# A CFD comparative study of bubble break-up models in a turbulent multiphase jet

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## Abstract

In this paper several bubble break-up models are compared. They have been implemented in the CFX-4.4 fluid dynamic commercial code, which uses the population balance equations for describing liquid/gas multi-phase flows. The models have been assessed against published experimental data, obtained for air bubble break-up within a turbulent water jet. The model of Martínez-Bazán, based on purely kinematics arguments, has shown better agreement with the experimental data. The capabilities of using these models coupled to a CFD code for multiphase flow prediction in industrial applications have been demonstrated.

## Keywords

Bubble Size Nozzle Diameter Computational Fluid Dynamic Code Bubble Size Distribution Population Balance Equation## List of symbols

- C
_{D} drag coefficient

*C*_{TD}turbulent dispersion coefficient

*C*_{pdf}cumulative volume probability density function

*d*_{B}local bubble mean diameter (m)

*D*nozzle diameter (m)

*D*_{e}eddy size in the inertial sub-range (m)

*f*_{i}volume fraction of bubbles in the

*i*-th group (*f*_{ i }=*r*_{ i }/*r*_{g})*f*particle size distribution (m

^{−1}) or (m^{−3})*F*inter-phase momentum transfer (N m

^{−3})*g*break-up frequency (s

^{−1})*n*_{i}number of bubbles in the

*i*-th group per unit volume (m^{−3})*r*volume fraction of the phase

*Re*_{D}Reynolds number at the nozzle section \(\left(Re _{D} = \frac{{\rho _{l} U_{0} D}}{\mu }\right)\)

*u*velocity of the phase (m s

^{−1})*U*mean axial velocity of the single phase jet (m s

^{−1})*U*_{C}mean axial velocity at the jet axis (m s

^{−1})*U*_{0}mean axial velocity at the nozzle section (ms

^{−1})*v*_{i}volume of the bubbles in the

*i*-th group (m^{3})*X*axial distance to the jet nozzle section (m)

## Greek letters

- ɛ
dissipation rate of turbulent energy (m

^{2}s^{−3})- μ
dynamic viscosity (Pa s)

- ρ
density of the phase (kg m

^{−3})- σ
surface tension (N m

^{−2})

## Subscripts

- c
critical bubble

- g
gas phase

*i*bubble size

*k*phase k

- l
liquid phase

*m**m*-th phase- 0
mother bubble

- 1
first daughter bubble

- 2
complementary daughter bubble

## Superscripts

- D
drag term

- T
turbulent term

## Notes

### Acknowledgments

Authors wished to acknowledge the support from the Fifth Framework Program of the European Commission under the Energy, Environment and Sustainable Development Contract EVG1-CT-2001-00042 (EXPRO). Moreover, authors wished to thank Mr. Francisco Herráez for his assistance in the simulations.

## References

- 1.AEA Technology plc (2000) CFX 4.4: Solver. CD-ROM, CFX International, AEA Technology, HarwellGoogle Scholar
- 2.Batchelor GK (1956) The theory of homogeneous turbulence. Cambridge University Press, LondonGoogle Scholar
- 3.Kolev NI (1993) Fragmentation and coalescence dynamics in multiphase flows. Exp Thermal Fluid Sci 6:211–251CrossRefGoogle Scholar
- 4.Konno M et al (1980) Simulations model for break-up process in an agitated tank. J Chem Eng Jpn 16:312–319Google Scholar
- 5.Kurul N, Podowski MZ (1990) Multi-dimensional effects in sub-cooled boiling. In: Proceedings of 9th heat transfer conferenceGoogle Scholar
- 6.Lasheras JC, Eastwood C, Martínez-Bazán C, Montañes JL (2002) A review of statistical models for the break-up of an immiscible fluid immersed into a fully developed turbulent flow. Int J Multiphase Flow 28:247–278CrossRefGoogle Scholar
- 7.Lo S (1996) Application of population balance to CFD modelling of bubbly flow via the MUSIG model. AEA Technology. AEAT-1096Google Scholar
- 8.Luo H, Svendsen F (1996) Theoretical model for drop and bubble break-up in turbulent dispersions. AIChE J 42:1225–1233CrossRefGoogle Scholar
- 9.Martinez-Bazán C et al (1999a) On the break-up of an air bubble injected into a fully developed turbulent flow Part I: Break-up frequency. J Fluid Mech 401:157–182zbMATHCrossRefGoogle Scholar
- 10.Martinez-Bazán C et al (1999b) On the break-up of an air bubble injected into a fully developed turbulent flow Part II: Size pdf of the resulting daughter bubbles. J Fluid Mech 401:183–207CrossRefGoogle Scholar
- 11.Pope SB (2000) Turbulent flows. Cambridge University Press, CambridgezbMATHGoogle Scholar
- 12.Sato Y, Sekoguchi K (1975) Liquid velocity distribution in two-phase bubbly flow. Int J Multiphase Flow 2:79–95zbMATHCrossRefGoogle Scholar
- 13.Tsouris C, Tavlarides LL (1994) Breakage and coalescence models for drops in turbulent dispersions. AIChE J 40:395–406CrossRefGoogle Scholar