Effect of Pipe Wall Wear Defects on the Flow Characteristics of Slurry Shield Discharge Pipe

Abstract

During slurry shield tunneling in hard rock or cobble strata, the discharge pipes suffer serve wear and damage. However, the effect mechanism of pipe wall wear defects on the flow characteristics of two-phase flow is unclear. In this study, a three-dimensional slurry particle model of pipeline transport was established using the coupled computational fluid dynamics–discrete element method (CFD-DEM) considering the pipe wall wear defect, and the typical pipeline forms of straight pipe and 90° elbow pipe were selected as the research targets. The results indicated that the localized wear defect of pipes can lead to increased inhomogeneity in the velocity distribution, generating localized low-flow zones and resulting in a reduced flow rate or stagnancy in parts of the pipe. Meanwhile, the wear defect of the pipe results in local shape changes, so that the fluid flow path through the pipe is no longer smooth, causing more vortex/turbulence and secondary flow, where an increased vortex promotes localized kinetic energy reduction and creates larger pressure losses at the elbow. In addition, for the elbow pipe without wear defect, the pressure drop of the elbow increases quadratically from an increase of 6.5% to an increase of 16.9%, with the maximum wear depth increasing from 4 mm to 19 mm. For the straight pipe without wear defect, the pressure drop of the elbow increases linearly, from an increase of 2.2% to an increase of 10.2% with the maximum wear depth increasing from 4 mm to 19 mm. The paper investigates the potential mechanism of pipe flow characteristics influenced by wear defect and provides practical guidelines for the efficient operation of a slurry shield circulating system.

1. Introduction

Exploring underground spaces on a large scale is crucial for accelerating urban development and fostering sustainable economic growth [1]. Recently, there has been a surge in underground projects globally [2]. The slurry pressure balance shield machine (SPB shield machine), a fully mechanized tunneling technique, combines soil cutting, soil discharging, lining, and deviation correction [3]. Its high efficiency and safety make it widely used in constructing subway, highway, and railway tunnels, particularly in cross-river and underwater projects [4]. During the tunneling process with a SPB shield machine, fresh bentonite slurry is introduced into the excavation chamber in stages through feed pipelines to manage soil and water pressure at the tunnel face. Concurrently, large quantities of muck are transported to the surface through discharge pipelines, where they are screened and filtered, allowing for the recycling of the bentonite slurry. Accordingly, slurry pipelining plays essential roles in safe and efficient slurry shield tunneling [5].

However, the pipe wall will suffer severe damage and wear due to the impact and interaction between the rock chip particles and the pipe wall during shield tunneling in hard rock or cobble strata, resulting in the worn failure of the pipe wall (see Figure 1a,b) [6]. On the one hand, the leaked pipe wall will eventually lead to slurry leakage (see Figure 1c), resulting in slurry TBM breakdown and reducing the construction efficiency. On the other hand, the wear and damage of the pipe will change the internal cross-sectional shape of the pipe from a circular cross-section to an irregular shape. This localized cross-sectional change affects the flow characteristics of the slurry, as well as the rock chip particles movement properties.

To date, pipe wear has always been a hot topic in hydraulic transport, and numerous investigations have been carried out on the wear behavior of pipes using numerical modeling [7] and field test [8]. Fang et al. [9] investigated the wear- and vibration-induced failure of slurry discharge pipes. Through field data and computational fluid dynamics–discrete element method (CFD-DEM) simulations, the wear patterns were identified and an early warning system for detecting pipe wear was proposed, with elbow joints being particularly vulnerable to fatigue damage and leakage. Li et al. [10] presented a model to predict the pipe wear caused by collision and contact of large-sized slag particles by means of direct and indirect in situ observations. The results indicated that the observed wear rates in different types of ground had varied constants, and the wear rates were higher for pipes in rock ground than for those in a pebble layer. Su and Zhang [11] examined the premature wear and leakage in an adsorbent transport pipeline after a 30° elbow. And the surface morphology analysis and CFD simulations were employed to determine that erosive wear caused by adsorbent particles was the main factor, resulting in pipeline thinning and eventual perforation, particularly on the upper wall. Wang et al. [12] investigated the wear characteristics of a pipeline transporting cemented paste backfill containing coarse aggregates, and a power–law relationship was found between the wear rate and both flow velocity and coarse aggregate size, while mechanical wear was identified as the primary contributor to overall wear, especially at higher flow velocities. Yu et al. [13] predicted gas–solid erosion wear on bionic surfaces using machine learning, with support vector regression as the most accurate model, and improved Harris’s hawks optimization was integrated to enhance erosion prediction under varying conditions like particle size, velocity, and impact angle.

Furthermore, numerous research studies have also been conducted on pipeline flow characteristics using model test and numerical simulation, including the pipeline pressure drop [14], particle trajectory mode [15], particle critical velocity, etc. Xu et al. [16] investigated the laws of pipeline pressure loss during the transportation of large-size gangue slurry and optimal gangue slurry ratios were determined through experiments, and it was found that factors such as mass concentration, flow velocity, and particle size significantly influenced the pressure loss in both straight and bent pipe sections. Li et al. [17] examined the hydraulic transport of non-spherical particles in a vertical–bend–horizontal pipeline using a CFD-DEM simulation. Lower particle sphericity was found to increase velocity, reduce fluid flow, and intensify wall erosion, particularly at the elbow. Qiu et al. [18] investigated the impact of particle shape on clogging behavior in fluid-driven flows through pipelines using a coupled CFD-DEM simulation, and found that irregular particles significantly influenced clogging due to sieving, locking, and friction mechanisms, which led to the formation of clogging arches and increased porosity in the filter cake. Wan et al. [19] investigated the pressure drop in a solid–liquid two-phase pipe flow for deep-sea mining using machine learning techniques, and an ensemble algorithm was developed to accurately predict the pressure drop based on variables such as particle concentration, diameter, and flow velocity, outperforming traditional models.

As mentioned above, the existing investigations on pipe wear mainly focus on the analysis of the wear distribution characteristics and the prediction of the pipeline wear amount. The objective of this study is to investigate the effect mechanism of pipe wall wear defects on flow characteristics of slurry particle flow. In this study, a three-dimensional slurry–particle model of pipeline transport was established using the coupled CFD-DEM method considering the pipe wall wear defect, and the typical pipeline form of a straight pipe and a 90° elbow pipe were selected as the research targets. Comparing the pipe without wear defect, the effect of pipe wall wear defect on the pressure drop, flow trajectory, and particle critical velocity was revealed, respectively. The paper investigates the potential mechanism of pipe flow characteristics influenced by wear defect and provides practical guidelines for the efficient operation of slurry shield circulating systems.

2. Description of the Wear Pattern of Pipes

2.1. Wear Pattern of Straight Pipe

During slurry shield tunneling in hard rock or cobble stratum, large-diameter rock or cobble particles sink to the bottom of the pipe due to gravity, continuously rubbing and impacting the pipe wall. Due to their larger mass, these particles exert relatively greater impact forces on the pipe wall, leading to more severe wear at the bottom of the pipe. According to the investigation of Li et al. [10], a significant amount of wear occurred within the lower half of the pipe, which can be described by a central angle of 120° (see Figure 2a), the wear amount prediction model was proposed based on a field test (see Figure 2b), and the relationship between the maximum wear amount and the wear amount at any polar angle θ was given in Equation (1).

$$\delta ={\delta }_{\max }{\displaystyle \frac{\cos \alpha +\sin \theta }{\cos \alpha +1}}\cos ({\displaystyle \frac{3\pi }{2}}-\theta )$$

(1)

where δ is the wear depth of the pipe wall, δ_max is the maximum wear depth of the pipe wall, and α is the central angle. Figure 3 describes the microstructures and morphologies of worn straight pipe. As indicated in Figure 3, SEM image at a scale bar of 50 μm reveals the obvious scratches on the surface of the worn straight pipe wall. These are caused by the small angle of impact between the rock particles and the wall of the pipe.

2.2. Wear Pattern of 90° Elbow Pipe

A 90° elbow is a common structure in piping systems, especially when transporting media containing rock or cobble particles, such as slurry and rock. The wear issue is particularly severe in these cases. The most significant wear occurs on the outer side of the elbow, where the radius of curvature is largest. This is because, as the fluid passes through the elbow, rock or cobble particles tend to continue in their original direction due to inertia, causing them to collide with the outer side of the elbow. This inertial impact is especially pronounced for large rock or cobble particles, leading to concentrated wear in the outer region. Additionally, as the fluid flows through the 90° elbow, its flow pattern changes, often resulting in turbulence. This flow instability causes irregular particle motion inside the elbow, particularly on the outer side, where turbulence and vortices increase particle-wall collisions, further intensifying elbow wear. As indicated in the study of Fang et al. [9], both the CFD-DEM outcomes and field results demonstrate that the maximum wear location is located at the initial position of the 90° elbow pipe, with a central angle of approximately 3°, and the wear distribution of 90° elbow during transporting large rock or cobble particles was revealed. Figure 4 describes the microstructures and morphologies of worn 90° elbow pipe. As indicated in Figure 4, SEM image at a scale bar of 50 μm reveals the obvious dent on the surface of the worn 90° elbow pipe wall. This is caused by the direct impact (the impact angle is close to vertical) between the rock particles and the wall of the pipe.

3. CFD-DEM Modeling

The coupled CFD-DEM simulations were performed via two commercial software packages: ANSYS FLUENT 2021 for simulating the slurry flow and EDEM for simulating the slag particle migration. The following operation sequence was performed:

(1)

Initializing fluid domain (including velocities, pressures, etc.) via CFD solver;

(2)

Initializing particle domain (including interaction forces, mass flow rate, and volume fraction) via DEM solver;

(3)

Particle domain volume fraction and initial interaction information on the DEM solver and transferred to the CFD solver;

(4)

CFD solver time step correction to obtain an integral multiple of the DEM solver time step;

(5)

One CFD solution time step and n DEM solution time steps are executed in parallel;

(6)

Interaction information (DEM cell-averaged values), such as interaction forces, solid phase volume fraction, solid phase velocity transfer from the DEM solver to the CFD solver;

(7)

Velocity, pressure, and physical properties for each mesh cell (CFD primary phase values) are transferred from the CFD solver to the DEM solver;

(8)

Repeating the process until the total simulation time is terminated. It was noted that when any of the modules (CFD or DEM) reaches a set termination condition (CFD is the same as DEM), the whole coupled simulation terminates. This means that after CFD reaches t_final, the DEM computation also stops, although it has not yet reached t_final.

3.1. CFD Simulation

In CFD simulations, slurry is treated as a uniform fluid phase. Consequently, the flow process of the slurry adheres to the principles of mass conservation and momentum conservation [20]. The rheological properties of slurry is better represented by the Herschel–Bulkley (H-B) model [21]. In this study, the H-B model was employed to characterize the rheological properties of slurry. And the constitutive equations were given as follow. And the rheological parameters were measured by a rheometer, and the experimental device and results were indicated in Figure 5. It was noted that the fitted results under low and high shear rates were not particularly satisfactory. But on the whole, the regression coefficient R² was higher than 0.98, and the H-B fitted parameters can provide an accurate description for slurry rheology.

$$\tau ={\tau }_0+k{\dot{\gamma }}^n (\left|\tau \right|>{\tau }_0)$$

(2)

$$\dot{\gamma }=0 (\left|\tau \right|\le {\tau }_0)$$

(3)

where $\dot{\gamma }$ is the shear rate, τ is the shear stress, τ₀ is the yield stress, k is the viscosity coefficient, and n is power law index.

The slurry–particle two-phase flow within the discharge pipeline is a typical turbulent flow. The k-ε turbulence model, developed by Launder and Spalding [22], was widely applied in engineering fields because of its reliability, strong convergence properties, and low memory demand. Furthermore, as reported by Yang et al. [23], the k-ε model more accurately captures the turbulent characteristics of slurry–rock flow. Thus, it was used in our study to simulate the turbulence behavior.

3.2. DEM Simulation

The large rock/cobble particles within the pipe are represented as the solid phase; they are subject to interactions with the slurry, pipe wall, and other particles. Their movement and interactions can be described by Newton’s second law using DEM [24].

In the discharge pipe, the shape and size of particles larger than 20 mm are critical for simulation. To accurately represent the true characteristics of these pebbles in DEM, 3D scanning was performed on randomly sampled typical rocks to create corresponding digital geometric models, as shown in Figure 6. For slag particles smaller than 20 mm, they can be simplified as spherical particles. In addition, the Hertz–Mindlin no-slip model was employed to characterize the contact behavior between particles and pipe wall and the other particles [25], which has been widely used to describe the interactions between the particles during slurry transporting [9].

3.3. Fluid-Particle Interaction

The interaction forces between rock particles and bentonite slurry mainly consists of the buoyancy force F_b, the drag force F_d [26], and the pressure gradient force F_p, which are given as follows:

$${\mathit{F}}_b=-{\displaystyle \frac{{\rho }_f}{{\rho }_p}}\mathit{g}$$

(4)

$${\mathit{F}}_d={\displaystyle \frac{18\mu }{{\rho }_p{d}_V^2}}{\displaystyle \frac{C_{D}R{e}_p}{24}}({\mathit{U}}_f-{\mathit{U}}_p)$$

(5)

$${\mathit{F}}_p=-{\displaystyle \frac{1}{{\rho }_p}}\nabla p_f$$

(6)

where ρ_f is the fluid phase density, U_f is the velocity vector of fluid phase, U_p is the velocity vector of particle phase, ρ_p is the particle density, d_V is the diameter of the volume-equivalent sphere, μ is the fluid viscosity, p_f is pressure of fluid phase, Re_p is the particle Reynolds number, g is the gravity acceleration, and C_D is the drag coefficient that can be calculated as below:

$$C_D=a_1+{\displaystyle \frac{a_2}{Re}}+{\displaystyle \frac{a_3}{R{e}^2}}$$

(7)

where Re is the fluid Reynolds number; a₁, a₂, a₃ are constants as indicated by Morsi and Alexander [27], as below:

$$a_1,a_2,a_3=\left\{\begin{array}{ll}0,24,0& 0<Re<0.1\\ 3.690,22,0.0903& 0.1<Re<1\\ 1.222,29.1667,-3.8889& 1<Re<10\\ 0.6167,46.50,-116.67& 10<Re<100\\ 0.3644,98.33,-2778& 100<Re<1000\\ 0.357,148.62,-47500& 1000<Re<5000\\ 0.46,-490.546,578700& 5000<Re<10000\\ 0.5191,-1662.5,5416700& Re\ge 10000\end{array}\right.$$

(8)

3.4. Boundary Conditions

As shown in Figure 7, the coupled CFD-DEM models considering the wear defect were established to investigate the effect of wear defect on the pipe flow characteristics, and the pipe diameter was 500 mm. For straight pipe, the length of the pipe was 5 m, and the wear defect was considered according to the study of Li et al. [10]. For the 90° elbow pipe, the wear defect was considered according to the study of Fang et al. [9]. The maximum wear amount was set 19 mm (pipe wall thickness of 20 mm). The inlet was set as a mass flow inlet (191 kg/s), and the outlet was set as a pressure outlet, which was equivalent to the default outlet connecting with atmospheric pressure. In the literature, there are models assuming boundary of slip condition [28] or non-slip condition [5]. Compared to slip boundary conditions, non-slip boundary conditions can improve the stability of numerical computation and the accuracy of the simulation results. In the simulation process, if slip boundary conditions are used, it may lead to instability or dispersion of the numerical solution, especially when dealing with complex multi-phase flow problems. In this study, the wall boundary was regarded as a non-slip wall, which can describe the bentonite slurry flow well. In addition, the nodes and elements number of fluid mesh are given in

Table 1. Fluid mesh information.

Pipe Type	Elements Number	Nodes Number
Straight pipe with wear defect	35,743	190,567
90° elbow pipe with wear defect	33,480	177,886
Straight pipe without wear defect	9349	48,920
90° elbow pipe without wear defect	6155	32,045

. Within the DEM model, the pipe wall geometric model was established via rigid wall elements, which is complementary to the fluid domain mesh. And a circular particle factory was created at the pipe inlet to produce particles of different sizes and shapes.

According to Tsuji et al. [29], the time step of a fluid phase can be 10–100 times the time step of the particle phase. In this study, the fluid time step was set to 0.001 s, and the particle time step was set to 1 × 10⁻⁵ s. The data are automatically saved every 0.05 s during the 3 s-long simulation, and the detailed simulation parameter settings are given in

Table 2. Parameter settings in the CFD-DEM coupling simulation.

Parameters	Value
Fluid density (kg/m3)	1150
Yield stress of fluid (Pa)	4.598
Viscosity coefficient of fluid (Pa·sn)	0.886
Power law index of fluid	0.654
Particle density (kg/m3)	2500
Poisson ratio of particle	0.13
Shear modulus of particle (Pa)	2.212 × 1010
Pipe wall density (kg/m3)	7800
Poisson ratio of pipe wall	0.25
Shear modulus of pipe wall (Pa)	8 × 1010
Particle–particle static friction coefficient	0.35
Particle–particle rolling friction coefficient	0.01
Particle–pipe wall static friction coefficient	0.35
Particle–pipe wall rolling friction coefficient	0.01
Coefficient of restitution	0.05

.

4. Results and Analysis

4.1. Effect of Wear Defect on the Flow Characteristics of 90° Elbow Pipe

The velocity and dynamic pressure of slurry phase can directly reflect the flow ability and muck carrying capacity of the discharge pipe. Figure 8 demonstrates the comparisons of velocity and dynamic pressure distribution between the 90° elbow pipe with or without wear defect. It can be observed that there is no significant difference in the velocity field distribution in front of the elbow (see the comparison of section 1-1). In the vicinity of the 90° elbow (2-2 section), the area of low velocity zone (less than 3 m/s) of the elbow with wear defect only covers about 15% of the total cross-section area. However, the area of low velocity zone of the elbow with wear defect covers about 35% of the total cross-section area, and the area of low velocity zone of the elbow with wear defect is obviously larger compared to that of the elbow without wear defect (see the comparison of section 2-2). This indicates that the localized wear defect of the elbow can lead to increased inhomogeneity in the velocity distribution, generating localized low-flow zones, and resulting in a reduced flow rate or stagnancy in parts of the elbow. From the perspective of dynamic pressure comparisons, it is similar to the law of velocity distribution, and the area of the low dynamic pressure zone (less than 8750 Pa) elbow with wear defect is obviously larger compared to that of the elbow without wear defect (see the comparison of section 2-2). This is caused by the wear defect of the elbow resulting in local shape changes, so the fluid flow path through the elbow is no longer smooth, resulting in greater flow resistance.

To further investigate the key flow field characteristics of the 90° elbow pipe with or without wear defect, the flowing paths of slurry phase were given in Figure 9. It can be found that there is an obvious low velocity zone in the local area of the elbow with wear defect, and the fluid flow path is no longer smooth where elbow wear is the largest. As a result, the wear defect can cause more vortex/turbulence and secondary flow as the fluid flows through the elbow, especially in areas of high wear amount, where increased vortex promotes localized kinetic energy reduction and creates larger pressure losses at the elbow.

The particle migration trajectory can also reflect the flow characteristics of pipe. Figure 10 indicates the comparisons of particle migration trajectories between pipe with or without wear defect. It can be found that the slag moves along the outer wall of the pipe as it passes through the elbow for both the elbow pipes with or without wear defect. Compared with previously published research [9], a similar particle pattern can be observed. However, the number of particles passing through the elbow with wear defect is slightly less than the number of particles passing through the elbow without wear defect due to the lower slurry velocity in the elbow with wear defect compared to that in the elbow without wear defect, indicating that the elbow with wear defect leads to a certain degree of clogging and stagnation of the particles. It was noted that since the differences in Figure 10 are not obvious and intuitive, and the velocities of particles of different sizes were counted. Figure 11 shows the numbers of different sized particles at different velocities (representing the magnitude of velocity, that is, the square-root of the sum of squares of each component). It can be found that for the elbow pipe with wear defect, the velocities of irregular particles are mainly concentrated around 2.0 m/s, and the number of particles with velocities greater than 2.2 m/s is higher than the number of particles with velocities greater than 2.2 m/s in the elbow pipe without wear defect. For spherical particles (smaller than 20 mm), their velocities are mainly concentrated around 2.3 m/s, and similarly to irregular particles, the number of spherical particles with velocities greater than 2.5 m/s in the elbow with wear defect is higher than the number of particles with velocities greater than 2.5 m/s in the elbow pipe without wear defect. Accordingly, the elbow pipe wear defect will cause a decrease in the velocity of particles passing through the elbows, which is more pronounced with large-sized irregular particles, increasing the potential risk of elbow blockage and clogging.

Figure 12 indicates the mass flow rate of particles passing through the elbow with/without wear defect, and the detailed monitoring location is also given in Figure 12. For the elbow pipe without wear defect, the stable value (final value) of the mass flow rate is slightly higher than the stable value of mass flow rate for the elbow pipe with wear defect. It was noted that there are some transient flows, leading to the mass flow rate changing from zero to the final value.

The pressure drop is also key index for evaluating the flow characteristics of pipes. Figure 13 shows the effect of maximum wear depth on the pressure drop of elbow pipe. For the elbow pipe without wear defect, the pressure drop is approximately 3021 Pa, and with the maximum wear depth increasing from 4 mm to 19 mm, the pressure drop of the elbow increases quadratically, from an increase of 6.5% to an increase of 16.9%, and the quadratic relationship between the maximum wear depth and the pressure drop of the elbow pipe is given as Equation (9):

$$P_e=1.09{\delta }_{\max }^2-4.88{\delta }_{\max }+3223.6$$

(9)

where the P_e is the pressure drop of the elbow pipe. It is noted that Equation (9) is limited to one pipe diameter of 500 mm, which is due to the fact the commonly used diameter of the slurry discharge pipeline of the slurry shield is 500 mm, which is the result of a comprehensive consideration of pumping capacity, screening capacity, and shield advancing capacity. The increase in pressure loss is due to local shape changes caused by elbow wear defects, so that the fluid flow path through the elbow is no longer smooth, resulting in greater flow resistance. Meanwhile, in the wear of the local area, the increase in vortex means that the local kinetic energy is rapidly lost to internal energy, resulting in increased pressure loss. In order to maintain continuous and stable pipeline transportation, the multi-stage centrifugal pump systems need to provide higher pumping pressures, and frequent pressure fluctuations and increased resistance result in increased centrifugal pump maintenance requirements.

4.2. Effect of Wear Defect on the Flow Characteristics of Straight Pipe

Figure 14 compares the velocity and dynamic pressure distributions between straight pipes with/without wear defect. It can be found that the difference in velocity distribution within the pipe is more pronounced in the vicinity of the inlet (section 1-1), and the velocity (3.0 m/s) within the straight pipe with wear defect is slightly lower than that (3.5 m/s) within the straight pipe without wear defect. In the vicinity of the straight pipe outlet, the difference in velocity distribution within the center of the pipe (section 2-2) is not obvious, and only near the edge of the pipe wall, the velocity in the pipe with wear defects is just slightly lower than the velocity in the pipe without wear defects. This is due to the fact that the cross-section A of pipe with wear defect is larger than that of pipe without wear defect, resulting in a lower velocity (v = Q/A) within the pipe with wear defect under the same flow rate, Q. From the perspective of differences in dynamic pressure distribution, it can be concluded that the dynamic pressure on the upper and lower sides of the normal straight pipe is approximately symmetrical along the central axis of the pipe. However, the dynamic pressure distribution within the pipe with wear defect is uneven and irregular, which is due to the fact that the wear is mainly concentrated at the bottom of the pipe, and the internal cross-section of the pipe will no longer be a regular circle but a slightly elliptical shape. This asymmetry causes the fluid flow inside the pipe to become uneven, with typical turbulence is generated at localized locations.

Figure 15 indicates the particles migration trajectories of the straight pipe with/without wear defect. It can be seen that the average velocity (about 2.8 m/s, color in brown) of suspended particles within the straight pipe with wear defect is slightly lower than that (about 3.1 m/s, color in red) of suspended particles within the normal straight pipe. And the numbers of spherical and irregular particles deposited on the bottom of the worn pipe is also higher than the number of spherical and irregular particles deposited on the bottom of the normal pipe, as indicated in Figure 16. This is due to the fact that wear at the bottom of the pipe will generate an area similar to a groove, which results in a further reduction in the velocity of the slurry in the bottom area (v = Q/A, for the same flow rate Q, the larger the cross-sectional area A, the smaller the slurry velocity v). The reduced velocity makes it easier for large particles to be deposited and accumulated. Once the particles are deposited in the bottom wear zone, it is difficult for the particles to be carried forward by the slurry due to the reduced velocity, leading to an accumulation of particles at the bottom of the pipe, further increasing the risk of clogging.

Figure 17 indicates the mass flow rate of particles passing through the straight pipe with/without wear defect, and the detailed monitoring location is also given in Figure 17. For the straight pipe without wear defect, the stable value (final value) of mass flow rate is slightly higher than the stable value of mass flow rate for the elbow pipe with wear defect, which is similar to the rule of the elbow pipe.

Figure 18 shows the effect of maximum wear depth on the pressure drop of the straight pipe. For the straight pipe without wear defect, the pressure drop is approximately 1810 Pa, and with the maximum wear depth increasing from 4 mm to 19 mm, the pressure drop of the elbow increases linearly, from an increase of 2.2% to an increase of 10.2%, and the linear relationship between the maximum wear depth and pressure drop of straight pipe is given as Equation (10):

$$P_s=1821.63{\delta }_{\max }+222.18$$

(10)

where the P_s is the pressure drop of the straight pipe. The wear zone can be regarded as a locally extended zone within the pipe. According to Bernoulli’s equation, the local cross-section changes lead to flow fluctuations and kinetic energy changes, causing the local pressure losses. The more severe the wear, the higher the local pressure loss, which is due to flow separation, vortexing, and kinetic energy loss. At the same time, in the wear zones, the conversion between kinetic and pressure energy of the fluid is no longer uniform due to cross-sectional inhomogeneities and the presence of deposits.

5. Discussion

Based on above analysis, the wear defect of the pipe has significant influences on the flow characteristics of discharge pipe including the pressure drop, flow trajectory, and particle critical velocity. The influences can be attributed to two aspects, the first of which is changes in fluid dynamics. The flow of fluid can be significantly altered by changes in cross-section due to wear defect at the bottom of the pipe. Normally, the fluid flow in a pipe is uniformly distributed by the circular cross-section of the pipe. Wear causes the bottom cross-section to expand, changing the boundary conditions of the fluid, especially near the boundary layer where typical turbulence and secondary flows may be generated. The change in the boundary layer leads to a slowing down of the fluid flow at the bottom of the pipe, which significantly affects the transport of particles. The second aspect is the change in the rheological properties of slurry. The changes in the pipe shape of the wear zone can change the rheological properties of the fluid. The shear rate and shear stress distribution of the slurry can change significantly in the wear zone. This affects the rheological behavior of the slurry, especially at low shear rates, where the dynamic equilibrium between deposition and resuspension is upset, leading to more particle deposition. It should be noted that Equations (9) and (10) proposed in this study are limited to one pipe diameter of 500 mm, and in future research, it will be necessary to investigate the effect of wear defects on pipe flow characteristics under different pipe diameters.

6. Conclusions

In this study, a three-dimensional slurry-particle model of pipeline transport was established using a coupled CFD-DEM method considering the pipe wall wear defect, and the typical pipeline form of straight pipe and 90° elbow pipe were selected as the research targets. The potential mechanism of pipe flow characteristics influenced by wear defect was revealed. Some main conclusions could be drawn as follows:

• The wear defect of pipe can lead to increased inhomogeneity in the velocity distribution, generating localized low-flow zones, and resulting in a reduced flow rate or stagnancy in parts of the pipe. Meanwhile, the wear defect of the pipe leads to local shape change, causing more turbulence, where increased vortex promotes localized kinetic energy reduction and creates larger pressure losses at the elbow.
• Pipe wear defect causes a decrease in the velocity of particles passing through the pipes, and the reduced velocity makes it easier for large particles to be deposited and accumulated, further increasing the potential risk of clogging and blockage.
• For the elbow pipe with wear defect, the pressure drop of the elbow increases quadratically, from an increase of 6.5% to an increase of 16.9% with the maximum wear depth increasing from 4 mm to 19 mm. For the straight pipe with wear defect, the pressure drop of the elbow increases linearly, from an increase of 2.2% to an increase of 10.2% with the maximum wear depth increasing from 4 mm to 19 mm.