Research on the multiphase flow in a sludge concentrated tank and its structural optimization

With the acceleration of industrialization and urbanization, sewage treatment has become an urgent task. However, the slow sedimentation rate of sludge limits the removal efficiency of pollutants in sewage and seriously affects the overall water quality of the environment. To improve the efficiency of sewage treatment and reduce the impact on the environment, it is urgent to further study the sludge sedimentation technology, optimize the technology, reduce energy consumption, and chemical consumption, so as to achieve the purpose of energy saving and emission reduction. Therefore, it is of great significance to optimize the design of large-scale sludge settling and thickening equipment to achieve efficient settling of sludge particles, and it is also the core research point in this study.

At present, in the research and design of sludge settlement equipment, many excellent scholars have proposed and developed settlement technology and methods. Dominiak et al. (2011) applied residual sludge on the reed bed and adjusted the sludge load, concentration, or sludge pretreatment to optimize the drainage process. Romero-Güiza et al. (2022) described the use of three advanced process control strategies to upgrade the sludge line of a full-scale wastewater treatment plant over a period of 6 years (2015–2021). The results show that advanced control strategies greatly improve resource utilization (Romero-Güiza et al., 2022). Mazhar et al. (2021) proposed that the removal efficiency of suspended particles by the Up-flow Anaerobic Sludge Blanket–Down-flow Hanging Sponge system was increased by 92.88%. The systematic scheme has good removal efficiency of sludge particles (Mazhar et al., 2021). Trelles et al. (2017) developed a simple method to predict the settling curve of pilot and industrial plants through laboratory-scale results. This method has good applicability for industrial wastewater treatment facilities with a sludge volume index ranging from 30 to 240 mL/g (Trelles et al. 2017). In addition, the main reason for the difficulty in sludge dewatering is the high content of organic and colloidal substances in the solid phase of the sludge, which leads to the high compressibility and particle deformation of the coagulated sludge during the mechanical dewatering stage, hindering the formation of high concentration solid filter cakes. The key to solving this problem lies in improving the filtration performance of sludge and studying the role of physical regulators (Qi et al. 2011). The core content of these studies mainly focuses on sludge settlement efficiency and control methods, involving mixing intensity, anaerobic digestion, sustainable sewage treatment, and flocculation. Through in-depth research in these areas, the sludge settlement technology can be further optimized to improve the efficiency and effectiveness of sewage treatment, thus achieving better environmental protection and economic benefits.

In addition, on the basis of theoretical and experimental studies, with the development of computational technology, the researchers used the two-phase flow method in computational fluid mechanics to simulate the sedimentation and concentration of sludge particles under different conditions, including different particle concentrations, fluid velocities, and particle sizes and shapes. Through these simulations, they analyzed parameters such as particle trajectory, velocity distribution, and pressure gradient and explored the mechanism of particle–fluid interaction. It provides theoretical support for further research on the mechanism of sludge particle settlement. Hirom et al. provided a comprehensive review of numerical simulation methods used to study sludge settlement in wastewater treatment processes, indicating the application value and significance of numerical methods for sludge particle settlement concentration (Hirom & Devi 2022). Xu et al. (2017) have developed new functions for fluid dynamic resistance, solid pressure, and shear stress. This force-based model provides a more convenient and useful tool for improving active sludge settlement design and operational optimization (Xu et al. 2017). The research of Bürger et al. (2011) establishes a consistent modeling approach (CMM) that combines classical concepts with mathematical applications to provide more accurate models for simulating and predicting various phenomena in wastewater treatment processes. In CMM, the actual process is transformed into a mathematical model, usually ordinary differential equations or partial differential equations, and then simulated on a computer using numerical methods, which helps one to better understand the dynamic behavior of the process and predict future trends (Bürger et al. 2011). Latsa et al. (1999) proposed a two-phase model for simulating settlement processes. This model solves the continuity equation and momentum equation for the pure transparent liquid phase and sludge phase, and is validated for a well-known benchmark problem that has an analytical solution. A typical one-dimensional batch settling process of monodisperse particles is numerically simulated, and the results are in agreement with experimental data and model predictions from other researchers. By further extending this model to two dimensions, it can predict the dynamic behavior of settlers and the impact of inclination on the settlement process (Latsa et al. 1999).

These studies demonstrate the importance of numerical methods in the study of sludge settling and concentration. Further numerical simulation can better understand the dynamic behavior and mechanism of sludge treatment process, and predict and control sludge settlement and concentration effect more accurately, so as to optimize the treatment process and improve efficiency. Mir developed a computational fluid dynamics (CFD) model based on the Takacs index function to simulate the effectiveness of mixing and settling in sludge ponds. Based on this model, a new operation method was developed that can effectively reduce the energy consumption of the mixer by 55% (Mir et al. 2018). More importantly, the numerical method can not only simulate the complex flow and mixing phenomenon but also consider the influence of different factors such as fluid parameters, particle properties, and chemical reactions on the sludge settlement and concentration, so as to comprehensively understand the sludge treatment process and provide a more reliable basis for practical application. Especially with the development of particle flow technology, the multiphase flow method has been applied to the study of sludge particle settlement and concentration, so as to more realistically simulate the complex flow and mixing phenomena occurring in the sludge treatment process (Zheng et al. 2001). Furthermore, models such as the two-fluid model (TFM) and CFD-discrete element method can be used to simulate these phenomena more accurately and provide more reliable prediction results. To better understand the behavior of sludge particles in the flow and mixing process and explore the interaction mechanism with the fluid, so as to optimize the treatment process, which provides important theoretical and technical guidance for practical production.

Based on the application of this numerical method in sludge particle flow, this study adopts the CFD two-phase flow method to simulate the particle flow and settling phenomenon in a sludge thickening tank. The influence of internal structure changes, such as the width of the branch of the diversion cone and the extension plate of the branch flow, on the concentration of settling particles at the bottom is discussed. This reveals the potential of internal structural optimization for improving sludge concentration and water purification effectiveness. The research results will provide important theoretical guidance for further improving the internal structure design of the sludge thickening tank and realizing more efficient energy saving and emission reduction.

This formula takes into account the equilibrium relationship between particle gravity, buoyancy, and fluid resistance. In multiphase flow, the interaction between particles is also one of the important factors affecting the settling behavior. The collision, coalescence, and fragmentation between particles can alter the distribution and dynamic characteristics of particle groups, thereby affecting the overall settlement effect. Therefore, when studying the theory of particle settling in multiphase flow, it is also necessary to consider the interaction mechanism between particles.

In addition, the theory of multiphase flow particle settling also needs to consider the influence of factors such as fluid turbulence, temperature field, and concentration field. These factors can alter the physical properties and flow state of the fluid, thereby affecting the settling behavior of the particles. To more accurately describe the settling process of multiphase flow particles, it is necessary to establish a mathematical model that includes the above factors and verify the accuracy and reliability of the model through experiments. In this regard, the TFM is considered an important method for dealing with large-scale particle motion in multiphase flow, and its computational results have been proven (Schneiderbauer 2018; Ahadi et al. 2019).

Currently, the TFM remains the mainstream of the development of CFD at engineering scales for two-phase flows. As the particle phase is treated as a quasi-fluid, the particle phase should have viscosity and pressure defined as those of a fluid. The closure method of the equation system will have a decisive impact on the simulation results of the TFM.

where u_s and ρ_p are the average velocity and density of the solid phase, respectively; u_f and ρ_f are the average velocity and density of the fluid phase, respectively; ε_s and ε_f are the volume fractions of the solid and fluid phases, respectively; τ_s is the stress tensor of the solid phase; τ_f is the stress tensor of the fluid phase; and F_fs is the volume average of the force exerted by the surrounding fluid on the particles.

Here, d_p,i is the diameter of the particle; v_p,i and u_s are the solid particle velocity and flow velocity, respectively; ρ_f is the density of the fluid; and C_d,i is the drag coefficient.

In the formula, k represents turbulent kinetic energy; ε is the dissipation rate of turbulent energy consumption; P_k is the turbulent kinetic energy generation term caused by the average velocity gradient (Jing et al. 2022); G_k is the turbulent kinetic energy generation term caused by buoyancy (Charrondière et al. 2020); μ is the turbulent viscosity coefficient (Di Nucci et al. 2020); are constants with a dimension of one, with values of 1.44, 1.92, and 0.85, respectively; σ_t is the turbulent Prandtl number of turbulent kinetic energy (Basu & Holtslag 2021), with a value of 1.0; and σ_z is the turbulent Prandtl number of turbulent energy dissipation rate, with a value of 1.2.

In this study, the flow port width (300, 400, 500 mm) formed at the bottom of the conical guide area and the wall surface, as well as the presence or absence of an extended guide plate, are analyzed and discussed to investigate the impact of the distance between the cone bottom and the wall surface in the guide chamber and the presence or absence of an extended plate on deposition efficiency. First, a three-dimensional model of the control system is established. The internal design and structural optimization methods and flow patterns of the sludge tank are further explained through three-dimensional internal structural models. This study mainly consists of the following steps. Establishing a three-dimensional model: Using CAD software, a three-dimensional model of the guide chamber is established based on the actual size and structure of the sludge tank. The model includes guide areas, cones, walls, and flow port widths of 300, 400, and 500 mm. Numerical calculations: The three-dimensional model is imported into CFD to simulate fluid flow in the guide chamber. Setting simulation conditions: In the CFD code, physical conditions for the simulation are set, including sludge fluid types (liquid phase and solid phase), fluid density, viscosity, inlet velocity, and other parameters. Appropriate boundary conditions are also established. Mesh generation: The model is meshed using appropriate mesh types and sizes, ensuring that the mesh is dense enough to meet the requirements of irrelevance for accurate simulation results (Nan et al. 2024). Simulation calculation: After setting up simulation conditions and meshing, simulations are conducted. By solving fluid dynamic equations, data on fluid velocity fields, pressure fields, and particle concentration fields in the guide chamber are obtained.

On the basis of the three-dimensional model constructed, the fine numerical simulation of the entire sludge particle settlement process inside the entire sludge concentration tank can be achieved by setting model boundaries and computational parameters. This allows for the effective analysis of fluid velocity fields, pressure fields, and vortex structure distribution under different guide chamber structures (such as the width of the flow port, the presence or absence of flow extension plates, etc.). It further aids in understanding the flow characteristics within the guide chamber, such as turbulence intensity and flow directionality. It explores how guide structures impact the uniformity of sludge particle flow and possible flow dead zones or vortexes. It also studies how changes in internal structures affect the overall particle settling efficiency. By comparing differences in simulation results under different design scenarios, the impact of each design on flow patterns and particle settlement efficiency can be evaluated.

The main physical parameters of mixed sludge in this study and the setting parameters for CFD calculation of sludge flow are shown in Tables 1 and 2.

In the analysis of numerical results of sludge settling, the distribution of sludge particle content and the flow changes of the entire flow field are the main considerations. Four monitoring surfaces and four monitoring points are set up in the three-dimensional model of the sludge tank. The coordinates of the monitoring surfaces and points are shown in Tables 3 and 4.

Figure 7 shows the concentration changes of a₁, b₁, c₁, and d₁ at the monitoring points in Table 4. With the increase of time, the concentration gradually increases. At the upper monitoring points fig 7(a) and (b), there is no particularly significant difference in concentration with the increase of time. However, at the lower position fig 7(c), it can be seen that at 300 s, the concentrations of 400 and 500 mm are higher than that of 300 mm. At point fig 7(d), under the condition of 500 mm guide cone bottom outlet width, the concentration of sludge particles deposited with time shows a significant sludge concentration effect. Its concentration is 21.8% higher than that of 400 mm width, and its concentration is 48.9% higher than that of 300 mm width. This indicates that the guide port width has a significant improvement on the deposition and concentration effect of sludge at the bottom position.

According to the velocity change on the velocity measurement line corresponding to the profile in Figure 8 (the transversal line at z = 2.76 m), it can be seen that the velocity on the velocity measurement line at the outlet of the guide cone flow decreases with the increase of the width of the diversion outlet, and the velocity change trend is basically the same with the extension of time (from 100 to 300 s). That is, the outlet flow rate under the width of 300 mm is greater than 400 and 500 mm. The opposite trend occurred on the monitoring line at the base of the cone. This is the speed change of the monitoring line at the base of the cone.

At the 300 s moment, the monitoring of sludge concentration shows that the distribution range of all is between 0.012 and 0.015, and the concentration distribution is close, with an average value around 0.0134. By further comparing the concentration difference range, it can be found that the overall concentration of S-500 mm is higher than that of 50 mm, and the overall concentration difference is 0.00105. This once again indicates that the internal structure design of S-500 mm has advantages in the sludge settlement effect.

Figure 14(a) and 14(b) clearly shows the changes in the Reynolds number of the internal flow field of the sludge tank, especially in the high Reynolds number range outside the guide cylinder. As the width of the cone bottom outlet increases, the high Reynolds number range decreases. Therefore, the change in the bottom width of the guide cone has a significant impact on the changes in flow velocity and turbulence development in the flow field, which further affects the settlement and concentration of sludge particles.

It can be seen from Figure 16(a)–16(c) that at points b and a, the concentration changes over time are higher than those at points c and d, regardless of the structure. In addition, the concentration at point b is significantly highest. Moreover, except for the case of a 400 mm guide cone outlet width, where the concentration at point b decreased, when the guide cone bottom outlet width is 500 mm, the sludge concentration value increases from 0.0112 at 300 mm to 0.0129, and it also increases to 0.0134 with an extension plate by Figure 16(c) and Figure 16(d) representing an increase of approximately 15.2 and 19.6%, respectively.

It can be seen from Figure 17(a) that the effect of sludge concentration inside the flow field changes. The most obvious one is that the sludge concentration inside the flow guide barrel is concentrated, which makes the sludge concentration inside the flow guide barrel significantly higher than that at the bottom width of the flow guide cone of other widths without extension for 300 s as shown in Figure 6. In addition, it can be seen from the top view and section view in Figure 17(a) that the concentration of sludge in the latter two sections also increases significantly. Therefore, it can be determined that the addition of the extension plate has a promoting effect on the concentration of the bottom sludge. In addition, the Reynolds number distribution and flow line distribution in Figure 17(b) and 17(c) show that the range of high Reynolds number in the upper barrel wall is significantly reduced, and the flow line in Figure 17(c) also reduces the range and vortex of the eddy flow line in the cylinder wall. This result indicates that the addition and extension of the flow guide plate can significantly reduce the turbulence phenomenon near the water purification outlet outside the barrel wall and realize the purification of sewage at the outlet. The above data analysis can provide an important basis for design optimization of the sludge thickening system and help improve the performance and efficiency of the sludge thickening tank.

Based on the above research content, the influence of internal structure and sewage flow is further discussed. The increase of the bottom outlet width of the guide cone will have a certain influence on the flow field and then affect the sludge concentration effect. When the outlet width increases, the flow velocity will relatively decrease, which will lead to a decrease in the carrying capacity of the fluid for sludge particles. This is mainly because as the vortex scale on the outer side of the cylinder wall decreases, the buoyancy of the sludge particles decreases, and under the action of gravity, the particles deposit at the bottom, resulting in concentration of sludge particles at the bottom. In this case, larger sludge particles will be more likely to settle at the outlet, thereby increasing the sludge concentration at the bottom. In addition, as the outlet width increases, the water purification capacity at the outlet will also be improved.

It can be seen from Figure 19(a) that the effluent sludge content is significantly reduced by optimizing the guide vane structure. After structure optimization, the water purification effect obviously increased by 7.41, 35.8, and 40.7%. This shows that the optimized guide vane structure can guide the water flow more effectively, reduce the formation of large eddy current and the impact force of water flow on the outlet, and thus reduce the sludge flowing out of the outlet with water. The optimized guide vane structure can improve the flow state of water and reduce unnecessary energy consumption (as shown in Figure 19(b), the energy consumption is significantly reduced by 3.7, 27.4, and 35.5%), thus achieving energy saving of the equipment.

Through the discussion, it can be seen that the optimization of diversion structure has multiple significance in improving sludge settling efficiency and realizing equipment energy saving. In the design and study of sludge structure, it is necessary to consider the influence mechanism of guide cone base width and guide cone extension plate on the water purification effect and sludge settling efficiency. Through the in-depth study of the influence of these two factors, it can provide a more accurate basis for optimizing the structural design, so as to improve the performance and efficiency of the sludge thickening tank.

In this study, the influence of the internal structure of the sludge tank (the width of the diversion outlet and the existence of the diversion extension plate) on the sedimentation rate of the sludge and the purification effect of the water outlet was explored through the multiphase flow numerical simulation method, so as to formulate the optimal internal structure. The whole study shows that increasing the width of the diversion outlet and adding the diversion extension plate can significantly improve the sedimentation efficiency at the bottom and outlet of the sludge tank. The specific conclusions are as follows.

• (1) The increase of the bottom outlet width of the diversion cone will lead to further attenuation of the upper eddy current scale, thus affecting the sludge concentration effect and water purification capacity. With the increase of the outlet width, the sludge concentration at the bottom increases, and the sludge concentration efficiency increases by 37% under the condition that the width of 500 mm is higher than that of 300 mm, and the water purification capacity is improved.

• (2) The presence or absence of an extension plate has a significant impact on sludge concentration and flow field. The extension plate can improve the flow field distribution, increase the residence time, eliminate the effect of eddy current, and significantly reduce the turbulence around the water outlet, and the sludge thickening efficiency at the bottom outlet is increased by 19.6%, which greatly promotes the settling and thickening of sludge. In addition, the internal structural design of the S-500 mm has advantages in terms of sludge settling. This conclusion is of great significance for optimizing wastewater treatment process and improving treatment efficiency.

• (3) The addition of an extension plate can eliminate the floating of sludge particles caused by eddy currents outside the cylinder wall to a large extent and significantly reduce the sludge content in the water flow at the upper outlet.

• (4) The tolerance of the bottom width of the diversion cone is the basis for exploring the influence mechanism of the diversion extension plate, and considering the water purification effect and sludge settling efficiency is the key point.

The above conclusions provide an important basis for the internal design of a sludge tank to improve the performance and efficiency of a sludge thickening tank. In future applications, combined with the internal optimization suggestions of this study, the influence mechanism of the effluent width, the length and shape of the extension plate, and other factors on the entire sludge system can be comprehensively considered in one step, and then the optimization scheme of the system can be realized.

This work was supported by the National Natural Science Foundation of China (project number: 52169027, 52069013), Tiandi Science and Technology Co. Ltd Science and Technology Innovation Venture Capital Special Project (2023-TD-ZD004-003GC-23-TZK05), Research on Efficient COD Degradation Technology in Mine Water Purification (GC-22-TZK02), Science and Technology Innovation Fund of Xi'an Research Institute of CCTEG (2023XAYJS11), and Nanchang Key Laboratory (NCZDSY-007).

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.