Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-26T05:42:50.905Z Has data issue: false hasContentIssue false
  • English
  • Français

Stabilizing effect of surrounding gas flow on a plane liquid sheet

Published online by Cambridge University Press:  18 February 2011

OUTI TAMMISOLA ,
ATSUSHI SASAKI ,
FREDRIK LUNDELL ,
MASAHARU MATSUBARA  and
L. DANIEL SÖDERBERG
OUTI TAMMISOLA
Affiliation:
Linné Flow Centre, KTH Mechanics, Royal Institute of Technology, SE-100 44 Stockholm, Sweden
ATSUSHI SASAKI
Affiliation:
Mechanical Systems Engineering, Shinshu University, Nagano 380-8553, Japan
FREDRIK LUNDELL*
Affiliation:
Linné Flow Centre, KTH Mechanics, Royal Institute of Technology, SE-100 44 Stockholm, Sweden Wallenberg Wood Science Center, KTH Mechanics, Royal Institute of Technology, SE-100 44 Stockholm, Sweden
MASAHARU MATSUBARA
Affiliation:
Mechanical Systems Engineering, Shinshu University, Nagano 380-8553, Japan
L. DANIEL SÖDERBERG
Affiliation:
Wallenberg Wood Science Center, KTH Mechanics, Royal Institute of Technology, SE-100 44 Stockholm, Sweden Innventia AB, Box 5604, SE-114 86 Stockholm, Sweden
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The stability of a plane liquid sheet is studied experimentally and theoretically, with an emphasis on the effect of the surrounding gas. Co-blowing with a gas velocity of the same order of magnitude as the liquid velocity is studied, in order to quantify its effect on the stability of the sheet. Experimental results are obtained for a water sheet in air at Reynolds number Rel = 3000 and Weber number We = 300, based on the half-thickness of the sheet at the inlet, water mean velocity at the inlet, the surface tension between water and air and water density and viscosity. The sheet is excited with different frequencies at the inlet and the growth of the waves in the streamwise direction is measured. The growth rate curves of the disturbances for all air flow velocities under study are found to be within 20% of the values obtained from a local spatial stability analysis, where water and air viscosities are taken into account, while previous results from literature assuming inviscid air overpredict the most unstable wavelength with a factor 3 and the growth rate with a factor 2. The effect of the air flow on the stability of the sheet is scrutinized numerically and it is concluded that the predicted disturbance growth scales with (i) the absolute velocity difference between water and air (inviscid effect) and (ii) the square root of the shear from air on the water surface (viscous effect).

JFM classification

Flow Control: Instability control Interfacial Flows (free surface): Interfacial Flows (free surface) Wakes/Jets: Jets
Type
Papers
Information
Journal of Fluid Mechanics , Volume 672 , 10 April 2011 , pp. 5 - 32
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

Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability, 3rd edn. Dover.Google Scholar
Eggers, J. & Villermaux, E. 2008 Physics of liquid jets. Rep. Prog. Phys. 71, 036601.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
Li, X. 1993 Spatial instability of plane liquid sheets. Chem. Engng Sci. 48 (16), 2973–2981.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.Google Scholar
Lozano, A., Barreras, F., Hauke, G. & Dopazo, C. 2001 Longitudinal instabilities in an air-blasted liquid sheet. J. Fluid Mech. 437, 143–173.Google Scholar
Mansour, A. & Chigier, N. 1991 Dynamic behavior of liquid sheets. Phys. Fluids A 3, 2971–2980.CrossRefGoogle Scholar
Park, J., Huh, K. Y., Li, X. & Renksizbulut, M. 2004 Experimental investigation on cellular breakup of a planar liquid sheet from an air-blast nozzle. Phys. Fluids 16 (3), 625–632.CrossRefGoogle Scholar
Rayleigh, Lord 1878 On the instability of jets. Proc. Lond. Math. Soc. 10 (1), 4–13.CrossRefGoogle Scholar
Sakiadis, B. C. 1961 a Boundary-layer behaviour on continuous solid surfaces. I. Boundary-layer equations for two-dimensional and axisymmetric flow. AIChe J. 7 (1), 26–28.CrossRefGoogle Scholar
Sakiadis, B. C. 1961 b Boundary-layer behaviour on continuous solid surfaces. II. The boundary layer on a continuous flat surface. AIChe J. 7 (2), 221–225.CrossRefGoogle Scholar
Sander, W. & Weigand, B. 2008 Direct numerical simulation and analysis of instability enhancing parameters in liquid sheets at moderate Reynolds numbers. Phys. Fluids 20, 053301.Google Scholar
Schmid, P. J. & Henningson, D. S. 2001 Stability and Transition in Shear Flows. Springer.CrossRefGoogle Scholar
Söderberg, L. D. 2003 Absolute and convective instability of a relaxational plane liquid jet. J. Fluid Mech. 493, 89–119.Google Scholar
Söderberg, L. D. & Alfredsson, P. H. 1998 Experimental and theoretical stability investigations of plane liquid jets. Eur. J. Mech. B/Fluids 17 (5), 689–737.CrossRefGoogle Scholar
Squire, H. B. 1953 Investigation of the instability of a moving liquid film. Br. 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
Weber, C. 1931 Zum Zerfall eines Flüssigkeitsstrahles. Z. Angew. Math. Mech. 11, 136–154.CrossRefGoogle Scholar