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Bubbling and jetting regimes in planar coflowing air–water sheets

Published online by Cambridge University Press:  13 July 2011

R. BOLAÑOS-JIMÉNEZ ,
A. SEVILLA ,
C. GUTIÉRREZ-MONTES ,
E. SANMIGUEL-ROJAS  and
C. MARTÍNEZ-BAZÁN
R. BOLAÑOS-JIMÉNEZ
Affiliation:
Área de Mecánica de Fluidos, Departamento de Ingeniería Mecánica y Minera, Universidad Jaén, Campus de las Lagunillas, 23071 Jaén, Spain
A. SEVILLA*
Affiliation:
Área de Mecánica de Fluidos, Departamento de Ingeniería Térmica y de Fluidos, Universidad Carlos III de Madrid, 28911 Leganés, Spain
C. GUTIÉRREZ-MONTES
Affiliation:
Área de Mecánica de Fluidos, Departamento de Ingeniería Mecánica y Minera, Universidad Jaén, Campus de las Lagunillas, 23071 Jaén, Spain
E. SANMIGUEL-ROJAS
Affiliation:
Área de Mecánica de Fluidos, Departamento de Ingeniería Mecánica y Minera, Universidad Jaén, Campus de las Lagunillas, 23071 Jaén, Spain
C. MARTÍNEZ-BAZÁN
Affiliation:
Área de Mecánica de Fluidos, Departamento de Ingeniería Mecánica y Minera, Universidad Jaén, Campus de las Lagunillas, 23071 Jaén, Spain
*
†Email address for correspondence: [email protected]
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Abstract

The dynamics of a plane air sheet surrounded by a coflowing water film, discharging into stagnant air, is investigated by means of experiments and linear stability theory. For fixed values of the water-to-air thickness ratio, h = hw,0*/ha,0* ≃ 5.27, and of the air-to-water density ratio, S = ρa/ρw ≃ 0.0012, two different flow regimes are experimentally observed depending on the values of two control parameters, namely the Weber number, defined as We = ρwuw,0*2ha,0*/σ, and the velocity ratio, Λ = uw,0*/ua,0*, where uw,0* and ua,0* are the water velocity and the mean air velocity at the exit slit, respectively, and ha,0* and hw,0* are the half-thicknesses of the air and water sheets at the exit. The study focuses on the characterization of the transition between the two regimes found experimentally: a bubbling regime, leading to the periodic breakup of the air sheet, and a jetting regime, where both sheets evolve slowly downstream without breaking. With the aim of exploring whether the transition from the jetting to the bubbling regime is related to a convective/absolute instability transition, we perform a linear spatiotemporal stability analysis. The base flow is described by a simple model that incorporates the downstream evolution of the sheets, which shows excellent agreement with our experiments if the existence of a sufficiently long region of absolute instability, of the order of one absolute wavelength evaluated at the nozzle exit, is imposed as an additional requirement. Finally, we show that the transition is also properly captured by two-dimensional numerical simulations using the volume of fluid technique.

JFM classification

Instability: Absolute/convective instability Drops and Bubbles: Breakup/coalescence Multiphase and Particle-laden Flows: Gas/liquid flow
Type
Papers
Information
Journal of Fluid Mechanics , Volume 682 , 10 September 2011 , pp. 519 - 542
Copyright
Copyright © Cambridge University Press 2011

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References

REFERENCES

Ambravaneswaran, B., Subramani, H. J., Phillips, S. D. & Basaran, O. A. 2004 Dripping–jetting transitions in a dripping faucet. Phys. Rev. Lett. 93, 034501.CrossRefGoogle Scholar
Chuang, S. C. & Goldschmidt, V. W. 1970 Bubble formation due to a submerged capillary tube in quiescent and coflowing streams. Trans. ASME D: J. Basic Engng 92, 705–711.CrossRefGoogle Scholar
Clanet, C. & Lasheras, J. C. 1999 Transition from dripping to jetting. J. Fluid Mech. 383, 307–326.CrossRefGoogle Scholar
Couairon, A. & Chomaz, J.-M. 1999 Fully nonlinear global modes in slowly varying flows. Phys. Fluids 11, 3688–3703.CrossRefGoogle Scholar
Dombrowski, N. & Johns, W. R. 1963 The aerodynamic instability and disintegration of viscous liquid sheets. Chem. Engng Sci. 18, 203–214.CrossRefGoogle Scholar
Gordillo, J. M., Gañán-Calvo, A. M. & Pérez-Saborid, M. 2001 Monodisperse microbubbling: Absolute instabilities in coflowing gas–liquid jets. Phys. Fluids 13, 3839–3842.CrossRefGoogle Scholar
Gordillo, J. M., Sevilla, A. & Martínez-Bazán, C. 2007 Bubbling in a coflow at high Reynolds numbers. Phys. Fluids 19, 077102.CrossRefGoogle Scholar
Hagerty, W. W. & Shea, J. F. 1955 A study of the stability of plane fluid sheets. J. Appl. Mech. 22, 509–514.CrossRefGoogle Scholar
Hauke, G., Dopazo, C. Lozano, A., Barreras, F. & Hernández, A. H. 2001 Linear stability analysis of a viscous liquid sheet in a high-speed viscous gas. Flow Turbul. Combust. 67, 235–265.CrossRefGoogle Scholar
Ibrahim, E. A. 1998 Instability of a liquid sheet of parabolic velocity profile. Phys. Fluids 10, 1034–1036.CrossRefGoogle Scholar
Le Dizès, S. 1997 Global modes in falling capillary jets. Eur. J. Mech. B/Fluids 16, 761–778.Google Scholar
Lesshafft, L., Huerre, P. & Sagaut, P. 2007 Frequency selection in globally unstable round jets. Phys. Fluids 19 (5), 054108.CrossRefGoogle Scholar
Lesshafft, L., Huerre, P., Sagaut, P. & Terracol, M. 2006 Nonlinear global modes in hot jets. J. Fluid Mech. 554, 393–409.CrossRefGoogle Scholar
Lezzi, A. M. & Prosperetti, A. 1991 Stability of an air film in a liquid flow. J. Fluid Mech. 226, 319–347.CrossRefGoogle Scholar
Li, X. 1993 Spatial instability of plane liquid sheets. Chem. Engng Sci. 48 (16), 2973–2981.CrossRefGoogle Scholar
Li, X. & Bhunia, A. 1996 Temporal instability of plane gas sheets in a viscous liquid medium. Phys. Fluids 8, 103–111.CrossRefGoogle Scholar
Li, X. & Bhunia, A. 1997 Instability of plane compressible gas sheets. Acta Mechanica 123, 117–133.CrossRefGoogle Scholar
Li, X. & Tankin, R. S. 1991 On the temporal instability of a two-dimensional viscous liquid sheet. J. Fluid Mech. 226, 425–443.CrossRefGoogle Scholar
Lin, S. P. 1981 Stability of a viscous liquid curtain. J. Fluid Mech. 104, 111–118.CrossRefGoogle Scholar
Lin, S. P., Lian, Z. W. & Creighton, B. J. 1990 Absolute and convective instability of a liquid sheet. J. Fluid Mech. 220, 673489.CrossRefGoogle Scholar
Longuet-Higgins, M. S., Kerman, B. R. & Lunde, K. 1991 The release of air bubbles from an underwater nozzle. J. Fluid Mech. 230, 365–390.CrossRefGoogle Scholar
Lozano, A., Barreras, F., Hauke, G. & Dopazo, C. 2001 Longitudinal instabilities in an air-blasted liquid sheet. J. Fluid Mech. 437, 143–173.CrossRefGoogle Scholar
Oguz, H. N. & Prosperetti, A. 1993 Dynamics of bubble growth and detachment from a needle. J. Fluid Mech. 257, 111–145.CrossRefGoogle Scholar
Sevilla, A., Gordillo, J. M. & Martínez-Bazán, C. 2002 The effect of the diameter ratio on the absolute and convective instability of free coflowing jets. Phys. Fluids 14, 3028–3038.CrossRefGoogle Scholar
Sevilla, A., Gordillo, J. M. & Martínez-Bazán, C. 2005 a Bubble formation in a coflowing air–water stream. J. Fluid Mech. 530, 181–195.CrossRefGoogle Scholar
Sevilla, A., Gordillo, J. M. & Martínez-Bazán, C. 2005 b Transition from bubbling to jetting in a coaxial air–water jet. Phys. Fluids 17, 018105.CrossRefGoogle Scholar
Squire, H. B. 1953 Investigation on the instability of a moving liquid film. Brit. J. Appl. Phys. 4, 167–169.CrossRefGoogle Scholar
Teng, C. H., Lin, S. P. & Chen, J. N. 1997 Absolute and convective instability of a viscous liquid curtain in a viscous gas. J. Fluid Mech. 332, 105–120.CrossRefGoogle Scholar
York, J. L., Stubbs, H. E. & Tek, M. R. 1953 The mechanisms of disintegration of liquid sheets. Trans. ASME 75, 1279–1286.Google Scholar