Difference between revisions of "BubbleFoam"

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	=== Overview ===		=== Overview ===
		+	The two-fluid equations solved by the bubbleFoam solver are described in this chapter.
		+	The general two-fluid continuity and momentum equations are introduced, the closure
		+	expressions for the phase stress tensor and the momentum transfer term are presented,
		+	and the transport equations of the turbulence model are summarized.
	=== Governing equations ===		=== Governing equations ===

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Revision as of 03:16, 12 February 2010

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1 Introduction and applications

The bubbleFoam solver is a two-phase solver based on the Euler-Euler two-fluid methodology [1, 2, 3, 4, 10], suitable to compute dispersed gas-liquid and liquid-liquid flows. In the Euler-Euler two-fluid approach, the phases are treated as interpenetrating continua, which are capable of exchanging properties, like momentum, energy and mass one with the other. Typical applications of the two-fluid approach, as implemented in bubbleFoam, are:

• bubble columns
• stirred tank reactors
• static mixers

2 bubbleFoam capabilities and limitations

2.1 bubbleFoam capabilities

The bubbleFoam solver implements the two-fluid equations derived in [10, 8] for the simulation of gas-liquid flows. The model undergoes the following assumptions:

• Phases are incompressible
• The dispersed phase particle diameter is constant
• The flow is isothermal
• Only momentum exchange is accounted for in the momentum transport equations

The main features of the solver are the following:

• Capability to solve for dispersed two-phase flows with strong density ratio
• Robust solution algorithm, able to deal with complete flow separation
• Turbulence modelling through κ − ε model and standard wall functions.

2.2 bubbleFoam limitations

The bubbleFoam solver currently has the following limitations:

• Only one dispersed phase and a continuous phase can be described. It is not possible to account for multiple dispersed phases (i.e. represent a dispersed phase diameter distribution)
• The diameter of the particles1 constituting the dispersed phase is assumed to be constant. Aggragation, breakage and coalescence phenomena are not accounted for
• The drag coefficient is computed as a blend of the drag coefficients evaluated for each phase on the basis of the phase fractions, and no alternative drag models are available
• The interaction between the phases happens only through the momentum exchange term in the corresponding momentum equations:
  • It is not possible to model the heat transfer between the phases
  • It is not possible to model the mass transfer between the phases
  • No chemical reaction model is available.

3 bubbleFoam theory

3.1 Overview

The two-fluid equations solved by the bubbleFoam solver are described in this chapter. The general two-fluid continuity and momentum equations are introduced, the closure expressions for the phase stress tensor and the momentum transfer term are presented, and the transport equations of the turbulence model are summarized.

3.2 Governing equations

3.2.1 Turbulence model

4 bubbleFoam implementation

4.1 Numerical methodology

4.1.1 Phase momentum equation

4.1.2 Phase continuity equation

4.1.3 Pressure equation

4.2 Solution procedure

4.3 Code representation

4.3.1 Implementation of the phase momentum equation

4.3.2 Implementation of the phase continuity equation

4.3.3 Implementation of the pressure equation

5 bubbleFoam setup and solution strategy

5.1 Case structure

5.2 Initial conditions

5.3 Solver configuration

5.3.1 The environmentalProperties dictionary

5.3.2 The RASProperties dictionary

5.3.3 The transportProperties dictionary

5.4 Solver controls

5.4.1 The controlDict dictionary

5.4.2 The fvSchemes dictionary

5.4.3 The fvSolution dictionary

6 References

1. D. A. Drew. Averaged equations for two-phase flows. Studies in Applied Mathematics, L(3):205 – 231, 1971.
2. D. A. Drew. Continuum modeling of two-phase flows. In R. Meyer, editor, Theory of dispersed multiphase flow, pages 173 – 190. Academic Press, 1983.
3. H. Enwald, E. Peirano, and A. E. Almstedt. Eulerian two-phase flow theory applied to fluidization. International Journal of Multiphase Flow, 22:21 – 66, 1996.
4. D. P. Hill. The computer simulation of dispersed two-phase flow. PhD thesis, Imperial College of Science, Technology and Medicine, London, U.K., 1998.
5. J. P. Oliveira and R. I. Issa. Numerical aspects of an algorithm for Eulerian simulation of two-phase flows. International Journal for Numerical Methods in Fluids, 43:1177 – 1198, 2003.
6. OpenCFD. OpenFOAM - The Open Source CFD Toolbox - Programmer’s Guide. OpenCFD Ltd., United Kingdom, 1.4 edition, 11 April 2007.
7. OpenCFD. OpenFOAM - The Open Source CFD Toolbox - User’s Guide. OpenCFD Ltd., United Kingdom, 1.4 edition, 11 April 2007.
8. H. Rusche. Computational fluid dynamics of dispersed two-phase flows at high phase fractions. PhD thesis, Imperial College of Science, Technology and Medicine, London, 2002.
9. L. Schiller and A. Naumann. Uber die grundlegenden Berechnungen bei der Schwerkraftaufbereitung. Zeitschrift des Vereins deutscher Ingenieure, 77(12):318, 1933.
10. H. G. Weller. Derivation, modelling and solution of the conditionally averaged two-phase flow equations. Technical report, OpenCFD Ltd., United Kingdom, 23 February 2005.