a1 Instituto de Ingeniería, Universidad Nacional Autónoma de México, Calle 21 No. 97A, Colonia Itzimná, 97100 Mérida, Mexico
a2 Institut de Mécanique des Fluides, Institut National Polytechnique de Toulouse Allée du Professeur Camille Soula, 31400 Toulouse, France
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.
(Received July 05 2010)
(Revised January 28 2011)
(Accepted March 28 2011)
(Online publication May 19 2011)