Turbulent statistics and scales involved in turbulent kinetic energy budget in bubble plumes

Existence of bubble plumes in nature and their wide range of applications in engineering have driven the advancement of our understanding of this unique multiphase fluid mechanics problem in the past few decades. However, bubble induced turbulence is not fully understood due to the incomplete understanding of turbulent scales involved in the interaction between bubble and water. Specifically, the mechanisms of turbulent kinetic energy (TKE) production, transport, and dissipation in both spatial and spectral spaces, are not adequately characterized. To address this knowledge gap, we conducted a series of experiments using fluorescent particle image velocimetry and measured flow field and turbulent statistics within the bubble plume. To support analysis of spatial scales, shadow-graphic imaging was used to measure bubble size distribution. The data indicate that bubble size plays a significant role in mechanisms of turbulence production and transport. The analysis suggests some similarities but differences in turbulent statistics and TKE budget compared to single-phase jets and plumes. Spectral analysis of the TKE budget elucidates the hypothesis of an inverse energy cascade in the bubble plume, a mechanism to transfer TKE from small to large eddies. This is attributed to the direct injection of TKE by bubble passages across a wide range of scales, in contrast to canonical shear production of TKE in large scales.