# Computational Fluid Dynamics Simulation of Suspended Solids Transport in a Secondary Facultative Lagoon Used for Wastewater Treatment

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## Abstract

**:**

^{−1}and 0.115 m·s

^{−1}, respectively). Additionally, the dispersion number of each model showed that the single-phase model (0.478) exhibited a better behavior of complete mixing reactor than the two-phase model (0.403). These results can be attributed to the effect of the drag and slip forces of the solids on the velocity of the fluid. In conclusion, the fluid of FL in these models is better represented as a two-phase fluid in which the particle–fluid interactions are represented by drag and slip forces.

## 1. Introduction

## 2. Material and Methods

#### 2.1. Location of the Conventional Facultative Lagoon

^{3}·d

^{−1}and was regulated using an automatic globe valve (KSB SE & CO, Frankenthal, Germany). The inlet and outlet structures were submerged tubes 0.0546 m in diameter and were oriented parallel to the longest side of the lagoon. The surface area of this constructed ecosystem is 83.22 m

^{2}, and has the following dimensions: depth = 1.48 m, width = 5.70 m and length = 14.60 m. The operating flow rate produces a hydraulic retention time of 3.99 days. The FL was designed for an organic load of 279 kg BOD·ha

^{−1}·d

^{−1}.

#### 2.2. Experimental Tracer Studies

^{−1}and 300 μg·kg

^{−1}and wavelengths between 550–570 nm. The data were used to reconstruct the experimental residence time density function for the FL. In the CFD model, the tracer injection was implemented using the chemical species model (Species) and the pulse input method. The output concentration was monitored using an “area-weighted averaged concentration” monitor, taking into account the velocity distribution across the cross-section [23].

#### 2.3. Experimental Suspended Solid Concentrations

^{®}Loveland, CO, USA).

#### 2.4. Validation of Data from Research

## 3. CFD Model Specifications

#### 3.1. Geometry and Discretization

^{®}, Release 16.1 on a Dell Precision TX3500 workstation with an Intel

^{®}Xeon

^{®}X3470 processor (8 MB Cache, 2.93 GHz, Turbo, HT). The 3D geometry of the experimental FL was built using ANSYS Design Modeler

^{®}software Release 16.1. The finite volume method was used for discretization. The computational domain was divided into 161,890 hexagonal elements of 0.05 m, using the Ansys Inc

^{®}ICEM CFD™ meshing software Release 16.1. The quality of the mesh elements was evaluated using the determinant and internal angle methods. The first method guarantees an element quality of greater than 0.5, and the second an internal angle greater than 9°. This procedure was performed to favor solution accuracy and model convergence. Figure 1 displays the geometry and mesh of the CFD model.

#### 3.2. Boundary Conditions

#### 3.3. Drag and Slip Forces Models

#### 3.4. Properties of the Materials

^{−3}and the dynamic viscosity (ν) was 0.0011 kg·m

^{−1}·s

^{−1}[27]. The suspended solids density (ρ) was 1170 kg·m

^{−3}[28] and three-particle diameters (1 × 10

^{−5}, 5 × 10

^{−5}and 8 × 10

^{−5}m) were used for SS [29], which spans the potential range that would occur in the full-scale FL.

#### 3.5. Governing Equations

- Continuity equation

- Equation for momentum

- Turbulence model

#### 3.6. Mesh Independence Test

## 4. Results and Discussion

#### 4.1. Mesh Independence Test

#### 4.2. Tracer Studies: CFD Models vs. Experimental Results

^{2}= 3057) than the variances of the experimental data and two-phase model (see Table 3). The absence of suspended particles in the single-phase model changes the fluid velocity distribution in the FL. When solids are introduced into the flow domain, the interaction between the particles in suspension and the fluid (drag and slide forces) reduce the velocity distribution, and lead to greater mixing and dispersion. These results support the conclusions of [31] that showed multiphase CFD models that include appropriate particle–particle interactions and drag models significantly improve the final predictions of the solids transport in reactors.

^{2}= 4602), single-phase (σ

^{2}= 3057) and two-phase model (σ

^{2}= 4607). Results of this analysis showed that there was no statistically significant difference between the experimental and two-phase model variances (p < 0.05).

#### 4.3. Single-Phase CFD Model vs. Two-Phase CFD Model

^{−1}at the ecosystem inlet and 0.088 m·s

^{−1}in adjacent zones for the two-phase CFD model. Based on the velocity profiles, the previous zones are directly influenced by the mixing generated from the fluid entry into the lagoon, which, in the absence of structures such as baffles or screens, causes this type of hydraulic failure [33]. The higher velocities predicted in the single-phase model (i.e., 0.127 m·s

^{−1}) provide an explanation for the early release of tracer concentration and the absence of the third recirculation zone that was predicted with the two-phase model.

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Residence time distribution obtained experimentally and with the CFD models (single-phase and two-phase).

**Figure 3.**Velocity magnitudes and streamlines obtained with Fluent for the single-phase (

**a**) and two-phase (

**b**) models.

**Figure 4.**Distribution of the solids concentration in the FL: (

**a**) inlet side depth wise profile (

**b**) lengthwise centerline profile.

Zone | Boundary | Value | Units | Observations |
---|---|---|---|---|

Inlet | Velocity inlet | 0.115 | m·s^{−1} | Turbulence Intensity = 5.29% Dh = 0.0546 m Re = 5822 I = 0.053% k = 5.78 × 10 ^{−5} J·kg^{−1}ε = 8.00 × 10 ^{−6} m^{2}·s^{−3}Conc.: 0.041% w/v, UDF |

Outlet | Outflow | 1.0 Fraction | N.A | Turbulence Intensity = 7.3% Re = 506 I = 0.073 (%) k = 8.00 × 10 ^{−7} J·kg^{−1}ε = 1.00 × 10 ^{−8} m^{2}·s^{−3} |

Walls | Stationary Wall | --- | N.A | Polyethylene of low density |

Surface | Free surface | 0.81 | m·s^{−1} | The prevailing direction of the wind was used with an average speed of 0.81 m·s^{−1} and northeast (NE) direction. |

**Table 2.**Predicted effluent suspended solids concentration and velocity from each mesh evaluated in CFD model.

Mesh No. | Mesh Cell Size (m) | Velocity of Fluid (m·s ^{−1}) | Suspended Solids Concentration (% w/v) |
---|---|---|---|

1 | 0.500 | 0.01340 | 0.2930 |

2 | 0.050 | 0.01120 | 0.2240 |

3 | 0.025 | 0.01123 | 0.2221 |

Parameter | Study 1 | Single-Phase CFD Model | Two-Phase CFD Model |
---|---|---|---|

Experimental retention time (h) | 75 | 62 | 70 |

Theoretical retention time (h) | 95.76 | 95.76 | 95.76 |

Error (%) | 22 | 35 | 26 |

Variance (σ^{2}) | 4602 | 3057 | 4607 |

Dispersion number (δ) | 0.436 | 0.478 | 0.403 |

Depth (m) | PL/2 | PL/2 | ||||||
---|---|---|---|---|---|---|---|---|

Average Concentration | UDF “Define Profile” | |||||||

Concentration (% w/v) | ||||||||

Exp. | SD | Sim. | SD | %E | Sim. | SD | %E | |

0.05 | 0.017 | 0.0023 | 0.026 | 0.0014 | 48 | 0.019 | 0.0010 | 12 |

0.45 | 0.016 | 0.0032 | 0.053 | 0.0037 | 230 | 0.019 | 0.0017 | 18 |

1.40 | 0.097 | 0.0023 | 0.094 | 0.0016 | 3 | 0.099 | 0.0009 | 2.1 |

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**MDPI and ACS Style**

Zapata Rivera, A.M.; Ducoste, J.; Peña, M.R.; Portapila, M. Computational Fluid Dynamics Simulation of Suspended Solids Transport in a Secondary Facultative Lagoon Used for Wastewater Treatment. *Water* **2021**, *13*, 2356.
https://doi.org/10.3390/w13172356

**AMA Style**

Zapata Rivera AM, Ducoste J, Peña MR, Portapila M. Computational Fluid Dynamics Simulation of Suspended Solids Transport in a Secondary Facultative Lagoon Used for Wastewater Treatment. *Water*. 2021; 13(17):2356.
https://doi.org/10.3390/w13172356

**Chicago/Turabian Style**

Zapata Rivera, Andres Mauricio, Joel Ducoste, Miguel Ricardo Peña, and Margarita Portapila. 2021. "Computational Fluid Dynamics Simulation of Suspended Solids Transport in a Secondary Facultative Lagoon Used for Wastewater Treatment" *Water* 13, no. 17: 2356.
https://doi.org/10.3390/w13172356