Summary
A linear analysis has been carried out for the temporal instability of an annular viscous liquid jet moving in an inviscid gas medium, which includes three limiting cases of a round liquid jet, a gas jet and a plane liquid sheet. It is found that there exist two independent unstable modes, which become the well-known sinuous and varicose modes for plane liquid sheets as annular jet radii approach to infinity. Hence, they are named as para-sinuous and para-varicose. It is shown that an ambient gas medium always enhances the annular jet instability. The curvature effects in general increase the disturbance growth rate, and may not be neglected for the breakup process of an annular or conical liquid sheet. An annular jet with a sufficiently small thickness tends to break up much faster than the corresponding plane liquid sheet, in accordance with existing experimental observations. Liquid viscosity has complicated dual effects on the instability. It is also found that there exists a critical Weber number below which surface tension is the source of instability. Whereas above it, instability is suppressed by surface tension effect and it promoted by aerodynamic interaction between the liquid and gas phase. For the practical importance of large Weber numbers such as related to liquid atomization, the para-sinuous mode is always predominant.
Similar content being viewed by others
References
Kendall, J. M.: Hydrodynamic performance of an annular liquid jet: production of spherical shells. In: Proc. 2nd Int. Colloquium on Drops and Bubbles (LeCroissette, D. H., ed.), pp. 79–87, Monterey, CA, 1982. Jet Propulsion Laboratory Publication 82-7.
Lee, C. P., Wang, T. G.: A theoretical model for the annular jet instability. Phys. Fluids29, 2076–2085 (1986).
Kendall, J. M.: Experiments on annular liquid jet instability and on the formation of liquid shells. Phys. Fluids29, 2086–2094 (1986).
Lee, C. P., Wang, T. G.: The theoretical model for the annular jet instability — revisited. Phys. FluidsA1, 967–974 (1989).
Walker, G., East, R. A.: Shock tube studies of a water sheet inertial energy absorber to reduce blast overpressure. In: Proc. Symp. Shock and Blast Wave Phenomena, Cranfield, U.K. (1984) Paper C-2, pp. 16.
Masters, K.: Spray drying handbook, 4th ed. New York: Wiley 1985.
Lefebvre, A. H.: Atomization and sprays. New York: Hemisphere 1989.
Binnie, A. M., Squire, H. B.: Liquid jets of annular cross section. Engineer171, 236–238 (1941).
Lance, G. N., Perry, R. L.: Water bells. Proc. Phys. Soc.B66, 1067–1072 (1953).
Baird, M. H. I., Davidson, J. F.: Annular jets — I: Fluid dynamics, — II: Gas absorption. Chem. Eng. Sci.17, 467–472, 473–480 (1962).
Tuck, E. O.: Annular water jets. IMA J. Appl. Math.29, 45–58 (1982).
Gardner, G. C., Lloyd, T.: Annular buoyant jets. Int. J. Multiphase Flow10, 635–641 (1984).
Sanz, A., Meseguer, J. H.: One-dimensional linear analysis of the compound jet. J. Fluid Mech.159, 55–68 (1985).
Crapper, G. D., Dombrowski, N., Pyott, G. A. D.: Kelvin-Helmholtz wave growth on cylindrical sheets. J. Fluid Mech.68, 497–502 (1975).
Meyer, J., Weihs, D.: Capillary instability of an annular liquid jet. J. Fluid Mech.179, 531–545 (1987).
Lee, J. G., Chen, L. D.: Linear stability analysis of gas-liquid interface. AIAA J.29, 1589–1595 (1991).
Keller, J. B., Rubinow, S. I., Tu, Y. O.: Spatial instability of a jet. Phys. Fluids16, 2052–2055 (1973).
Li, X.: Spatial instability of plane liquid sheets. Chem. Eng. Sci.48, 2973–2981 (1993).
Squire, H. B.: Investigation of the instability of a moving liquid film. Br. J. Appl. Phys.4, 167–169 (1953).
Hagerty, W. W., Shea, J. F.: A study of the stability of plane fluid sheets. J. Appl. Mech.22, 509–514 (1955).
Li, X., Tankin, R. S.: On the temporal instability of a two-dimensional viscous liquid sheet. J. Fluid Mech.226, 425–443 (1991).
Li, X.: On the instability of plane liquid sheets in two gas streams of unequal velocities. Acta Mech.106, 137–156 (1994).
Taylor, G. I.: Formation of thin flat sheets of water. Proc. R. Soc. London Ser.A259, 1–17 (1960).
Weihs, D.: Stability of thin, radially moving liquid sheets. J. Fluid Mech.87, 289–298 (1978).
Levich, V. G.: Physicochemical hydrodynamics. New York: Prentice-Hall 1962.
Rayleigh, L.: On the instability of cylindrical fluid surfaces. Scientific Papers, vol. iii, pp. 594–596, Cambridge, England, 1902.
Lin, S. P., Kang, D. J.: Atomization of a liquid jet. Phys. FluidsA30, 2000–2006 (1987).
Sterling, A. M., Sleicher, C. A.: The instability of capillary jets. J. Fluid Mech.68, 477–495 (1975).
Lin, S. P., Creighton, B.: Energy budget in atomization. Aerosol Sci. Tech.12, 630–636 (1990).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Shen, J., Li, X. Instability of an annular viscous liquid jet. Acta Mechanica 114, 167–183 (1996). https://doi.org/10.1007/BF01170402
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01170402