Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-27T00:37:57.407Z Has data issue: false hasContentIssue false

Turbulence modulation in buoyancy-driven bubbly flows

Published online by Cambridge University Press:  03 December 2021

Vikash Pandey
Affiliation:
TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, Gopanpally, Hyderabad 500046, India
Dhrubaditya Mitra
Affiliation:
Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, 10691 Stockholm, Sweden
Prasad Perlekar*
Affiliation:
TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, Gopanpally, Hyderabad 500046, India
*
Email address for correspondence: [email protected]

Abstract

We present a direct numerical simulation (DNS) study of buoyancy-driven bubbly flows in the presence of large-scale driving that generates turbulence. On increasing the turbulence intensity: (a) the bubble trajectories become more curved and (b) the average rise velocity of the bubbles decreases. We find that the energy spectrum of the flow shows a pseudo-turbulence scaling for length scales smaller than the bubble diameter and a Kolmogorov scaling for scales larger than the bubble diameter. We conduct a scale-by-scale energy budget analysis to understand the scaling behaviour observed in the spectrum. Although our bubbles are weakly buoyant, the statistical properties of our DNS are consistent with the experiments that investigate turbulence modulation by air bubbles in water.

Type
JFM Papers
Copyright
© The Author(s), 2021. Published by 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

REFERENCES

Alexakis, A. & Chibbaro, S. 2020 Local energy flux of turbulent flows. Phys. Rev. Fluids 5, 094604.CrossRefGoogle Scholar
Almeras, E., Mathai, V., Lohse, D. & Sun, C. 2017 Experimental investigation of the turbulence induced by a bubble swarm rising within incident turbulence. J. Fluid Mech. 825, 10911112.CrossRefGoogle Scholar
Almeras, E., Mathai, V., Sun, C. & Lohse, D. 2019 Mixing induced by a bubble swarm rising through incident turbulence. Intl J. Multiphase Flow 114, 316322.CrossRefGoogle Scholar
Alméras, E., Risso, F., Roig, V., Cazin, S., Plais, C. & Augier, F. 2015 Mixing by bubble-induced turbulence. J. Fluid Mech. 776, 458474.CrossRefGoogle Scholar
Balachandar, S. & Eaton, J.K. 2010 Turbulent dispersed multiphase flow. Annu. Rev. Fluid Mech. 42, 111133.CrossRefGoogle Scholar
Bhatnagar, A., Gupta, A., Mitra, D., Perlekar, P., Wilkinson, M. & Pandit, R. 2016 Deviation-angle and trajectory statistics for inertial particles in turbulence. Phys. Rev. E 94, 063112.CrossRefGoogle ScholarPubMed
Borue, V. & Orszag, S.A. 1998 Local energy flux and subgrid-scale statistics in three-dimensional turbulence. J. Fluid Mech. 366, 131.CrossRefGoogle Scholar
Bunner, B. & Tryggvason, G. 2002 a Dynamics of homogeneous bubbly flows part 1. Rise velocity and microstructure of the bubbles. J. Fluid Mech. 466, 1752.CrossRefGoogle Scholar
Bunner, B. & Tryggvason, G. 2002 b Dynamics of homogeneous bubbly flows part 2. Velocity fluctuations. J. Fluid Mech. 466, 5384.CrossRefGoogle Scholar
Cano-Lozano, J.C., Martínez-Bazán, C., Magnaudet, J. & Tchoufag, J. 2016 Paths and wakes of deformable nearly spheroidal rising bubbles close to the transition to path instability. Phys. Rev. Fluids 1, 053604.CrossRefGoogle Scholar
Canuto, C., Hussaini, M.Y., Quarteroni, A.M. & Zang, T.A. 2012 Spectral Methods in Fluid Dynamics. Springer.Google Scholar
Chandrasekhar, S. 1981 Hydrodynamic and Hydromagnetic Stability. Dover.Google Scholar
Chen, Q., Chen, S., Eyink, G.L. & Holm, D.D. 2003 Intermittency in the joint cascade of energy and helicity. Phys. Rev. Lett. 90, 214503.CrossRefGoogle ScholarPubMed
Clift, R., Grace, J.R. & Weber, M.E. 1978 Bubbles, Drops and Particles. Academic.Google Scholar
Cox, S.M. & Matthews, P.C. 2002 Exponential time differencing for stiff systems. J. Comput. Phys. 176, 430455.CrossRefGoogle Scholar
Deckwer, W.-D. 1992 Bubbles Column Reactors. Wiley.Google Scholar
Eyink, G.L. 1995 Local energy flux and the refined similarity hypothesis. J. Stat. Phys. 78, 335351.CrossRefGoogle Scholar
Frisch, U. 1997 Turbulence, A Legacy of A. N. Kolmogorov. Cambridge University Press.Google Scholar
Hadamard, J. 1911 Mouvement permanent lent d'une sphere liquide et visqueuse dans un liquide visqueux. C. R. Acad. Sci. Paris 152, 17351738.Google Scholar
Innocenti, A., Jaccod, A., Popinet, S. & Chibbaro, S. 2021 Direct numerical simulation of bubble-induced turbulence. J. Fluid Mech. 918, A23.CrossRefGoogle Scholar
Ishihara, T., Gotoh, T. & Kaneda, Y. 2009 Study of high–Reynolds number isotropic turbulence by direct numerical simulation. Annu. Rev. Fluid Mech. 41, 165180.CrossRefGoogle Scholar
Kolmogorov, A.N. 1941 The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl. Acad. Nauk SSSR 30, 914.Google Scholar
Kraichnan, R.H. 1974 On Kolmogorov's inertial-range theories. J. Fluid Mech. 62, 305330.CrossRefGoogle Scholar
Lance, M. & Bataille, J. 1991 Turbulence in the liquid phase of a uniform bubbly air–water flow. J. Fluid Mech. 222, 95118.CrossRefGoogle Scholar
Loisy, A. & Naso, A. 2017 Interaction between a large buoyant bubble and turbulence. Phys. Rev. Fluids 2, 014606.CrossRefGoogle Scholar
Ma, T., Ott, B., Fronhlich, J. & Bragg, A.D. 2021 Scale-dependent anisotropy, energy transfer and intermittency in bubble-laden turbulent flows. arXiv:2104.00449.Google Scholar
Machiels, L. 1997 Predictability of small-scale motion in isotropic fluid turbulence. Phys. Rev. Lett. 79, 34113414.CrossRefGoogle Scholar
Mathai, V., Lohse, D. & Sun, C. 2020 Bubbly and buoyant particle-laden turbulent flows. Annu. Rev. Fluid Mech. 11, 529559.Google Scholar
Meneveau, C. & Katz, J. 2000 Scale-invariance and turbulence models for large-eddy simulation. Annu. Rev. Fluid Mech. 32, 132.CrossRefGoogle Scholar
Mercado, J.M., Gomez, D.G., Gils, D.V., Sun, C. & Lohse, D. 2010 On bubble clustering and energy spectra in pseudo-turbulence. J. Fluid Mech. 650, 287306.CrossRefGoogle Scholar
Mudde, R.F. 2005 Gravity-driven bubbly flows. Annu. Rev. Fluid Mech. 37, 393423.CrossRefGoogle Scholar
Pandey, V., Ramadugu, R. & Perlekar, P. 2020 Liquid velocity fluctuations and energy spectra in three-dimensional buoyancy-driven bubbly flows. J. Fluid Mech. 884, R6.CrossRefGoogle Scholar
Perlekar, P. 2019 Kinetic energy spectra and flux in turbulent phase-separating symmetric binary-fluid mixtures. J. Fluid Mech. 873, 459474.CrossRefGoogle Scholar
Petersen, M.R. & Livescu, D. 2010 Forcing for statistically stationary compressible isotropic turbulence. Phys. Fluids 22, 116101.CrossRefGoogle Scholar
Pope, S. 2012 Turbulent Flows. Cambridge University Press.Google Scholar
Popinet, S. 2018 Numerical models of surface tension. Annu. Rev. Fluid Mech. 50, 128.CrossRefGoogle Scholar
Prakash, V.N., Mercado, J.M., van Wijngaarden, L., Mancilla, E., Tagawa, Y., Lohse, D. & Sun, C. 2016 Energy spectra in turbulent bubbly flows. J. Fluid Mech. 791, 174190.CrossRefGoogle Scholar
Ramadugu, R., Pandey, V. & Perlekar, P. 2020 Pseudo-turbulence in two-dimensional buoyancy-driven bubbly flows: a DNS study. Eur. Phys. J. E 43, 73.CrossRefGoogle ScholarPubMed
Riboux, G., Risso, F. & Legendre, D. 2010 Experimental characterization of the agitation generated by bubbles rising at high Reynolds number. J. Fluid Mech. 643, 509539.CrossRefGoogle Scholar
Risso, F. 2011 Theoretical model for $k^-3$ spectra in dispersed multiphase flows. Phys. Fluids 23, 011701.CrossRefGoogle Scholar
Risso, F. 2016 Physical interpretation of probability density functions of bubble-induced agitation. J. Fluid Mech. 809, 240263.CrossRefGoogle Scholar
Risso, F. 2018 Agitation, mixing, and transfers induced by bubbles. Annu. Rev. Fluid Mech. 50, 2548.CrossRefGoogle Scholar
Risso, F., Roig, V., Amoura, Z., Riboux, G. & Billet, A.-M. 2008 Wake attenuation in large reynolds number dispersed two-phase flows. Phil. Trans. R. Soc. Lond. A 366 (1873), 21772190.Google ScholarPubMed
Roghair, I., Annaland, M.V.S. & Kuipers, H.J.A.M. 2013 Drag force and clustering in bubble swarms. AIChE J. 59 (5), 17911800.CrossRefGoogle Scholar
Roghair, I., Mercado, J.M., Annaland, M.V.S., Kuipers, H., Sun, C. & Lohse, D. 2011 Energy spectra and bubble velocity distributions in pseudo-turbulence: numerical simulations vs experiments. Intl J. Multiphase Flow 37, 10931098.CrossRefGoogle Scholar
Rosti, M.E. & Brandt, L. 2018 Suspensions of deformable particles in a couette flow. J. Non-Newtonian Fluid Mech. 262, 311.CrossRefGoogle Scholar
Rosti, M.E, Brandt, L. & Mitra, D. 2018 Rheology of suspensions of viscoelastic spheres: deformability as an effective volume fraction. Phys. Rev. Fluids 3, 012301.CrossRefGoogle Scholar
Rosti, M.E., Ge, Z., Jain, S.S., Dodd, M.S. & Brandt, L. 2019 Droplets in homogeneous shear turbulence. J. Fluid Mech. 876, 962984.CrossRefGoogle Scholar
Rybczynski, D. 1911 Uber die fortschreitende bewegung einer flussigen kugel in einem zahen medium. Bull. Acad. Sci. Cracovie 1, 4046.Google Scholar
Said, E. 2019 Direct numerical simulation of turbulent flows laden with droplets or bubbles. Annu. Rev. Fluid Mech. 51, 217244.Google Scholar
Salibindla, A.K.R., Masuk, A.U.M., Tan, S. & Ni, R. 2020 Lift and drag coefficients of deformable bubbles in intense turbulence determined from bubble rise velocity. J. Fluid Mech. 894, A20.CrossRefGoogle Scholar
Shukla, I., Kofman, N., Balestra, G., Zhu, L. & Gallaire, F. 2019 Film thickness distribution in gravity-driven pancake-shaped droplets rising in a Hele-Shaw cell. J. Fluid Mech. 874, 10211040.CrossRefGoogle Scholar
Tabib, M.V., Roy, S.A. & Joshi, J.B. 2008 CFD simulation of bubble column-an analysis of interphase forces and turbulence models. Chem. Engng J. 139, 589614.CrossRefGoogle Scholar
Tryggvason, G., Bunner, B., Esmaeeli, A., Juric, D., Al-Rawahi, N., Tauber, W., Han, J., Nas, S. & Jan, Y.-J. 2001 A front-tracking method for the computations of multiphase flow. J. Comput. Phys. 169, 708759.CrossRefGoogle Scholar
Verma, M.K. 2019 Energy Transfers in Fluid Flows. Cambridge University Press.CrossRefGoogle Scholar
Yi, L., Toschi, F. & Sun, C. 2021 Global and local statistics in turbulent emulsions. J. Fluid Mech. 912, A13.CrossRefGoogle Scholar
Yousefi, A., Ardekani, M.N. & Brandt, L. 2020 Modulation of turbulence by finite-size particles in statistically steady-state homogeneous shear turbulence. J. Fluid Mech. 899, A19.CrossRefGoogle Scholar