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Interaction of two oscillating bubbles rising in a thin-gap cell: vertical entrainment and interaction with vortices
- Audrey Filella, Patricia Ern, Veronique Roig
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- Journal:
- Journal of Fluid Mechanics / Volume 888 / 10 April 2020
- Published online by Cambridge University Press:
- 06 February 2020, A13
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We present an exploratory study of the hydrodynamical interaction between two bubbles rising at high Reynolds numbers in a thin-gap cell. When they are isolated, the bubbles exhibit oscillatory motions and develop an unsteady wake with periodic release of vortices. Experiments combine bubble tracking and measurements of the liquid velocity field through volumetric time-resolved particle image velocimetry. This enabled us to analyse the kinematics of the bubbles during their interaction in relationship with the liquid flow field induced by their motion and governing their behaviour. We first investigate how the kinematics of a bubble, already submitted to the intrinsic instability of its path and wake, is modified by the interaction, i.e. by the presence of a liquid flow field generated by the companion bubble. Two main effects are highlighted in association with (i) the role of the ascending flow generated by the leading bubble, and of its spatial evolution, leading to a slowly varying vertical entrainment of the trailing bubble, and (ii) the role of the vortices released by the leading bubble inducing strong localized horizontal deviations on a bubble in line or in oblique positioning. In the latter case, two major scenarios are identified: deviations of the trailing bubble towards the wake centre line (centring in the wake) or away from it (ejection from the wake). We also show that a regular succession of ejections and re-alignments events may take place (cyclic alternation of ejections and centrings). The analysis is built on the knowledge of the behaviour of isolated bubbles, which is used as the basis for comparison to characterize the effect of the interaction, for the modelling of the vertical entrainment, and for the definition of a criteria on a dimensionless parameter characterizing the ability of a vortex to drive the bubble motion. In turn, we investigate the effect of a bubble passage in the liquid flow field generated by the companion bubble, highlighting the destruction or reinforcement of vortices. We show in particular that both effects can occur without a significant impact on the bubble kinematics.
Oscillatory motion and wake of a bubble rising in a thin-gap cell
- Audrey Filella, Patricia Ern, Véronique Roig
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- Journal:
- Journal of Fluid Mechanics / Volume 778 / 10 September 2015
- Published online by Cambridge University Press:
- 30 July 2015, pp. 60-88
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We investigate the characteristics of the oscillatory motion and wake of confined bubbles freely rising in a thin-gap cell ($h=3.1~\text{mm}$ width). Once the diameter $d$ of the bubble in the plane of the cell is known, the mean vertical velocity of the bubble $V_{b}$ is proportional to the gravitational velocity $(h/d)^{1/6}\sqrt{gd}$, where $g$ is the gravitational acceleration. This velocity is used to build the Reynolds number $Re=V_{b}d/{\it\nu}$ that characterizes the flow induced by the bubble in the surrounding liquid (of kinematic viscosity ${\it\nu}$), and which determines at leading order the mean deformation of the bubble given by the aspect ratio ${\it\chi}$ of the ellipse equivalent to the bubble contour. We then show that in the reference frame associated with the bubble (having a fixed origin and axes corresponding to the minor and major axes of the equivalent ellipse) the characteristics of its oscillatory motion in the plane of the cell display remarkable properties in the range $1200<Re<3000$ and $h/d<0.4$. In particular, the velocity of the bubble presents along its path an almost constant component along its minor axis (fluctuations in time of approximately 5 %), given by $V_{a}/V_{b}\simeq 0.92$ for all $Re$. The dimensionless amplitude of oscillation of the angular velocity is also constant for all $Re$, $\tilde{r}d/V_{b}\simeq 0.75$, while that of the transverse velocity of the bubble (along its major axis) is given by $\tilde{V}_{t}/V_{b}\simeq 0.32{\it\chi}$, reaching values comparable to those of the axial velocity $V_{a}$ for the most deformed bubbles (${\it\chi}\approx 3$). Furthermore, the frequency $f$ of oscillation scales with the inertial time scale based on the transverse velocity of the bubble $\tilde{V}_{t}$, corresponding to a constant Strouhal number $St^{\ast }=fd/\tilde{V}_{t}\simeq 0.27$. Using high-frequency particle image velocimetry, we investigate in detail the properties of the wake associated with the oscillatory motion of sufficiently confined bubbles. We observe that vortex shedding occurs for a maximal transverse velocity $V_{t}$ of the bubble, corresponding to a maximal drift angle of the bubble. Furthermore, the measured vorticity of the vortex at detachment corresponds to the estimation $V_{b}{\it\chi}^{3/2}/d$ of the vorticity produced at the bubble surface. Three stages then emerge concerning the evolution in time of the wake generated by the bubble. For one to two periods of oscillation $T_{x}$ following the release of a vortex, a rapid decay of the vorticity of the released vortex is observed. Meanwhile, the released vortex located initially at a distance of approximately one diameter from the bubble centre moves outwards from the bubble path and expands. At intermediate times, the vortex street undergoes vortex pairing. When viscous effects become predominant at a time of the order of the viscous time scale ${\it\tau}_{{\it\nu}}=h^{2}/(4{\it\nu})$, the vortex street becomes frozen and decays exponentially in place.