The emergence of bubble-induced scaling in thermal spectra in turbulence

TL;DR

This study investigates how large bubbles in turbulent flows modify the temperature fluctuation spectra, revealing a bubble-induced $-3$ spectral scaling that extends with increased gas volume fraction, differing from classical turbulence spectra.

Contribution

It uncovers the bubble-induced $-3$ spectral scaling in passive scalar temperature spectra within turbulent bubbly flows, a novel observation in multiphase turbulence research.

Findings

The $-3$ spectral scaling emerges at higher gas volume fractions.

The transition frequency from $-5/3$ to $-3$ scaling depends on gas volume fraction.

The $-3$ scaling coincides with velocity fluctuation spectra in bubbly flows.

Abstract

We report on the modification of the spectrum of a passive scalar inside a turbulent flow by the injection of large bubbles. While the spectral modification through bubbles is well known and well analyzed for the velocity fluctuations, little is known on how bubbles change the fluctuations of an approximately passive scalar, in our case temperature. Here we uncover the thermal spectral scaling behavior of a turbulent multiphase thermal mixing layer. The development of a $-3$ spectral scaling is triggered. By injecting large bubbles ($\text{Re}_{\text{bub}} = \mathcal{O}(10^2)$) with gas volume fractions $\alpha$ up to 5\%. For these bubbly flows, the $-5/3$ scaling is still observed at intermediate frequencies for low $\alpha$ but becomes less pronounced when $\alpha$ further increases and it is followed by a steeper $-3$ slope for larger frequencies. This $-3$ scaling range extends with increasing gas volume fraction. The $-3$ scaling exponent coincides with the typical energy spectral scaling for the velocity fluctuations in high Reynolds number bubbly flows. We identify the frequency scale of the transition from the $-5/3$ scaling to the $-3$ scaling and show how it depends on the gas volume fraction.