# Optimal Design of Water Treatment Contact Tanks

## Abstract

**:**

## 1. Introduction

## 2. Computational and Optimization Models

#### 2.1. Flow Model

_{i}and x

_{j}are Cartesian coordinates. Reynolds-averaged Navier-Stokes (RANS) equations are closed using k-ε turbulence closure model for the solution of turbulent flow in the contact tank. Reynolds stresses are approximated by the following Boussinesq hypothesis:

_{ij}is the Kronecker delta, k is the turbulence kinetic energy, and ${\mathrm{v}}_{\mathrm{t}}$ is the turbulent viscosity, which is defined as,

_{μ}is the model constant and selected as 0.09. Two transport equations are sequentially solved for $\mathrm{k}$ and $\mathsf{\epsilon}$ using appropriate boundary conditions as given in Section 2.3. Further details of these models can be found in the general fluid mechanics literature and in [12,13].

#### 2.2. Conservative Tracer Model

_{init}is the injected tracer concentration (C

_{init}= 1), T

_{injection}is the injection time, θ = t/τ is the dimensionless time and τ is the MRT.

#### 2.3. Computational Domain and Boundary Conditions

^{−4}for pressure, 1 × 10

^{−5}for velocity and turbulence quantities, and the steady-state flow field in the flow domain was achieved around (~2586; ~2080) iterations for the given convergence parameters for the baffle configurations used in the analysis. The mesh cell numbers given above slightly varied for various baffle geometries considered in this study in the range 7M to 4M. The use of structured mesh application also facilitated the simulation-optimization computations since the re-meshing that was necessary during the optimization computations were achieved within few seconds on an Intel Core I7/144 Hz computer with 1 TB SSD. The complete cycle of each iteration of a typical application of the simulation-optimization sequence took ~10 h execution time on the desktop computer and this execution time reduces as the iteration process progresses towards convergence. This performance was achieved on a guest Oracle VM/Virtual Box running Ubuntu 64-bit-30 GB VT-x/AMD-V-Nested paging system hosted on the Windows11 platform for the OpenFOAM9 application [23]. A typical mesh used in the analysis can be seen in Figure 2.

#### 2.4. Optimization Model

#### 2.5. Simulation-Optimization Procedure

## 3. Results

#### 3.1. Baffle without Slots

#### 3.2. Finite Width Slot Baffle Population

#### 3.3. Full Width Slot Baffle Population

#### 3.4. Optimal Baffle Geometry

^{3}of water is treated (Figure 16) with a reliability of $\mathrm{r}\left(\mathrm{X}\right)=0.87$ (Figure 16). The convergence of the optimal results is achieved within about 57 iterations as seen in Figure 14.

## 4. Discussion

## 5. Conclusions

- The multidimensional design concept introduced is important in the overall design of the contact tanks since it provides a platform to include multiple design criteria that would contribute to the overall performance of contact tank design beyond a one-dimensional approach of baffle geometry design to improve mixing.
- The appropriate development of the optimization algorithm is important since a multitude of optimization solution strategies exist in the literature for the solution of multi-dimensional optimization problems, such as multi-objective approaches. The strategy recommended in this study, which is the use of a single objective function approach, performed well for the problem considered in this case without artificial controls on the final selection.
- Simulation-optimization techniques have been previously used in the literature. The recommended CFD analysis combined with PGA assisted genetic algorithm approach provided a preferable and efficient computational platform for the application considered in this case and may be adopted in future studies.
- The optimum contact tank design achieved that would satisfy the four design objectives in a smart manner, and using a single objective function, yielded a new contact tank baffle design that was not reported in the earlier literature. This indicates that the multidimensional analysis concept developed in this study is an important concept which may be adopted in future studies.

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Schematic view of the contact tank: (

**a**) baffle without slots case; (

**b**) slot-baffle case [14].

**Figure 2.**Computational mesh generated using the blockMesh utility for one of the finite slot width cases: (

**a**) mesh geometry used for the full contact tank; (

**b**) left half perspective of the contact tank mesh cut at the middle of the center vertical baffle.

**Figure 6.**Velocity magnitude and concentration distributions in the contact tank for the classic design (without slot baffle case): (

**a**) Flow distribution; (

**b**) Flow distribution with velocity vectors; (

**c**) Concentration distribution at 200 s; (

**d**) Concentration distribution at 300 s.

**Figure 7.**E(θ) and F(θ) plots (Equations (7) and (8)) obtained from tracer simulations for classic contact tank.

**Figure 8.**Typical contact tank baffle configuration for baffles with slots (w = 120 mm, h = 10, 12, 14 mm random) case.

**Figure 9.**Typical velocity magnitude and concentration distributions in the contact tank with finite with slots (w = 120 mm, h = 10, 12, 14 mm random) case: (

**a**) Flow distribution; (

**b**) Flow distribution with velocity vectors; (

**c**) Concentration distribution at 200 s; (

**d**) Concentration distribution at 300 s.

**Figure 10.**E(θ) and F(θ) plots obtained from tracer simulations for contact tank with finite width slots and classic design cases.

**Figure 11.**Typical contact tank baffle configuration for baffles with full width slots (w = 230 mm, h = 12, 16, 14 mm random placement) case.

**Figure 12.**Typical velocity magnitude and concentration distributions in the contact tank with full width slots (w = 230 mm, h = 12, 16, 14 mm random placement) case: (

**a**) Flow distribution; (

**b**) Flow distribution with velocity vectors; (

**c**) Concentration distribution at 200 s; (

**d**) Concentration distribution at 300 s.

**Figure 13.**E(θ) and F(θ) plots obtained from tracer simulations for contact tank with full width slots (w = 230 mm, h = 12, 16, 14 mm random) case.

**Figure 17.**Convergence trend for the treated volume of water within ${\mathrm{t}}_{\mathrm{d}}$ period.

Variables | Boundary Conditions Used | |||
---|---|---|---|---|

Inlet Region | Outlet Region | Atmosphere Boundary | Wall Regions | |

U | mapped | inletOutlet | symmetryPlane | noSlip |

p | mapped | inletOutlet | symmetryPlane | zeroGradient |

k | mapped | inletOutlet | symmetryPlane | kqRWallFunction |

ε | mapped | inletOutlet | symmetryPlane | epsilonWallFunction |

nut | mapped | inletOutlet | symmetryPlane | nutkWallFunction |

Parameters | Cases Considered | |||
---|---|---|---|---|

Baffle 1 | Baffle 2 | Baffle 3 | Options | |

Number of Slots | 1, 2, 3, 4 | 1, 2, 3, 4 | 1, 2, 3, 4 | PGA Elim. 1, 2, 4 |

Finite Slot (w-mm) | 100, 110, 120, 160 | 100, 110, 120, 160 | 100, 110, 120, 160 | Random |

Finite Slot (h-mm) | 10, 12, 14, 16 | 10, 12, 14, 16 | 10, 12, 14, 16 | Random |

Full Slot (h-mm) | 10, 12, 14, 16 | 10, 12, 14, 16 | 10, 12, 14, 16 | Random |

Space between slots (mm) | 40, 42, 44, 46 | 40, 42, 44, 46 | 40, 42, 44, 46 | Random Sym. |

Parameters | PGA Parameters |
---|---|

Value | |

Population Size | 60 |

Crossover Ratio | 0.8 |

New Member Generation Ratio | 0.3 |

Elitism Ratio | Best Member |

Mutation Ratio | 0.2 |

Maximum generation for each Subdomain | 40 |

Slot Number | Optimal Slot Geometry |
---|---|

(w, h) (mm) | |

Slot 1 | (230, 12) |

Slot 2 | (230, 16) |

Slot 3 | (230, 14) |

Slot 4 | (230, 14) |

Slot 5 | (230, 16) |

Slot 6 | (230, 12) |

Slot 7 | (230, 12) |

Slot 8 | (230, 16) |

Slot 9 | (230, 14) |

Spacing between slots | (39, 38) |

Distance from base to first slot | (45) |

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Aral, M.M.
Optimal Design of Water Treatment Contact Tanks. *Water* **2022**, *14*, 973.
https://doi.org/10.3390/w14060973

**AMA Style**

Aral MM.
Optimal Design of Water Treatment Contact Tanks. *Water*. 2022; 14(6):973.
https://doi.org/10.3390/w14060973

**Chicago/Turabian Style**

Aral, Mustafa M.
2022. "Optimal Design of Water Treatment Contact Tanks" *Water* 14, no. 6: 973.
https://doi.org/10.3390/w14060973