Effect of rising motion on the damped shape oscillations of drops and bubbles

Abstract

The objective of this work is to determine the effect of the rising motion on the dynamics of inertial shape oscillations of drops and bubbles. We have carried out axisymmetric direct numerical simulations of an ascending drop (or bubble) using a level-set method. The drop is initially elongated in the vertical direction and therefore performs shape oscillations. The analysis is based on the decomposition of the interface into spherical harmonics, the time evolutions of which are processed to obtain the frequency and the damping rate of the oscillations. As the drop accelerates, its shape flattens and oscillations no longer take place around a spherical equilibrium shape. This causes the eigenmode of oscillations to change, which results in the appearance of spherical harmonics of high order that all oscillate at the same frequency. For both drops and bubbles, the frequency, which remains controlled by the potential flow, slightly decreases with the rising velocity. The damping rate of drops, which is controlled by the dissipation within boundary layers at the interface, strongly increases with the rising velocity. At terminal velocity, the damping rate of bubbles, which results from the dissipation by the potential flow associated with the oscillating motion, remains close to that of a non-rising bubble. During the transient, the rate of deformation of the equilibrium shape of bubbles can be comparable to the oscillation frequency, which causes complex evolutions of the shape. These results extend the description of shape oscillations to common situations where gravity plays a role. In particular, the present conclusions are useful to interpret experimental results where the effect of the rising motion is often combined with that of surfactant.

Direct numerical simulation of nucleate pool boiling at large microscopic contact angle and moderate Jakob number

“…Temporal integration is carried out with a second order Runge Kutta scheme. In recent works [28,30] accurate comparisons between experimental data and Direct Numerical Simulations on oscillations of bubble rising have been presented by using these numerical methods. It is noteworthy that in the following papers [5,37,47], an alternative method is proposed to compute the distance function by using a subcell fix in the grid cells that are crossed by the interface.…”

Paths and wakes of deformable nearly spheroidal rising bubbles close to the transition to path instability

“…Both predictions compare very well with those recently obtained with a level-set approach on a uniform three-dimensional grid with 48 cells per bubble diameter [36], namely, χ T = 1.91 and Re T = 142. To evaluate how the characteristics of the oscillations evolve in such a configuration, effects of the variation of the mean bubble shape must be removed [37]. We achieved this by considering a succession of time windows and separating the time-averaged and time-dependent contributions to the amplitude of mode (2,0) in each of them.…”

An investigation of the influence of initial deformation on fluid dynamics of toluene droplets in water

“…(9) (cf. Lalanne et al, 2013). Thus, the theoretical and the simulated case differ significantly and a perfect match of the frequencies cannot be expected.…”

“…The same applies to the experimental and numerical study of toluene droplets in water by Eiswirth et al (2011). Lalanne et al (2013) studied the influence of the rising movement on the shape oscillations of droplets and bubbles. Simulations were performed with a level set based method in an axisymmetric setting.…”