Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-12-01T08:53:04.508Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  19 May 2011

BERNARDO FIGUEROA-ESPINOZA  and
JEAN FABRE
BERNARDO FIGUEROA-ESPINOZA
Affiliation:
Instituto de Ingeniería, Universidad Nacional Autónoma de México, Calle 21 No. 97A, Colonia Itzimná, 97100 Mérida, Mexico
JEAN FABRE*
Affiliation:
Institut de Mécanique des Fluides, Institut National Polytechnique de Toulouse Allée du Professeur Camille Soula, 31400 Toulouse, France
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

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.

JFM classification

Drops and Bubbles: Bubble dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 679 , 25 July 2011 , pp. 432 - 454
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Benkenida, A. 1999 Développement et validation d'une méthode de simulation d'écoulement diphasique sans reconstruction d'interface. Application à la dynamique des bulles de Taylor. Thesis, INP Toulouse, France.Google Scholar
Benkenida, A. & Magnaudet, J. 2000 Une méthode de simulation d'écoulements diphasiques sans reconstruction d'interfaces. C. R. Acad. Sci. IIb 328, 25–32.Google Scholar
Birkhoff, G. & Carter, D. 1957 Rising plane bubbles. J. Math. Mech. 6, 769–779.Google Scholar
Bonometti, T. 2003 Développement d'une méthode de simulation d'écoulements à bulles et à gouttes. Thesis, INP Toulouse, France.Google Scholar
Bonometti, T. & Magnaudet, J. 2007 An interface-capturing method for incompressible two-phase flows: validation and application to bubble dynamics. Intl J. Multiphase Flow 33, 109–133.CrossRefGoogle Scholar
Clanet, C., Héraud, P. & Searby, G. 2004 On the motion of bubbles in vertical tubes of arbitrary cross-sections: some complements to the Dumitrescu–Taylor problem. J. Fluid Mech. 519, 359–376.CrossRefGoogle Scholar
Collins, R. 1965 A simple model of the plane gas bubble in a finite liquid. J. Fluid Mech. 22, 763–771.CrossRefGoogle Scholar
Collins, R., de Moraes, F. F., Davidson, J. F. & Harrison, D. 1978 The motion of large bubbles rising through liquid flowing in a tube. J. Fluid Mech. 89, 497–514.CrossRefGoogle Scholar
Couët, B. & Strumolo, G. S. 1987 The effects of surface tension and tube inclination on a two-dimensional rising bubble. J. Fluid Mech. 184, 1–14.CrossRefGoogle Scholar
Davies, R. M. & Taylor, G. I. 1950 The mechanics of large bubbles rising through extended liquids and through liquids in tubes. Proc. R. Soc. Lond. A 200, 375–390.Google Scholar
Dumitrescu, D. T. 1943 Strömung an einer Luftblase in senkrechten Rohr. W. Angew. Math. Mech. 23, 139–149.CrossRefGoogle Scholar
Dupont, J. B. & Legendre, D. 2010 Numerical simulation of static and sliding drop with contact angle hysteresis. J. Comput. Phys. 229, 2453–2478.CrossRefGoogle Scholar
Engquist, B. & Majda, A. 1977 Absorbing boundary conditions for the numerical simulations of waves. Maths Comput. 31, 629–651.CrossRefGoogle Scholar
Esmaeeli, A. & Tryggvason, G. 1998 Direct numerical simulations of bubbly flows. Part 1. Low Reynolds number arrays. J. Fluid Mech. 377, 313–345.CrossRefGoogle Scholar
Fabre, J. & Liné, A. 1992 Modeling of two-phase slug flow. Annu. Rev. Fluid Mech. 24, 21–46.CrossRefGoogle Scholar
Garabedian, P. R. 1957 On steady-state bubbles generated by Taylor instability. Proc. R. Soc. Lond. A 241, 423–431.Google Scholar
Griffith, P. & Wallis, G. B. 1961 Two phase slug flow. J. Heat Trans. 83, 307–320.CrossRefGoogle Scholar
Ha Ngoc, H. 2003 Etude théorique et numérique du mouvement de poches de gaz en canal et en tube. Thesis, INP Toulouse, France.Google Scholar
Ha Ngoc, H. & Fabre, J. 2004 a The velocity and shape of 2D long bubbles in inclined channels or in vertical tubes. Part I. In a stagnant liquid. Multiphase Sci. Technol. 16 (1–3), 175–188.Google Scholar
Ha Ngoc, H. & Fabre, J. 2004 b The velocity and shape of 2D long bubbles in inclined channels or in vertical tubes. Part II. In a flowing liquid. Multiphase Sci. Technol. 16 (1–3), 189–204.Google Scholar
Ha Ngoc, H. & Fabre, J. 2006 A boundary element method for calculating the shape and velocity of two-dimensional long bubble in stagnant and flowing liquid. Engng Anal. Bound. Elem. 30, 539–552.CrossRefGoogle Scholar
Harlow, F. H. & Welch, J. E. 1965 Numerical calculation of time-dependent viscous incompressible flows of fluid with free surface. Phys. Fluids 8, 2182–2189.CrossRefGoogle Scholar
Hirt, C. W. & Nichols, B. D. 1981 Volume of fluid (VOF) methods for the dynamics of free boundaries. J. Comput. Phys. 39, 201–225.CrossRefGoogle Scholar
Kull, H. J. 1983 Bubble motion in the nonlinear Raleigh–Taylor instability. Phys. Rev. Lett. 51, 1434–1437.CrossRefGoogle Scholar
Layzer, D. 1955 On the instability of superposed fluids in a gravitational field. Astrophys. J. 122, 1–12.CrossRefGoogle Scholar
Lu, X. & Prosperetti, A. 2006 Axial stability of Taylor bubbles. J. Fluid Mech. 568, 173–192.CrossRefGoogle Scholar
Magnaudet, J., Rivero, M. & Fabre, J. 1995 Accelerated flows past a rigid sphere or a spherical bubble. Part 1. Steady straining flow. J. Fluid Mech. 284, 97–135.CrossRefGoogle Scholar
Maneri, C. & Zuber, N. 1974 An experimental study of plane bubbles rising at inclination. Intl J. Multiphase Flow 1, 623–645.CrossRefGoogle Scholar
Mao, Z. S. & Dukler, A. E. 1990 The motion of Taylor bubbles in vertical tubes I: a numerical simulation for the shape and rise velocity of Taylor bubbles in stagnant and flowing liquids. J. Comput. Phys. 91, 132–160.CrossRefGoogle Scholar
Martin, C. S. 1976 Vertically downward two-phase slug flow. J. Fluids Engng 98, 715–722.CrossRefGoogle Scholar
Nicklin, D. J., Wilkes, J. O. & Davidson, J. F. 1962 Two phase flow in vertical tubes. Trans. Inst. Chem. Engng 40, 61–68.Google Scholar
Polonsky, S., Shemer, L. & Barnea, D. 1999 The relation between the Taylor bubble motion and the velocity field ahead of it. Intl J. Multiphase Flow 25, 957–975.CrossRefGoogle Scholar
Taha, T. & Cui, Z. F. 2006 CFD modelling of slug flow in vertical tubes. Chem. Engng Sci. 61, 665–675.CrossRefGoogle Scholar
Vanden-Broëck, J. M. 1984 Rising bubbles in a two-dimensional tube with surface tension. Phys. Fluids 27, 2604–2607.CrossRefGoogle Scholar
Wallis, G. B. 1969 One-Dimensional Two-Phase Flow. MacGraw-Hill.Google Scholar

Figueroa-Espinoza supplementary movie

Symmetry breaking of a long bubble rising in a vertical channel at Σ = 0.018 in downward liquid flow. The black arrows display the velocity profile at a finite distance from the tip in a frame moving with the bubble. The additional dimensionless vorticity is displayed: red area (Δω≥2), green area (1<Δω<2), blue area (Δω≤1).

Download Figueroa-Espinoza supplementary movie(Video)
Video 1.4 MB