Simulation of Water-in-Oil Emulsion Flow with OpenFOAM using Validated Coalescence and Breakage Models

Simulation of Water-in-Oil Emulsion Flow with OpenFOAM using Validated Coalescence and Breakage Models Gabriel G. S. Ferreira*, Jovani L. Favero*, Luiz Fernando L. R. Silva +, Paulo L. C. Lage* Laboratório de Termofluidodinâmica *Programa de Engenharia Química, COPPE, Universidade Federal do Rio de Janeiro + Escola de Química, Universidade Federal do Rio de Janeiro

Presentation Topics Institution Overview Introduction Goals Methodology Results Conclusion and next steps

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 following research 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 of continuous mixtures Transport Phenomena

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.

Introduction The adequate simulation of a polydispersed multiphase flow depends on the development of accurate numerical algorithms but also on the usage of validated and physically consistent breakage and coalescence models. The existence of accurate methods for the solution of the PBE are computationally too expensive for usage coupled to the CFD solution, especially when more sophisticated aggregation and breakage models are used.

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 Núcleo de Separadores Compactos of the Instituto de Engenharia Mecânica of the Universidade Federal de Itajubá (UNIFEI).

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.

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 the volumetric drop distribution used in this work, corresponding to mass flow rate of 3 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.

Methodology The PBE is formulated as: where: and:

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 and n 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.

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

Results Comparison of 0-D simulation along the residence time of the experiment for the Sauter mean diameter (d 32 ) and volumetric mean diameter (d 43 ):

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.

Results Simulated contour plot for the Sauter mean diameter (d 32 ) using N=2: The bulk value of the d 32 calculated on the outlet was about 31.3 µm, the experimental value was 12.1 µm and model 0-D (N=6) predicted 14 µm (value at inlet is 55.4 µm).

Results Simulated contour plot of the volumetric mean diameter (d 43 ) using N=2: The bulk value of the d 43 calculated on the outlet was 34.2 µm, the experimental value is 20 µm and model 0-D (N=6) predicted 18 µm (value at inlet is 73.0 µm).

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/cm 2 and the experimental value was 1.74 Kgf/cm 2.

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.

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. 2653 2666 (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. 43 73 (2005).

Thank You! Emails to contact: Paulo Laranjeira da Cunha Lage: paulo@peq.coppe.ufrj.br Luiz Fernando Lopes Rodrigues Silva: lflopes@eq.ufrj.br