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Flow topologies in bubble-induced turbulence: a direct numerical simulation analysis

  • Josef Hasslberger (a1), Markus Klein (a1) and Nilanjan Chakraborty (a2)

Abstract

This paper presents a detailed investigation of flow topologies in bubble-induced two-phase turbulence. Two freely moving and deforming air bubbles that have been suspended in liquid water under counterflow conditions have been considered for this analysis. The direct numerical simulation data considered here are based on the one-fluid formulation of the two-phase flow governing equations. To study the development of coherent structures, a local flow topology analysis is performed. Using the invariants of the velocity gradient tensor, all possible small-scale flow structures can be categorized into two nodal and two focal topologies for incompressible turbulent flows. The volume fraction of focal topologies in the gaseous phase is consistently higher than in the surrounding liquid phase. This observation has been argued to be linked to a strong vorticity production at the regions of simultaneous high fluid velocity and high interface curvature. Depending on the regime (steady/laminar or unsteady/turbulent), additional effects related to the density and viscosity jump at the interface influence the behaviour. The analysis also points to a specific term of the vorticity transport equation as being responsible for the induction of vortical motion at the interface. Besides the known mechanisms, this term, related to surface tension and gradients of interface curvature, represents another potential source of turbulence production that lends itself to further investigation.

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Corresponding author

Email address for correspondence: josef.hasslberger@unibw.de

References

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Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.
Brackbill, J. U., Kothe, D. B. & Zemach, C. 1992 A continuum method for modeling surface tension. J. Comput. Phys. 100 (2), 335354.
Brøns, M., Thompson, M. C., Leweke, T. & Hourigan, K. 2014 Vorticity generation and conservation for two-dimensional interfaces and boundaries. J. Fluid Mech. 758, 6393.
Brücker, C. 1999 Structure and dynamics of the wake of bubbles and its relevance for bubble interaction. Phys. Fluids 11 (7), 17811796.
Bunner, B. & Tryggvason, G. 2002a Dynamics of homogeneous bubbly flows. Part 1. Rise velocity and microstructure of the bubbles. J. Fluid Mech. 466, 1752.
Bunner, B. & Tryggvason, G. 2002b Dynamics of homogeneous bubbly flows. Part 2. Velocity fluctuations. J. Fluid Mech. 466, 5384.
Chakraborty, N., Wang, L., Konstantinou, I. & Klein, M. 2017 Vorticity statistics based on velocity and density-weighted velocity in premixed reactive turbulence. J. Turbul. 18, 825853.
Chong, M. S., Perry, A. E. & Cantwell, B. J. 1990 A general classification of three-dimensional flow fields. Phys. Fluids A 2 (5), 765777.
Chong, M. S., Soria, J., Perry, A. E., Chacin, J., Cantwell, B. J. & Na, Y. 1998 Turbulence structures of wall-bounded shear flows found using DNS data. J. Fluid Mech. 357, 225247.
Clift, R., Grace, J. R. & Weber, M. E. 2005 Bubbles, Drops, and Particles. Courier Corporation.
Davidson, P. 2015 Turbulence: An Introduction for Scientists and Engineers. Oxford University Press.
Davies, R. M. & Taylor, G. 1950 The mechanics of large bubbles rising through extended liquids and through liquids in tubes. Proc. R. Soc. Lond. A 200, 375390.
Desjardins, O. & Pitsch, H. 2010 Detailed numerical investigation of turbulent atomization of liquid jets. Atomiz. Sprays 20 (4), 311336.
Dixit, H. N. & Govindarajan, R. 2010 Vortex-induced instabilities and accelerated collapse due to inertial effects of density stratification. J. Fluid Mech. 646, 415439.
Dopazo, C., Martín, J. & Hierro, J. 2007 Local geometry of isoscalar surfaces. Phys. Rev. E 76 (5), 056316.
Elsinga, G. E. & Marusic, I. 2010 Universal aspects of small-scale motions in turbulence. J. Fluid Mech. 662, 514539.
Farsoiya, P. K., Mayya, Y. S. & Dasgupta, R. 2017 Axisymmetric viscous interfacial oscillations: theory and simulations. J. Fluid Mech. 826, 797818.
Feng, J. & Bolotnov, I. A. 2017 Evaluation of bubble-induced turbulence using direct numerical simulation. Intl J. Multiphase Flow 93, 92107.
Grötzbach, G. 2011 Revisiting the resolution requirements for turbulence simulations in nuclear heat transfer. Nucl. Engng Des. 241 (11), 43794390.
Haase, K., Kück, U. D., Thöming, J. & Kähler, C. J. 2017 On the emulation of bubble-induced turbulence using randomly moving particles in a grid structure. Chem. Engng Technol. 40 (8), 15021511.
Koebe, M., Bothe, D., Pruess, J. & Warnecke, H.-J. 2002 3D direct numerical simulation of air bubbles in water at high Reynolds number. In Proceedings of the 2002 ASME Fluids Engineering Division Summer Meeting. Montreal, Quebec, Canada. American Society of Mechanical Engineers.
Koebe, M., Bothe, D. & Warnecke, H.-J. 2003 Direct numerical simulation of air bubbles in water/glycerol mixtures: shapes and velocity fields. In Proceedings of the 4th ASME/JSME Joint Fluids Engineering Conference. Honolulu, Hawaii, USA. American Society of Mechanical Engineers.
Lance, M. & Bataille, J. 1991 Turbulence in the liquid phase of a uniform bubbly air–water flow. J. Fluid Mech. 222, 95118.
Ling, Y., Fuster, D., Zaleski, S. & Tryggvason, G. 2017 Spray formation in a quasiplanar gas–liquid mixing layer at moderate density ratios: a numerical closeup. Phys. Rev. Fluids 2 (1), 014005.
Ling, Y., Zaleski, S. & Scardovelli, R. 2015 Multiscale simulation of atomization with small droplets represented by a Lagrangian point-particle model. Intl J. Multiphase Flow 76, 122143.
Ma, T., Santarelli, C., Ziegenhein, T., Lucas, D. & Fröhlich, J. 2017 Direct numerical simulation-based Reynolds-averaged closure for bubble-induced turbulence. Phys. Rev. Fluids 2 (3), 034301.
Ooi, A., Martin, J., Soria, J. & Chong, M. S. 1999 A study of the evolution and characteristics of the invariants of the velocity-gradient tensor in isotropic turbulence. J. Fluid Mech. 381, 141174.
Perry, A. E. & Chong, M. S. 1987 A description of eddying motions and flow patterns using critical-point concepts. Annu. Rev. Fluid Mech. 19 (1), 125155.
Popinet, S. 2009 An accurate adaptive solver for surface-tension-driven interfacial flows. J. Comput. Phys. 228 (16), 58385866.
Popinet, S. 2018 Numerical models of surface tension. Annu. Rev. Fluid Mech. 50, 4975.
Sadhal, S. S., Ayyaswamy, P. S. & Chung, J. N. 2012 Transport Phenomena with Drops and Bubbles. Springer.
Sakamoto, H. & Haniu, H. 1990 A study on vortex shedding from spheres in a uniform flow. Trans. ASME J. Fluids Engng 112, 386392.
Taylor, T. D. & Acrivos, A. 1964 On the deformation and drag of a falling viscous drop at low Reynolds number. J. Fluid Mech. 18 (3), 466476.
Toutant, A., Labourasse, E., Lebaigue, O. & Simonin, O. 2008 DNS of the interaction between a deformable buoyant bubble and a spatially decaying turbulence: a priori tests for LES two-phase flow modelling. Comput. Fluids 37 (7), 877886.
Tripathi, M. K., Sahu, K. C. & Govindarajan, R. 2014 Why a falling drop does not in general behave like a rising bubble. Nat. Sci. Rep. 4, 4771.
Tryggvason, G., Scardovelli, R. & Zaleski, S. 2011 Direct Numerical Simulations of Gas–Liquid Multiphase Flows. Cambridge University Press.
Tsinober, A. 2000 Vortex Stretching versus Production of Strain/Dissipation. Cambridge University Press.
Wacks, D. H., Chakraborty, N., Klein, M., Arias, P. G. & Im, H. G. 2016 Flow topologies in different regimes of premixed turbulent combustion: a direct numerical simulation analysis. Phys. Rev. Fluids 1 (8), 083401.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
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