Abstracts - KTH Mechanics

The evolution of energy in flow driven through rising bubbles
Enrico Calzavarini ∗ , Detlef Lohse † ,IreneMazzitelli ‡ and Federico Toschi §
We investigate by direct numerical simulations the flow that rising bubbles cause
in initially quiescent fluid. We employ the Eulerian-Lagrangian 1 method and embody
the two-phase coupling by retaining the bubbles like point sources (see figure 1(a)).
The effects of added mass, buoyancy, drag and lift are included in the model equation
for the bubble dynamics. The possibility of bubble-bubble interaction (4-way
coupling) is analyzed in detail. Our analysis is confined to bubble of small Reynolds
number, Reb ∼ O(1), corresponding to micro-bubbles in water.
The present results suggest that a large scale motion is generated in the initial stages
of the flow evolution, owing to an inverse energy cascade from the small to the large
scale, later on the flow reaches a statistically steady condition where no relevant large
scale fluctuations are present, see figure 1(b). Our analysis at relatively low gaseous
volume fractions, α 1%, suggests that the vorticity induced by the gas on the liquid
phase is not strong enough to enhance bubble accumulation in vortices and therefore
bubbles remain spreaded. The lift force and collision term play a major role in
reducing the degree of clusterization in the high vorticity regions of the flow.
∗Department of Applied Physics, University of Twente, 7500 AE Enschede, The Netherlands.
† Department of Applied Physics, University of Twente, 7500 AE Enschede, The Netherlands.
‡ Department of Applied Physics, University of Twente, 7500 AE Enschede, The Netherlands.
§ Istituto per le Applicazioni del Calcolo, CNR, Viale del Policlinico 137, I-00161 Roma, Italy.
1I. M. Mazzitelli, D. Lohse and F. Toschi, J. Fluid Mech. 483, 283 (2003) and Phys. Fluids 15,
L5-L8 (2003).
Figure 1: (a) Effect of the bubble feedback on still fluid, vertical section of the velocity
field. (b) Evolution of the velocity spectra in a typical run, void fraction α =0.016, a
transient characterized by relatively large velocity fluctuations (solid line) is followed
by a state of almost equi-partition of energy (the time evolution is as follows: dashed,
dotted and dot-dashed lines).
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