# (587e) Numerical Simulation of Drops in a Disc and Doughnut Pulsed Column

- Conference: AIChE Annual Meeting
- Year: 2015
- Proceeding: 2015 AIChE Annual Meeting
- Group: Separations Division
- Session:
- Time:
Wednesday, November 11, 2015 - 4:55pm-5:20pm

The disc and doughnut pulsed column is one of the best choices in solvent extraction processes because of its much smaller footprints and low investment compared to the most commonly used mixer-settler type extraction units among various types of solvent extraction units [1-9]. The low mass transfer efficiency of commercial pulsed column is the only disadvantage, especially for systems with very low interfacial surface tension, and severe axial back-mixing [9]. A large interfacial area is needed for increased mass transfer efficiency. The optimal design of a pulsed column needs an intensive understanding of the multiphase flow dynamics.

Hydrodynamics of single and two phase fluid flow in a disc and doughnut pulsed column is studied in literature using experimental, modelling and simulation techniques [3-8]. The velocity profile, liquid holdup and the size distribution drops of in the column are investigated experimentally [3, 5, 6, 7]. The velocity contours and stream functions of the continuous phase and the hold-up distribution of both the phases in a single stage are determined using numerical simulations [8]; however, to the best of our knowledge, simulations reported in the literature, are performed only on a two dimensional geometry of a single stage.

The objective of the present work is to investigate the pulsatile flow of single and multi-phase fluids in a disc and doughnut column using the techniques of computational fluid dynamics, in order to understand the effect of the operating conditions on the drop dynamics and the geometric parameters on the distribution of the drop size of the dispersed phase and deformation, coalescence and breakage of the droplets.

A disc and doughnut pulsed column can be described as a circular column with an internal fitting that has several units stacked vertically in a repeated manner. Each unit comprises of a doughnut placed between two discs. The height between the disc and doughnut remains uniform throughout the column. All the geometric parameters such as diameter of the disc, height between the doughnut and the disc and aperture of the doughnut are non-dimensionalised by the column diameter. The model geometry for the present simulations is selected based on the dimensional analysis of the large scale columns.

The usual macroscopic mass and momentum conservation laws form the set of governing equations as all the phases are assumed to be interpenetrating continua. The low Reynolds number k-ε model is used to see the effect of turbulence in the continuous phase. The interaction between the phases is modelled using the “Schiller-Naumann” drag law. The effect of drop size distribution on the macroscopic hold up of the liquids is simulated considering multi group description of the dispersed phase. Two pairs of immiscible fluids i.e. water-toluene & water-butanol [4] are considered for the simulations.

In another set of simulations performed on a single stage of the column, the deformation, coalescence and breakage mechanism of the droplets is investigated using the volume of fluid (VOF) method. The effect of shear stress on the interface is neglected while tracking the surface. The boundary conditions at the inlet and outlet of the domain is selected based on the profiles at the central stage, obtained from the earlier simulation. The size distribution of droplets obtained from these simulations is used to form the multi-groups.

The governing equations along with the boundary conditions are solved using the finite volume method as implemented in the commercial software Ansys (Fluent) 14.0/14.5. Uniform structured mesh is created in the computational domain using the ICEM CFD 14.0. The first order upwind scheme is used to discretize the governing equations. The absolute convergence criteria are set at 1x10^{-9} (unit of field variables) in the analysis.

Single-phase simulations are carried out on a pulsed column with three stages, which is found to be the minimum number of stages to be simulated in order to ensure the periodic nature in the central unit. The velocity profiles and contours of the fluid in the central stage is compared with that reported in literature [3] and are found to be in good agreement with each other. Next, the flow of two immiscible liquids is simulated. The velocity contours and phase distribution obtained from the simulations are compared with the experimental observations [6].

Simulations based on the volume of fluid method show that the stable droplets form at the doughnut surface in the column after the flow reaches a stationary state. The drop is found to be sensitive to the flow intensity of the continuous phase. The fluctuations of the droplet surface increase with the flow intensity of continuous phase. The simulation result also indicates that probability of breakage and coalescence increases with the number density of the drops. Effect of the distribution of the drop size on the liquid hold-up in the column will be discussed in the presentation.

*Key words*: Disc and doughnut pulsed column, pulsating flow, volume of fluid.

*References:*

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