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Simulation of Water-in-Oil Emulsion Flow with

OpenFOAM using Validated Coalescence and

Breakage ModelsGabriel G. S. Ferreira*, Jovani L. Favero*, Luiz Fernando L. R. Silva+, Paulo L. C. Lage*

Laboratrio de Termofluidodinmica

*Programa de Engenharia Qumica, COPPE, Universidade Federal do Rio de Janeiro

+Escola de Qumica, Universidade Federal do Rio de Janeiro

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Presentation Topics

Institution Overview

Introduction

Goals

Methodology

Results

Conclusion and next steps

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Institution Overview

COPPE hosts most of the Engineering graduate courses at UFRJ

PEQ is the Chemical Engineering Program at COPPE, responsible for the

master and doctoral courses in Chemical Engineering at UFRJ

The Thermo Fluid Dynamics Laboratory (LTFD) develops the followingresearch lines:

Modeling and Simulation of Multiphase Flows

Modeling and Simulation of Non-Newtonian Fluid Flows

Population Balance modeling of polydisperse systems

Numerical Methods: CFD, Population Balance and Thermodynamics ofcontinuous mixtures

Transport Phenomena

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Introduction

Polydispersed flows are of great importance in

many research areas and industrial

applications, to cite a few: aerosol dynamics,

bubble column reactors, crystallization,

combustion, emulsion flow, among others.

There are many important properties that can

be considered to characterize the dispersed

phase: particle volume, area, temperature,

mass of components, etc (Ramkrishna [1]).

An acceptable way to treat this kind of problems

is to use CFD to solve the multi-fluid model in an

Eulerian-Eulerian approach coupled with the

solution of the PBE.

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Introduction

The adequate simulation of a polydispersed

multiphase flow depends on the development of

accurate numerical algorithms but also on the

usage ofvalidated and physically consistentbreakage and coalescence models.

The existence of accurate methods for the

solution of the PBE are computationally too

expensive for usage coupled to the CFDsolution, especially when more sophisticated

aggregation and breakage models are used.

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Goals

Solution of the PBE in a coupled manner with CFD

simulations for real cases: using validated breakage and

coalescence models.

Verify the ability of these simulations to predict the

properties of the droplet size distribution in the emulsion

flow through an accident.

Compare the simulation results with experimental emulsion

flow data obtained in the Ncleo de Separadores

Compactos of the Instituto de Engenharia Mecnica of the

Universidade Federal de Itajub (UNIFEI).

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Methodology

In a recent work, Mitre et al. [2] proposed

new models for micro-droplets

coalescence and breakage in emulsion

flow.

They validated these models using

experimental data for the flow of water in

oil emulsions through a duct with a square

cross section and three movable drawers.

The overall accident generates a localized

pressure drop, similarly to a mixing valve.

The model parameters for the proposed

breakage and coalescence models were

estimated using optimization.

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Methodology

The experiments were made using

different experimental conditions,

varying the flow rate, emulsion

concentration and position of the

movable drawers. The measure of the pressure drop

and the volumetric drop

distribution were obtained before

and after the accident.

In the Figure is shown thevolumetric drop distribution used in

this work, corresponding to mass

flow rate of3 kg/mim, water

concentration of 8% and the

opening drawers being 2.5 mm.

Volumetric drop distribution before

and after the accident and error on

the adjustment of the model

parameters.

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Methodology

The PBE is formulated as:

where: and:

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Methodology

The coalescence and breakage models proposed by Mitre et al. [2] using a 0-

D Lagrangean model were extended to use local variables, i.e., the

turbulence kinetic energy and the residence time were calculated locally for

each one of the finite volume controls on the mesh.

These models were implemented on the solver developed by Silva and Lage

[3], named multiPhasePbeFoam.

This solver treat a polydispersed multiphase flow with one continuous andn dispersed phases. It was implemented in OpenFOAM [4].

The PB-CFD coupling was performed using the Direct Quadrature Method of

Moments (DQMoM) [5] following the MUSIG approach.

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Results

The geometry used to model

the duct accident. The

calculated residence time

for the conditions used for

this simulation case was

about 4.1 ms.

Geometry and mesh used

on the simulations: 2-D

model with 8k cells

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Results

Comparison of 0-D simulation along the residence time of the experiment for

the Sauter mean diameter (d32

) and volumetric mean diameter (d43

):

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Results

Simulated contour plot for the volumetric phase fraction using N=2:

Simulation of 0.5s of real time takes around 5 days of CPU time using 2 i7-2600K

processors.

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Results

Simulated contour plot for the Sauter mean diameter (d32

) using N=2:

The bulk value of the d32calculated on the outlet was about 31.3 m, the

experimental value was 12.1 m and model 0-D (N=6) predicted 14 m (value at

inlet is 55.4 m).

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Results

Simulated contour plot of the volumetric mean diameter (d43

) using N=2:

The bulk value of the d43 calculated on the outlet was 34.2 m, the experimental

value is 20 m and model 0-D (N=6) predicted 18 m (value at inlet is 73.0 m).

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Results

Simulated contour plot of the relative pressure through the duct accident

using N=2:

The pressure drop through the duct accident was about 2.04 Kgf/cm2 and the

experimental value was 1.74 Kgf/cm2.

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Conclusion and next working steps

The simulated results shown large values of the dispersed-phase fraction in

regions where recirculation zones entrap the droplets

Mean diameter results clearly show the existence of droplet breakage in

accident region and dominance of coalescence in the vortex region. The results are not in very good agreement with experimental data.

Improvements on the obtained results might be achieved by:

Mesh convergence analysis.

Improvement in the adaptation of Mitre et al. [2] models to

multidimensional problems.

Simulation of the full 3-D case.

Increasing the number of disperse phases.

Use a new method instead of DQMoM to improve accuracy and reduce

CPU time.

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References

[1] D. Ramkrishna, Population Balances - Theory and Applications to Particulate Systems in

Engineering. Academic Press, San Diego (2000).

[2] J. F. Mitre et al., Modeling droplet breakage and coalescence in the turbulent flow of

water-in-oil emulsions (in preparation) (2012).

[3] L. F. L. R. Silva and P. L. C. Lage, Development and implementation of a polydispersed

multiphase flow model in OpenFOAM.Comp. & Chem. Eng.35, pp. 26532666 (2011).

[4] OpenFOAM, The Open Source CFD Toolbox, User Guide, http://www.openfoam.org/docs/

(2012).

[5] D. L. Marchisio and R. O. Fox, Solution of population balance equations using the direct

quadrature method of moments.Journal of Aerosol Science, 36, pp. 4373 (2005).

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Thank You!Emails to contact:

Paulo Laranjeira da Cunha Lage: paulo@peq.coppe.ufrj.br

Luiz Fernando Lopes Rodrigues Silva: lflopes@eq.ufrj.br

mailto:paulo@peq.coppe.ufrj.brmailto:lflopes@eq.ufrj.brmailto:lflopes@eq.ufrj.brmailto:paulo@peq.coppe.ufrj.br