, it was difficult to change their motion and allow them to flow smoothly out of the pump. When analyzing the trajectory of fibers with different lengths, it was found that the length would change the position of the fibers staying in the sewage pump. In order to further analyze this phenomenon, the average position changes of different fibers were quantitatively analyzed. Figure 16 is a graph of the position of fibers with three lengths on the X-axis and the Y-axis with time. The abrupt change in the curve was due to the change in the average position of the fibers caused by the normal flow of fibers in and out of the pump. Compared with (a) and (b), it was found that the 80 mm fibers always took the lead in position change, entered the flow channel faster, and made a circular motion with the rotation of the impeller; however, the trajectories of the 120 and 160 mm fibers were very consistent before they entered the impeller passage smoothly, and they changed only after entering the impeller passage. Comparing the motion of the 120 and 160 mm fibers, it was found  Figure 15c shows the movement position change of C-type fibers in the pump. C-type fibers stayed at the blade head after entering the impeller. It can be seen from the figure that the displacement of fibers in the Z-axis direction first decreased and then increased, finally stabilizing at about Z = 0 mm. C-type fibers tended to move in the Z-axis neutral position after entering the flow channel, which was caused by the fast flow velocity; as can be seen from the displacement changes in the Xand Y-axes, the fibers moved to the blade head after entering the impeller, and it can be seen from the peak movement that the retention position was 34 mm away from the center point. Analysis of the diagram showed that once the fibers were caught at the blade head, it was difficult to change their motion and allow them to flow smoothly out of the pump.
When analyzing the trajectory of fibers with different lengths, it was found that the length would change the position of the fibers staying in the sewage pump. In order to further analyze this phenomenon, the average position changes of different fibers were quantitatively analyzed. Figure 16 is a graph of the position of fibers with three lengths on the X-axis and the Y-axis with time. The abrupt change in the curve was due to the change in the average position of the fibers caused by the normal flow of fibers in and out of the pump. Compared with (a) and (b), it was found that the 80 mm fibers always took the lead in position change, entered the flow channel faster, and made a circular motion with the rotation of the impeller; however, the trajectories of the 120 and 160 mm fibers were very consistent before they entered the impeller passage smoothly, and they changed only after entering the impeller passage. Comparing the motion of the 120 and 160 mm fibers, it was found that the circular motion time of the 160 mm fibers was longer, i.e., the smooth outflow time of the 160 mm fibers was longer, which led to a large number of fibers accumulating and forming a blockage in the pump when the fiber flow rate was too high.

Velocity Vector Analysis
The fluid medium conveyed in the fluid machinery generally has a fast flow rate, and the internal flow state is relatively complex, which will generate a large number of vortices, thereby affecting the flow stability. Since the position of the vortex could be seen intuitively from the velocity vector analysis, this section analyzes the velocity vector to obtain the relationship between the vortex and the fiber blockage. At the same time, the vorticity was analyzed in the next subsection to obtain further relevant conclusions. The reflux vortex was obviously affected by the flow rate and was hardly affected by the fiber length, so only different flow conditions were analyzed here. Figure 17 is a velocity vector diagram under different flow rates. From the diagram, it can be seen that there are a large number of backflow vortices in the pump, among which the four vortices A, B, C, and E in the diagram mainly affected the fiber movement. In Figure 17a, because of the existence of stall vortex A, fibers wandered at the impeller inlet, and long-term accumulation led to blockage at the impeller inlet; the recirculation vortex B appeared between the pressure surface of the blade and the wall of the volute, where the flow velocity along the outer direction of the volute was larger, and the fibers involved in it flowed along the inner wall of the volute; the recirculation vortex E appeared on the suction surface of the blade. Through the analysis of the fiber trajectory before, it was known that long fibers were easily caught here. With the increase of flow rate, the stall vortex A began to weaken, and the risk of fiber blockage at the impeller inlet decreased; the scope of reflux vortex B enlarged with the increase of flow rate, and it was easier to involve fibers in it. Therefore, when fibers flowed through the diaphragm tongue, they were easily stuck on the volute tongue under the action of reflux vortex B; the reflux vortex C also showed a weakening trend with the increase of flow rate, which indicated that increasing the flow rate can reduce the risk of fiber retention here.

PEER REVIEW 14 of 19
that the circular motion time of the 160 mm fibers was longer, i.e., the smooth outflow time of the 160 mm fibers was longer, which led to a large number of fibers accumulating and forming a blockage in the pump when the fiber flow rate was too high.

Velocity Vector Analysis
The fluid medium conveyed in the fluid machinery generally has a fast flow rate, and the internal flow state is relatively complex, which will generate a large number of vortices, thereby affecting the flow stability. Since the position of the vortex could be seen intuitively from the velocity vector analysis, this section analyzes the velocity vector to obtain the relationship between the vortex and the fiber blockage. At the same time, the vorticity was analyzed in the next subsection to obtain further relevant conclusions. The reflux vortex was obviously affected by the flow rate and was hardly affected by the fiber length, so only different flow conditions were analyzed here. Figure 17 is a velocity vector diagram under different flow rates. From the diagram, it can be seen that there are a large number of backflow vortices in the pump, among which the four vortices A, B, C, and E in the diagram mainly affected the fiber movement. In Figure 17a, because of the existence of stall vortex A, fibers wandered at the impeller inlet, and long-term accumulation led to blockage at the impeller inlet; the recirculation vortex B appeared between the pressure surface of the blade and the wall of the volute, where the flow velocity along the outer direction of the volute was larger, and the fibers involved in it flowed along the inner wall of the volute; the recirculation vortex E appeared on the suction surface of the blade. Through the analysis of the fiber trajectory before, it was known that long fibers were easily caught here. With the increase of flow rate, the stall vortex A began to weaken, and the risk of fiber blockage at the impeller inlet decreased; the scope of reflux vortex B enlarged with the increase of flow rate, and it was easier to involve fibers in it. Therefore, when fibers flowed through the diaphragm tongue, they were easily stuck on the volute tongue under the action of reflux vortex B; the reflux  Figure 17b is the velocity vector diagram of the XY section of the impeller. It can be seen from the diagram that there were two symmetrical reflux vortices C at the head of the suction surface of the blade head, which was one of the reasons for fiber adsorption onto the suction surface of blade.

Vorticity Analysis
In order to further study the relationship between vortex and fiber blockage in the pump, this section quantitatively analyzes it by vorticity. Figure 18 is a vorticity diagram under different flow rates. It can be seen from Figure 18b that with the continuous increase of flow rate, the overall vorticity intensity in the pump began to weaken gradually, but there were still several regions with strong vorticity. From the analysis of Figure 18a, it can be seen that after the fluid medium entered from the inlet, it experienced the first obvious vorticity change in region A, that is, the place where the stall vortex exists in the upper section, so fiber blockage easily occurred. Secondly, region E and region B were the tail of the suction surface of the blade and the tongue of the volute, respectively, and there was also a strong vortex, which easily trapped fibers in it. From the analysis in Figure 18b, it is obvious that there was a very strong vortex at the head of the suction surface of the blade, which easily involved fibers. This was also the reason why fibers stayed on the suction surface of the blades. In addition, by comparing the vorticity in region C under different flow rates, it was clearly observed that with the increase of flow rate, the range of region C began to decrease. It can be seen from the above analysis that increased flow rate can alleviate the fiber blockage in region C, which is basically consistent with Zhang et al. [31].

Vorticity Analysis
In order to further study the relationship between vortex and fiber blockage in the pump, this section quantitatively analyzes it by vorticity. Figure 18 is a vorticity diagram under different flow rates. It can be seen from Figure 18b that with the continuous increase of flow rate, the overall vorticity intensity in the pump began to weaken gradually, but there were still several regions with strong vorticity. From the analysis of Figure 18a, it can be seen that after the fluid medium entered from the inlet, it experienced the first obvious vorticity change in region A, that is, the place where the stall vortex exists in the upper section, so fiber blockage easily occurred. Secondly, region E and region B were the tail of the suction surface of the blade and the tongue of the volute, respectively, and there was also a strong vortex, which easily trapped fibers in it. From the analysis in Figure 18b, it is obvious that there was a very strong vortex at the head of the suction surface of the blade, which easily involved fibers. This was also the reason why fibers stayed on the suction surface of the blades. In addition, by comparing the vorticity in region C under different flow rates, it was clearly observed that with the increase of flow rate, the range of region C began to decrease. It can be seen from the above analysis that increased flow rate can alleviate the fiber blockage in region C, which is basically consistent with Zhang et al. [31].

Pressure Fluctuation Analysis
In order to further analyze the characteristics of vortex generation in the internal flow field, pressure fluctuations at detection points were analyzed. Since pressure was only slightly affected by changes in fiber length, only the effect of different flow rates was discussed. Figure 19 shows the distribution of monitoring points, set to P1, P2, P3, and P4.
The pressure fluctuation diagrams of monitoring points under different flow conditions were compared transversely, as illustrated in Figure 20. The pressure fluctuation amplitude of P1, P3, and P4 decreased with the increase of flow rate, while that of P2 increased. The pressure fluctuation amplitude of P2 nearly doubled from small flow to rated flow. At P1, the pressure fluctuation amplitude was relatively small due to the accumulation and development of bubbles at the tongue where the fluid was impacted. The stall vortex development and fusion at P2 reached the maximum, and the flow was the most disordered at this time, resulting in a large pressure pulsation. At P3, the pressure fluctuation amplitude under small flow condition was larger than that at P2, and with the increase of flow, the amplitude of the pressure pulsation was smaller than that at P2 because the stall vortex area was larger under the small flow condition and moved in the opposite direction of the impeller. Under the rated flow and large flow, the stall vortex did not change greatly with the increase of flow. It was the largest at P2 and gradually decreased along the opposite direction of the impeller rotation. Therefore, the flow also tended to stabilize from disorder, and the pressure on the volute wall gradually decreased.

Pressure Fluctuation Analysis
In order to further analyze the characteristics of vortex generation in the internal flow field, pressure fluctuations at detection points were analyzed. Since pressure was only slightly affected by changes in fiber length, only the effect of different flow rates was discussed. Figure 19 shows the distribution of monitoring points, set to P1, P2, P3, and P4.

Pressure Fluctuation Analysis
In order to further analyze the characteristics of vortex generation in the internal flow field, pressure fluctuations at detection points were analyzed. Since pressure was only slightly affected by changes in fiber length, only the effect of different flow rates was discussed. Figure 19 shows the distribution of monitoring points, set to P1, P2, P3, and P4.  increase of flow, the amplitude of the pressure pulsation was smaller than that at P2 because the stall vortex area was larger under the small flow condition and moved in the opposite direction of the impeller. Under the rated flow and large flow, the stall vortex did not change greatly with the increase of flow. It was the largest at P2 and gradually decreased along the opposite direction of the impeller rotation. Therefore, the flow also tended to stabilize from disorder, and the pressure on the volute wall gradually decreased.

Conclusions
At present, most of the solid-liquid two-phase flow in sewage pumps is based on solid particles, but less research has been done based on fibers. In this study, in order to

Conclusions
At present, most of the solid-liquid two-phase flow in sewage pumps is based on solid particles, but less research has been done based on fibers. In this study, in order to better study the effect of fiber impurities on the clogging mechanism of sewage pumps, the CFD-DEM coupling method was used to study the motion characteristics of fiber impurities in self-priming sewage pumps. Specifically, after a reasonable verification, this study simulated and compared the fiber motion by changing the flow rates and fiber length at first, and then analyzed and summarized the fiber motion characteristics and flow field motion characteristics obtained by the simulation. The main conclusions were as follows:

•
Influence of flow rate on the movement of fiber in the pump: under the condition of small flow rate, fiber was easily caught at the impeller inlet and blade head, which caused blockage; under large flow conditions, fibers were easily trapped at the impeller inlet and wound up at the volute tongue; • The influence of fiber length on the movement characteristics of the pump: First, the long fiber more readily adhered to the suction surface of the blade. Second, it took longer to flow out from the pump, which made it more likely to cause fiber accumulation and blockage in the pump; • Vortex in flow field could easily cause fiber clogging, and the main positions were at the impeller inlet, the blade head, and the middle of the blade suction surface. Concerning the position of the vortex, the vortex at the impeller inlet was the place where fiber was most easily blocked; • From the analysis of vorticity intensity, it was seen that the vorticity intensity at the inlet of the impeller, the suction surface of the blade, and the volute tongue was large, which made the vorticity more likely to cause fiber blockage. However, with the increase of flow rate, the vorticity in some regions began to decrease.