Energy cascade in a homogeneous swarm of bubbles rising in a vertical channel

The cascade of kinetic energy is a defining characteristic of fluid turbulence. For single-phase flows, the Richardson-Kolmogorov phenomenology provides a satisfactory first approximation of the energy cascade with which many existing turbulence models/theories are based. However, the phenomenology has not been demonstrated in two-phase flows where the production by the dispersed phase is an additional source of liquid turbulent kinetic energy.

We use bubble-resolved, direct numerical simulations to investigate the energy cascade in homogeneous swarms of air bubbles rising a vertical channel. We consider millimeter-sized bubbles with a bubble Reynolds number of 500. The von Karman-Howarth-Monin (K-H-M) equation is adapted for the two-phase flow and used to quantify the interscale energy transfer and to compute the scale-by-scale energy budget.