1. 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.
At present, researchers have done a lot of research on the solid–liquid two-phase flow of pumps. Sha et al. [
14] divided the energy consumption caused by the internal resistance of the vortex pump into two parts, i.e., mechanical loss and hydraulic loss, in order to study the hydraulic conveying characteristics of the solid–liquid two-phase flow vortex pump. At the same time, the performance tests of water, rapeseed, wheat, and soybean hydraulic transport were carried out on the vortex pump. Tan et al. [
15] used high-speed photography technology to track the motion law of single particles in the solid–liquid two-phase flow of coarse particles in a double-paddle pump and analyzed the influence of particle size and particle density on the passing and collision characteristics of particles. Wang et al. [
16] used experimental methods to study the effect of different coating thicknesses on the operating characteristics of sand-containing solid–liquid two-phase flow centrifugal pumps.
With the development of numerical simulation technology in the study of solid–liquid two-phase flow, the combination of computational fluid dynamics (CFD) and discrete element method (DEM) has been greatly developed and applied. Because the CFD–DEM coupling method can simulate particle suspension efficiently and conveniently, it has become the most promising numerical simulation method in the field of solid–liquid two-phase flow research and has been applied by a large number of researchers [
17,
18]. Hu et al. [
19] studied the solid–liquid two-phase flow of particles with different particle sizes in a two-stage centrifugal pump by CFD–DEM coupling method. It was found that larger particles with particle sizes ranging from 10 to 30 mm could maintain better reflux performance. Li et al. [
20] simulated solid–liquid two-phase flow in a centrifugal pump by CFD–DEM coupling method and carried out two-phase performance and wear tests under different flow rates and particle concentrations. The results showed that the instantaneous wear rates of the impeller, volute, and wear plate in the pump changed periodically with the rotation of the impeller. Deng et al. [
21] obtained the transport characteristic curve, particle transport characteristics, and distribution characteristics of slurry in a six-stage centrifugal pump by CFD–DEM simulation. The simulation method was verified by experimental data. It was found that the particle transport in the diffuser was nonuniform, the particle transport in the diffuser was in unit of strands, and the particle transport in the pump was in pulse mode, and the particle transport characteristics in the latter stage were similar to those in the previous stage. Tang et al. [
22] considered the movement characteristics of particles and simulated the solid–liquid flow in a single-channel pump by CFD–DEM coupling method. The results showed that the smaller the particles, the wider the velocity distribution range and peak value; the larger the particle, the greater the contact force.
A number of particle-based two-phase flow mechanism conclusions can be drawn from the above studies. However, the fluid medium conveyed by the sewage pump has complex impurity conditions and a wide variety of solid impurities. In addition to the usual particulate matter, it also carries a large number of fibrous impurities, which have a great impact on the pump. In recent years, with the development of CFD technology, the CFD–DEM method has been applied to fiber flow. Guo et al. [
23] established a flexible fiber model based on the discrete element method (DEM) and Cundall’s bonded particle model, considering the bending, tensile, and torsional conditions of fibers under static load and dynamic vibration. Sulaiman et al. [
24] established a fiber model consisting of a group of spherical beads. The transport, deformation, and buckling events of isolated elastic fibers in the Taylor–Green vortex were numerically studied, and the dynamic characteristics of filaments in uniform isotropic turbulence were studied. Imasaka et al. [
25] used the CFD–DEM coupling, motion capture, and PIV methods to study the clogging mechanism of flexible fibers in pumps. The results showed that the fiber motion simulated by this method is accurate and effective.
As shown by the above research results, many scholars have studied the effect of particles in sewage pumps, but there is not enough theory about the effect of fibers in pumps. The present work studied the influence of different flow rates and fiber lengths on the fiber clogging mechanism, which is relatively basic but has not been reported. This study adopted the following methods to carry out further research: the fiber model was established by means of the CFD–DEM coupling method. Then the numerical simulation calculation was carried out and the calculation results were compared with the visualization experiment of Imasaka [
25] to verify its feasibility. By changing the factors of sewage pump flow and fiber length, the transport mechanism of fibers, fiber motion characteristics, and flow field characteristics were explored. This research could provide theoretical support for the development of a sewage pump suitable for fiber suspension flow.
4. 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).
4.1. Trajectory Analysis
Figure 12 shows the fiber distribution in the pump at 1/4
T, 1/2
T, 3/4
T, 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.
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 0.8
Q and
Q, the fibers easily remained in the impeller head, such as C in the figure; when the flow rate increased to 1.2
Q, 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 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.
4.2. 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
X- and
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
X- and
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
X- and
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.
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
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 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.
4.3. 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.
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.
4.4. 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].
4.5. 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.