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Research Article | Open Access

Efficient simulation of bubble dispersion and resulting interaction

Xinghao Yang1,2( )Mark-Patrick Mühlhausen2Jochen Fröhlich1
Institute of Fluid Mechanics, TU Dresden, George-Bähr Str. 3c, 01062 Dresden, Germany
CoC Fluid Dynamics, Bosch Rexroth, Partensteiner Str. 23, 97816 Lohr am Main, Germany
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In this work, an efficient model for simulating bubble dispersion and coalescence due to turbulence is developed in the Euler-Lagrange framework. The primary liquid phase is solved on the Euler grid with the RANS turbulence model. Bubble motion is computed with the force balance equations. One-way coupling between two phases is assumed and the framework is designed for the computation of disperse bubbly flows at low Eötvös number. The turbulent dispersion of the dispersed phase is reconstructed with the continuous random walk (CRW) model. Bubble-bubble collisions and coalescence are accounted for deterministically. To accelerate the time-consuming search for potential collision partners in dense bubbly flows, the sweep and prune algorithm is employed, which can be utilized in arbitrary mesh types and sizes. Validation against experiments of turbulent pipe flows demonstrates that the one-way coupled EL-CRW dispersion model can well reproduce the bubble distribution in a typical dense bubbly pipe flow. Good agreement of the bubble size distribution at the pipe outlet between the simulation and the experiment is obtained.


T. R. Auton,, J. C. R. Hunt,, M. Prud’Homme, 1988. The force exerted on a body in inviscid unsteady non-uniform rotational flow. J Fluid Mech, 197: 241-257.
D. Baraff, 1992. Dynamic simulation of non-penetrating rigid bodies. Ph.D. Thesis. Cornell University.
T. L. Bocksell,, E. Loth, 2001. Random walk models for particle diffusion in free-shear flows. AIAA J, 39: 1086-1096.
T. L. Bocksell,, E. Loth, 2006. Stochastic modeling of particle diffusion in a turbulent boundary layer. Int J Multiphase Flow, 32: 1234-1253.
M. Breuer,, M. Alletto, 2012. Efficient simulation of particle-laden turbulent flows with high mass loadings using LES. Int J Heat Fluid Fl, 35: 2-12.
M. Breuer,, H. T. Baytekin,, E. A. Matida, 2006. Prediction of aerosol deposition in 90 bends using LES and an efficient Lagrangian tracking method. J Aerosol Sci, 37: 1407-1428.
G. Capannini,, T. Larsson, 2018. Adaptive collision culling for massive simulations by a parallel and context-aware sweep and prune algorithm. IEEE T Vis Comput Gr, 24: 2064-2077.
G. Capannini,, T. Larsson, 2016. Efficient collision culling by a succinct bi-dimensional sweep and prune algorithm. In: Proceedings of the 32nd Spring Conference on Computer Graphics, 25-32.
A. Chesters, 1991. The modelling of coalescence processes in fluid-liquid dispersions: A review of current understanding. Chem Eng Res Des, 69: 259-270.
A. K. Chesters,, G. Hofman, 1982. Bubble coalescence in pure liquids. Appl Sci Res, 38: 353-361.
C. Colin,, J. Fabre,, A. E. Dukler, 1991. Gas-liquid flow at microgravity conditions—I. Dispersed bubble and slug flow. Int J Multiphase Flow, 17: 533-544.
C. Colin, 1990. Écoulements diphasiques à bulles et à poches en micropesanteur. Ph.D. Thesis. Toulouse, INPT, thse de doctorat dirige par Fabre, Jean Mcanique des fluides Toulouse, INPT.
C. Colin,, J. Fabre,, A. Kamp, 2012. Turbulent bubbly flow in pipe under gravity and microgravity conditions. J Fluid Mech, 711: 469-515.
C. T. Crowe,, M. P. Sharma,, D. E. Stock, 1977. The particle-source-in cell (PSI-CELL) model for gas-droplet flows. J Fluid Eng, 99: 325-332.
K. D. Danov,, D. S. Valkovska,, I. B. Ivanov, 1999. Effect of surfactants on the film drainage. J Colloid Interf Sci, 211: 291-303.
D. Darmana,, N. G. Deen,, J. A. M. Kuipers, 2006. Parallelization of an Euler-Lagrange model using mixed domain decomposition and a mirror domain technique: Application to dispersed gas-liquid two-phase flow. J Comput Phys, 220: 216-248.
A. Dehbi, 2008. Turbulent particle dispersion in arbitrary wall-bounded geometries: A coupled CFD-Langevin-equation based approach. Int J Multiphase Flow, 34: 819-828.
P. C. Duineveld, 1995. The rise velocity and shape of bubbles in pure water at high Reynolds number. J Fluid Mech, 292: 325-332.
J. Fang,, J. J. Cambareri,, C. S. Brown,, J. Feng,, A. Gouws,, M. Li,, I. A. Bolotnov, 2018. Direct numerical simulation of reactor two-phase flows enabled by high-performance computing. Nucl Eng Des, 330: 409-419.
Fluent Theory Guide. 2019. Ansys Fluent v19.2 - CFD Software — ANSYS.
A. D. Gosman,, E. loannides, 1983. Aspects of computer simulation of liquid-fueled combustors. J Energy, 7: 482-490.
S. Heitkam,, A.-E. Sommer,, W. Drenckhan,, J. Fröhlich, 2017. A simple collision model for small bubbles. J Phys: Condens Matter, 29: 124005.
S. Heitkam,, A.-E. Sommer,, W. Drenckhan,, J. Fröhlich, 2020. Corrigendum: A simple collision model for small bubbles (2017 J. Phys.: Condens. Matter 29 124005). J Phys: Condens Matter, 32: 289501.
M. A. Hopkins,, M. Y. Louge, 1991. Inelastic microstructure in rapid granular flows of smooth disks. Phys Fluids A: Fluid, 3: 47-57.
F. Hoppe,, M. Breuer, 2018. A deterministic and viable coalescence model for Euler-Lagrange simulations of turbulent microbubble-laden flows. Int J Multiphase Fl, 99: 213-230.
I. Iliopoulos,, T. Hanratty, 1999. Turbulent dispersion in a non-homogeneous field. J Fluid Mech, 392: 45-71.
J. N. Israelachvili, 2011. Intermolecular and Surface Forces. Elsevier Science.
S. A. K. Jeelani,, S. Hartland, 1991. Effect of approach velocity on binary and interfacial coalescence. Chem Eng Res Des, 69: 271-281.
A. M. Kamp,, A. K. Chesters,, C. Colin,, J. Fabre, 2001. Bubble coalescence in turbulent flows: A mechanistic model for turbulence-induced coalescence applied to microgravity bubbly pipe flow. Int J Multiphase Flow, 27: 1363-1396.
S. Laín,, D. Bröder,, M. Sommerfeld,, M. F. Göz, 2002. Modelling hydrodynamics and turbulence in a bubble column using the Euler-Lagrange procedure. Int J Multiphase Flow, 28: 1381-1407.
C. J. Lawn, 1971. The determination of the rate of dissipation in turbulent pipe flow. J Fluid Mech, 48: 477-505.
Y. Liao,, D. Lucas, 2010. A literature review on mechanisms and models for the coalescence process of fluid particles. Chem Eng Sci, 65: 2851-2864.
M. D. Mattson,, K. Mahesh, 2012. A one-way coupled, Euler- Lagrangian simulation of bubble coalescence in a turbulent pipe flow. Int J Multiphase Flow, 40: 68-82.
R. Mei,, J. F. Klausner, 1994. Shear lift force on spherical bubbles. Int J Heat Fluid Flow, 15: 62-65.
A. Ormancey,, J. Martinon, 1984. Prediction of particle dispersion in turbulent flows. Physico Chemical Hydrodynamics, 5: 229-244.
S. Orvalho,, M. C. Ruzicka,, G. Olivieri,, A. Marzocchella, 2015. Bubble coalescence: Effect of bubble approach velocity and liquid viscosity. Chem Eng Sci, 134: 205-216.
S. B. Pope, 2000. Turbulent Flows. Cambridge University Press.
M. J. Prince,, H. W. Blanch, 1990. Bubble coalescence and break-up in air-sparged bubble columns. AIChE J, 36: 1485-1499
A. M. Reynolds,, G. Lo Iacono, 2004. On the simulation of particle trajectories in turbulent flows. Phys Fluids, 16: 4353-4358.
C. P. Ribeiro,, D. Mewes, 2006. On the effect of liquid temperature upon bubble coalescence. Chem Eng Sci, 61: 5704-5716.
A. Rousset,, A. Checkaraou,, Y. C. Liao,, X. Besseron,, S. Varrette,, B. Peters, 2018. Comparing broad phase interaction detection algorithms for multi-physics DEM applications. AIP Conf Proc, 1978: 270007.
P. G. Saffman, 1965. The lift on a small sphere in a slow shear flow. J Fluid Mech, 22: 385-400.
C. Santarelli,, J. Fröhlich, 2015. Direct Numerical Simulations of spherical bubbles in vertical turbulent channel flow. Int J Multiphase Flow, 75: 174-193.
SciPy. 2019. SciPy 1.4.1 reference guide.
E. Shams,, J. Finn,, S. V. Apte, 2011. A numerical scheme for Euler-Lagrange simulation of bubbly flows in complex systems. Int J Numer Method Flow, 67: 1865-1898.
M. Sommerfeld, 2001. Validation of a stochastic Lagrangian modelling approach for inter-particle collisions in homogeneous isotropic turbulence. Int J Multiphase Flow, 27: 1829-1858.
D. J. Thomson, 1987. Criteria for the selection of stochastic models of particle trajectories in turbulent flows. J Fluid Mech, 180: 529-556.
A. Tomiyama,, I. Kataoka,, I. Zun,, T. Sakaguchi, 1998. Drag coefficients of single bubbles under normal and micro gravity conditions. JSME Int J Ser B, 41: 472-479.
A. Tomiyama,, H. Tamai,, I. Zun,, S. Hosokawa, 2002. Transverse migration of single bubbles in simple shear flows. Chem Eng Sci, 57: 1849-1858.
Experimental and Computational Multiphase Flow
Pages 152-170
Cite this article:
Yang X, Mühlhausen M-P, Fröhlich J. Efficient simulation of bubble dispersion and resulting interaction. Experimental and Computational Multiphase Flow, 2021, 3(3): 152-170.








Web of Science




Received: 09 April 2020
Revised: 29 June 2020
Accepted: 29 July 2020
Published: 09 September 2020
© The Author(s) 2020

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