Dynamics of a two-dimensional upflowing mixing layer seeded with bubbles: Bubble dispersion and effect of two-way coupling

Abstract

The evolution and structure of a spatially evolving two-dimensional mixing layer seeded with small bubbles are numerically investigated. The one-way coupling approach is first employed to show that characteristics of bubble dispersion are dominated by the possibility for sufficiently small bubbles to be captured in the core of the vortices. A stability analysis of the ordinary differential equation system governing bubble trajectories reveals that this entrapment process is governed by the presence of stable fixed points advected by the mean flow. Two-way coupling simulations are then carried out to study how the global features of a two-dimensional flow are affected by bubble-induced disturbances. The local interaction mechanism between the two phases is first analyzed using detailed simulations of a single bubbly vortex. The stability of the corresponding fixed point is found to be altered by the collective motion of bubbles. For trapped bubbles, the interphase momentum transfer yields periodic sequences of entrapment, local reduction of velocity gradients, and eventually escape of bubbles. Similar mechanisms are found to take place in the spatially evolving mixing layer. The presence of bubbles is also found to enhance the destabilization of the inlet velocity profile and to shorten the time required for the rollup phenomenon to occur. The most spectacular effects of small bubbles on the large-scale flow are a global tilting of the mixing layer centerline towards the low-velocity side and a strong increase of its spreading rate. In contrast, no significant modification of the flow is observed when the bubbles are not captured in the large-scale vortices, which occurs when the bubble characteristics are such that the drift parameter defined in the text exceeds a critical value. These two contrasted behaviors agree with available experimental results.

Modelling bubble clusters in compressible liquids

“…Magnaudet & Eames (2000) present a complete review of available models. For the particular case of bubbles in liquids, the works by Parlitz et al (1999) and Climent & Magnaudet (2006) are two relevant examples of experimental studies of the influence of different forces on the bubble motion. The drag force, lift force, Bjerknes forces, and inertial force are some examples of typical forces usually considered to predict the bubble motion.…”

Preferential accumulation of bubbles in Couette-Taylor flow patterns

“…This criterion is met in all entrapment processes of bubbles in vortical structures. 29 The second parameter, H =4͑uЈ / U ͒ 2 R 1 / e, compares the opposite trends of the inertial effects induced by the added mass, pressure gradient, and lift forces. The acceleration U 2 / R 1 based on the Couette flow pushes bubbles toward the inner cylinder, while u · ٌ 2 u tends to capture them within the vortex cores.…”

“…The corresponding stability analysis is performed following the method described in Ref. 29. The set of ordinary differential equations is similar to that encountered in the latter reference with the addition of the centripetal attraction −U 2 / re r .…”

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.…”