Abstract
The study of hydraulic characteristics of water flow affected by blocked sediment is vital to assess discharge capacity in pipes with sediment sand to understand the process of pollutant and fine sand aggregation. The aim of this paper is to study the blocking effect of permeable sediments on non-full flow in circular pipe and to analyze hydraulic characteristics with backwater. Experiments and numerical simulations were performed and the porous media model is used to simulate the flow in permeable blocked sediments. To evaluate the degree of congestion, the backwater ratio β is proposed. The backwater ratio is positively proportional to blocked sediment height and inversely proportional to blocked sediment particle size and flow value. Cross-sectional velocity in the backwater zone decreases significantly and tends to be uniform as backwater ratio increases. Furthermore, the development of secondary flows and velocity distributions influenced by backwater height is discussed. The dimensionless shear velocity in backwater zone shows an exponential decrease as the backwater ratio increases, which greatly increases the possibility of further sediment deposition.
HIGHLIGHTS
The backwater ratio β is proposed to evaluate the effect of blocked sediment and to study the relationship between backwater height and blockage parameters.
The porous media model is used to simulate the flow in permeable blocked sediments.
The changes of flow field are observed under different backwater ratio.
INTRODUCTION
The drainage network is an important infrastructure for public health and safety and environmental protection. During the long-term operation of the urban sewer network, solid particles on the urban surface enter the drainage pipes with the rainwater catchment. As a result, deposition of suspended particles and pollutants is common in the pipeline. A study of some drainage pipes in Beijing city found that 60% of the drainage pipes had sediments, and the amount of sediment increased with the increase of the pipe diameter (Li et al. 2011). The sediment deposition rate in European drainage pipes can reach 30–50 
(Yuan et al. 2010), while the sediment deposit thickness exceeds 30 cm in drainage pipes with a diameter of 1.25 m or more in French (Chebbo et al. 1995). Although many self-cleaning models have been proposed (Safari et al. 2018; Carrera & La Motta 2020; Montes et al. 2020; Safari & Aksoy 2021), sediment in gravity sewers is always present. Even if the slope of the pipeline is very steep, there will still be some coarse sand deposited at the bottom during the recession stage (Butler et al. 1996). Therefore, self-cleaning models are enriched, and sewers with larger pipe diameters can be designed to allow for certain optimized deposit thicknesses to maximize their sediment transport capacity (Ab Ghani 1993; Nalluri & Ghani 1996; Safari et al. 2017). Sluggishness of flow are responsible for increased possibility for sediment deposition and accumulation in sewers leading to blockages. Therefore, it is necessary to study the hydraulic characteristics of the flow in the presence of blocked sediments in the pipeline, which assess the discharge capacity in drainage pipes with sediments and help to understand the processes of pollutant and fine sand aggregation.
The hydraulic performance of open channel flow in circular pipes with sediment has been widely studied. Some researchers have studied boundary shear stress distribution in circular pipes with flat sediment beds and estimated the roughness and resistance coefficients (Perrusquía et al. 1995; Sterling & Knight 2000). Nalluri et al. (1994) investigated the effect of permanent deposits on the invert of pipe channels on sediment carrying capacity and hydraulic resistance to flow. Hoohlo (1994) predicted the hydraulic characteristics of composite sections for different sediment bed roughness. Magura (2007) conducted numerous experimental studies on the velocity field of culverts filled with granular materials. Banasiak (2008) studied experimentally the influence of non-cohesive and partly cohesive deposits on hydraulic performance of sewer pipes. Fathy et al. (2020) obtained an equation to estimate the system efficiency as a function of blockage ratios and system discharges. However, a proportion of the total volume of any sediment, loose or cemented, consists of empty space. The previous studies neglected the permeability of sediments.
At the same time, sediments accumulation and blockage cause the upstream water level to increase and backwater in front of blocked sediment in pipe. The hydraulic characteristics of the partially filled pipe flow are inextricably linked to water depth in pipe (Zeyu et al. 2007; Yoon et al. 2012; Ng et al. 2018). However, the relationship of bank-up water height and hydraulic characteristics in circular pipes with blocked sediment is rarely discussed.
The aim of this paper is to study the blocking effect of permeable sediments on circular pipe with non-full flow and to analyze hydraulic characteristics with backwater. Experiments and numerical simulations were performed to investigate turbulent flow in sewer pipes with blocked sediments. The porous media model is used to simulate the flow in permeable blocked sediments and the simulated data are compared with the experimental data to verify the validity of the model. Furthermore, the backwater ratio is proposed to evaluate the degree of congestion and to study the relationship between backwater height and blockage parameters including particle size and height of blocked sediment. The changes of flow field are observed under different backwater ratio simultaneously.
MATERIALS AND METHODS
Experimental measurement
The experimental system for this research was installed in the Hydraulics Laboratory of Water Conservancy Engineering of Zhengzhou University, as shown in Figure 1. The pipe of the experiment equipment is made of transparent organic glass pipe with an inner diameter of 0.152 m, length of 10 m long. And the top of pipe is open to lay sediment conveniently. The bottom slope of pipe is 0.3%. Gravels of uniform particle size are laid horizontally at the bottom of the pipe to represent the sediment in actual drainage pipe. During the experiment, the water level of the water supply tower was kept stable, and the room temperature was 20 °C. The flow valve was adjusted to control the inlet flow. There is sufficient time to develop a steady flow. A tailgate is set up to control the constant tailwater level downstream. A needle water level gauge is used to measure the water level of the pipe flow with a measurement accuracy of 0.1 mm. The flow velocity above bed surface was measured using an acoustic doppler velocimeter (ADV).
Schematic diagram of the experimental apparatus.
is the thickness of the deposition, m; D is the pipe diameter, m. Therefore, the flow in a clean and non-deposited pipe was set as the control group, and flows with sediment deposit length of 4 m and sediment ratios of 0.1, 0.2 and 0.3 were experimented. Using the flow rate of inlet, sediment sizes, and sediment thickness as variables, we compared and analyzed the banked-up water effect and the hydrodynamic characteristics in backwater conditions in a total of 36 conditions, as shown in Table 1.Summary of experimental working conditions
| Particle size (mm) |  | Q (L/s) |  | Q (L/s) |  | Q (L/s) |
|---|---|---|---|---|---|---|
3 ( ) | 0.1 | 1.02 | 0.2 | 1.01 | 0.3 | 1.00 |
| 2.01 | 2.00 | 2.01 | ||||
| 2.99 | 3.02 | 3.01 | ||||
| 4.00 | 4.01 | 3.98 | ||||
| 4.98 | 4.98 | 4.99 | ||||
| 5.97 | 5.99 | 5.98 | ||||
5 ( ) | 0.1 | 1.01 | 0.2 | 1.02 | 0.3 | 1.01 |
| 2.02 | 2.01 | 2.01 | ||||
| 3.00 | 3.01 | 3.00 | ||||
| 4.01 | 3.98 | 3.97 | ||||
| 5.01 | 5.01 | 4.99 | ||||
| 5.99 | 5.98 | 5.98 |
| Particle size (mm) | | Q (L/s) | | Q (L/s) | | Q (L/s) |
|---|---|---|---|---|---|---|
| 3 () | 0.1 | 1.02 | 0.2 | 1.01 | 0.3 | 1.00 |
| 2.01 | 2.00 | 2.01 | ||||
| 2.99 | 3.02 | 3.01 | ||||
| 4.00 | 4.01 | 3.98 | ||||
| 4.98 | 4.98 | 4.99 | ||||
| 5.97 | 5.99 | 5.98 | ||||
| 5 () | 0.1 | 1.01 | 0.2 | 1.02 | 0.3 | 1.01 |
| 2.02 | 2.01 | 2.01 | ||||
| 3.00 | 3.01 | 3.00 | ||||
| 4.01 | 3.98 | 3.97 | ||||
| 5.01 | 5.01 | 4.99 | ||||
| 5.99 | 5.98 | 5.98 |
Numerical simulation
Governing equations and turbulent flow model
, 
are the flow velocity components (m/s), i = 1, 2, 3, j = 1, 2, 3; 
, 
are the coordinate components (m); p is the pressure (Pa); 
is the mass force (
); 
is the kinematic viscosity coefficient (
).
can be given as formulated in Equation (4).
is the convection term; 
is the turbulent diffusion, 
is the molecular diffusion, 
and 
are the stress and buoyancy production rate of 
, respectively, 
is the pressure strain, 
is the dissipation, 
is the production by system rotation, and 
is the user-defined source term, which depends on the study case.
is the turbulent viscosity,
component of the unit normal to the wall, 
is a constant.
is the slow pressure-strain which representing a return to isotropy by purely turbulent interactions, 
is the rapid pressure-strain taking account of the return to isotropy by the interaction between the turbulence and the mean velocity gradients, and 
is the wall-reflection term that is responsible for the damping of the velocity fluctuation component. Each component of the pressure strain can be formulated as following Equations (9)–(11):
is the component of the unit normal to the wall, d is the normal distance to the wall, 
is the turbulent kinetic energy, 
, 
, 
, and 
are constants.Porous media model
is the permeability and 
is the inertial resistance factor. One technique for deriving the appropriate constants involves the use of the Ergun equation, a semi-empirical correlation applicable over a wide range of Reynolds numbers and for many types of packing:
is the viscosity, 
is the mean particle diameter, L is the bed depth, and 
is the void fraction, defined as the volume of voids divided by the volume of the packed bed. The void fraction of gravels with the average particle size of 5 and 3 mm were 0.39 and 0.37, respectively, as measured by in-water weighing experimental method.
So the permeability coefficient and inertial drag coefficient are determined by the average particle size and void fraction of the sediment.
Numerical analysis conditions
As shown in the Figure 2, we use ANSYS Design Modeler to build a geometric model of the non-full flow of circular pipe with a pipe diameter of 0.152 m and length of 10 m. A porous media area with length of 4 m is set at the bottom of the pipe to simulate the blocking effect of the deposited bed. The height of porous media area is determined by sediment ratio. The grids are divided in ANSYS ICEM. Three mesh sizes in cross section of 8, 4 and 2 mm are set respectively for simulation calculation. Considering the calculation efficiency and calculation accuracy, the grid size is set to 4 mm in the cross section and 15 mm along the flow direction.
Schematic diagram of the model setup, meshing and boundary conditions.
The model boundary conditions are as follows: Upstream was set as velocity inlet to control the entry flow rate. Downstream was set as the pressure outlet to keep non-pressure flow in the pipe. Gravity is decomposed into longitudinal and vertical components to represent the effect of slope on water flow. The treatment of the free water surface uses the VOF method to calculate the equation of the volume rate function of the water body at the free interface. The wall boundary condition is set to no-slip solid wall condition, and the flow velocity distribution near the wall is calculated using the standard wall function. The blocked sediment area is set up as a porous domain to achieve the continuity of the fluid domain in the pipe. Input for the numerical analysis is set according to experimental variables.
RESULTS AND DISCUSSION
Comparison of numerical model results and experimental data
To validate the reliability of the simulation, the numerical data are compared with the experimental results of water depths along the pipe and average velocity. By comparing the measured and simulated water surface, the simulation data has a good agreement with the experimental results of the water surface as shown in Figure 3. Firstly, water flow is banked up in the upstream of the pipe near the sediment section, the water depth increases and velocity decreases. And then the water depth gradually declines along the sediment pipeline, the water crossing section shrinks and velocity gradually increases. When water flows over blocked sediment, the water depth drops rapidly and fluctuates sharply.
Comparison of the free water surface line between the simulation and experiment. (Z is the axis along the pipe with the sediment start point as the origin).
Comparison of the free water surface line between the simulation and experiment. (Z is the axis along the pipe with the sediment start point as the origin).
Table 2 shows the comparison of calculated and measured average velocity with a sediment ratio of 0.1 for different discharges. Where 
is experimental velocity value, 
is simulated velocity value, 
is the relative error between calculated and measured average velocity. As shown in the table, the relative error distribution is within 5%, the maximum absolute value of the error is 4.15%, and the average absolute value of the error is 1.66%. It is shown that the mathematical model and parameters used can accurately simulate the hydraulic characteristics of the flow with blocked sediment.
Comparison of calculated and measured average velocity with 
0.1
| Q (L/s) | Z (m) |   |   |   | Q (L/s) | Z (m) |   |   |   |
|---|---|---|---|---|---|---|---|---|---|
| 1 | −1 | 0.142 | 0.142 | 0.28 | 4 | −1 | 0.326 | 0.316 | 3.19 |
| 0 | 0.138 | 0.136 | 1.36 | 0 | 0.312 | 0.307 | 1.52 | ||
| 1 | 0.142 | 0.140 | 1.32 | 1 | 0.320 | 0.317 | 1.03 | ||
| 2 | 0.145 | 0.149 | −2.65 | 2 | 0.336 | 0.338 | −0.65 | ||
| 3 | 0.162 | 0.168 | −3.72 | 3 | 0.372 | 0.378 | −1.59 | ||
| 2 | −1 | 0.218 | 0.212 | 2.98 | 5 | −1 | 0.359 | 0.358 | 0.38 |
| 0 | 0.206 | 0.203 | 1.64 | 0 | 0.349 | 0.349 | 0.14 | ||
| 1 | 0.211 | 0.209 | 1.12 | 1 | 0.355 | 0.360 | −1.43 | ||
| 2 | 0.226 | 0.222 | 1.76 | 2 | 0.372 | 0.384 | −3.14 | ||
| 3 | 0.250 | 0.249 | 0.41 | 3 | 0.410 | 0.427 | −4.15 | ||
| 3 | −1 | 0.273 | 0.266 | 2.44 | 6 | −1 | 0.395 | 0.394 | 0.25 |
| 0 | 0.262 | 0.258 | 1.59 | 0 | 0.387 | 0.386 | 0.30 | ||
| 1 | 0.262 | 0.266 | −1.39 | 1 | 0.390 | 0.398 | −2.04 | ||
| 2 | 0.281 | 0.284 | −0.90 | 2 | 0.416 | 0.422 | −1.39 | ||
| 3 | 0.322 | 0.318 | 1.27 | 3 | 0.452 | 0.469 | −3.68 |
| Q (L/s) | Z (m) | | | | Q (L/s) | Z (m) | | | |
|---|---|---|---|---|---|---|---|---|---|
| 1 | −1 | 0.142 | 0.142 | 0.28 | 4 | −1 | 0.326 | 0.316 | 3.19 |
| 0 | 0.138 | 0.136 | 1.36 | 0 | 0.312 | 0.307 | 1.52 | ||
| 1 | 0.142 | 0.140 | 1.32 | 1 | 0.320 | 0.317 | 1.03 | ||
| 2 | 0.145 | 0.149 | −2.65 | 2 | 0.336 | 0.338 | −0.65 | ||
| 3 | 0.162 | 0.168 | −3.72 | 3 | 0.372 | 0.378 | −1.59 | ||
| 2 | −1 | 0.218 | 0.212 | 2.98 | 5 | −1 | 0.359 | 0.358 | 0.38 |
| 0 | 0.206 | 0.203 | 1.64 | 0 | 0.349 | 0.349 | 0.14 | ||
| 1 | 0.211 | 0.209 | 1.12 | 1 | 0.355 | 0.360 | −1.43 | ||
| 2 | 0.226 | 0.222 | 1.76 | 2 | 0.372 | 0.384 | −3.14 | ||
| 3 | 0.250 | 0.249 | 0.41 | 3 | 0.410 | 0.427 | −4.15 | ||
| 3 | −1 | 0.273 | 0.266 | 2.44 | 6 | −1 | 0.395 | 0.394 | 0.25 |
| 0 | 0.262 | 0.258 | 1.59 | 0 | 0.387 | 0.386 | 0.30 | ||
| 1 | 0.262 | 0.266 | −1.39 | 1 | 0.390 | 0.398 | −2.04 | ||
| 2 | 0.281 | 0.284 | −0.90 | 2 | 0.416 | 0.422 | −1.39 | ||
| 3 | 0.322 | 0.318 | 1.27 | 3 | 0.452 | 0.469 | −3.68 |
Backwater ratios and shear velocities with sediment of particle size of 
 | Q(L/s) |  |  (cm/s) |  | Q(L/s) |  |  (cm/s) |
|---|---|---|---|---|---|---|---|
| 0.1 | 1 | 2.16 | 0.781 | 0.2 | 4 | 1.87 | 1.260 |
| 2 | 1.90 | 1.115 | 5 | 1.79 | 1.430 | ||
| 3 | 1.78 | 1.446 | 6 | 1.78 | 1.510 | ||
| 4 | 1.68 | 1.709 | 0.3 | 1 | 3.05 | 0.449 | |
| 5 | 1.61 | 1.911 | 2 | 2.45 | 0.600 | ||
| 6 | 1.59 | 2.059 | 3 | 2.19 | 0.763 | ||
| 0.2 | 1 | 2.78 | 0.602 | 4 | 2.04 | 0.904 | |
| 2 | 2.24 | 0.862 | 5 | 1.94 | 1.025 | ||
| 3 | 2.03 | 0.966 | 6 | 1.93 | 1.183 |
| Q(L/s) | | (cm/s) | | Q(L/s) | | (cm/s) |
|---|---|---|---|---|---|---|---|
| 0.1 | 1 | 2.16 | 0.781 | 0.2 | 4 | 1.87 | 1.260 |
| 2 | 1.90 | 1.115 | 5 | 1.79 | 1.430 | ||
| 3 | 1.78 | 1.446 | 6 | 1.78 | 1.510 | ||
| 4 | 1.68 | 1.709 | 0.3 | 1 | 3.05 | 0.449 | |
| 5 | 1.61 | 1.911 | 2 | 2.45 | 0.600 | ||
| 6 | 1.59 | 2.059 | 3 | 2.19 | 0.763 | ||
| 0.2 | 1 | 2.78 | 0.602 | 4 | 2.04 | 0.904 | |
| 2 | 2.24 | 0.862 | 5 | 1.94 | 1.025 | ||
| 3 | 2.03 | 0.966 | 6 | 1.93 | 1.183 |
(Z
0.5 m).
Backwater in front of blocked sediment
is normal water depth of uniform flow without sediment.
Figure 4 shows the relationship between β and the sediment height, particle size of sediment as well as flow value. It can be found that the backwater ratio decreases with the increasing of flow, and the trend becomes slower. And this trend indicates that the smaller the amount of water in the pipe, the greater the negative effect of the same sediment on flow, which is obviously unfavorable to the actual operation. In addition, it is evident that the backwater ratio increases as the height of blocked sediment increase for the same discharge. This is mainly because the flow needs to cross over higher blocked sediments and water depth becomes higher. It is very small and difficult to observe the effect of permeability of the sediments on the backwater ratio. Sediments with larger particle size show greater permeability characteristics. Less permeable sediments cause greater backwater effect.
Backwater ratio relation with discharge. (Z = 0 m).
Discharge capacity affected by the backwater effect
Velocity profiles on mid-perpendiculars
The discharge capacity of drainage pipeline is very sensitive to the water level, which is greatly affected by the backwater effect. To ensure the representativeness and accuracy of velocity profiles, the XY section with sharp water surface fluctuation in the direction of flow is not suitable as a typical cross section to observe velocity distribution. Therefore, we choose the cross sections of Z = −0.5 m and Z = 2 m as typical of backwater section and sedimentary section, respectively. Figure 5(a) shows velocity profiles on mid-perpendiculars of different backwater ratio in the backwater section. The flow velocity within backwater zone is greatly reduced compared to uniform flow for same flow rate. Cross-sectional velocity decreases significantly as the backwater ratio increases and becomes more uniform along the depth of water.
Velocity profiles on mid-perpendiculars of different backwater ratios. ((a) Comparison of different sediment ratios with sediment particle size of 
for Q = 3 L/s, Z = −0.5 m; (b) Comparison of different sediment particle size and discharge for 
, Z = 2 m).
Velocity profiles on mid-perpendiculars of different backwater ratios. ((a) Comparison of different sediment ratios with sediment particle size of for Q = 3 L/s, Z = −0.5 m; (b) Comparison of different sediment particle size and discharge for , Z = 2 m).
Figure 5(b) shows velocity profiles on mid-perpendiculars of two sediment types in sediment section. The velocity over sediment with particle size of 5 mm is slightly larger than that with particle size of 3 mm for a fixed flow rate. The seepage velocity in blocked sediment increases as discharge increase. Compared with small particle size sediments, large particle size sediments are more loosely structured and have increased permeability for the large void fraction. The seepage flow in large particle size sediments bear less viscous resistance, and seepage velocity in the large particle size sediments is faster than that in the small particle size sediments. As a consequence, pollutants through large particle size sediments can transport faster.
Figure 6 shows the comparison of seepage flow of the two types of sediments at two cross-sections. It can be seen that seepage flow in sediments of small particle size is approximately 40% of that in sediments with large particle size. The seepage flow in sediments is proportional to the discharge of pipe. The seepage discharge increases with the increasing of sediment ratio, resulting from that amounts of sediment have more voids to allow flow through.
Seepage discharge under different deposition conditions.
Velocity structure in partial sedimentary section
When the backwater effect occurs in rectangular open channels, the cross-sectional shape of flow area is still rectangular as the depth of flow increases (Mulahasan et al. 2021). However, when it occurs in a partially filled circular pipe with sediment, the cross-sectional shape of flow area keeps changing as the depth of flow increases. Backwater height determines the degree of filling in the pipe. Due to the presence of the sediment bed and curved side walls for the sediment section, it is found that there is a secondary flow on cross section.
Figure 7 shows the velocity field of the sediment section in an XY plane. For three cases, in-plane flow structures symmetric about the y-axis are observed clearly. For the case that the water depth in pipe is approximately 2/5 of pipe diameter, the secondary flow structure with counter-rotating vortex pair are present near water-sediment interface, directing up in the pipe centerline and down at the pipe walls. Affected by secondary flows, water flow above sediment bed move to two sides, and it effectively creates two localize areas of maximum velocity above the edges of the gravel bed. Referring to Figure 7(a) and 7(b), the secondary flow pattern caused by the non-circular cross section are directed in the opposite direction when the water depth slightly greater than the radius of the pipe. It can be found that the core of this secondary flow appears above the sides of the sediment bed. And this secondary flow had a large impact on flow structure, making the area of maximum flow velocity back to the center of the pipe. For the third case, the filling degree is up to 2/3 pipe diameter, the secondary flow pattern is directed up at the pipe walls and down in the pipe centerline. The influence of the secondary flow just formed further expands. The scope of secondary flow becomes larger and the core of the secondary flow moves upward. It can be seen that the maximum velocity appears at the middle of water surface and velocity decreases toward the pipe wall and blocked sediment bed. In addition, the trend can be found that the region of high velocity moves down from the water surface as the filling degree rises according to the change of velocity contour.
Velocity contour and XY plane velocity vector of cross section with sediment of 0.1 D thickness. (Z = 2 m, (a), (b) and (c) are velocity contour for discharge of 1 L/s, 3 L/s, 6 L/s; (d), (e) and (f) are velocity vector in XY plane for discharge of 1 L/s, 3 L/s, 6 L/s.).
Velocity contour and XY plane velocity vector of cross section with sediment of 0.1 D thickness. (Z = 2 m, (a), (b) and (c) are velocity contour for discharge of 1 L/s, 3 L/s, 6 L/s; (d), (e) and (f) are velocity vector in XY plane for discharge of 1 L/s, 3 L/s, 6 L/s.).
Shear velocity in the backwater zone
, can be defined as follows:
is the bed shear stress, and ρ is the fluid density.
is longitudinal fluctuating velocity; and 
is vertical fluctuating velocity.We selected a cross section of Z = −0.5 m as the characteristic section of backwater to analyse the relationship between the degree of congestion and shear velocity as shown in Tables 3 and 4. The table shows backwater ratios and shear velocities of the two types of sediments at the characteristic sections.
Backwater ratios and friction velocities with sediment of particle size of 
 | Q(L/s) |  |  (cm/s) |  | Q(L/s) |  |  (cm/s) |
|---|---|---|---|---|---|---|---|
| 0.1 | 1 | 2.22 | 0.668 | 0.2 | 4 | 1.94 | 1.192 |
| 2 | 1.97 | 1.075 | 5 | 1.83 | 1.332 | ||
| 3 | 1.83 | 1.398 | 6 | 1.80 | 1.431 | ||
| 4 | 1.73 | 1.576 | 0.3 | 1 | 3.09 | 0.437 | |
| 5 | 1.68 | 1.747 | 2 | 2.48 | 0.553 | ||
| 6 | 1.63 | 1.873 | 3 | 2.22 | 0.698 | ||
| 0.2 | 1 | 2.78 | 0.579 | 4 | 2.09 | 0.805 | |
| 2 | 2.28 | 0.818 | 5 | 2.02 | 0.907 | ||
| 3 | 2.07 | 1.000 | 6 | 1.96 | 1.064 |
| Q(L/s) | | (cm/s) | | Q(L/s) | | (cm/s) |
|---|---|---|---|---|---|---|---|
| 0.1 | 1 | 2.22 | 0.668 | 0.2 | 4 | 1.94 | 1.192 |
| 2 | 1.97 | 1.075 | 5 | 1.83 | 1.332 | ||
| 3 | 1.83 | 1.398 | 6 | 1.80 | 1.431 | ||
| 4 | 1.73 | 1.576 | 0.3 | 1 | 3.09 | 0.437 | |
| 5 | 1.68 | 1.747 | 2 | 2.48 | 0.553 | ||
| 6 | 1.63 | 1.873 | 3 | 2.22 | 0.698 | ||
| 0.2 | 1 | 2.78 | 0.579 | 4 | 2.09 | 0.805 | |
| 2 | 2.28 | 0.818 | 5 | 2.02 | 0.907 | ||
| 3 | 2.07 | 1.000 | 6 | 1.96 | 1.064 |
(Z
0.5 m).
As shown in the tables, shear velocity tends to decrease as backwater ratio increases. To investigate the relationship between the shear velocity and backwater ratio, the dimensionless shear velocity, 
, is introduced to establish the relationship with backwater ratios where 
is shear velocity under uniform flow condition.
Relationship between dimensionless shear velocity and backwater ratio.
According to the relationship between shear velocity and the shear stress, the relationship between the dimensionless shear stress and the backwater ratio can also be determined. Where 
is shear stress under uniform flow condition. It can be seen from equations that the magnitude of shear velocity is closely related to backwater ratio. For the first reason, flow velocity distribution of the cross sections in the backwater zone becomes uniform due to backwater, then the shear stress of flow layers caused by the velocity difference becomes smaller. For the second reason, the turbulence intensity of flow in backwater zone is less than the flow without sediment, then the Reynolds stress caused by turbulence also becomes smaller. Therefore, both components of the water flow shear stress become smaller due to the backwater. Consequently, the dimensionless shear velocity and the dimensionless shear stress show an exponential decrease as the backwater ratio increases, which greatly increases the possibility of further sediment deposition.
CONCLUSION
In this study, experiments and numerical simulations were performed to investigate turbulent flow in sewer pipes with blocked sediment. The porous media model is used to simulate the flow in permeable blocked sediment. The backwater ratio is proposed to evaluate the degree of congestion and to study the relationship between backwater height and blockage parameters including particle size and height of blocked sediment. The changes of flow field are observed under different backwater ratios. The following conclusions were obtained from this analysis:
- (1)
The backwater ratio increases greatly as the height of blocked sediment increase for the same discharge. Blocked sediments of small particle size with less permeability have a stronger congestion effect and a greater backwater ratio. And the backwater ratio for the same blocked sediments tends to be greater when discharge flow is low.
- (2)
Cross-sectional velocity in front of the blocked sediment decreases considerably and tends to be uniform with increasing backwater ratio, which is conducive to producing more sediment. The seepage velocity in blocked sediment increases as backwater ratio increase.
- (3)
The backwater ratio largely determines the depth of water flowing through the sediment cross-section. The different secondary flows caused by backwater height on sediment section greatly affect cross-sectional velocity distribution. When depth of flow does not exceed pipe radius, the maximum velocity point is shifted upward due to the presence of sediments, and it effectively creates two localize areas of maximum velocity above the edges of the sediment bed. When depth of flow exceeds pipe radius, the region with higher velocity moves downward.
- (4)
The shear velocity of flow in backwater zone affected by blockage is dramatically reduced. The dimensionless shear velocity shows an exponential decrease as the backwater ratio increases, which greatly increases the possibility of further sediment deposition.
It is found that the variation of flow field including flow velocity, shear stress and water level in deposited bed conditions are quite essential for modeling sediment transport in deposited bed sewers. The seepage process within a porous medium is simplified by momentum loss of water flow in this study. A complex model that considers the characters of pore microstructure and fluid in porous media needs to be studied for the permeability and porosity of porous media.
ACKNOWLEDGEMENTS
This research was supported by the National Key Research and Development Program of China (No. 2017YFC1501204), the National Natural Science Foundation of China (No. 52008375, 51909242, 52009125), the Program for Science and Technology Innovation Talents in Universities of Henan Province (No. 19HASTIT043), the Key scientific research projects of colleges and universities in Henan Province (No. 21A570007), the Youth talent promotion project of Henan Province (No. 2021HYTP021).
DISCLAIMER
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
DATA AVAILABILITY STATEMENT
All relevant data are included in the paper or its Supplementary Information.
CONFLICT OF INTEREST STATEMENT
The authors declare there is no conflict.
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