Numerical Method and Test Verification for Temporary Sludge Pipeline Transportation

In response to the problems of poor stability and low efficiency in the transportation of temporary sludge in Shanghai Laogang, based on indoor experimental data, numerical simulation was used to predict the pressure drop characteristics of pipelines with different solid content, pipe diameters, and flow velocities, the numerical results show that at the same flow rate and pipe diameter, the pressure drop increases with the increase of solid content; The pressure drop gradually increases with the increase of flow rate at the same pipe diameter and solid content, and when the the flow state inside the pipe changes, there is a turning point in the flow rate pressure drop curve; At the same flow rate and solid content, the pressure drop decreases with the increase of pipe diameter. Combined with test for pipe pressure drop, the numerical method was verified, which provides guidance for the optimization and improvement of sludge transportation plans and the selection of transportation pumps.


Introduction
At present, there is a huge amount of temporary sludge storage in major cities, the reserves in multiple places are approaching the upper limit, and further treatment is urgently needed [1][2][3].The sludge stored in the temporary storage area of Shanghai Laogang is generally characterized by high solid content and strong viscosity.Pump suction is the main method of sludge transportation, but for some high solid content sludge with high viscosity, it is difficult to transport and poor stability.However, sludge with low solid content becomes relatively easy to transport, but the transportation efficiency is low.Therefore, it is particularly important to study the pipeline transportation characteristics of sludge and improve transportation efficiency.
At present, many domestic and foreign scholars have conducted extensive scientific research on sludge pipeline transportation, Sadeghi [4] used the Euler Euler CFD model combined with particle dynamics theory to study the transport of particles in turbulent non-Newtonian carriers.The results of CFD prediction of pressure drop are in good agreement with experimental data.Joshi et al. [5] used the Euler two-phase model and RNG k-ε.The turbulence model studied the flow characteristics of slurry through a horizontal bend under different Prandtl numbers, and the research results showed that the pressure drop increased with the increase of flow velocity and Prandtl number.Liu [6] analyzed the flow characteristics of sludge in urban sewage treatment plants and established a theoretical calculation model for sludge pipeline transportation under homogeneous conditions.Huang et al. [7] used a segmented fitting method to obtain the initial yield stress and critical shear rate of municipal sludge, and obtained a full range of sludge rheological curves, and they conducted numerical simulations of circular pipe flow for sludge pipeline transportation and found that pipe diameter, flow velocity, and rheological index have a significant impact on pipeline flow.Lu [8] quantitatively predicted the heterogeneous flow resistance of urban sludge pipeline transportation based on the rheological properties of sludge, and established an annual conversion cost model for sludge pipeline transportation system as the basis of hydraulic calculation.Zhang et al. [9] theoretically analyzed the calculation formula for sludge flow velocity and the resistance coefficient along the pipeline, and analyzed and studied the effects of sludge moisture content, pipe diameter, flow velocity, etc. on the resistance characteristics of the pipeline.However, there is currently limited numerical simulation research on the pipeline transportation of temporary sludge.
On the basis of existing experimental results and combined with CFD commercial software, this paper simulated and analyzed the effects of different solid content, pipe diameter, and flow velocity on the pressure drop characteristics of pipeline transportation of temporary sludge.Pressure drop tests were conducted on construction sites, and the test results verified the reliability of the numerical method, providing theoretical support for stable and efficient sludge transportation in the future.

Rheological Model
By measuring on site, it was found that the solid content of the temporary sludge is about 10.6%.By substituting it into the rheological model in reference [10], it can be obtained that the yield stress (σs) is 2.4321, the viscosity coefficient (ηHB) is 1.2982 and the rheological index (n) is 0.4382.the rheological model with a solid content (P) of 10.6% is shown in equation (1).

Flow State Judgment
The characteristics of the rheological model mentioned in the previous section are closer to power-law fluids, so the sludge flow state is judged based on power-law fluids.The critical generalized Reynolds number ((Re)c) of power-law fluids [11], as shown in equation ( 4).
The generalized Reynolds number (Re) formula for power-law fluids [11], as shown in equation (5).
In the above formula, ρ is the density of sludge, D is the pipe diameter, v is the flow velocity.Obtain the Re of a sludge sample with a solid content of 5% -15% at a certain pipe diameter (Ø 287mm) and different flow velocities through equation ( 5), as shown in figure 2. It can be seen that under the same flow velocity, the higher the solid content, the smaller the Re; When the solid content is less than or equal to 10.6%, the Re of the sludge sample is higher than the (Re)c, and the flow state of the transported sludge is turbulent; When the solid content is 12.5%, when the flow velocity is greater than 2m/s, the Re is much higher than the (Re)c, and the flow state is turbulent.When the flow velocity is less than 2m/s, the Re is much lower than the (Re)c, and the flow velocity is laminar; When the solid content is 15%, when the flow velocity is greater than 3.5m/s, the Re is much higher than the (Re)c, and the flow state is turbulent.When the flow velocity is less than 3.5m/s, the Re is much lower than the (Re)c, and the flow velocity is laminar.From equation ( 5), it can be seen that at the same flow velocity, the Re increases with the increase of pipe diameter.

Mesh Partitioning and Independence Verification
The structured hexahedral mesh is chosen for solving the computational model, as shown in figure 4.During the meshing process, the distribution of wall shear force is adjusted by setting boundary layers.The shear rate of laminar wall is shown in equation ( 6) [12], the turbulent wall shear rate is shown in equation ( 7) [13].
f is the Fanning resistance coefficient, which can be obtained through the semi empirical formula proposed by Reed & Philevari [14], as shown in equation ( 8), Δ is the roughness of pipeline.Taking the pressure drop as the solution target, calculate the pressure drop by taking a 10m pipe section near the outlet of the pipeline, and convert it into the pressure drop at a pipe length of 500m.Calculate the pressure drop for different grid cell numbers (0.37million, 0.96million, 1.92 million, 3.09 million), as shown in figure 5. ∆P in the figure represents the pressure drop for a pipe length of 500m (the same below).From the figure, it can be seen that when the number of mesh elements is around 2 million, the pressure drop remains almost unchanged when the grid number is increased.

Numerical Methods and Computation Schemes
Some commercial software is used for numerical analysis of the computation model.The k-w turbulence model and laminar model are used to solve the turbulent and laminar flow fields, respectively, to achieve closed solution of the equation system.The convergence accuracy is set to 10E-6.The wall roughness is set to 0.5mm, and the boundary conditions are set to velocity inlet and average static pressure outlet.The computation scheme is shown in the table 1

Effect of Solid Content on Pressure Drop
Figure 6 shows the calculation results of pressure drop under different solid content and flow velocities when the pipe diameter is 287mm.It can be seen from the figure that under the same flow velocity, the pressure drop increases with the increase of solid content; When the solid content is the same, the pressure drop gradually increases with the increase of flow velocity.Compared to the solid content of 5% and 10.6%, when the solid content is 15%, there is an inflection point in the curve of pressure drop changing with flow velocity.Before the inflection point, the pressure drop flow velocity slope is small, and after the inflection point, the pressure drop flow velocity slope is large.This is mainly because the sludge flow state in the pipe changes from laminar flow to turbulent flow with the increase of flow velocity.
Figure 6.Pressure drop at different solid contents.

Effect of Pipe Diameters on Pressure Drop
Figure 7 shows the calculation results of pressure drop under different pipe diameters and flow velocities when the solid content is 10.6%.From the figure, it can be seen that under the same flow velocity, the pressure drop decreases with the increase of pipe diameter; When the pipe diameter is the same, the pressure drop gradually increases with the increase of flow velocity.

Effect of Pipe Diameters on Flow Field
Figure 11 shows the distribution of outlet velocity under different pipe diameters (P = 10.6%, v = 3m/s).
It can be seen from the figure that the change in pipe diameter has a small impact on the distribution of flow velocity inside the pipe, and the velocity field can be approximately considered to be proportionally enlarged.

Test and Verification
To verify the reliability of the numerical method, pipeline testing was conducted at the construction site of the Laogang Project Department.All instruments and meters are installed on the discharge pipeline, with an inner diameter of 287mm.Figure 13 shows the pressure gauge installed on the discharge pipeline.
There are two pressure gauges installed on the discharge pipeline, with a distance of approximately 500m between the two gauges.The solid content of the backend mud sample was determined to be about 10.6%.Two on-site tests were conducted, with 60 sets of data collected for each test.Considering the fluctuation of on-site data, the test data was averaged.Table 2 shows the average data tested.Table 3 shows the comparison between numerical simulation data and experimental data.It can be seen when the flow velocities are about 1.94m/s and 2.48m/s, compared to the measured results of pipeline pressure drop, the relative deviations of the numerical simulation results of pressure drop are 0.4% and 1.3%, respectively, which verified the reliability of the numerical method.(Relative deviation of pressure drop=(｜pressure drop under numerical simulation -pressure drop on test｜) / pressure drop on test × 100%)

Conclusion
By comparing and analyzing the effects of solid content, pipe diameter, and flow velocity on pressure drop, it can be seen that at the same flow velocity and pipe diameter, the pressure drop increases with the increase of solid content.The pressure drop gradually increases with the increase of flow velocity, and there is a turning point in the phase velocity pressure drop curve when the flow state inside the pipe changes.At the same flow velocity and solid content, the pressure drop decreases with the increase of pipe diameter.By comparing and analyzing the effects of solid content, pipe diameter, and flow velocity on the flow field of the pipeline, it can be concluded that there is a high viscosity region in the center of the pipeline.When the solid content is the same and the pipe diameter is the same, the high viscosity area decreases and the highest viscosity value decreases with the increase of flow velocity.Under the same flow velocity and the same pipe diameter, the viscosity in the high-velocity area of the pipe center, the lowvelocity area of the pipe wall, and the same position all increase with the increase of solid content.When the flow velocity and solid content are the same, the change in pipe diameter has little effect on the distribution of flow velocity and viscosity inside the pipe.
By comparing and analyzing the numerical results with the on-site test results, the numerical simulation results of the pressure drop are in good agreement with the measured results, verifying the reliability and accuracy of the numerical method and providing strong support for future engineering applications.

Figure 1 .
Figure 1.(Re)c varies with n.Figure 2. (Re)c varies with v at different solid contents.

Figure 2 .
Figure 1.(Re)c varies with n.Figure 2. (Re)c varies with v at different solid contents.4. Computation Model Figure 3 is a schematic diagram of the computation model, The length of pipe model is 50m.The left side shows the inlet and the right side shows the outlet.

Figure 7 .
Figure 7. Pressure drop at different pipe diameters.

Figure 10
Figure 10 shows the distribution of outlet dynamic viscosity under different solid content (D = 287mm, v = 3m/s).It can be seen from the figure that as the solid content increases, the viscosity of the same position in the pipe area increases.

Figure 10 .
Figure 10.Distribution of outlet dynamic viscosity under different solid contents.

Figure 11 .
Figure 11.Distribution of outlet velocity under different pipe diameters.

Figure 12 Figure 12 .
Figure12shows the distribution of outlet dynamic viscosity under different pipe diameters (P = 10.6%, v = 3m/s).It can be seen from the figure that as the pipe diameter increases, the high viscosity

Table 3 .
Comparison between numerical simulation and test.