Buoyancy driven bubbly flows: role of meso-scale structures on the relative motion between phases, and scaling of velocities in bubble columns operated up to the heterogeneous regime

Y Mezui (1) , Martin Obligado (1) , Alain H Cartellier (1)

1 LEGI - Laboratoire des Écoulements Géophysiques et Industriels [Grenoble]

The hydrodynamics of bubble columns is revisited, with an emphasis on the origin of the increase in the relative velocity observed in the heterogeneous regime. We focus on air-water systems, with no or limited coalescence and a quasi-fully developed region where the flow self-organizes when it reaches the heterogeneous regime. We show from dimensional analysis that, in the heterogeneous regime, buoyancy equilibrates inertia, and that velocities scale as (gDε) 1/2 , where D is the bubble column diameter, ε the void fraction and g the gravitational acceleration. This scaling holds for both liquid and gas mean velocities and for their standard deviations, and it is valid over a large range of column diameter and of gas superficial velocities, corresponding to Froude numbers F r = V sg /(gD) 1/2 from 0.02 to 0.5. To investigate further the analogy with turbulent convection, experiments are performed in a 0.4m diameter column with O(10 3) particle Reynolds numbers bubbles. The self-organization prevailing in the heterogeneous regime is confirmed, with a recirculating liquid flow rate that only depends on the column diameter D. The void fraction at small scales is analysed using Voronoï tessellations, that allow to identify meso-scale structures (clusters), void and intermediate regions. A series of arguments are presented that demonstrate that the large relative velocity observed in the heterogeneous regime originates from the presence of meso-scale structures. Concerning velocity fluctuations, a flow picture is presented that seems consistent with a fast track mechanism which, for moderate Rouse numbers, leads to liquid velocity fluctuations proportional to the relative velocity.

Domaines: Mécanique des fluides [physics.class-ph]

Y Mezui, Martin Obligado, Alain H Cartellier. Buoyancy driven bubbly flows: role of meso-scale structures on the relative motion between phases, and scaling of velocities in bubble columns operated up to the heterogeneous regime. 2022. ⟨hal-03615797⟩