# The Whole Process CFD Numerical Simulation of Flow Field and Suspended Solids Distribution in a Full-Scale High-Rate Clarifier

^{1}

^{2}

^{3}

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^{5}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. The Full-Scale High-Rate Clarifier Geometry

^{3}of wastewater following the secondary settling tank is treated by this high-rate clarifier. The clarifier is mainly composed of the reaction tank and the settling tank as shown in Figure 1. The wastewater inlet was at the central bottom of the reaction tank. The wastewater was mixed with the chemicals in the reaction tank and the mechanical agitation of stirred paddle improved the kinetic energy of the fluid. Then, the fluid flowed to the settling tank by passing through the overflow wall and the under-through channel. The sludge would settle and separate from the water in the settling tank by inclined tube sedimentation. The entire high-rate clarifier tank is composed of complex structures and multiple sizes in this study. The reaction tank and the settling tank of the high-rate clarifier were simultaneously studied.

#### 2.2. Mathematical Modeling

#### 2.2.1. CFD Model

#### 2.2.2. Governing Equations

_{m}—mass averaged velocity vector (m/s);

^{3});

^{3});

_{k}—velocity vector of phase k (m/s);

^{2});

#### 2.2.3. Boundary Conditions

^{3}, 90 μm, and 3.08 mPa∙s, respectively. The slip velocity between the liquid phase and solid phase was introduced through the user-defined function. The SS settling velocities were described by Equation (6) (Takács double exponential equation) in the CFD model for the two-phase flow. On the one hand, the velocity inlet was applied and calculated according to the treatment capacity and cross-sectional area at the inlet. As such, the inlet was set to 0.614 m/s. On the other hand, the wastewater outlet and the sludge outlet were set as pressure outlet boundary conditions of 0 Pa in the settling tank. The approach of MRF (multiple reference frames) was introduced for the rotation of stirred paddle simulation [50,51]. The static walls, including the external wall and central hollow cylinder with four baffles, were defined. However, the moving walls of the rotational paddles were defined and simulated at 1.466 rad/s based on the local operational conditions in WWTP.

#### 2.3. Experimental Measurements

#### 2.3.1. Flow Field Measurements

#### 2.3.2. Other Measurements

#### 2.4. Statistical Analysis

_{si}—the simulated result of the i-th parameter;

_{mi}—experimental data of the i-th parameter.

## 3. Results and Discussion

#### 3.1. Comparison of the Simulated and the Measured Flow Velocities

#### 3.1.1. Comparison of the Simulated and the Measured Flow Velocities in the Reaction Tank

#### 3.1.2. Comparison of the Simulated and the Measured Flow Velocities in the Settling Tank

#### 3.2. Contour Profiles of Velocities and SS Concentrations of the High-Rate Clarifier

#### 3.2.1. Contours of Velocity Profiles of the High-Rate Clarifier Simulated by the Two-Phase Model

#### 3.2.2. Contours of SS Concentration Profiles of the High-Rate Clarifier Simulated by the Two-Phase Model

## 4. Conclusions

- (1)
- The simulated results of the developed CFD model were in good agreement with the experimental data obtained in the high-rate clarifier. The normalized standard error was less than 7.66%. The consistency between the simulated results and the measured data further proved that the flow field could be accurately simulated by the CFD model.
- (2)
- Through the analysis of the flow field distribution in the five typical sections, it was found that the overall flow velocities in the settling tank were much smaller than that in the reaction tank. After the fluid passed through the diversion effect of the overflow wall and the under-through channel, the overall kinetic energy loss was relatively large.
- (3)
- Through the analysis of the SS concentration distribution in the five typical sections, the sludge sedimentation happened at the edge of the settling tank due to the vertical angle between the plug-flow fluid and the outlet.
- (4)
- The successful construction of the CFD model demonstrated that hydraulic characteristics of the high-rate clarifier could be simulated and studied at a low cost and in a short time. This could be an insight into the sedimentation process and pollutant removal mechanism in-depth and lay the foundation for the next step of the high-rate clarifier optimization operation and research on pollutant removal.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**The schematic diagram of the high-rate clarifier (

**a**), sectional diagram 1-1 of the central line along the reaction tank (

**b**), and sectional diagram 2-2 of the effluent along the overflow wall (

**c**) (Unit: mm).

**Figure 4.**The schematic diagram of the eight sampling sites in the reaction tank and the six sampling sites in the settling tank (Unit: mm).

**Figure 5.**Comparisons of the simulated and measured flow velocities of eight sampling sites in the reaction tank: (

**a**) R1, (

**b**) R2, (

**c**) R3, (

**d**) R4, (

**e**) R5, (

**f**) R6, (

**g**) R7, and (

**h**) R8 at the top layer, middle layer, and bottom layer (6.0, 4.0, and 2.6 m above the bottom, respectively).

**Figure 6.**Comparisons of the simulated and measured flow velocities of six sampling sites in the settling tank: (

**a**) S1, (

**b**) S2, (

**c**) S3, (

**d**) S4, (

**e**) S5, and (

**f**) S6 at the top layer, middle layer, and bottom layer (6.0, 4.0, and 2.6 m above the bottom, respectively).

**Figure 8.**The contours of velocity profiles at the top layer, middle layer, and bottom layer (6.0, 4.0, and 2.6 m above the bottom, respectively) of the high-rate clarifier simulated by the two-phase model.

**Figure 9.**The contours of velocity profiles at Y = 0 mm section of the high-rate clarifier simulated by the two-phase model.

**Figure 10.**The contours of SS concentration profiles at the top layer, middle layer, bottom layer (6.0, 4.0, and 2.6 m above the bottom, respectively), and the bottom of the high-rate clarifier simulated by the two-phase model.

**Figure 11.**The contours of SS concentration profiles at Y = 0 mm section of the high-rate clarifier simulated by the two-phase model.

SS (mg/L) | 874 | 1747 | 2184 | 2730 | 3413 | 4266 |

Settling velocity (×10^{−4} m/s) | 8.89 | 5.97 | 4.72 | 3.71 | 2.60 | 2.28 |

Regions | Sampling Sites * | Coordinates (mm) |
---|---|---|

Reaction tank | R1 | (−3000, −1080) |

R2 | (−3000, 1080) | |

R3 | (3000, −1080) | |

R4 | (3000, 1310) | |

R5 | (−1750, −4000) | |

R6 | (−3800, −1080) | |

R7 | (−3800, 1080) | |

R8 | (3200, −3800) | |

Settling tank | S1 | (4700, −3500) |

S2 | (4700, 3500) | |

S3 | (5600, −1100) | |

S4 | (5600, 1330) | |

S5 | (7300, −1100) | |

S6 | (7300, 1330) |

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**MDPI and ACS Style**

Xu, Q.; Luo, X.; Xu, C.; Wan, Y.; Xiong, G.; Chen, H.; Zhou, Q.; Yan, D.; Li, X.; Li, Y.;
et al. The Whole Process CFD Numerical Simulation of Flow Field and Suspended Solids Distribution in a Full-Scale High-Rate Clarifier. *Sustainability* **2022**, *14*, 10624.
https://doi.org/10.3390/su141710624

**AMA Style**

Xu Q, Luo X, Xu C, Wan Y, Xiong G, Chen H, Zhou Q, Yan D, Li X, Li Y,
et al. The Whole Process CFD Numerical Simulation of Flow Field and Suspended Solids Distribution in a Full-Scale High-Rate Clarifier. *Sustainability*. 2022; 14(17):10624.
https://doi.org/10.3390/su141710624

**Chicago/Turabian Style**

Xu, Qi, Xi Luo, Chengjian Xu, Yanlei Wan, Guangcheng Xiong, Hao Chen, Qiuhong Zhou, Dan Yan, Xiang Li, Yingxi Li,
and et al. 2022. "The Whole Process CFD Numerical Simulation of Flow Field and Suspended Solids Distribution in a Full-Scale High-Rate Clarifier" *Sustainability* 14, no. 17: 10624.
https://doi.org/10.3390/su141710624