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Settlers are broadly used by industries for separating components with different densities, because they show operational facilities and high efficiency. As they use the action of gravity, they can treat great quantities of effluents with lower energy expenditure. However, the performance of the settler depends on the streamlines inside the equipment, which, in turn, are influenced by the characteristics of the suspended solids, the geometry, and dimensions of the tank. In this paper, the effect of the settler geometry properties on the hydrodynamic in a vertical circular cylindrical tank was investigated. The evaluated parameters were the feed pipe design, the dimensions of the piece of equipment, and the structure of settler bottom. The numerical simulations were performed using the package ANSYS-CFX 16.0. It was considered a turbulent, isothermal, and stationary flow. The Euler-Euler multiphase model and BSL-RSM model turbulence were applied. The recirculation zones were influenced by the separation tank geometrical form. The modification of the feed pipe in the original project reduced the mixture inside the feedwell. The increase of the sedimentation tank diameter improved the performance of water and solid separation, elevating the efficiency by 10.48%, whilst the increase of the tank depth reduced the separation efficiency by 16.72%, in comparison to the original project.

Sedimentation promotes the separation of particles suspended in the fluid by the action of gravity as well as the difference in density of involved components. This unit operation is an integral part of any water and sewer treatment station. Sedimentation tanks are some of the main equipment in a treatment station, especially in the purification of turbid flows [

However, the characteristics of the suspended solids are not the only factors that influence the separation performance of tanks. Fluid dynamics has a prominent role: the uniform flow field is essential to increase the efficiency of the sedimentation tank, allowing particles to settle within a shorter time [

Computational fluid dynamics (CFD) has been largely employed in the study of fluids behavior in settlers, replacing part of some slow and expensive experiments. CFD can be used to increase the basic understanding of the internal processes and their interactions inside the tank, which can optimize projects and propose adaptations to reduce fluid recirculation zones and, consequently, increase the separation efficiency. However, to ensure that the results are consistent, the CFD model must be validated with experimental data or theoretical results [

Several authors have been studying sedimentation tanks by using CFD, in order to predict flow patterns. Al-Sammarraee et al. [

Furthermore, different numerical studies aim to find new and useful methods to increase separation efficiency. White et al. [

Goula et al. [

Al-Sammarraee and Chan [

Rostami et al. [

Shahrokhi et al. [

Panda et al. [

It is worth mentioning that, although the scrapers are essential in the transport of bed material to the underflow, they do not significantly influence the flow that occurs in the sedimentation region in wastewater treatment tanks [^{ }

From this situation presented, the aim of this paper is to evaluate how the geometry of a vertical cylindrical settler tank affects the separation efficiency. The parameters evaluated were the feed pipe design, diameter and depth dimensions of the equipment and the inclination of the settler tank base. In order, we used the ANSYS-CFX 16.0 package to perform tridimensional simulations. The analysis of fluid dynamics was performed by flow lines, turbulent kinetic energy, the volumetric fraction of solids and separation efficiency.

The multiphase flow within the settler may be modelled based on the Euler-Euler [^{ }

As there are regions with high concentrations of solid phase in settlers, the Euler-Euler multiphase model is the appropriate one to be used. This model assumes that the momentum equations are solved for each phase and the coupling among them is given by interfacial transference [

The following assumptions were made 1) Newtonian and incompressible fluid with constant physicochemical properties; 2) isothermal, stationary and turbulent flow; 3) mass transfer and mass generation were not considered; 4) lift force, wall lubrication force, virtual mass force, and solid pressure force were neglected; 5) smooth and static wall; 6) model of particle interfacial transfer considered, and 7) dispersed phase with a constant diameter size of the particle.

With these considerations, the Reynolds-averaged Navier-Stokes (RANS) equations become:

∇ ⋅ ( f α ρ α U ¯ α ) = 0 (1)

∇ ⋅ [ f α ( ρ α U ¯ α ⊗ U ¯ α ) ] = − f α ∇ p α + ∇ ⋅ { f α [ μ α ( ∇ U ¯ α + ( ∇ U ¯ α ) T ) − ρ α u ′ i u ′ j ¯ ] } + S ¯ M α + M ¯ α β (2)

where the α subscript represents one phase of the suspension. f, ρ and U ¯ are the volumetric fraction, specific mass and velocity, respectively; p is the pressure; μ and − ρ u ′ i u ′ j ¯ represent dynamic viscosity and Reynolds stress tensor, respectively. S ¯ M β represents the sum of the gravitational force per unit volume of the phase and a buoyancy force per unit volume of the phase (on the solid). On the liquid, S ¯ M α represents the sum of the gravitational force per unit volume and the opposite reaction of the buoyancy force per unit volume. M ¯ α β is the sum of the interfacial forces per unit volume of the phase, here defined by the sum of the drag force per unit volume of the phase ( M ¯ α β D ) and turbulent dispersion force per unit volume of the phase ( M ¯ α β T D ) (Equation (3)):

M ¯ α β = M ¯ α β D + M ¯ α β T D (3)

The drag force is given by the model proposed by Gidaspow [

M ¯ α β D = { 3 4 C D ρ α f β | U ¯ β − U ¯ α | d β ( U ¯ β − U ¯ α ) f α − 1.65 ; f α ≥ 0.8 [ 150 ( 1 − f α ) 2 μ α f α d β 2 + 7 ( 1 − f α ) ρ α | U ¯ α − U ¯ β | 4 d β ] ( U ¯ β − U ¯ α ) ; f α < 0.8 (4)

where d_{β} is the particle diameter and C_{D} is the drag coefficient, determined by Equation (5) [

C D = { 24 f α × R e [ 1 + 0.15 ( f α × R e ) 0.687 ] ; f α × R e < 1000 0.44 ; f α × R e ≥ 1000 (5)

where Re is the Reynolds number.

The turbulent dispersion force used here was proposed by Lopez de Bertodano et al. [

M ¯ α β T D = − C T D ρ α κ α ∇ f β (6)

where κ represents the turbulent kinetic energy. C_{TD} is the turbulent dispersion coefficient that considers the average of the turbulent tensions in all directions.

For this study, the BSL-RSM turbulence model was used, which is a model capable of accurately predicting the oscillations that were generated from the turbulent flow inside settler tanks [

∇ ⋅ [ ρ u ′ i u ′ j ¯ ⊗ U ¯ ] = P + Φ + ∇ ⋅ [ ( μ + μ t σ κ ) ∇ ρ u ′ i u ′ j ¯ ] − 2 3 δ ρ ω κ β ′ (7)

where P is the term of rate production of Reynolds stresses; Φ is the correlation term of pressure—strain, determined by the LRR-QI model [_{k} = 1.0 and β' = 1.3. μ_{t} is the turbulent viscosity given by:

μ t = ρ κ ω (8)

The BSL-RSM model uses the modified turbulence frequency transport equation to determine the turbulent dissipation rate. The model consists of a combined function for the equation of turbulent dissipation, transforming it into a ε-equation for the external flow region and into a ω-equation treatment closer to the wall.

The design of the used prototype followed the geometry of the industrial circular clarifiers that can serve as thickeners [^{−3} m^{3}, also studied by Luna et al. [

The dimensions of the circular prototype were defined from the high-rate settlers, which present dimension ratios not so long; thus, the diameter-depth ratio may vary from 1:1 to 5:1 [

settler. However, according to Metcalf et al. [

A structured mesh with hexahedral elements was generated using ICEM-CFD version 16.0. The blocking construction strategy was employed. Some meshes were created (sizes between 0.4 and 3.5 million volume elements) and some tests were performed to ensure the independence of results concerning the refinement used and to determine the best commitment among precision, numerical stability, convergence, and computational time. The mesh selected was composed of 2,450,410 cells (

The modifications in the original geometry of the settler tank were proposed, and the fluid dynamics were analyzed through the streamlines, the solid volumetric fraction and the turbulent kinetic energy, factors related to the separation efficiency. As depicted in

1) Suspension inlet structure (

Cases | Feed Pipe | Settler Diameter (m) | Settler Depth (m) | Settler Base | Mesh size (millions) |
---|---|---|---|---|---|

Case 01 | No change | 0.200 | 0.170 | No change | 2.45 |

Case 02 | Centralized | 0.200 | 0.170 | No change | 2.45 |

Case 03 | Without tube | 0.200 | 0.170 | No change | 2.16 |

Case 04 | Increased 50% | 0.200 | 0.170 | No change | 2.60 |

Case 05 | No change | 0.200 | 0.204 | No change | 2.94 |

Case 06 | No change | 0.200 | 0.238 | No change | 3.44 |

Case 07 | No change | 0.240 | 0.170 | No change | 3.54 |

Case 08 | No change | 0.280 | 0.170 | No change | 4.82 |

Case 09 | No change | 0.200 | 0.170 | Conical-Inclination 1˚ | 2.46 |

Case 10 | No change | 0.200 | 0.170 | Conical-Inclination 5˚ | 2.49 |

Case 11 | No change | 0.200 | 0.170 | Conical-Inclination 8˚ | 2.52 |

2) Dimensions of the settler: four configurations were studied. Two cases (cases 05 and 06) with increased settler depth, but with fixed tank diameter. And two cases (cases 07 and 08) with larger tank diameter and original depth.

3) Settler bottom: three new designs of tanks with the conical bottom of different inclination angles with the horizontal (1˚, 5˚, and 8˚) were studied, as shown in

The blocking used for generating new meshes was the same as for the original settler, making only the necessary associations of points, edges, and surfaces. The meshes obtained followed the same methodology adopted for the original tank. For each case, the mesh refinement test was performed, resulting in the appropriate mesh sizes, described in

The equations of mass conservation, momentum conservation, and turbulence were solved by the finite volume method, using the ANSYS-CFX package (version 16.0). The coupling between velocity and pressure is handled implicitly by a solver. The advection terms are discretized using the High-Resolution Scheme, which is second-order accurate. For all the simulations, the values of y^{+} were less than 1 (around 0.8).

The Root Mean Square (RMS) convergence criterion adopted was 10^{−5}. Furthermore, the solid flow in the clarified outlet was monitored; the convergence was reached when the number of particles in this tank output did not present alteration.

Concerning boundary conditions, in the inlet, were specified the suspension flow (water and solid particles) equal to 43.5 g∙s^{−1}. And in the sludge and clarified outlets, it was established a flow rate of 15.5 g∙s^{−1} and a mean static pressure of 1 atm, respectively, also used in the experimental study. The inlet volume fraction was studied with the constant values between 1% and 20% of the solid phase; the carbonate diameter was assumed constant and equal to 25 μm.

To quantify the equipment separation efficiency was employed the Equation (9), also used by Al-Sammarraee et al. [

E ( % ) = 100 ⋅ ( 1 − C L C o ) (9)

where E corresponds to the liquid/solid separation efficiency; C_{L} and C_{o} is the mass fraction of the solid particles in the clarified outlet and the mass fraction of solids in the settler feeding, respectively.

All simulations were performed considering the BSL RSM turbulence model, which accurately represented the velocity profiles in the settler tank, validated with experimental data from PIV (Particle Image Velocimetry) in a previous paper [

Luna et al. [

The Euler-Euler multiphase approach allowed the accurate evaluation of the separation efficiency, and, it was possible to observe agreement between the separation efficiency values obtained numerically and experimentally [

The turbulent kinetic energy, on an XY plane, going through the settler central axis (z = 0), is exhibited (

was zero (at the top) for the settler with an increased feed pipe (

In the external region of the feedwell, the settler without feed pipe is observed to present a volumetric fraction of solid values lower than the ones observed in the other settlers for the positions 0.777 H and 0.559 H,

For all the cases, there was a deposit of solid particles at the bottom of the feedwell, totally undesirable for the process, these particles deposited inside the settler can be resuspended by fluid recirculations, and be directed to the clarified outlet, reducing the efficiency of separating the tank. The ideal for the process is that all particles be collected in the sludge outlet. The accumulation was elevated with the increase of the feed pipe (

With the increase of the sedimentation tank diameter, the recirculations of the sedimentation region were verified to be reduced; conversely, with the increase of the settler depth, the vortexes were intensified.

Inside the feedwell, all the cases presented similar behaviors: in

Ratio (H/D)* | Separation Efficiency (%) | |
---|---|---|

Case 06** | 1.19 | 44.08 |

Case 05** | 1.02 | 50.44 |

Case 01** | 0.85 | 60.80 |

Case 07** | 0.71 | 66.68 |

Case 08** | 0.61 | 71.28 |

*H = Settler depth; D = Settler diameter. **For the cases with volume fraction of carbonate equal to 1% in the inlet.

XY plane going through the settler central axis (z = 0). It was observed that the increase of the inclination in the conical region elevated the turbulent kinetic energy value near the sludge outlet. The increase of the inclination angle lengthens the height of the studied settler.

Conical base | Separation Efficiency (%) | |
---|---|---|

Case 01* | Original settler | 49.05 |

Case 09* | 1˚ | 48.64 |

Case 10* | 5˚ | 47.73 |

Case 11* | 8˚ | 46.82 |

*For the cases with volume fraction of carbonate equal to 10% in the inlet.

The CFD simulations enable a more detailed analysis of the fluid dynamics inside the equipment, and allow design changes, that in turn may optimize the liquid-solid separation. Three aspects were evaluated: 1) feed pipe-positioning and dimension; 2) settler dimensions and 3) inclination of the tank base.

The streamlines allowed observing that the centralization and increase of the feed pipe (length) reduced the solid recirculation inside the feedwell. Consequently, the solid volumetric fraction did not spread within this region in any of the cases, which can be a disadvantage in the sedimentation process. Accumulation of solids in the feedwell base of the original settler was also verified, and all the cases presented variations in the inlet structure.

The increase of the settler depth intensified fluid recirculations inside the equipment and raised the turbulent kinetic energy near the sludge outlet, consequently reducing the equipment’s separation efficiency. Conversely, the elevation of the sedimentation tank diameter reduced the turbulent kinetic energy, and enlarged the sedimentation area, resulting in tanks more efficient and profitable.

The addition of a conical region to the original settler base increased the turbulent kinetic energy near the sludge outlet and reduced the separation efficiency. The addition extended the settler’s depth, which can justify the higher values of turbulent kinetic energy near the sludge outlet.

Considering the results pointed out in this paper, it is suggested that the following topics be considered for further studies:

1) Quantify the presence of baffles inside the settler tank;

2) Analyze the behavior of fluid dynamics in the settler in transient solver and considering mixing with polydispersed systems, together with the flocculation and segregation of the particles.

The authors acknowledge Brazilian National Research Council (CNPq) for the financial support.

This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior—Brazil (CAPES)—Finance Code 001.

The authors declare no conflicts of interest regarding the publication of this paper.

de Luna, F.D.T., da Silva, A.G. and dos Santos Vianna Júnior, A. (2020) The Influence of Geometry on the Fluid Dynamics of Continuous Settler. Open Journal of Fluid Dynamics, 10, 164-183. https://doi.org/10.4236/ojfd.2020.103011