Research Progress on Numerical Simulation of Heterogeneous Flow Resistance in Sludge Conveying System

: Sludge pipeline transportation is increasingly used in different fields. Flow resistance is an important influencing factor in the pipeline transportation of solid-liquid two-phase flow slurry, and studying its characteristics is of great significance for optimizing pipeline design, reducing pipeline erosion and wear, and reducing transportation energy consumption. In view of the complexity of sludge as the resistance characteristics of solid-liquid two-phase flow, it is often necessary to analyze the inline mechanism of solid-liquid two-phase flow in slurry with the help of high-precision turbulent flow model in computational fluid dynamics (CFD), which has become the research focus of heterogeneous solid-liquid two-phase flow pipeline transportation. This paper analyzes and summarizes the CFD simulation status of heterogeneous solid-liquid two-phase flow resistance in pipelines, points out the future research direction, and provides reference for the analysis of heterogeneous flow resistance of sludge pipeline transportation and the optimization design of conveying system.


Introduction
Sludge is a heterogeneous solid-liquid two-phase flow is a fluid mixed with liquid and solid particles, which is widely present and used in various natural worlds and various fields such as energy, chemical industry, petroleum, water conservancy, such as coal water slurry hydraulic transportation. The conveying of heterogeneous solidliquid two-phase flow of sludge is also commonly referred to as slurry conveying, in which the concentration of particulate matter is generally high and has significant viscoelastic rheological properties. In recent years, more and more scholars have used computational fluid dynamics technology to study the transport characteristics of slurry in pipelines [1,2]. Ekambara K [3] (2009) conducted CFD numerical simulation of the slurry pipeline transportation experiment conducted by Roco and Shook et al., and found that the pressure drop and concentration distribution obtained by the simulation were highly consistent with the actual values measured by the experimental results. Kaushal D R [4] et al. (2012) established a two-phase Eulerian model for a volume concentration of 9% to 42%, a pipe diameter of 0.05m to 0.263m, and a particle size of 90 to 440 μ m. The slurry with a flow rate of 3 m/s~6.5 m/s was simulated for pressure drop during pipeline transportation. The simulated pressure distribution nephogram shows that the slurry pressure always reaches the maximum at the bottom of the pipe, consistent with expectations. The simulation results show that the CFD Euler two-phase flow model's prediction of pressure drop for slurry flow is in good agreement with experimental data. Gopaliya MK [5] et al.
(2016) conducted a three-dimensional CFD analysis of two-phase mud flow (sand water). The simulation results were compared with experimental data with a velocity range of 4.7 m/s to 5.0 m/s, a pipe diameter of 263 mm, and a concentration of 9.95% to 34%. The simulation results were in good agreement with the pressure drop, concentration, and velocity corresponding to the measured values. Xiongting [6] conducted resistance simulations of slurries with different particle sizes, and compared the differences between the numerical simulation and the Durand model's calculated values. It was found that the Durand model exaggerated the energy loss of the slurry, resulting in a relatively large resistance loss calculated by the model, and it was proved that the trend of the simulated value and the measured value was consistent. Chen Jianhong [7] compared the simulation of slurry resistance in the pipeline with the measured results, and the comparison showed that the maximum error between the two was about 5%, proving that numerical simulation can accurately predict the slurry resistance in the pipeline. Compared with traditional experimental methods, computational fluid dynamics can quickly and accurately obtain ideal research results through computer numerical calculation and image display methods for various complex flow physical phenomena, and has the advantages of not being limited by experimental conditions, low cost, fast calculation speed, high accuracy and good fitting. Therefore, it is of great significance to accurately predict the friction head loss by computational fluid dynamics for different actual conveying conditions, which is of great significance to the optimal design of sludge pipeline transportation system.

Mathematical model of slurry pipeline transportation CFD simulation 2.1 Euler model
The Euler model theory method is a differential method for solid-phase particles, which treats the liquid phase and solid-phase particles as continuous media and occupies a certain space, so 1. Both solid-liquid phases meet the mass conservation equation, momentum conservation equation and energy equation, and the phase and phase have different motion properties, and the concepts of pressure and viscosity are introduced into the solid-liquid two phases, and the resulting solid-liquid twophase mass conservation equation is as follows: Among them,t-time;g-acceleration of gravity; pfluid local pressure; , -concentrations of liquid and solid phases; ∇-Laplace operator; , -densities of liquid and solid phases, respectively; , -velocities of liquid and solid phases; , -shear stress tensor of liquid and solid phases; -exchange coefficient of solid and liquid phases.

Turbulence model
Turbulent kinetic energy and turbulent dissipation rate are calculated using the k-ε model. The k-ε model has a wider range of applicability and is used in both boundary layer flow and uniform shear flow, and is more applicable to this paper to study the design selection and parameter study for optimizing sludge pipe network transportation.
Among them, -turbulent kinetic energy generated by the turbulent kinetic energy due to the average velocity gradient; -turbulent kinetic energy generated by buoyancy; -effect of compressible turbulent arterial kinetic expansion on the total dissipation rate; , , -empirical coefficients =1.44, =1.92, =0.09; -turbulent viscosity coefficient.

Research progress on the influence of flow characteristics on flow resistance
Flow velocity has a direct effect on the flow pattern and transport resistance. Liu Qingqing [8] used CFD to simulate the velocity vectors at the inlet and outlet sections of the pipeline for sludge at different flow rates. The sludge density was set to 1013 kg/m3, the total solids concentration was 3.45%, the pipe diameter D was taken as 100 mm, the pipe length L was taken as 2 m, and the inlet flow rates were 0.5-3.5 m/s. By observing the simulated cloud diagram, it can be seen that as the flow rate increases, the pipeline pressure increases continuously, almost linearly. When the sludge flow rate increases from 0.5m/s to 3.5m/s, the sludge pressure increases by 3.45 times, as shown in Figure 1.Wu Guoying [9] conducted a CFD-based numerical study of the pressure in a solid-liquid two-phase flow pipeline for a solid-liquid two-phase flow with a pipe diameter of 0.6 m and a turning angle of 32° containing 10% sand, and simulated the pressure in the pipeline under different flow conditions by CFD. The pressure clouds with inlet flow velocities of 1m/s, 2m/s, 3m/s and 4m/s show that when the inlet flow velocity increases from 1m/s to 2m/s, the maximum pressure at the inlet concave wall in the pipe increases by 1055 Pa; when the inlet flow velocity increases from 2m/s to 3m/s, the pressure increases by 2300 Pa. The maximum pressure of the pipe increases with the increase of the flow velocity. This indicates that the conveying flow velocity is as close as possible to the critical flow velocity without slurry deposition to reduce the friction loss during the conveying process and reduce energy consumption while satisfying the transport efficiency. Xiao-Xi Qiao [10] et al. found that the pressure at various locations of the pressure cloud obtained from CFD simulation increased with the increase of flow velocity under the same other working conditions, indicating that with the gradual increase of flow velocity, the magnitude of pressure at the turning surface was significantly affected and the particle impact energy became larger, which intensified the head loss and slurry erosion wear on the pipe and was not conducive to the maintenance of the pipe. Ji Cheng [11] simulated the pipeline transportation of slurry through CFD to obtain the inlet particle concentration nephogram under different inlet flow rates.Combining the data obtained from CFD, it can be observed more intuitively that the hydraulic gradient gradually increases with the continuous improvement of flow velocity. Therefore, when selecting the flow rate, the appropriate critical flow rate should be selected based on the combination of pipe length, pipe diameter, slurry concentration, particle size gradation and viscosity.

Research progress on the influence of pipe characteristics on flow resistance
Qingqing Liu used CFD to simulate the slurry pipeline conveying conditions with the same concentration, all flow rates of 1 m/s, and pipe diameters D of 50 mm, 65 mm, 80 mm, 100 mm, 150 mm, 200 mm, and 300 mm, respectively, and the velocity vector diagram and pressure cloud distribution at the outlet derived from them, and based on the simulated pressure drop in the sludge in the pipe versus the diameter of the circular pipe It can be seen that the pressure drop in the pipe decreases with the increasing diameter of the pipe. When a larger pipe diameter is selected, the pressure drop in the pipe decreases more slowly compared to the smaller pipe diameter, while when a smaller pipe diameter is selected, the trend of pressure reduction is more significant. When v=2.5m/s, the pressure drop in the pipe decreases from 13629.32Pa to 10113.8Pa when the pipe diameter D increases from 65mm to 80mm, which is 25.79%; and when the pipe diameter increases from 150mm to 300mm, the reduction rate of the pressure is 13.04%, and this trend is more obvious when the transport flow rate is small.In the conveying process and the actual project should be combined with the construction cost and operating cost of the conveying system to choose the economic pipe diameter. Figure 2 shows the pressure drop changes under different pipe diameters.

Research progress on the influence of slurry properties on flow resistance
The slurry characteristics directly affect its friction loss in pipeline transportation. The concentration of the slurry is the most critical factor. The increase of the concentration makes the gap between the particles decrease, the degree of interaction intensifies, the flocculated mesh structure is easily formed, the viscosity of the slurry increases, and the friction loss increases. Most of the existing studies tend to study the inter-particle resistance in the pipe wall and slurry, while the energy dissipation caused by the particleto-particle collision inside the slurry is less studied. Zhong Lin [12]compared the influence law of effluent valve erosion and wear based on CFD numerical simulation for solid-liquid two-phase flow with the same flow rate and pipe diameter and different sand concentration, and it is known from the pressure cloud diagram that the maximum erosion rate and the average erosion rate of the effluent valve show a linear growth trend with the increase of particle concentration. Mz A [13]simulated the hydraulic transport process of coarse particles in a vertical pipe and investigated the effect of coarse particle concentration on the pipeline transport characteristics, showing that the axial liquid velocity and axial solid phase velocity decreased with increasing solid phase concentration in the feed and led to an increase in pressure drop.Combined with the above mentioned research results, it can be found that inelastic collision between particles is the main reason for the increase of energy loss due to the high concentration of the transported slurry in the project. With the increase of slurry concentration, it makes the gap between the particles decrease, which in turn leads to the increase of mutual collision between the particles and between the particles and the pipe wall, increasing the probability of inelastic collision. The high concentration slurry requires more energy for the particle material to do suspension motion compared with the low concentration slurry, while the settling resistance loss increases and the hydraulic slope increases.

Conclusions
In this paper, the research progress of numerical simulation of heterogeneous flow resistance in sludge pipeline conveying system is analyzed and summarized, and the following conclusions are drawn: (1) Numerical simulation can well simulate the flow state of slurry in the pipeline, and the simulated values of pressure drop and velocity distribution have good consistency with the measured values. When the sludge is transported in the pipeline, the appropriate flow rate should be controlled, and the high energy consumption caused by excessive speed should be avoided while preventing solid material deposition.
(2) When designing sludge conveying pipelines, the rheological parameters of sludge are obtained through experiments, and the pressure drop, flow rate, concentration distribution and change laws of different positions in the pipeline are obtained by numerical simulation, which can effectively predict the more serious abrasion of the pipeline and targeted post-maintenance, balance the conveying efficiency and conveying energy consumption and reduce the operating cost. It is recommended to go deep into the actual sludge pipeline transportation project, such as the sewage treatment plant, take samples and analyze on the spot, and combine the actual situation to widely provide a basis for the design of solid-liquid two-phase slurry conveying system, in order to be widely promoted in related design and application fields.