Velocity fluctuations for bubbly flows at small Re

TL;DR

This paper experimentally studies how the Reynolds number influences turbulence caused by bubbles in a fluid, revealing a transition from $k^{-3}$ to $k^{-5/3}$ energy spectrum scaling as Re decreases.

Contribution

It provides experimental evidence of the spectral transition in bubble-induced turbulence at low Reynolds numbers, highlighting the non-universality of energy spectra.

Findings

At Re ~ 100, energy spectra slope depends on gas volume fraction.

At Re < 10, the spectra shift from $k^{-3}$ to $k^{-5/3}$ scaling.

Energy spectra at low Re depend on bubble count, indicating non-universality.

Abstract

We experimentally investigate the effect of Reynolds number (Re) on the turbulence induced by the motion of bubbles in a quiescent Newtonian fluid at small Re. The energy spectra, $E(k)$, is determined from the decaying turbulence behind the bubble swarm obtained using particle image velocimetry (PIV). We show that when Re $\sim$ $O$(100), the slope of the normalized energy spectra is no longer independent on the gas volume fraction and the $k^{-3}$ subrange is significantly narrower, where $k$ is the wavenumber. This is further corroborated using second-order longitudinal velocity structure function and spatial correlation of the velocity vector behind the bubble swarm. On further decreasing the bubble Reynolds number ($O(1) < $ Re $ < O(10)$), the signature $k^{-3}$ of the energy spectra for the bubble induced turbulence is replaced by $k^{-5/3}$ scaling. Thus, we provide experimental evidence to the claim by \citet{mazzitelli2003effect} that at low Reynolds numbers the normalized energy spectra of the bubble induced turbulence will no longer show the $k^{-3}$ scaling because of the absence of bubble wake and that the energy spectra will depend on the number of bubbles, thus non-universal.