Evolution of energy in flow driven by rising bubbles

Abstract

We investigate by direct numerical simulations the flow that rising bubbles cause in an originally quiescent fluid. We employ the Eulerian-Lagrangian method with two-way coupling and periodic boundary conditions. In order to be able to treat up to 288000 bubbles, the following approximations and simplifications had to be introduced, as done before, e.g., by Climent and Magnaudet, Phys. Rev. Lett. 82, 4827 (1999). (i) The bubbles were treated as point particles, thus (ii) disregarding the near-field interactions among them, and (iii) effective force models for the lift and the drag forces were used. In particular, the lift coefficient was assumed to be 1/2, independent of the bubble Reynolds number and the local flow field. The results suggest that large-scale motions are generated, owing to an inverse energy cascade from the small to the large scales. However, as the Taylor-Reynolds number is only in the range of 1, the corresponding scaling of the energy spectrum with an exponent of -5/3 cannot develop over a pronounced range. In the long term, the property of local energy transfer, characteristic of real turbulence, is lost and the input of energy equals the viscous dissipation at all scales. Due to the lack of strong vortices, the bubbles spread rather uniformly in the flow. The mechanism for uniform spreading is as follows. Rising bubbles induce a velocity field behind them that acts on the following bubbles. Owing to the shear, those bubbles experience a lift force, which makes them spread to the left or right, thus preventing the formation of vertical bubble clusters and therefore of efficient forcing. Indeed, when the lift is artificially put to zero in the simulations, the flow is forced much more efficiently and a more pronounced energy that accumulation at large scales (due to the inverse energy cascade) is achieved.

Voronoï analysis of bubbly flows via ultrafast X-ray tomographic imaging

“…According to his study, the increase in temperature hinders the bubble alignment. Similar results were obtained from other numerical studies (Bunner and Tryggvason 2002;Mazzitelli and Lohse 2009;Santarelli and Fröhlich 2013), but also proven by experiments such as the work of Zenit et al (2001). They concluded clustering by means of velocity variance and verified it by analyzing video images.…”

Effect of vapor bubbles on velocity fluctuations and dissipation rates in bubbly Rayleigh-Bénard convection

“…Several papers exist on the buoyant rise of gas bubbles and their effect on the liquid motion [6][7][8][9][10][11]. What distinguishes the present work is that the mechanical coupling between the bubbles and the liquid is augmented and influenced by the thermal coupling, which causes the bubble volume to change.…”

“…Note that here the turbulence intensity is larger than in the case of pseudoturbulence without heating and with periodic boundary conditions in all directions [9], where u t,V /V r was found to be of the order of 6%. In that work [9], which was quantitatively confirmed by independent simulations by Calzavarini [22], the bubbles did not grow and the drag law was pure Stokes. We have repeated our simulations with Ja = 0 and the same drag law, still finding considerably larger velocity fluctuations than reported for the case of pseudoturbulence with periodic boundary conditions and no heating.…”

“…Thus we conclude that the reason for this difference lies in the nature of the two flows investigated. The work of [9] concerns the rise of fixed-radius bubbles in a quiescent liquid in a cube with periodic boundary conditions not only on the sides but also on the top and bottom. In that system the only liquid flow is induced by the bubbles and, in a frame of reference with zero mean flow, the bubbles rise while, by continuity, the liquid descends.…”

Effects of particle settling on Rayleigh-Bénard convection

“…For this purpose we extended the standard point-bubble model already used for isothermal bubbly flows by several researchers [see e.g. 17,18] to deal with the thermal effects associated with phase change phenomena.…”