# Predicting Sedimentation in Urban Sewer Conduits

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{2}) of 0.899. This satisfied the aims of this study, to obtain a higher discharge capacity and a plan for the design of urban drainage systems.

## 1. Introduction

## 2. Methodologies

#### 2.1. Overview

- The two-phase flow of a single sewer conduit was simulated
- The pipe channel instead of open channel was used for simulations
- The mixture and turbulent flows was assumed
- The same diameter of particle flows to a single sewer conduit.

#### 2.2. Governing Equations

_{c}and F

_{d}in Equations (3) and (4) represent the drag force and the lift force due to the interactions between the fluids and soil particles, respectively, for which commercial programs provide various models as options. This study applied the Syamlal–O’Brien model [30] as a particle viscosity and pressure model [31,32,33,34], and it was also used as a drag force model. The continuity equations are shown as Equations (1) and (2), and the momentum equations as Equations (3) and (4):

#### 2.3. Model for Analysis

_{t}can be obtained through k and ε in Equation (5):

_{u}is a model constant that takes a value of 0.09 in general [24]. In local areas, depending on the generation of sedimentation in conduits, turbulent stress can be modeled by computing k and ε using two transport equations, such as Equations (6)–(8):

#### 2.4. Boundary Conditions

#### 2.5. Validation of Model

## 3. Slurry Flow in Sewer Conduits

#### 3.1. Changes to Flow Velocity and Fraction of Slurry Volume in Conduit

#### 3.2. Changes in Pattern of Slurry Volume at Outlet

## 4. Prediction Model for Height of Particle Deposition in Sewer Conduits

^{2}) of 0.877 was obtained. However, in the region where the soil deposition rate y/D was relatively high at 0.4, the deviation in the predictions increased. The rate of deposition increased as the soil volume fraction and particle size increased. Thus, in the analysis, the interaction between the fluids and particles increased, and the deposition height showed small changes compared with various other conditions. Equation (12) can thus be used within the conditions of this analysis, and the flow of soil and slurry had various shapes and sizes of particles. Thus, these results as well as wider operation conditions should be reflected in modeling in future studies.

## 5. Conclusions

- As the inflow velocity of soil particles in slurry is slow and the particle diameter is large, particles incline to the bottom of the conduit.
- If the soil particles in slurry deposits near the inlet, flow velocity at the deposit increases, according to which the transportation of the deposited soil particles occurs.
- As the flow velocity of incoming slurry is low and the diameter of the soil particles large, the amount of the deposit increases and the stable transportation of slurry is interrupted.
- The relations between the height of the soil deposited and the inlet flow velocity of mixtures, volume fraction of inflowing particle size, which were non-dimensionalized, were derived as a correlation formula.
- Linear regression analysis between the deposit height and the model confirmed a correlation coefficient (R
^{2}) of 0.877.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 3.**Comparison of the velocity of the simulated mixture (m/s) with that in experimental results [7].

**Figure 4.**Comparison of the simulated soil volume fraction (%) with that in experimental results [7].

**Figure 6.**Sedimentation results for soil of diameter 1.0 mm according to changes in volume fraction; (

**a**) Volume fraction 10%; (

**b**) Volume fraction 30%; (

**c**) Volume fraction 50%.

**Figure 7.**Sedimentation results for soil of diameter 20.0 mm according to changes in volume fraction. (

**a**) Volume fraction 10%; (

**b**) Volume fraction 30%; (

**c**) Volume fraction 50%.

**Figure 8.**Sedimentation results for soil of diameter 1.0 mm according to changes in inlet velocity. (

**a**) 1.0 m/s inlet velocity; (

**b**) 2.0 m/s inlet velocity; (

**c**) 3.0 m/s inlet velocity.

**Figure 9.**Sedimentation results for soil of diameter 20.0 mm according to changes in inlet velocity. (

**a**) 1.0 m/s inlet velocity; (

**b**) 2.0 m/s inlet velocity; (

**c**) 3.0 m/s inlet velocity.

**Figure 10.**Soil velocity and soil diameter according to change in volume fraction. (

**a**) Soil velocity distribution at a volume fraction of 10%; (

**b**) Soil velocity distribution at a volume fraction of 30%; (

**c**) Soil velocity distribution at a volume fraction of 50%.

**Figure 11.**Flow patterns and characteristics diagram in sewer. (

**a**) Moderately damped oscillation; (

**b**) Oscillation pattern; (

**c**) Highly damped oscillation pattern.

${\mathit{C}}_{\mathit{u}}$ | ${\mathit{C}}_{\mathit{\epsilon}\mathbf{1}}$ | ${\mathit{C}}_{\mathit{\epsilon}\mathbf{2}}$ | ${\mathit{\delta}}_{\mathit{k}}$ | ${\mathit{\delta}}_{\mathit{\epsilon}}$ |
---|---|---|---|---|

0.09 | 1.44 | 1.92 | 1.0 | 1.3 |

Condition | Setting |
---|---|

Type | Fluid |

Material | Water |

Turbulence Model | k–ε standard |

Inlet | Velocity = 1.0–3.0 m/s |

Outlet | Relative pressure = 0 (Pa) |

Wall Influence of Flow | No slip |

Surface Influence of Flow | Free slip |

Title | Soil–Water Transport |
---|---|

Geometry | 10.55 m × 0.015 m |

Model | Eulerian–eulerian model, Turbulent flow |

Mixture boundary Conditions | Inlet velocity: 3 m/s, Inlet volume fraction: 30% |

Soil | Density: 2650 kg/m^{3}, Particle diameter: 0.2 mm |

Water | Density: 1000 kg/m^{3}, Dynamic viscosity: 0.001004 Pa·s |

Titles | Conditions | |
---|---|---|

Geometry | 0.6 m (D) × 10 m (L) | |

Model | Eulerian–eulerian model, Turbulent flow | |

Mixture boundary Conditions | Inlet Velocity (m/s): | 1.0, 2.0, 3.0 |

Inlet Volume Fraction (%): | 10, 30, 50 | |

Soil | Density (kg/m^{3}): | 2650 |

Particle Diameter (mm): | 0.5, 1.0, 3.0, 5.0, 7.0, 15.0, 20.0 | |

Water | Density (kg/m^{3}): | 1000 |

Dynamic Viscosity (Pa·s): | 0.001004 |

**Table 5.**Sedimentation results for soil of diameter 1.0 mm and 20.0 mm according to changes in volume fraction (where the soil deposition rate h/D).

Volume Fraction | 10 | 30 | 50 | |
---|---|---|---|---|

D (mm) | ||||

1.0 | 0.160 | 0.365 | 0.884 | |

20.0 | 0.629 | 0.938 | 0.967 |

**Table 6.**Sedimentation results for soil of diameter 1.0 mm according to changes in inlet velocity (where the soil deposition rate h/D).

Velocity (m/s) | 1.0 | 2.0 | 3.0 | |
---|---|---|---|---|

D (mm) | ||||

1.0 | 0.160 | 0.053 | 0.047 | |

20.0 | 0.629 | 0.552 | 0.518 |

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**MDPI and ACS Style**

Song, Y.H.; Yun, R.; Lee, E.H.; Lee, J.H.
Predicting Sedimentation in Urban Sewer Conduits. *Water* **2018**, *10*, 462.
https://doi.org/10.3390/w10040462

**AMA Style**

Song YH, Yun R, Lee EH, Lee JH.
Predicting Sedimentation in Urban Sewer Conduits. *Water*. 2018; 10(4):462.
https://doi.org/10.3390/w10040462

**Chicago/Turabian Style**

Song, Yang Ho, Rin Yun, Eui Hoon Lee, and Jung Ho Lee.
2018. "Predicting Sedimentation in Urban Sewer Conduits" *Water* 10, no. 4: 462.
https://doi.org/10.3390/w10040462