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Liquid velocity fluctuations and energy spectra in three-dimensional buoyancy-driven bubbly flows

Published online by Cambridge University Press:  17 December 2019

Vikash Pandey ,
Rashmi Ramadugu  and
Prasad Perlekar Open the ORCID record for Prasad Perlekar [Opens in a new window]
Vikash Pandey
Affiliation:
TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, Hyderabad, 500107, India
Rashmi Ramadugu
Affiliation:
TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, Hyderabad, 500107, India
Prasad Perlekar*
Affiliation:
TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, Hyderabad, 500107, India
*
†Email address for correspondence: [email protected]
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Abstract

We present a direct numerical simulation (DNS) study of pseudo-turbulence in buoyancy-driven bubbly flows for a range of Reynolds ($150\leqslant Re\leqslant 546$) and Atwood ($0.04\leqslant At\leqslant 0.9$) numbers. We study the probability distribution function of the horizontal and vertical liquid velocity fluctuations and find them to be in quantitative agreement with the experiments. The energy spectrum shows a $k^{-3}$ scaling at high $Re$ and becomes steeper on reducing $Re$. To investigate spectral transfers in the flow, we derive the scale-by-scale energy budget equation. Our analysis shows that, for scales smaller than the bubble diameter, the net transfer because of the surface tension and the kinetic energy flux balances viscous dissipation to give $k^{-3}$ scaling of the energy spectrum for both low and high $At$.

JFM classification

Drops and Bubbles: Bubble dynamics Multiphase and Particle-laden Flows: Multiphase flow Turbulent Flows: Turbulence simulation
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 884 , 10 February 2020 , R6
Copyright
© 2019 Cambridge University Press

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Pandey et al. supplementary movie 1

Time evolution of bubbles for our simulations R1 (Movie1.m4v). The bubbles are initially spherical in shape and their center-of-mass are distributed randomly over the entire simulation domain. The time evolution is shown from $t=0$ to $t=54 \tau_\lambda$.

Download Pandey et al. supplementary movie 1(Video)
Video 6.3 MB

Pandey et al. supplementary movie 2

Time evolution of bubbles for our simulations R4 (Movie2.m4v). The bubbles are initially spherical in shape and their center-of-mass are distributed randomly over the entire simulation domain. The time evolution is shown from $t=0$ to $t=27 \tau_\lambda$ .

Download Pandey et al. supplementary movie 2(Video)
Video 5.4 MB

Pandey et al. supplementary movie 3

Time evolution of bubbles for our simulations R6 (Movie3.m4v). The bubbles are initially spherical in shape and their center-of-mass are distributed randomly over the entire simulation domain. The time evolution is shown from $t=0$ to $t=20 \tau_\lambda$.

Download Pandey et al. supplementary movie 3(Video)
Video 6.3 MB