## 1. Introduction

Over 50% drinking water was supplied to the Taiwan’s public by sludge blanket clarifiers (Chen * et al.*, 2003; Lin

*., 2004). The sludge blanket performs dual functions as a filter as well as a particle coagulator. Coagulation, the chemistry-based treatment stage, controls the characteristics of the generated sludge layer, whereas sedimentation, the hydrodynamic treatment stage, controls sludge layer stability. The existence of a sludge blanket in clarifiers is thereby essential to produce quality effluent water. In addition, the flow dynamics is an important parameter for the design of clarifiers.*et al

The use of solids flux theory continues in many studies in the design and operation of sludge treatment processes (Takacs * et al*., 1991; Daigger, 1995; Wett, 2002). Ekama and Marais (2004) gave a survey on the development of one dimensional (1D) settler modeling. Although application of solids flux theory is good for studying the performance of clarifiers, it does not adequately describe the effect of hydrodynamic behavior in clarifiers (Narayanan

*., 2000). Computational fluid dynamics (CFD) has shown to be a powerful tool for resolving complex practical problems in engineering. (Hsu et al., 2007; Videla et al., 2008; Lin et al., 2008; Tao et al., 2008; Yang et al., 2007) Therefore some studies attempted to simulate full clarifiers via CFD (Deininger*et al

*, 1998; Burger*et al.

*, 2005; Fan et al., 2007). Recently Wu*et al.

*. (2007) simulated flow pattern in a clarifier with porous medium as sludge blanket by 3D CFD. The first work to utilize a 3D, multiphase flow simulation for a clarifier is by Wu*et al

*. (2008). Weiss*et al

*. (2007) utilized non-Newtonian flow to model a circular secondary clarifier and showed that viscosity of sludge dominates the flow in clarifier. This study attempts to improve clarifier effluent quality by altering its geometric construction. The simulation is based on the sludge blanket clarifier at the Bansin Water Treatment Plant, Taiwan.*et al

Bansin Water Treatment Plant (BWTP) is in Banchiao City, Taipei County, Taiwan. About every 20 minutes sludge blanket overturns somewhere and effluent solid flux increases. The turbidity of the clarified water is generally too high to produce quality clean water after sand filtering. In this work, four types of constructions of clarifiers are simulated by 3D, multiphase flow model to improve clarifier effluent quality. * Type A* is the conventional clarifier used in BWTP.

*changes inlet pipe to a large one (1.6 folds).*Type B

*changes reaction well angle from 120*Type C

^{0}to 90

^{0}.

*changes reaction well angle from 120*Type D

^{0}to 60

^{0}. As shown in previous research (Yang

*, 2008) that, the velocity of suspension in the reaction well is one of the factors affecting the quality of water discharge, so the improved method of*et al.

*is expected to slow the velocity of flow by enlarging diameter of inlet pipe. The improvement method of*Type B

*is the angle of 90*Type C

^{0}of reaction cover. It is hoped that the backflow could be limited within the reaction well, so that the residence time of suspension in the reaction well can be increased. The improved method for

*reverses the whole reaction cover, so the water quality may not deteriorate for reason of easy outflow of the suspension from the reaction well.*Type D

## 2. Geometry and meshes

Figure 1 indicates the geometry of the sludge blanket clarifier. The clarifier is 19×19×5.5 m^{3}, with an impeller with 16 blades and diameter of 3 m. The impeller is located in center top of the clarifier. The inlet pipe is 0.9 m in diameter. The inlet pipe is connected to a draft tube 2.4 m in diameter. The inlet water velocity was typically operated at 0.34 m/s. The draft tube comprises the first reaction zone. The second reaction zone is outside the first reaction zone and inside a reaction well with upper and lower diameters of 8 and 13 m, respectively. The reaction well is 3.8 m high. Figure 2 shows all grids in the clarifier.

## 3. Governing equations and boundary conditions

### 3.1. Conservation equations.

Volume fractions represent the space occupied by each phase, and the laws of conservation of mass and momentum are satisfied by each phase individually. The volume of phase * q*,

where * α* is phase volume fraction occupied by each phase, and

The effective density of phase * q* is

where * q*. In this work, only water and solid phases are considered.

The continuity equation for phase * q* is

where * q* and

*to*p

*phase, and*q

*to phase*q

*, hence*p

The momentum balance for water phase * w* yields

where * P* is the pressure shared by all phases, and

Here

The momentum balance for solid phase * s* yields

where

The solids stress tensor contains shear and bulk viscosities arising from particle momentum exchange due to translation and collision. The collisional and kinetic parts are added to give the solids shear viscosity. The solids bulk viscosity accounts for the resistance of the granular particles to compression and expansion.

### 3.2. Phase interactions.

FLUENT uses a simple interaction term of the following form:

where

where

where

For the Syamlal-O'Brien model (1989),

where the drag function and relative Reynolds number have the following forms:

This model is based on measurements of the terminal velocities of particles in fluidized or settling beds.

Lift forces act on a particle mainly due to velocity gradients in the primary-phase flow field. The lift force will be more significant for larger particles. Thus, the inclusion of lift forces is not appropriate for closely packed particles or for very small particles. When a secondary phase * p* accelerates relative to the primary phase

*, the inertia of the primary phase mass encountered by the accelerating particles exerts a virtual mass force on the particles. The virtual mass effect is significant when the secondary pahse density is much smaller than the primary phase density. Therefore virtual mass force is not either considered in this work. In order to make the calculation simple, the acting force between water and particle is dominated by the drag force, which is shown in the*q

### 3.3. Boundary conditions.

The boundary conditions are as follows:

Equation (15a) and (15b) state that the inlet suspension is moving at a constant speed and has a solid volume fraction equal to 0.005. Equation (15c) describes no slip boundary conditions for water and solid phases. Equation (15d) describes the gauge pressure at the water surface (top of the clarifier) is zero.

The computational fluid dynamics program FLUENT 6.1 (Fluent Inc., USA) solved the governing equations, together with the associated boundary conditions, using hybrid mesh volumes generated by GAMBIT. This work uses three groups of meshes of different quantities (1 million, 2 million, 2.5 million) for calculation. The relative error of the solid volume fraction at the overflow is smaller than 10%. Therefore the numbers of mesh volumes in the whole clarifier are used about 2,500,000. The calculations were carried out with maximum relative error of 10^{-4} in fluid velocity evaluation.

## 4. Results and discussion

### 4.1. Velocity vector of water flow.

Figure 3 plots the velocity vector of water in the clarifier (inlet velocity = 0.3 m/s, impeller rotation speed = 0.3 rad/s). When inlet water is flowing into the draft tube, it is sucked to the top of the clarifier, owing to the rotating impeller. Then it goes down along the inside of the well and separates into two streams. One stream inside the well makes a strong cycling flow (#1) in the secondary reaction well, the other stream rises along the wall of the clarifier, to water surface, and descends along the outside of the reaction well, making another weaker cycling flow (#2). Although this cycling flow (#2) is weaker than (#1), it is still a strong density current that the flocs will be elutriated, leading to an average 20 minutes overturn as reported in Chen * et al.* (2003). An idea is to treat the flocs into a strong and dense blanket.

## 5. Comparison with Bansin Water Treatment Plant (BWTP)

Bansin Water Treatment Plant (BWTP) adopted 16 sludge blanket clarifiers to treat its raw water. This type of clarifier is used by many regions to produce drinking water, but relevant references are very few. Figure 4 is a comparison between observation in BWTP and CFD results. An observer stood beside the clarifier, recorded which areas sludge blanket was floating. Thus in figures 4(a)-(d), blue color means that water surface is clean; while yellow color indicates that sludge suspension was on that surface. Figures 4(a)-(d) were the observation results at 0 s, 600 s, 900 s, and 1200 s. Figures 4(e)-(h) were volume fraction contours calculated by FLUENT at 2400 s, 3000 s, 3300 s, and 3600 s. The patterns are similar between BWTP observation and numerical calculation and that sludge overturns from edge and corner every 20 minutes. Circular clarifier might be a solution to solve this problem.

### 5.1. Twophase flow.

Figure 5 reveals the contour of volume fraction of solid phase of Eulerian two phase flow as time evolves. The primary phase is water phase, the secondary phase is solid phase with particle size 10 μm and density 1,005 kg/m^{3}. As time goes by, the solid particles were sucked from the draft tube to the top of the impeller, descends along the reaction well inside, be full of the whole reaction well, and overflow to the reaction well outside, making a relatively stable blanket at the bottom of the clarifier, and a dynamic upward particles’ surface. Compared with figures 5a to 5c, it is obviously shown that as time passes, the particles boundary becomes higher (white dash line), i.e., many particles rise and the loading of the following fast filtration becomes heavy.

In order to enunciate the geometric effects on the stability of the sludge blanket, the other three types (* Type B*,

*, and*Type C

*) of constructions of clarifiers were studied. Comparing with these figures it is shown that after 3600s’ operation, the lowest particle concentration at the effluent surface happens at the*Type D

*construction, the large inlet pipe.*Type B

As shown in Figure 6a, the increase of the caliber size of inlet pipes decelerate the fluid, thus, the intensity of backflow formed is smaller than the original structure (Fig. 3). The flow-up velocity outside of the reaction well is relatively small, and the volume fraction of particles carried upward by fluids is small as well. Finally, the quality of water discharge is favorable.

As shown in Figure 6b, the angle of the reaction well is a right angle, which is equivalent to an impinge flow when the suspension flows downward along the inside of the reaction well and approaches the bottom of the clarifier. The effective backflow cannot be formed, thus, the particles are prone to flow out of the reaction well to raise the concentration. In Figure 6c, it is expected that the suspension will be surrounded by the reversed reaction cover, thus preventing the particles from flowing out of the reaction well. However, a backflow zone is produced at the top of reaction well (as compared to the backflow zone appeared in the middle section of the reaction well in the original structure, Fig. 3). The upper backflow field at this position will hamper the backflow of the suspension under the reaction well so that it does not backflow into the reaction well, but leaving the reaction well. Thus, the concentration of the suspension outside the reaction well is raised.

Effluent upflow velocity (EUV) is proposed as an important parameter affecting clarifier performance (Narayanan * et al*., 2000). In this simulation work, effluent solid flux can be calculated in advance. The effluent solid flux is displayed in figure 7. For

*and*Type A

*, effluent solid flux increase steadily; while for*Type B

*and*Type C

*, effluent solid flux increase saw-toothed. This might due to the squeezed backflow in top of the reaction well causing unstable flow field outside the reaction well. Before 2500s, effluent solid flux is less than 0.05 kg/m*Type D

^{2}-s except for

*. After 2500s, effluent solid flux is increasing dramatically. It is suggested that BWTP could drain sludge away per hour according to this simulation work. At almost all the 3000s’ operations, the effluent solid flux is the lowest in*Type D

*construction.*Type B

## 9. Nomenclature

_{
D
}drag coefficient, -

* K*interphase momentum exchange coefficient, -

_{
s
}diameter of particle, m

* f*correlation factor, -

^{2}

*to*p

*phase, kg/m*q

^{3}-s

* P*pressure, N/m

^{2}

_{
s
}solid pressure, N/m^{2}

_{
s
}Reynols number, -

^{2}

* V*volume of each phase, m

^{3}

_{
r,s
}terminal velocity correlation, -

α volume fraction, -

μshear viscosity, kg/m-s

λbulk viscosity, kg/m-s

* ρ* density, kg/m

^{3}

^{3}

_{
S
}particulate relaxation time, s

^{2}Subscripts

* w*water phase

* s*solid phase

## 6. Conclusions

Blanket floc volumetric concentration is an important parameter in understanding the performance of sludge blanket clarifiers. 3D simulations of a clarifier using four different geometric constructions were studied in this work. From the simulation results of effluent solid flux, it is suggested that under the same daily throughput the large inlet pipe can reduce the flow velocity in the clarifier, hence reduce effluent solid flux and improve the quality of water. According to this simulation results, it is recommended that BWTP has to make large inlet pipe to obtain good quality water under the same daily throughput, or obtain large daily throughput under the same quality water.

The simulation results can only be interpreted qualitatively and not quantitatively since only hydrodynamic behavior is considered. Further work should concern the chemical based treatment, i.e., coagulation of flocs in clarifier. Nevertheless, the simulation results can show tendencies in the flow pattern due to changes in clarifier construction.

## Acknowledgments

The authors would like to thank the National Science Council of the Republic of China, Taiwan, for financially supporting this research under Contract No. NSC 96-2221-032-020.

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