Hostname: page-component-7bb8b95d7b-wpx69 Total loading time: 0 Render date: 2024-09-26T11:56:05.121Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  19 October 2018

Josef Hasslberger Open the ORCID record for Josef Hasslberger [Opens in a new window] ,
Markus Klein Open the ORCID record for Markus Klein [Opens in a new window]  and
Nilanjan Chakraborty
Josef Hasslberger*
Affiliation:
Institute of Mathematics and Applied Computing, University of the German Federal Armed Forces, Werner-Heisenberg-Weg 39, 85577 Neubiberg, Germany
Markus Klein
Affiliation:
Institute of Mathematics and Applied Computing, University of the German Federal Armed Forces, Werner-Heisenberg-Weg 39, 85577 Neubiberg, Germany
Nilanjan Chakraborty
Affiliation:
School of Engineering, Newcastle University, Claremont Road, Newcastle-upon-Tyne NE1 7RU, UK
*
†Email address for correspondence: josef.hasslberger@unibw.de
Get access Rights & Permissions [Opens in a new window]

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.

JFM classification

Drops and Bubbles: Bubble dynamics Multiphase and Particle-laden Flows: Multiphase flow Vortex Flows: Vortex dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 857 , 25 December 2018 , pp. 270 - 290
Check for updates
Copyright
© 2018 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.Google Scholar
Brackbill, J. U., Kothe, D. B. & Zemach, C. 1992 A continuum method for modeling surface tension. J. Comput. Phys. 100 (2), 335–354.Google Scholar
Brøns, M., Thompson, M. C., Leweke, T. & Hourigan, K. 2014 Vorticity generation and conservation for two-dimensional interfaces and boundaries. J. Fluid Mech. 758, 63–93.Google Scholar
Brücker, C. 1999 Structure and dynamics of the wake of bubbles and its relevance for bubble interaction. Phys. Fluids 11 (7), 1781–1796.Google Scholar
Bunner, B. & Tryggvason, G. 2002a Dynamics of homogeneous bubbly flows. Part 1. Rise velocity and microstructure of the bubbles. J. Fluid Mech. 466, 17–52.Google Scholar
Bunner, B. & Tryggvason, G. 2002b Dynamics of homogeneous bubbly flows. Part 2. Velocity fluctuations. J. Fluid Mech. 466, 53–84.Google Scholar
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, 825–853.Google Scholar
Chong, M. S., Perry, A. E. & Cantwell, B. J. 1990 A general classification of three-dimensional flow fields. Phys. Fluids A 2 (5), 765–777.Google Scholar
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, 225–247.Google Scholar
Clift, R., Grace, J. R. & Weber, M. E. 2005 Bubbles, Drops, and Particles. Courier Corporation.Google Scholar
Davidson, P. 2015 Turbulence: An Introduction for Scientists and Engineers. Oxford University Press.Google Scholar
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, 375–390.Google Scholar
Desjardins, O. & Pitsch, H. 2010 Detailed numerical investigation of turbulent atomization of liquid jets. Atomiz. Sprays 20 (4), 311–336.Google Scholar
Dixit, H. N. & Govindarajan, R. 2010 Vortex-induced instabilities and accelerated collapse due to inertial effects of density stratification. J. Fluid Mech. 646, 415–439.Google Scholar
Dopazo, C., Martín, J. & Hierro, J. 2007 Local geometry of isoscalar surfaces. Phys. Rev. E 76 (5), 056316.Google Scholar
Elsinga, G. E. & Marusic, I. 2010 Universal aspects of small-scale motions in turbulence. J. Fluid Mech. 662, 514–539.Google Scholar
Farsoiya, P. K., Mayya, Y. S. & Dasgupta, R. 2017 Axisymmetric viscous interfacial oscillations: theory and simulations. J. Fluid Mech. 826, 797–818.Google Scholar
Feng, J. & Bolotnov, I. A. 2017 Evaluation of bubble-induced turbulence using direct numerical simulation. Intl J. Multiphase Flow 93, 92–107.Google Scholar
Grötzbach, G. 2011 Revisiting the resolution requirements for turbulence simulations in nuclear heat transfer. Nucl. Engng Des. 241 (11), 4379–4390.Google Scholar
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), 1502–1511.Google Scholar
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.Google Scholar
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.Google Scholar
Lance, M. & Bataille, J. 1991 Turbulence in the liquid phase of a uniform bubbly air–water flow. J. Fluid Mech. 222, 95–118.Google Scholar
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.Google Scholar
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, 122–143.Google Scholar
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.Google Scholar
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, 141–174.Google Scholar
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), 125–155.Google Scholar
Popinet, S. 2009 An accurate adaptive solver for surface-tension-driven interfacial flows. J. Comput. Phys. 228 (16), 5838–5866.Google Scholar
Popinet, S. 2018 Numerical models of surface tension. Annu. Rev. Fluid Mech. 50, 49–75.Google Scholar
Sadhal, S. S., Ayyaswamy, P. S. & Chung, J. N. 2012 Transport Phenomena with Drops and Bubbles. Springer.Google Scholar
Sakamoto, H. & Haniu, H. 1990 A study on vortex shedding from spheres in a uniform flow. Trans. ASME J. Fluids Engng 112, 386–392.Google Scholar
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), 466–476.Google Scholar
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), 877–886.Google Scholar
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.Google Scholar
Tryggvason, G., Scardovelli, R. & Zaleski, S. 2011 Direct Numerical Simulations of Gas–Liquid Multiphase Flows. Cambridge University Press.Google Scholar
Tsinober, A. 2000 Vortex Stretching versus Production of Strain/Dissipation. Cambridge University Press.Google Scholar
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.Google Scholar