Numerical simulation of a rectangular clarifier using drift-flux model in OpenFOAM

A computation fluid dynamic (CFD) simulation of a rectangular clarifier is performed in this study using a drift-flux model in OpenFOAM CFD code. Using this model with 𝑘 − 𝜀 turbulence model, the key characteristics (re-circulation and sedimentation) of water-particle mixture flow in a rectangular clarifier are reasonably reproduced. A fairly good agreement is obtained between the simulation results and experimental data of the velocity profiles. Thus, with the demonstrated capability of this CFD model for the prediction of hydrodynamic and sedimentation behavior of water-particle mixture flow, several design issues such as the determination of the best location of baffle in a clarifier can be investigated and addressed. This method can not only provide general conceptual information at the initial design stage but can also be used to perform analysis of different configurations and the effect of changes in operational parameters.


Introduction
Water is one of the essential needs of humans. Water covers a very high percentage of the earth's surface. However, several pollutants contaminate the water, thereby making them impure in their raw form. The pollutants can be solid, liquid, or gaseous substances. Accordingly, several techniques have been devised over time to purify water for human needs. The techniques include filtration, distillation, flocculation-coagulation, and sedimentation. The sedimentation technique uses the passive method, gravity, to separate liquid and solid. It is an important technique that is widely applied in chemical, pharmaceuticals, and industrial processes because of its deployment in solid-fluid separation [1][2] [3]. Similarly, it has been widely applied for large-scale water treatment for several reasons, including simplicity and lower cost. The technique includes the use of settling tanks that are designed according to rules of overflow rate and detention period based on the assumption of an ideal settling basin [4]. Several other factors such as concentrations or density gradients, wind movement, flow variation, variation of shape of the tank, and in-let and out-let structure are considered to determine the behavior of sediment tanks during operation fully.
Researchers and practitioners have conducted several studies to improve sedimentation techniques. A finite difference method has been used to determine the vertical velocity field and sedimentation distribution of a sedimentation tank [4]. In a similar study, the finite element method is used to establish a relationship between sludge concentration distribution and flow velocity [5].
However, the finite difference method requires very high computation resources, including storage and time. Therefore, a more efficient technique that used a Strip Integral Method (SIM) has been applied to solve the governing differential equations of continuity, momentum, and mass transport [6]. Similarly, the spatial and temporal development of influent particle size distribution toward the out-let of a rectangular sedimentation basin is described with a computer simulation according to a fundamental governing mechanism of particle growth and motion. The general performance of the settling basin is predicted based on the model [7].
A study was conducted on cohesive sediment and the process of settling in a sedimentation tank [8]. In the study, a numerical investigation of three-dimensional settling process using CFD-DEM (Computational Fluid Dynamics-Discrete Element Method) considering inter-particle collision force, the van der Waals force, and the fluid-particle interaction forces was carried out to establish the exact influence of the characteristics of sediment particles such as the Bond number and particle size distribution on cohesive features. It was found that the cohesive silt characteristics in the settling process depend on the cohesion among silt particles and the particle polydispersity.
Ghawi and Josef carried out a study with the objective to improve the operational performance of large horizontal rectangular sedimentation tanks. They applied a full two-dimensional mass conservative model, which is based on computational fluid dynamics, to realize their objectives by analyzing and modeling the two-phase flow regime found in settling tanks and comparing the model with experimental data [6]. A CFD package FLUENT 6.3.26 was used to develop the novel CFD code technique that is used to analyze sediment transport for multiple particle sizes in sedimentation tanks of potable water.
Recently, Long Fan et al. studied the flow dynamics in a secondary sediment tank. A computational flow dynamics technique was used to establish the velocity profile and the solids concentration distribution in the tank [9]. The study further established the influence of the position of baffle in the secondary sedimentation tank. Similarly, an overflow rate technique was used to remove fine particles from a tertiary sedimentation tank. In the study, an adjustable baffle, which is inclined at different angles, was used to examine particle removal efficiency in the tank [10]. The study revealed that the sedimentation tank with an adjustable baffle at different angles is more effective for particle removal. Another study compared Lamella plate design, often called inclined plates, and a conventional design to examine sedimentation efficiency in a rectangular tank. The result indicated an improved sedimentation efficiency by the Lamella plate design relative to a conventional design [11].
Several numerical methods have been previously used to predict the behavior and performance of a settling tank. However, most of these CFD methods involve high computational cost. Thus, a simple drift-flux model which is an alternative mathematical formulation to the described methods in the previous section is used in the present work to capture both the flow and sedimentation characteristics of a rectangular settling tank to demonstrate the accuracy of the new CFD method proposed for the evaluation of the settling tank performance. Consequently, the challenge of high computational resources is solved.

Governing equations of the drift-flux model
Generally, for the type of multiphase flow problem described in the preceding section where solid particles are dispersed in a liquid. If the liquid is assumed to be continuous while the solid is considered dispersed within the liquid, the dynamics of the system can be comprehensively The most important phenomenon in settling tanks employed for water treatment is the sedimentation of particles in the water in the tank. As stated previously, the sedimentation or settling of particles causes the slip motion of particles. Therefore, the relative velocity of particles and base fluid resulting from the settling of particles is assumed to follow the Vesilind sedimentation model [12] given by Eq. (6) and Eq. (7).
where 0 and represents the reference settling velocity vector and settling coefficient which can be determined from the experimental data. In this study, the settling coefficient, = 285.84 and 0 = (0, −0.002198 / , 0) (values recommended by Vesilind).
To capture the physics of particle slip motion resulting from the sedimentation of particles in the base fluid (water in this case), a mixture model implemented in OpenFOAM CFD code version 6 is used in this study. The basic assumptions of this two-phase mixture modeling approach are: the particles and the base fluid are in local thermal equilibrium, the slip motion of particle due to sedimentation is considered and physical properties of the mixture are evaluated based on the local concentration of the particles. As a developmental basis, the drift flux solver (driftFluxFoam) implemented in OpenFOAM 6 is used to capture the mixture modeling concept.

Problem description, boundary conditions and numerical scheme
Flows in a settling tank is a two-phase turbulent flow which is characterized by the sedimentation of the solid particles in the flow field. Figure. 1(b) shows the geometry of the computation domain used in this study, which is the simplification of the experimental setup of Imam [4]. This geometry is typical of the settling zone and outlet zone of rectangular clarifier as can be seen in Fig. 1(a).
Although, flow in settling tank is generally three-dimensional, however, a two-dimensional is considered in this study because the inlet and outlet are separated in such a way to uniformly spread the width of the tanks, which makes the three-dimensional effect insignificant. The computation domain (see Fig. 1  This has not impact in this study since the steadystate calculation is sought. Thus, the absolute residuals of the key variables (velocity, temperature, pressure, and particle concertation) are restricted to the maximum of 10 -6 as the convergence criterion of the iteration process of the PIMPLE loop.

Discussion of simulation results
To  Fig. 2(a). With the suspended solid particles injected with the water at the inlet at 0.1% concentration, the predicted particle distribution shows the gradual settling of the particles at the bottom of the clarifier as the computation progresses with time until a steady-state solution is reached which is shown in Fig. 2(a). In addition, the hydrodynamic behavior of the water-particle mixture is also reasonably captured by the model. This is indicated by the flow filed shown in Fig. 2 Fig. 3, it can be said that the drift-flux mixture model is able to predict the entire flow field in terms of the velocity profiles reasonably well.

Conclusion
The computational fluid dynamic model (drift-flux mixture model) described in this study can substantially reproduce both the hydrodynamic and sedimentation behavior of water-water mixture flow in rectangular clarifier. With this model, several design issues such as the determination of the optimal location of baffle in the rectangular clarifier can be investigated and addressed at reasonable computational cost since it provides simplification (through reduction of conservation equations) of the full Eulerian multiphase model without compromising the model for key phenomena in clarifiers. This CFD method can also be used for the optimization of the design to achieve robust and stable operation of the sedimentation tank under divergent conditions given the economics, increasing availability of water and environmental responsibility.