Taylor bubble moving in a flowing liquid in vertical channel: transition from symmetric to asymmetric shape

Abstract

The velocity and shape of Taylor bubbles moving in a vertical channel in a Poiseuille liquid flow were studied for the inertial regime, characterized by large Reynolds numbers. Numerical experiments were carried out for positive (upward) and negative (downward) liquid mean velocity. Previous investigations in tube have reported that for upward flow the bubble is symmetric and its velocity follows the law of Nicklin, whereas for certain downward flow conditions the symmetry is broken and the bubble rises appreciably faster. To study the bubble motion and to identify the existence of a transition, a two-dimensional numerical code that solves the Navier-Stokes equations (through a volume of fluid implementation) was used to obtain the bubble shape and the rise velocity for different liquid mean velocities. A reference frame located at the bubble tip and an irregular grid were implemented to allow long simulation times without an excessively large numerical domain. It was observed that whenever the mean liquid velocity exceeded some critical value, bubbles adopted a symmetric final shape even though their initial shape was asymmetric. Conversely, if the mean liquid velocity was smaller than the critical value, a transition to a non-symmetric shape occurred, along with a correspondingly faster velocity. It was also found that surface tension has a stabilizing effect on the transition.

Taylor bubble rising in a vertical pipe against laminar or turbulent downward flow: symmetric to asymmetric shape transition

“…for R * c > 0.9 in tube flow and R * c > 0.6 in plane flow. (d) The three-dimensional results in tubes and the two-dimensional numerical simulations of Figueroa-Espinoza & Fabre (2011) in channels are remarkably similar. A theoretical study of two-dimensional channel flow should therefore be worthwhile, and has the added advantage that it should be easier to perform.…”

“…For channel flow, Figueroa-Espinoza & Fabre (2011) observed that the curvature radius of a symmetric bubble is smaller than the critical radius R * c ≈ 0.6 (see figure 12b). A similar conclusion can be drawn from the present results: bifurcation occurs at R * c ≈ 0.9 whether the velocity distribution is laminar or turbulent.…”

“…This excess is plotted versus Ω * 0 in figure 13(a) and the channel results, determined from the data of Figueroa-Espinoza & Fabre (2011), are shown in figure 13(b). The similarity between the tube and channel cases is remarkable for laminar flow.…”

“…They argued that the instability occurs because the relative velocity between the bubble and the liquid decreases with increasing downflow, resulting in a flattening of the bubble tip. Figueroa-Espinoza & Fabre (2011) recently reported two-dimensional numerical experiments on plane Taylor bubbles moving in vertical Poiseuille flow. They observed that below a critical mean liquid velocity, a transition to a non-symmetric, faster-moving, bubble occurs.…”

Improved locality of the phase-field lattice-Boltzmann model for immiscible fluids at high density ratios

“…In this section, the proposed model is used to simulate the rise of a planar Taylor bubble through stagnant fluid in an inertial regime. This case has been studied theoretically [47,48], numerically [49,50], and experimentally [48] by a number of authors, and a summary of these works can be found in [51]. Table I reproduces the findings of Ref.…”