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

Abstract

We present a direct numerical simulation (DNS) study of pseudo-turbulence in buoyancy driven bubbly flows for a range of Reynolds (Re) and Atwood (At) 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 the k −3 scaling at high Re and becomes steeper on reducing the Re. To investigate the 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 production because of the surface tension and the kinetic energy flux balances viscous dissipation to give the k −3 scaling of the energy spectrum for both low and high At.

Scalars in bubbly turbulence

“…As reviewed in Ref. [7] and the recent DNS work [91], this scaling is robust and is observed for a homogeneous bubble swarm for a wide range of parameters: 10 ≤ Re bub ≤ 1000 and 1 ≤ We ≤ 4 where We is the Weber number. In contrast, point particle simulations do not show k −3 scaling [25], because the wakes behind the bubbles are crucial for the emergence of a -3 scaling (in both frequency or wavenumber space) [7].…”

“…This means that the inverse of scalar diffusive time scale needs to be around the onset frequency of -3 subrange. A direct verification on the speculation may be done by the investigation on the diffusive, spectral transfer budgets of the spectral content of scalar fluctuations at the -3 subrange that can be analysed by direct numerical simulations similar to [91]. Another future investigation is to predict the critical α that leads to the saturation of the -3 scaling in passive scalar spectra for a general turbulent bubbly thermal mixing layer (for different incident turbulent intensities, mean temperature gradient forcing and high-Re bubble properties).…”

Direct numerical simulation of bubble-induced turbulence

“…For comparison, the very recent numerical results presented by Pandey et al (2020) are also shown for two Ar numbers. It is worth recalling that these results have been obtained with a lower resolution (24 points per diameter instead of 82 for the present simulation), and using a much lower density ratio of approximately 20, instead of 800 for the present simulation as for water/air.…”

“…Furthermore, in the first work (Roghair et al 2011) realistic physical properties are chosen but just a few bubbles are released, of the order of 10, while in the study by Pandey et al (2020) many bubbles are followed but with a very low density ratio between the fluid and the gas, between 1.1 and 20. The nonlinear interactions among bubbles are, however, key to the dynamics and their statistical study requires the presence of a large number of bubbles (Lance & Bataille 1991;Risso 2018).…”

“…of the velocity is analysed first and compared with previous experimental results (Riboux et al 2010). The spectrum of the kinetic energy is then computed and compared with experiments and results obtained very recently at a lower resolution by Pandey et al (2020). To gain physical insights and address the issues related to the cascade, we present a scale-by-scale analysis of the energy transfers in physical space, rather than in spectral space as commonly done in isotropic turbulence.…”