Research on the Influence of Particles and Blade Tip Clearance on the Wear Characteristics of a Submersible Sewage Pump

Abstract

A submersible sewage pump is designed for conveying solid–liquid two-phase media containing sewage, waste, and fiber components, through its small and compact design and its excellent anti-winding and anti-clogging capabilities. In this paper, the computational fluid dynamics–discrete element method (CFD-DEM) coupling model is used to study the influence of different conveying conditions and particle parameters on the wear of the flow components in a submersible sewage pump. At the same time, the energy balance equation is used to explore the influence mechanism of different tip clearance sizes on the internal flow pattern, wear, and energy conversion mechanism of the pump. This study demonstrates that increasing the particle volume fraction decreases the inlet particle velocity and intensifies wear in critical areas. When enlarging the tip clearance thickness from 0.4 mm to 1.0 mm, the leakage vortex formation at the inlet is enhanced, leading to increased wear rates in terms of the blade and volute. Consequently, the total energy loss and turbulent kinetic energy generation increased by 3.57% and 2.25%, respectively, while the local loss coefficient in regard to the impeller channel cross-section increased significantly. The findings in this study offer essential knowledge for enhancing the performance and ensuring the stable operation of pumps under solid–liquid two-phase flow conditions.

1. Introduction

Submersible sewage pumps are extensively utilized in urban sewage management, agricultural irrigation, and industrial water treatment, due to their compact design and superior anti-winding capabilities. These pumps effectively transport sewage media that contain solid particles and fiber materials. Due to velocity disparities between solid particles and the fluid medium, particle collisions with pump components induce wear, adversely affecting the hydraulic performance of the submersible sewage pump, which may lead to shutdown [1].

To date, researchers globally have conducted comprehensive investigations into the complexities of solid–liquid two-phase flow in pumps. For instance, Luo et al. [2] conducted an analysis of the energy conversion characteristics of solid–liquid two-phase flow in an in-line hybrid pump, using an integrated analysis method, based on entropy production theory and relative energy rotor enthalpy. Their findings revealed that the peak values of turbulent kinetic energy (TKE) and the entropy production rate were localized near the tongue, and the flow rate exerted a more significant influence on the TKE than the particle concentration. Tane et al. [3] employed the RANS–DEM method to analyze the motion characteristics of cylindrical particles in a slurry pump, revealing that the average velocity of cylindrical particles decreases with increasing particle density and concentration. Wang et al. [4,5] utilized the renormalization group k-ε model and the dense discrete phase model in Fluent to examine the characteristics of solid–liquid two-phase flow and wear in an open impeller centrifugal pump that handles dense, fine particles. Additionally, the CFD–DEM method was employed to examine the distribution of flow in terms of binary mixed particles within the pump, as well as to investigate particle–fluid interactions at varying volume concentrations. It was found that the linked reaction in terms of the fluid field on the particles decreased as the particle concentration increased, and the time taken to transport small particles decreased with the concentration. Zheng [6] developed a CFD–DEM coupling method, incorporating a fiber model, to analyze how the flow and fiber length affect fiber movement and blockage, revealing that fiber retention locations coincide with vortex sites, notably at the impeller inlet, blade tip, mid-blade, and pump tongue.

Wang et al. [7] studied the space distribution and motion characteristics of particles with varying diameters using the CFD–DEM coupling algorithm, indicating that increasing the particle diameter reduces stratification phenomena, while enhancing the vortex intensity and scale within the guide vane. Cao et al. [8] simulated the flow in pumps featuring diverse particle sizes and shapes by utilizing the CFD–DEM approach in conjunction with the Archard model, finding that larger particles and reduced sphericity resulted in heightened average wear in overflow areas. Wang et al. [9] used a dense discrete phase model to analyze particle–fluid flow and wall erosion in a slurry pump, suggesting that the volute experiences the most erosion and is generally less sensitive to the particle concentration. Guo [10] employed the Rosin–Rammler function to model the sand particle size distribution and investigated key factors influencing component wear in terms of a multiphase pump blade. They identified that the particle Reynolds number primarily affects wear on the pressure side of the blade, while the sand concentration plays a crucial role on the suction side. Peng et al. [11] examined impeller wear in a centrifugal slurry pump, using the Euler–Euler multiphase flow model. It was observed that increasing the particle concentration under identical conditions reduces the pump head and efficiency, while gradually increasing the particle slip velocity at the blade outlet. Cheng et al. [12] employed the Fluent and EDEM coupling approach to study solid–liquid two-phase flow within a pump, observing that high flow rates lead to particle aggregation in the flow channel, forming a long wear strip at the trailing edge of the blade on the pressure surface, with minimal wear on the suction side. Based on the four-way coupled Euler–Lagrangian method, Wang et al. [13] implemented a semi-open centrifugal pump to emulate the behavior of solid–liquid flow with varying particle sizes. They observed that due to effective particle tracking and suppression of the tip leakage vortex, particles readily impacted the trailing edge of the suction surface and the blade hub. As the particle size decreased, more particles flowed into the tip clearance area.

To mitigate friction between the dynamic and static components of the submersible sewage pump, a specific tip clearance is maintained between the blade tip and the pump shell in open impeller submersible sewage pumps. However, the tip clearance induces leakage flow during pump operation, resulting in a tip leakage vortex that impacts the hydraulic performance of the pump. Therefore, investigating the effect of the tip clearance size on the internal flow dynamics of the pump is crucial for optimizing its performance. Yang et al. [14] studied the combined effects of diverse two-phase flow patterns and different tip gap sizes on pump performance by using the multi-factor variance analysis method. The findings indicate that pump performance significantly deteriorates as the clearance size increases, and the sensitivity of the pump efficiency to the change in the tip clearance size depends on the flow rate. Ji et al. [15] carried out energy performance and pressure tests to investigate how tip clearance affects pressure pulsations in mixed-flow pumps, identifying low-frequency pulsations with concentrated energy at the impeller inlet as the primary interference frequency. Increasing the tip clearance expanded the high-amplitude region of the wavelet spectrum towards lower frequencies. Lin et al. [16] explored the fluctuation characteristics of the tip clearance leakage flow and pressure pulsation in response to different flow conditions. The observations indicate that with higher flow rates, the amplitude of the pressure fluctuations at the tip clearance increases initially and then declines, while the effect of the tip clearance size on the tip clearance flow rate becomes less significant.

Yang et al. [17] discussed the effects of tip clearance design on both the energy characteristics and flow dynamics, through a combination of numerical calculations and experimental verification, and found that the complicated mixing action of leakage and the mainstream flow is the main source of energy dissipation in a semi-open impeller. Guo [18] investigated the influence of four different tip clearance thicknesses in inducers on the high-speed performance of centrifugal pumps under various flow conditions. The findings indicate that increased tip clearance, particularly under high-flow conditions, enhances both the efficiency and pump head. Peng et al. [19] examined the impact of the tip gap between the impeller and blade tip on the hydraulic performance of a single-stage centrifugal pump, through experiments and numerical simulations. They observed that an increase in the tip clearance significantly reduced the impact losses at the tongue and gradually mitigated interference from water exiting the tip clearance at the impeller inlet. Li [20] investigated the impact of leakage flow through the tip clearance on the rotating stall and observed that the critical stall point shifted to higher flow rates under a smaller tip clearance, consequently reducing the stable operation scope of mixed-flow pumps. Han [21] discovered that increasing the tip clearance in submersible electric pumps decreases the energy performance. Specifically, at lower flow rates, increasing the tip clearance proportionally decreases the energy performance. Under higher flow conditions, a greater tip clearance results in significant leakage increases.

In conclusion, extensive research has been undertaken on solid–liquid two-phase flow and tip clearance within this field, yet the dynamics within pumps and the mechanisms governing phase interactions are still not fully understood. Furthermore, the interaction between particles and the tip clearance size under multiphase solid–liquid conditions, and their combined effects on the pump’s energy characteristics, have not been thoroughly investigated. Therefore, there is an urgent need for further exploration of the flow characteristics in terms of solid–liquid two-phase systems and their interaction mechanisms with tip clearance. In this study, an open impeller submersible sewage pump is taken as the research object and the CFD–DEM coupling model is deployed to explore the wear properties of the internal flow components under different transportation flow rates and particle parameters. Additionally, three different tip clearance sizes are considered to comprehensively analyze the tip leakage vortex structure, internal flow field patterns, and wear characteristics, across different configurations. Utilizing the energy balance equation, the relationship between the tip clearance and the energy conversion in the pump is deeply explored. The research in this paper can not only enrich the theory on solid–liquid two-phase flow within pump systems, but also serves as a reference for designing and optimizing the tip clearance of open impeller sewage pumps, possessing significant theoretical and practical engineering value.

2. Geometric Model and Parameters

This study focuses on an open impeller submersible sewage pump, characterized by a low specific speed, with a specific speed of n_s = 24.8, a design flow rate of Q_d = 10 m³/h, a design head of H_d = 28 m, and a rated speed of n = 2980 r/min. Figure 1 illustrates the two-dimensional and three-dimensional configuration of the pump. To mitigate the effects of inlet and outlet reflux, the inlet and outlet pipes are lengthened to five times their diameter. The key geometric parameters of the model pump are listed in

Table 1. The geometrical parameters of the submersible sewage pump.

Geometrical Parameters	Value	Geometrical Parameters	Value
Inlet pipe diameter Di/mm	58	Outlet pipe diameter Do/mm	50
Impeller inlet diameter D1/mm	71	Wrapping angle φ/°	194.57
Impeller outlet diameter D2/mm	180	Base circle diameter of volute D3/mm	180
Impeller outlet width b1/mm	7.62	Volute inlet width b2/mm	26
Number of blades Z	3	Diameter of volute outlet D4/mm	50
Blade inlet setting angle β1/°	16.3	Tip clearance width b3/mm	0.7
Blade outlet setting angle β2/°	13.15	Rear cover plate width b4/mm	0.5

.

3. Numerical Modeling

3.1. Particle Model

To ascertain the impact of the solid–liquid medium properties on the internal wear and flow dynamics in the submersible sewage pump, various solid particle configurations were employed within the solid–liquid two-phase flow, as detailed in

Table 2. Solid–liquid two-phase flow research plan.

Variables	Flow Conditions (Q/Qd)	Particle Volume Fractions (%)	Particle Shapes
Flow conditions	0.6, 1.0, 1.4	1	Long cylindrical particle
Particle volume fractions	1.0	1, 2, 3	Long cylindrical particle
Particle shapes	1.0	1	Spherical, short cylinder particle, long cylindrical particle, mixed particle

. Three variables, namely the flow conditions, particle volume fraction, and particle shape, were considered in the study. Figure 2 illustrates the three particle shapes: spherical particles with a diameter of 1 mm, two spherical particles piled up to form a short cylinder (length 2.5 mm), and four spherical particles piled up to form a long cylindrical particle (length 5 mm).

3.2. Numerical Simulation Method

To address potential issues arising from high local particle volume fractions during two-phase flow simulations, the following fluid control equations are implemented:

$${\displaystyle \frac{\partial }{\partial \mathrm{t}}}\left(\alpha {\rho }_{\mathrm{f}}\right)+\nabla \cdot \left(\alpha {\rho }_{\mathrm{f}}{\mathit{v}}_{\mathrm{f}}\right)=0$$

(1)

$${\rho }_{\mathrm{f}}{\displaystyle \frac{\partial }{\partial t}}(\alpha {\mathit{v}}_{\mathrm{f}})+\nabla \cdot \left(\alpha {\rho }_j{\mathit{v}}_{\mathrm{f}}{\mathit{v}}_{\mathrm{f}}\right)=-\nabla \cdot (\alpha P)+(\nabla \cdot \alpha \mu )\left(\nabla {\mathit{v}}_{\mathrm{f}}+{(\nabla {\mathit{v}}_{\mathrm{f}})}^T-{\displaystyle \frac{2}{3}}\nabla \cdot {\mathit{v}}_{\mathrm{f}}l\right)+{\rho }_{f}g+\mathit{F}$$

(2)

where ρ_f stands for fluid density; ν_f represents the fluid velocity vector; t is the time variable; P indicates pressure; g denotes gravitational acceleration; α is the volume fraction of the liquid phase; and F represents other additional forces (including the interaction force between discrete phases, etc.).

During the simulation of the fluid flow within the submersible sewage pump, the finite volume method and SST k-ω turbulence model are applied, and the rotation effect of the impeller is realized by applying the sliding grid method. In addition, the particles are discretized, according to the Euler–Lagrange method, to calculate the movement of the particle phase. In this study, the particle volume fraction is below 10%, which means that it belongs to a sparse solid–liquid two-phase flow. The solid particles are described by the following governing equation:

$$m_{\mathrm{s}}{\displaystyle \frac{d{\mathit{v}}_{\mathrm{s}}}{dt}}={\mathit{F}}_{\mathrm{drag}}+{\mathit{F}}_{\mathrm{g}}+{\mathit{F}}_{\mathrm{vm}}+{\mathit{F}}_{\mathrm{p}}+{\mathit{F}}_{\mathrm{saff}}+{\mathit{F}}_{\mathrm{Magn}}+{\mathit{F}}_{\mathrm{c}}$$

(3)

$$I_{\mathrm{s}}{\displaystyle \frac{d{\mathit{\omega }}_{\mathrm{s}}}{dt}}={\displaystyle \sum {\mathit{T}}_{\mathrm{c}}}+{\mathit{T}}_{\mathrm{f}}$$

(4)

$$I_{\mathrm{s}}=0.1m_{\mathrm{s}}{d}_{\mathrm{s}}^2$$

(5)

where F_drag represents the drag force on the particles; F_g denotes the resultant force of gravity and buoyancy acting on the particles; F_vm signifies the additional mass force on the particles; F_p denotes the pressure gradient force on the particles; F_saff accounts for the force generated by the difference in the vertical flow velocity between the particles; F_Magn represents the force on the particles due to rotation; F_c denotes the contact force between the particles and between the particles and the wall; I_s represents the moment of inertia of the particle; ω_s represents the angular velocity of the particle; T_c and T_f [22], respectively, represent the contact torque of the particle and the torque resulting from the fluid phase; and m_s indicates the mass of the particle, whereas d_s refers to its size.

Particles are primarily influenced by gravity and drag force during movement [23]. The Di Felice drag model, which considers the fluid volume fraction and porosity, is utilized to compute the drag force. The formula is given below:

$${\mathit{F}}_{\mathrm{drag}}={\displaystyle \frac{1}{8}}\mathsf{\pi }{d}_{\mathrm{s}}^2{\rho }_{\mathrm{f}}{C}_{\mathrm{D}}\left|{\mathit{v}}_{\mathrm{f}}+{\mathit{v}}_{\mathrm{f}}^{\prime }-{\mathit{v}}_{\mathrm{s}}\right|\left({\mathit{v}}_{\mathrm{f}}+{\mathit{v}}_{\mathrm{f}}^{\prime }-{\mathit{v}}_{\mathrm{s}}\right){\alpha }_{\mathrm{f}}^{\left(1-\alpha \right)}$$

(6)

$$\alpha =3.7-0.65exp\left[-{\displaystyle \frac{{\left(1.5-{\log }_{10}{\mathit{Re}}_{\mathrm{s},\mathsf{\alpha }}\right)}^2}{2}}\right]$$

(7)

where Re_s,α is the particle Reynolds number under the action of the fluid volume fraction, which can be expressed as:

$$R{e}_{\mathrm{s},\alpha }={\displaystyle \frac{{\rho }_{\mathrm{f}}{d}_{\mathrm{s}}\alpha \left|{\mathit{v}}_{\mathrm{f}}+{\mathit{v}}_{\mathrm{f}}^{\prime }-{\mathit{v}}_{\mathrm{s}}\right|}{{\mu }_{\mathrm{f}}}}$$

(8)

The combined force of gravity and buoyancy F_g can be expressed as follows:

$${\mathit{F}}_{\mathrm{g}}=m_{\mathrm{s}}\left({\displaystyle \frac{{\rho }_{\mathrm{s}}-{\rho }_{\mathrm{f}}}{{\rho }_{\mathrm{s}}}}\right)g$$

(9)

where ρ_s represents the particle density.

The pressure gradient force arises from the pressure differential induced by the accelerated fluid motion over the surface of the particles, resulting from the particle movement within the flow field with changing pressures. It can be expressed as follows:

$${\mathit{F}}_{\mathrm{p}}=-V_{\mathrm{s}}\nabla p$$

(10)

The additional mass force is the force required to push the fluid to accelerate when the particle velocity is greater than the fluid velocity, which can be expressed as:

$${\mathit{F}}_{\mathrm{vm}}={\displaystyle \frac{{\rho }_{\mathrm{f}}}{2{\rho }_{\mathrm{s}}}}\left[{\mathit{v}}_{\mathrm{s}}\nabla \left({\mathit{v}}_{\mathrm{f}}+{\mathit{v}}_{\mathrm{f}}^{\prime }\right)-{\displaystyle \frac{d{\mathit{v}}_{\mathrm{s}}}{dt}}\right]$$

(11)

when the ratio of the fluid density to the particle density exceeds 0.1, the effects of the virtual mass force and pressure gradient force on the particle motion become significant [24]. In this paper, the fluid density ρ_f = 998.2 kg/m³ and particle density ρ_s = 2650 kg/m³ ratio is greater than 0.1, thus necessitating the virtual mass force and pressure gradient force in regard to the coupling interface.

The F_saff is the vertical force on the particle due to the different fluid velocities across the upper and lower surfaces [25], which is expressed as:

$${\mathit{F}}_{\mathrm{saff}}=1.615d_{\mathrm{s}}^2{({\mu }_{\mathrm{f}}{\rho }_{\mathrm{f}})}^{1/2}{C}_{\mathrm{saff}}|{\mathit{w}}_c{|}^{1/2}({\mathit{v}}_{\mathrm{f}}-{\mathit{v}}_{\mathrm{s}}){\mathit{w}}_{\mathrm{c}}$$

(12)

where w_c is the vorticity of the fluid; C_saff denotes the slip-shear lift coefficient, which correlates closely with the particle Reynolds number, and can be expressed as:

$$C_{\mathrm{saff}} =\left\{\begin{array}{l}(1-0.3314\sqrt{\beta })exp\left[-{\displaystyle \frac{R{e}_s}{10}}\right]+0.3314\sqrt{\beta }, R{e}_{\mathrm{s}}\le 40\\ 0.0524\sqrt{\beta R{e}_s}, R{e}_{\mathrm{s}}>40\end{array}\right.$$

(13)

In the formula, the shear Reynolds number is expressed as Re_s = ρ_fd_s²|w_c|/μ_f and the coefficient is β = Re_s/2 Re_s,α.

The F_Magn is the force applied to the particle due to rotation, calculated according to the Kutta–Joukowski theorem [26]. The expression is:

$${\mathit{F}}_{\mathrm{Magn}}={\displaystyle \frac{1}{2}}{A}_{\mathrm{p}}{C}_{\mathrm{Magn}}{\rho }_{\mathrm{f}}{\displaystyle \frac{\left|\mathbf{V}\right|}{|\mathbf{\Omega }|}}(\mathbf{V}\times \mathbf{\Omega })$$

(14)

where A_p is the projection area of the particles; Ω signifies the angular velocity of the fluid in relation to the particles; V stands for the linear velocity of the particle as compared to the fluid; and C_Magn is the rotational lift coefficient, predominantly impacted by the rotational Reynolds number Re_s,r and the particle Reynolds number Re_s,α. It is given by:

$$C_{\mathrm{Magn}}=0.45+({\displaystyle \frac{R{e}_{\mathrm{s},\mathrm{r}}}{R{e}_{\mathrm{s},\alpha }}}-0.45)e^{(-0.057\pi )R{e}_{\mathrm{s},\mathrm{r}}^{0.4}R{e}_{\mathrm{s},\alpha }^{0.3})}$$

(15)

$$R{e}_{\mathrm{s},\mathrm{r}}={\displaystyle \frac{{\rho }_{\mathrm{f}}{d}_{\mathrm{s}}^2\left|{\mathbf{\omega }}_{\mathrm{c}}\right|}{{\mu }_{\mathrm{f}}}}$$

(16)

F_c denotes the force arising from mutual contact between the particles and can be formulated as:

$${\mathit{F}}_{\mathrm{c}}={\mathit{F}}_{\mathrm{c},\mathrm{n}}+{\mathit{F}}_{\mathrm{c},\mathrm{t}}$$

(17)

where F_c,n refers to the normal force exerted on the particle after collision and F_c,t represents the tangential force on the particle after collision, which can be calculated using the following expression:

$${\mathit{F}}_{\mathrm{c},\mathrm{n}}=1.5{\displaystyle \frac{Y}{1-{\mu }^2}}\sqrt{R_{1,2}}\sqrt{u_{\mathrm{n}}^3}$$

(18)

$${\mathit{F}}_{\mathrm{c},\mathrm{t}}=12(G_{1.2}\sqrt{R_{1.2}{u}_{\mathrm{n}}})\sqrt{u_{\mathrm{q}}^3}$$

(19)

where μ signifies Poisson’s ratio, Y defines the equivalent elastic modulus, R_1,2 represents the equivalent contact radius, u_n represents the normal displacement, G_1,2 represents the equivalent shear modulus, and u_q represents the tangential displacement.

The Archard wear model [27] is a wear model grounded in contact mechanics between the particles and the walls, used to characterize solid material interactions on frictional surfaces. It assumes that wear occurs due to the relative movement between small particles or surface protrusions, which break or detach upon contact, resulting in material loss. The semi-empirical formula is given by:

$$Q_{\mathrm{v}}={\displaystyle \frac{K}{H_{\mathrm{v}}}}{F}_{\mathrm{n}}{d}_{\mathrm{s}}$$

(20)

where Q_v represents the amount of wear, where the unit is mm³; H_v represents the hardness of the material surface, where the unit is N∙mm⁻²; K denotes the wear constant; F_n denotes the point load, in N; and d_s represents the sliding distance, where the unit is mm.

The wear amount is represented by the wear depth h, which can be expressed as:

$$h={\displaystyle \frac{Q_{\mathrm{v}}}{A}}$$

(21)

where A indicates the contact region between the wall and the particle, where the unit is mm².

3.3. Boundary Condition

The Fluent–EDEM coupling calculation simulates solid–liquid two-phase flow in pumps by treating the liquid phase continuously and the solid phase discretely. The Fluent 2022 R1 software computes the liquid flow field, while EDEM simulates particle motion. Figure 3 depicts the coupling mechanism used to transfer momentum between the solid and liquid phases. As demonstrated in our previous research [28], the Fluent–EDEM coupling calculation can effectively simulate the solid–liquid two-phase flow in the pump.

The Fluent simulation employs the SST k-ω turbulence model, with an inlet velocity of 1.0514 m/s, under the design conditions, while the outlet boundary condition is configured as free outflow (outflow). In the EDEM, the pump’s inlet surface is configured as a particle factory, generating a certain number of particles per second based on the computational parameters. The contact model between the particles and between the particle walls uses the Hertz–Mindlin (no-slip) model, and the wear rate of the wall in terms of the flow-through parts is calculated using the Archard wear model. The time step for the calculations is set to 1 × 10⁻⁶ s in the EDEM and 1 × 10⁻⁴ s in Fluent. Both simulations use a residual convergence criterion of 1 × 10⁻⁶.

Table 3. Key parameter settings for the submersible sewage pump in Fluent and EDEM.

Fluid properties	Parameters	Unit	Value
	Density	kg/m3	998.2
	Import speed	m/s	1.0514
	Free outflow	/	/
Particle properties	Density	kg/m3	2650
	Poisson’s ratio	/	0.3
	Young’s modulus	Pa	1.9 × 109
	Restitution coefficient	/	0.4
	Static friction coefficient	/	0.7
Wall properties	Density	kg/m3	7825
	Poisson’s ratio	/	0.285
	Young’s modulus	Pa	2 × 1011
	Restitution coefficient	/	0.5
	Static friction coefficient	/	0.4

presents the key parameters for the EDEM and the Fluent simulation.

3.4. Grid Division and Independence Analysis

The grid quantity and quality substantially affect both the speed and accuracy of numerical simulations of submersible sewage pumps. To optimize the computational resources, Fluent meshing was employed to mesh the components, including the inlet pipe, tip clearance, impeller, rear chamber, volute, and outlet pipe of a submersible sewage pump, featuring a 0.7 mm tip clearance, in clear water conditions. Five sets of polyhedral grids were examined for grid independence, all exhibiting a grid quality above 0.3. Figure 4 shows the details of the polyhedral grid generation.

The variations in the pump head and efficiency across different grid configurations were analyzed to determine the optimal mesh density for a submersible sewage pump. Based on the findings shown in

Table 4. Grid independence analysis.

Scheme	Grid Number	Head (m)	Efficiency (%)
1	402957	31.42	34.85
2	528825	31.14	34.23
3	652543	30.71	33.95
4	734542	30.68	33.89
5	875511	30.67	33.82

and Figure 5, the fluctuations in the efficiency and pump head remain within 1% when the grid count exceeds 652,543. Consequently, grid scheme group 3, comprising 652,543 grids, was selected as the most suitable configuration.

4. Analysis of the Influence of Particle Parameters on Pump Performance

4.1. The Influence of the Flow Rate on Flow Patterns and Wear Characteristics

The wear characteristics of the impeller and the volute of a submersible sewage pump, when subjected to long cylindrical particles at a volume fraction of 1%, are comprehensively investigated under varying flow conditions. Figure 6 illustrates the velocity vector distribution within the pump across different flow rates. It has been discerned that at lower flow rates in terms of solid–liquid two-phase flow, a significant low-speed region emerges on the suction side of the impeller near the tongue, leading to flow separation and the formation of small vortices that can potentially cause channel blockage. Conversely, the pressure side exhibits relatively stable flow conditions, with no distinct low-speed zone. Under conditions in terms of the designed flow rate and high flow rates, the fluid velocity within the impeller channels increases, causing a gradual weakening and migration of flow separation-induced vortices towards the blade’s pressure surface. The highest velocity area appears near the second section of the volute, and the peak decreases with increasing flow rates, while the velocity at the outlet of the volute gradually decreases with the increase in the flow rate.

Figure 7 depicts the TKE distribution within the pump across various solid–liquid two-phase flow conditions. The maximum turbulent kinetic energy is observed at the volute tongue and the middle section of the impeller channel. Under the design conditions, the high turbulent kinetic energy area is significantly reduced at lower and higher flow rates. The impeller channel exhibits a more uniform distribution in terms of the TKE, indicating more regular fluid movement. Near the volute outlet, the turbulent kinetic energy gradually increases with the flow rate, leading to a more disordered distribution. This phenomenon results from higher flow rates increasing the fluid velocity at the volute outlet, intensifying the turbulent kinetic energy in that region.

Figure 8 demonstrates the distribution pattern of the particles within the pump under varying flow rates. It can be observed that the inlet of the impeller is in a low-speed zone and the velocity of the particles is low. In this region, the impact of the particles on the leading edge of the blade, along with their subsequent rebound and further collisions, will be of particular significance. With the increase in the flow rate, the particle velocities increase, augmenting their travel distance per unit time and, thereby, diminishing particle aggregation towards the impeller inlet, resulting in enhanced dispersion. Consequently, the time required for particle concentration within the pump to stabilize is reduced. In addition, with the particle volume fraction held as constant, an increase in the flow rate leads to an increase in both the number of particles within the pump and the transport load on the impeller. The quantity of particles conveyed through each flow channel of the impeller is significantly increased, resulting in serious wear to the flow components in this area. Concurrently, particle aggregation intensifies along the volute wall surface with increasing flow rates, predicting a gradual increase in the wear rate. At the outlet pipe of the submersible sewage pump, significant particle aggregation is only observed at low flow rates. This phenomenon is primarily attributed to the inadequate fluid velocity within the outlet pipe at low flow rates, resulting in insufficient transportation capacity for solid particles.

Figure 9 illustrates the distribution of the wear rates for the blade and volute in the submersible sewage pump for various flow rates. From the diagram, it can be seen that the area with the largest wear rate on the blade is mainly distributed on the leading edge and tail of the blade. With a constant solid volume fraction, the leading-edge area exhibits progressively higher wear rates as the flow rate increases. This trend is primarily attributed to elevated particle velocities and increased particle counts associated with higher flow rates, leading to intensified wear. The rate of wear in the volute grows with the flow rate from section I to section V, while it decreases initially and then increases again from section V to section VIII. This is due to the small flow rate and the insufficient capacity of the submersible sewage pump to transport particles, resulting in the deposition of particles from section V to section VIII. The wear rate of the volute decreases as the flow rate increases, owing to the enhanced particle conveyance capacity of the pump. However, the excessive flow rate increases the particle velocity and quantity, accelerating volute wear and, consequently, increasing the wear rate.

4.2. The Influence of the Particle Volume Fraction on the Pump Wear Characteristics

To investigate the characteristics of the particle transportation by a submersible sewage pump for various particle volume fractions and particle distributions, the wear analyses were conducted at 1%, 2%, and 3% particle volume fractions. The flow rate was maintained in terms of the design condition and the particles were long cylinders in terms of their shape. Figure 10 illustrates the particle distribution within the submersible sewage pump at varying particle volume fractions. The number of particles transported per unit of time exhibited a linear increase with an increasing particle volume fraction. Collisions both among the particles and between the particles and the leading edge of the blade were considerably intensified, leading to a reduced particle velocity at the inlet and increased momentum loss. Therefore, a substantial number of particles accumulated at the impeller inlet, causing a blockage effect. Particles entering the impeller passage experienced significant collisions, predominantly at the leading edge of the blade’s pressure side and the trailing edge of the suction surface. The amount of particles transported through each flow channel of the impeller increases substantially with the increasing concentration. The primary accumulation zone for the particles extends from section V to section VIII, along the volute wall. Higher concentrations result in more pronounced particle aggregation within this region.

The wear rates of the blades and volute in the submersible sewage pump are shown in Figure 11, as influenced by varying particle volume fractions. The leading edge located on the pressure surface, the trailing edge on the suction surface, and the V–VIII region of the volute, are the main wear areas. The leading edge of the blade is where the initial particle collisions occur, thus causing heightened wear at the front edge of the blade’s pressure side and the trailing edge on the suction surface. An increase in particle volume fraction expands the wear area and significantly increases the wear depth, necessitating timely replacement of the impeller due to continuous operation under high volume concentrations. Figure 11b illustrates that as the concentration increases, the volute’s high-wear area experiences deeper wear, leading to substantial material removal from the wall and, thereby, reducing the volute’s lifespan considerably. Moreover, the tongue barrier intensifies particle collisions and increases the collision frequency. However, the volute exhibits a lower wear rate. This is mainly due to particles colliding with the tongue, which prevents direct impact on the volute wall and, thereby, reduces the wear on the volute tongue to some extent.

4.3. The Influence of Particle Shape on the Wear Characteristics

In practical solid–liquid fluid transportation applications, submersible sewage pumps are frequently employed to convey particles of varying shapes. This study simulates operational scenarios involving a submersible sewage pump, with a designed flow particle volume fraction of 1%, to investigate how different particle shapes affect the wear characteristics of the flow components. Additionally, the volume concentration of the particles generated per unit of time for different particle shapes is the same.

Figure 12 illustrates the particle distribution in the submersible sewage pump for various particle shapes. It reveals that at the same particle volume fraction, the pump transports different quantities of particles depending on their shapes. The order of the shapes, from the highest to the lowest number of particles, is spherical, mixed, short cylindrical, and long cylindrical. Upon observing the particle distribution, it was noted that the velocity distribution among the particles of different shapes in the submersible sewage pump is nearly uniform. However, the uniformity of the particle distribution within the impeller channel correlates notably with the particle shape. Spherical particles exhibit the most even distribution in the impeller channel, followed by mixed particles and then short cylindrical particles. Long cylindrical particles display the most chaotic distribution, consistent with their lower distribution value among the different particle shapes. The reason is that, on the one hand, the contact area with the fluid is expanded due to the increase in the surface area of the particles, which intensifies the interaction with the fluid and elevates the resistance of the particles. On the other hand, the equivalent diameter of spherical particles is smaller. Compared with long and short cylindrical particles and mixed-shape particles, the Stokes number (S_t number) of spherical particles is lower, and the drag force is dominant. Consequently, spherical particles demonstrate superior flowability and more uniform distribution and movement within the fluid.

The wear rate distribution in submersible sewage pumps for different particle shapes is shown in Figure 13. As evidenced by Figure 13a, the high wear rate area distribution in the submersible sewage pump when transporting the above four shapes of particles is consistent, primarily distributed along the pressure leading edge and suction surface trailing edge of the impeller blade. High wear is observed along the leading edge of the blade, extending rearward from the bottom. The wear rate significantly declines in the upper portion of the leading edge, while the center of the blade shows irregular, localized wear patterns.

The primary cause lies in the lower velocity of the particles at the bottom of the blade’s leading edge, leading to prolonged accumulation and severe wear in this region. In the middle of the blade, particles acquire higher kinetic energy, resulting in more random impacts and uneven wear patterns. At the trailing edge of the blade, the particle velocity peaks, significantly intensifying the blade impact and causing extensive high wear rates. As the particle surface area increases, the contact area between the particles and the fluid expands, leading to a higher wear rate on the blade. As illustrated in Figure 13a, the area with a high wear rate, for elongated cylindrical particles, is the most extensive, whereas for spherical particles, the high wear rate area is the smallest. From Figure 13b, it is evident that the impact of the particle shape on the wear rate distribution in the volute mirrors that of the impeller. Long cylindrical particles demonstrate the highest wear rate and deepest wear depth on the volute, followed by short cylindrical particles with a lower wear rate. Spherical particles exhibit the lowest wear rate, while mixed particles display intermediate wear rates between short cylindrical and spherical particles.

5. Analysis of the Influence of the Tip Clearance Size on Performance

To prevent friction between the dynamic and static components of open-type submersible sewage pumps, a specially designed tip clearance gap induces leakage flow of the working medium under a pressure differential, forming a tip leakage vortex that reduces the hydraulic performance. Thus, the following research investigates the effect of varying tip clearance thicknesses as the sole variable, employing long cylindrical particles in terms of the design condition, with a particle volume fraction of 1%, to simulate the influence of the tip clearance thickness change on the solid–liquid two-phase flow dynamics and energy dissipation by the pump. Various tip clearance parameter schemes are presented in

Table 5. Simulation scheme for different blade tip clearance parameters.

Scheme	Flow Rate (Q/Qd)	Particle Volume Fraction (%)	Particle Shape	Blade Tip Clearance (mm)
1	1.0	1	Long cylindrical particles	0.4
2	1.0	1	Long cylindrical particles	0.7
3	1.0	1	Long cylindrical particles	1.0

.

5.1. The Influence of Different Tip Clearances on Tip Leakage Vortex Structure

Figure 14 presents the color coding for the TKE that represents the distribution of the tip leakage vortices in a submersible sewage pump for varying tip clearances. As depicted, increasing the gap thickness, enlarges the leakage vortex at the tip clearance inlet and markedly expands the region of irregular small-scale vortices along the blade. Conversely, the TKE distribution within the vortex gradually diminishes with the increasing tip clearance thickness. This is attributed to the fact that enlarging the tip clearance thickness allows more fluid to reach the volute directly through the clearance, diminishing the driving effect of the blade on the fluid and leading to increased resistance as the fluid moves past the blade and, consequently, more turbulence. Additionally, the fluid velocity decreases, exacerbating energy dissipation. However, the reduced fluid velocity concurrently lowers the turbulent kinetic energy within the vortex.

Figure 15 examines the analysis of the tip leakage flow velocities for different tip clearances, to assess the impact on the performance of the submersible sewage pump. The tip leakage flow mainly travels from the pressure side to the suction side of the impeller, with its velocity affected by varying tip clearance thicknesses. Furthermore, under a constant tip clearance thickness, the tip leakage flow velocity increases progressively from the leading edge to the trailing edge of the blade, attaining its highest value at the trailing edge of the pressure surface, as illustrated. As the tip clearance thickness increases, the velocity distribution at identical positions along the tip clearance diminishes gradually, which aligns with the previously discussed TKE distribution analysis. This trend primarily stems from the augmented tip clearance thickness enabling greater fluid passage, thereby reducing the driving effect of the blade on the fluid.

5.2. The Influence of Different Tip Clearances on the Flow Pattern

The velocity and TKE distributions are used to describe the fluid motion and energy distribution within the pump, directly representing the internal flow pattern of the submersible sewage pump. Figure 16 presents the velocity distribution contour for various tip clearances. With the increasing tip clearance thickness, the maximum fluid velocity within the impeller and volute of the submersible sewage pump decreases gradually. The variation in the tip clearance significantly influences the fluid velocity within the impeller passages, particularly along the suction surface of the blades. A progressive increase in the fluid velocity at the suction surface of the blade is noted with an increase in the tip clearance. Moreover, under the same tip clearance, the maximum velocity region of the impeller in the submersible sewage pump is situated at the trailing edge of the pressure surface, with the greatest velocity region in the volute appearing in section II; the minimum velocity region of the impeller is observed at the impeller inlet, and a similar region is identified at the volute outlet.

Figure 17 depicts the distribution of the TKE within the impeller and volute in the submersible sewage pump for various tip clearances. The diagram shows that as the tip clearance enlarges, the TKE within the impeller in the submersible sewage pump gradually increases, especially in the region of the impeller flow channel adjacent to the volute tongue. This indicates that turbulence generated at the impeller in the submersible sewage pump increases with a greater tip clearance, resulting in increased energy loss and reduced operational stability. Meanwhile, the TKE value in the V to VIII section of the volute shows a gradual decrease with the increasing tip clearance.

5.3. The Influence of Different Tip Clearances on the Wear Characteristics

Figure 18 and Figure 19 depict the distribution of the particles and wear rate across the primary flow components for different tip clearances in terms of the pump. It is apparent from the figures that as the tip clearance increases, particle aggregation becomes more pronounced, accompanied by a gradual reduction in the particles within the impeller flow channel. Figure 19 reveals a consistent wear rate distribution trend on the impeller blades and volute in the submersible sewage pump for various tip clearances. The highest wear rates on the blades predominantly occur at the leading edge of the pressure region and the trailing edge of the suction region, while for the volute, they are concentrated in sections I and IV. Furthermore, as the tip clearance increases incrementally, the wear rates on the impeller blades and volute both exhibit a gradual increase, with the most notable increase observed at the trailing edge of the suction surface of the blade. The observed phenomenon can be explained by the alteration in the flow pattern and velocity distribution of the solid–liquid two-phase fluid between the impeller and volute caused by the increased tip clearance. This change induces greater eddy currents and turbulence, thereby intensifying the particle impact and surface friction on the impeller and volute surfaces, consequently elevating the wear rate. Moreover, the increased tip clearance facilitates greater direct contact between the particles and pump surfaces, further augmenting the wear severity.

5.4. The Influence of Different Tip Clearances on the Energy Loss Mechanism

During the design and operation of open-type submersible sewage pumps, the tip clearance thickness is closely linked to the pump’s energy conversion efficiency, directly influencing internal flow dynamics and energy conversion processes. Energy losses occur within the primary components, such as the impeller and volute, during the flow process of submersible sewage pumps. Using energy balance equation theory, the alterations in the energy loss for the flow components are evaluated, highlighting the relationship between the tip clearance thickness and the energy conversion process inside the pump and providing a reference for selecting the most suitable tip clearance in engineering practice.

Lu et al. [29] used the unsteady Reynolds-Averaged Navier–Stokes method to analyze local, unsteady losses using the energy equation. It was observed that, during non-rotating stall conditions, changes in the average flow kinetic energy had negligible influence on local energy losses within the pump; instead, the majority of losses were converted into turbulent kinetic energy. Building upon this finding and referencing Wilhelm et al.’s work [30], a simplified equation can be derived:

$$\begin{array}{r}{\displaystyle \frac{\partial \left[\left(\frac{\overline{p}}{\rho \mathrm{g}}+z+\frac{1}{2\mathrm{g}}{\left(\overline{{\mathit{v}}_{\mathrm{f} \mathrm{i}}}\right)}^2\right)\rho \mathrm{g}\overline{{\mathit{v}}_{\mathrm{f} \mathrm{j}}}\right]}{\partial x_{\mathrm{j}}}}=\underset{p1}{\underbrace{{\displaystyle \frac{\partial }{\partial x_{\mathrm{j}}}}\left((\overline{{\mathit{v}}_{\mathrm{f} \mathrm{i}}})(-\overline{\rho {\mathit{v}}_{\mathrm{f} \mathrm{i}}^{\prime }{\mathit{v}}_{\mathrm{f} \mathrm{j}}^{\prime }})\right)}}+\underset{p2}{\underbrace{\mu {\displaystyle \frac{\partial }{\partial x_{\mathrm{j}}}}\left((\overline{{\mathit{v}}_{\mathrm{f} \mathrm{i}}})(\overline{D_{\mathrm{ij}}})\right)}}\\ -\underset{p3}{\underbrace{(-\overline{\rho {\mathit{v}}_{\mathrm{f} \mathrm{i}}^{\prime }{\mathit{v}}_{\mathrm{f} \mathrm{j}}^{\prime }}){\displaystyle \frac{\partial \overline{{\mathit{v}}_{\mathrm{f} \mathrm{i}}}}{\partial x_{\mathrm{j}}}}}}-\underset{p4}{\underbrace{\mu (\overline{D_{\mathrm{ij}}}){\displaystyle \frac{\partial \overline{{\mathit{v}}_{\mathrm{f} \mathrm{i}}}}{\partial x_{\mathrm{j}}}}}}\end{array}$$

(22)

$$D_{\mathrm{ij}}=2S_{\mathrm{ij}}={\displaystyle \frac{\partial {\mathit{v}}_{\mathrm{fi}}}{\partial x_{\mathrm{j}}}}+{\displaystyle \frac{\partial {\mathit{v}}_{\mathrm{f} \mathrm{j}}}{\partial x_{\mathrm{i}}}}$$

(23)

$$-\overline{\rho {\mathit{v}}_{\mathrm{f} \mathrm{i}}^{\prime }{\mathit{v}}_{\mathrm{f} \mathrm{j}}^{\prime }}={\mu }_{\mathrm{t}}({\displaystyle \frac{\partial \overline{{\mathit{v}}_{\mathrm{f} \mathrm{i}}}}{\partial x_{\mathrm{j}}}}+{\displaystyle \frac{\partial \overline{{\mathit{v}}_{\mathrm{f} \mathrm{j}}}}{\partial x_{\mathrm{i}}}})-{\displaystyle \frac{2}{3}}{\delta }_{\mathrm{ij}}\rho k$$

(24)

where ρ represents the fluid density; g is the acceleration of gravity; z signifies the height of the fluid mass; μ stands for the fluid’s dynamic viscosity, in units of N·s/m²; ν_fi denotes the fluid velocity component in the direction of i; $\overline{{\mathit{v}}_{\mathrm{fi}}}$ is the average velocity component in the direction of i and ${\mathit{v}}_{\mathrm{fi}}^{\prime }$ is the fluctuating component of the velocity in the direction of i, both with units of m/s; $-\overline{\rho {\mathit{v}}_{\mathrm{f} \mathrm{i}}^{\prime }{\mathit{v}}_{\mathrm{f} \mathrm{j}}^{\prime }}$ represents the Reynolds stress, which can be expressed by the average velocity gradient and turbulent viscosity μ_t; and μ_t serves as a parameter in the SST k-ω turbulence model.

By adding up the local energy losses, the total energy dissipation within the pump is determined. The energy balance equation for the pump is formulated as:

$$\begin{array}{r}L=\mathrm{g}Q\mathsf{\Delta }H=-\underset{L1}{\underbrace{{\displaystyle {\iiint }_V\frac{\partial }{\partial x_{\mathrm{j}}}\left(-\overline{{\mathit{v}}_{\mathrm{f} \mathrm{i}}}\overline{\rho {\mathit{v}}_{\mathrm{f} \mathrm{i}}^{\prime }{\mathit{v}}_{\mathrm{f} \mathrm{j}}^{\prime }}\right)dV}}}-\underset{L2}{\underbrace{{\displaystyle {\iiint }_V\mu \frac{\partial \left(\overline{{\mathit{v}}_{\mathrm{f} \mathrm{i}}}\overline{D_{\mathrm{ij}}}\right)}{\partial x_{\mathrm{j}}}}dV}}\\ +\underset{L3}{\underbrace{{\displaystyle {\iiint }_V(-\overline{\rho {\mathit{v}}_{\mathrm{f} \mathrm{i}}^{\prime }{\mathit{v}}_{\mathrm{f} \mathrm{j}}^{\prime }})\frac{\partial \overline{{\mathit{v}}_{\mathrm{f} \mathrm{i}}}}{\partial x_{\mathrm{j}}}dV}}}+\underset{L4}{\underbrace{{\displaystyle {\iiint }_V\mu \overline{D_{\mathrm{ij}}}\frac{\partial \overline{{\mathit{v}}_{\mathrm{f} \mathrm{i}}}}{\partial x_{\mathrm{j}}}}dV}}\end{array}$$

(25)

where Q represents the mass flow, where the unit is kg/s; L represents the total energy loss term, where the unit is W; L1 and L2 denote the diffusion of kinetic energy through Reynolds stress and viscous stress, respectively, known as the Reynolds stress transfer term and viscosity transfer term. L3 represents the conversion of average kinetic energy into turbulent kinetic energy, termed turbulent kinetic energy generation. The TKE is eventually converted into heat through viscous dissipation by small-scale turbulence. L4 denotes the viscous dissipation of the average kinetic energy, referred to as the viscous dissipation term [31].

Illustrated in Figure 20 is the distribution of various energy loss types within the submersible sewage pump for different tip clearances. It can be observed from the diagram that under different tip clearance thicknesses, the turbulent kinetic energy generation term L3 has the highest value, while the viscous dissipation term L4 has the lowest value in terms of the two-phase flow condition in the submersible sewage pump. The value of L3 significantly exceeds that of the other terms, aligning with the transient flow characteristics observed in terms of the clear water conditions described earlier. This underscores that the generation of irregular turbulence under solid–liquid two-phase flow conditions constitutes the primary energy loss mechanism during the operation of submersible sewage pumps. The influence on the energy loss in the submersible sewage pump is primarily attributed to the turbulent kinetic energy generation term L3. As the tip clearance thickness gradually increases, the diagram illustrates a corresponding increase in the total energy loss term L within the submersible sewage pump, consistent with the trend observed in L3. The analysis indicates that higher fluid velocity differentials passing through the blade clearance are a result of the increase in the tip clearance, thereby elevating the turbulent kinetic energy generation term L3 and, consequently, increasing the total energy loss L. This also shows that to investigate the connection between the tip clearance change and energy conversion in the submersible sewage pump, it is necessary to further analyze the turbulent kinetic energy generation term L3 for each flow component.

Figure 21 depicts the variation in the turbulent kinetic energy generation term L3 among the principal flow components of the submersible sewage pump under solid–liquid two-phase flow conditions and different tip clearances. The diagram reveals that as the tip clearance thickness increases, the L3 values in regard to the tip clearance (BTC) and impeller (IMP) progressively increase, whereas the L3 value in terms of the volute (VOL) decreases gradually. The L3 value in the IMP exhibits the most significant change, increasing by 36.8 W. Conversely, L3 in the VOL decreases by 34.7 W for different tip clearances. The change in L3 for the BTC is less pronounced compared to the IMP and VOL, increasing by only 11.7 W. These results highlight that the variations in the tip clearance thickness primarily affect L3 in the impeller and volute. The slight increase in L3 in the BTC with the increasing tip clearance thickness is primarily attributed to enhanced leakage flow, intensifying the non-uniform fluid velocity distribution at the tip clearance and, consequently, augmenting L3. Due to the minor volume in terms of the tip clearance compared to the impeller and volute, changes in L3 are relatively insignificant. Additionally, an augmentation in the tip clearance directly enlarges the gap between the blade and the volute, and more fluid flows directly into the volute without the pressure and growth of the impeller, resulting in a more dramatic change in the fluid velocity gradient in the impeller, an irregular eddy current and turbulence increase, resulting in a considerable increase in the L3 value and a sharp increase in the energy loss. As the tip clearance thickness increases within the volute, L3 exhibits a gradual decrease, signifying enhanced fluid flow stability, reduced turbulence distribution, and diminished energy loss within this component.

5.5. The Influence of Different Tip Clearances on Local Energy Loss

To analyze the energy loss component along the cross-section, a local loss coefficient l_i is introduced to quantify the magnitude of the term pi (Equation (22)) within specific regions of the pump body. Its definition is as follows:

$$l_{\mathrm{i}}={\displaystyle \frac{p\mathrm{i}}{(\rho u_2^3)/\alpha D}}$$

(26)

where α is a constant with a value of 5.556; u₂ is defined as the circumferential velocity of the exit to the impeller, where the unit is m/s; D represents the impeller diameter, measured in meters; l₁ signifies the local loss coefficient for the Reynolds stress transfer term; l₂ denotes the local loss coefficient for the viscosity transfer term; l₃ indicates the local loss coefficient for the turbulent kinetic energy generation term; and l₄ represents the local loss coefficient for the viscous dissipation term.

Figure 22 depicts the distribution of the local loss coefficient l₃ for the turbulent kinetic energy generation term in the central region of the impeller and volute for different tip clearances. The regions of elevated l₃ are predominantly observed in the impeller inlet area, volute tongue area, and the junction of the trailing edge of the blade and the volute. The change in l₃ in the central flow channel area between the two blades near the volute tongue is more obvious, which indicates that the increasing tip clearance leads to a gradual diffusion of the turbulence from the impeller inlet to the center of the flow channel. This results in increased flow instability within the impeller, accompanied by higher operational energy losses.

The impeller and tip clearance in the submersible sewage pump have a cross-section along the x-axis and y-axis directions. The positional distribution of the four sections (P1 to P4) is illustrated in Figure 23.

The distribution of the local loss coefficient l₃ related to the turbulent kinetic energy generation term is shown in Figure 24 across the four sections (P1 to P4), highlighting the intensity of turbulent kinetic energy generation in the local area. According to the diagram, under different tip clearance thicknesses, the high l₃ regions in sections P1 through to P4 are primarily concentrated around the edge of the impeller blade. This situation is particularly evident in terms of the distribution of l₃ at the tip clearance, where a sharp decrease in l₃ is observed in regions not in contact with the blade. This reduction occurs due to the absence of blade contact, mitigating the flow separation phenomena and, subsequently, reducing the turbulent energy. With the increasing tip clearance thickness, the region with elevated l₃ values at the tip clearance steadily expands towards the midsection of the impeller passage. The most noticeable diffusion changes are observed in the X1 to X4 and Y1 to Y4 regions, as represented in the figure. It is apparent that in these regions of the impeller, the l₃ value increases gradually with the thicker tip clearance, accompanied by an expanding diffusion range. This demonstrates that as the tip clearance increases, the leakage flow increases, impacting the fluid velocity and pressure distribution. Concurrently, the turbulence intensity within the impeller flow channel shows an increasing trend, consistent with the earlier findings. Moreover, under an identical tip clearance thickness, the l₃ distribution is notably more intricate in the X3, Y2, and Y3 regions, with higher l₃ values compared to the other five regions marked by red circles. The main reason is that the cross-sections of P2 and P3 are adjacent to the volute tongue, and the impeller rotation interacts with the tongue to produce a dynamic and static coherence effect. As a result of the interference effect, the flow properties in the central region of the impeller channel undergo considerable changes, forming more complex turbulence.

6. Conclusions

In the present study, the CFD–DEM coupling methodology is employed to investigate how varying particle parameters and tip clearance thicknesses affect the performance of an open impeller submersible sewage pump, operating under solid–liquid two-phase flow conditions. Utilizing the energy balance equation, the tip leakage vortex structure, the internal flow pattern, and wear characteristics of the pump for various tip clearance thicknesses are compared and analyzed, including the effect on energy conversion within the pump. The following key findings are summarized:

• At a low flow rate, a substantial low-speed region develops on the suction surface of the impeller, leading to the formation of minor vortices. The highest velocity region is located near the second section of the volute, and this peak velocity diminishes gradually with an increasing flow rate. Furthermore, higher flow rates lead to more dispersed particle distribution, increasing the wear rates, particularly at the leading edge of the blade. Conversely, the wear rates impacting the volute decrease;
• The relationship between the particle parameters and pump wear characteristics is compared and analyzed. It is observed that increasing the particle volume fraction leads to decreased inlet particle velocity. Meanwhile, the extent of the wear on the blade pressure leading edge, the suction surface trailing edge, and the volute area become larger. The wear rate is highest for long cylindrical particles, with spherical particles exhibiting the lowest wear rate. A low particle velocity is observed at the leading edge of the blade, which prolongs the particle contact time and causes significant wear in that area. The velocity of the particles at the trailing edge of the blade reaches the maximum, the impact effect is significantly enhanced, and a large area related to a high wear rate area appears;
• Through comparing the tip clearance thickness of 0.4 mm, 0.7 mm, and 1.0 mm, changes in the internal flow and wear rates of the flow passage components were analyzed. Observations indicate that a greater tip clearance thickness intensifies the leakage vortex at the tip clearance inlet. The tip leakage flow velocity escalates from the leading to the trailing edge of the blade, peaking at the trailing edge of the pressure surface, which also makes the TKE on the impeller gradually increase. Moreover, an increased tip clearance exacerbates particle aggregation, leading to a gradual reduction in the particle concentration within the impeller channel, and the wear rate of the impeller and volute gradually increase;
• By applying the energy balance equation, the effect of varying tip clearance thicknesses on the energy dissipation in the pump is assessed under solid–liquid two-phase flow conditions. The results indicate that the turbulent kinetic energy generation term L3 exhibits the highest magnitude, while the viscous dissipation term L4 exhibits the smallest proportion, highlighting turbulence as the primary source of energy dissipation in submersible sewage pump operations. Simultaneously, regions with elevated values in terms of the local loss coefficient l₃ from turbulent kinetic energy generation are primarily concentrated at the impeller inlet and blade edges. Under the same tip clearance thickness, dynamic and static interference results in higher l₃ values in regions X3, Y2, and Y3 near the volute tongue, indicating more complex flow dynamics.