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

TL;DR

This study uses direct numerical simulations to analyze pseudo-turbulence in buoyancy-driven bubbly flows, revealing how velocity fluctuations and energy spectra behave across different Reynolds and Atwood numbers, with findings matching experimental data.

Contribution

It provides a detailed numerical analysis of velocity fluctuations and energy spectra in bubbly flows, including the derivation of a scale-by-scale energy budget equation and insights into spectral transfer mechanisms.

Findings

Velocity fluctuation PDFs match experimental results.

Energy spectrum exhibits a $k^{-3}$ scaling at high Reynolds numbers.

Surface tension and kinetic energy flux balance viscous dissipation at small scales.

Abstract

We present a direct numerical simulation (DNS) study of pseudo-turbulence in buoyancy driven bubbly flows for a range of Reynolds ($\Rey$) 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 $\Rey$ and becomes steeper on reducing the $\Rey$. 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 $\At$.