Skip to main content
×
Home
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 73
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Calderon-Ramos, Ismael and Morales, R. D. 2016. Influence of Turbulent Flows in the Nozzle on Melt Flow Within a Slab Mold and Stability of the Metal–Flux Interface. Metallurgical and Materials Transactions B, Vol. 47, Issue. 3, p. 1866.


    Khan, Afrasyab Sanaullah, Khairuddin Takriff, M. Sobri Zen, Hushairi Rigit, Andrew Ragai Henry Shah, Ajmal and Chughtai, Imran Rafiq 2016. Numerical and experimental investigations on the physical characteristics of supersonic steam jet induced hydrodynamic instabilities. Asia-Pacific Journal of Chemical Engineering, Vol. 11, Issue. 2, p. 271.


    Kim, Byoung Jae and Kim, Kyung Doo 2016. Rayleigh-Taylor instability of viscous fluids with phase change. Physical Review E, Vol. 93, Issue. 4,


    Kim, Byoung Jae Lee, Jong Hyuk and Kim, Kyung Doo 2016. Improvements of critical heat flux models for pool boiling on horizontal surfaces using interfacial instabilities of viscous potential flows. International Journal of Heat and Mass Transfer, Vol. 93, p. 200.


    Liang, H. Shi, B. C. and Chai, Z. H. 2016. Lattice Boltzmann modeling of three-phase incompressible flows. Physical Review E, Vol. 93, Issue. 1,


    Mohanta, Lokanath Cheung, Fan-Bill and Bajorek, Stephen M. 2016. Stability of coaxial jets confined in a tube with heat and mass transfer. Physica A: Statistical Mechanics and its Applications, Vol. 443, p. 333.


    Alkharashi, Sameh A. 2015. Dynamical System of Three Magnetic Layers in the Presence of Porous Media. Journal of Applied Mathematics and Physics, Vol. 03, Issue. 03, p. 310.


    Huang, Haishui and He, Xiaoming 2015. Fluid displacement during droplet formation at microfluidic flow-focusing junctions. Lab Chip, Vol. 15, Issue. 21, p. 4197.


    Kobald, Mario Verri, Isabella and Schlechtriem, Stefan 2015. Theoretical and experimental analysis of liquid layer instability in hybrid rocket engines. CEAS Space Journal, Vol. 7, Issue. 1, p. 11.


    Lee, Melanie Wang, Bo Wu, Zhentao and Li, K. 2015. Formation of micro-channels in ceramic membranes – Spatial structure, simulation, and potential use in water treatment. Journal of Membrane Science, Vol. 483, p. 1.


    Li, Wenming Yang, Fanghao Alam, Tamanna Khan, Jamil and Li, Chen 2015. Experimental and theoretical studies of critical heat flux of flow boiling in microchannels with microbubble-excited high-frequency two-phase oscillations. International Journal of Heat and Mass Transfer, Vol. 88, p. 368.


    Sanaullah, Khairuddin Khan, Afrasyab Takriff, Mohd Sobri Zen, Hushairi Shah, Ajmal Chughtai, Imran Rafiq Jamil, Tahir Fong, Lim Soh and Haq, Noaman Ul 2015. Determining potential of subcooling to attenuate hydrodynamic instabilities for steam–water two phase flow. International Journal of Heat and Mass Transfer, Vol. 84, p. 178.


    Amooey, A. A. Modarress, H. Dabir, B. and Dadvar, M. 2014. Transition Model of Stratified Oil-water Flow in a Horizontal Pipe. Petroleum Science and Technology, Vol. 32, Issue. 7, p. 878.


    Asthana, Rishi Awasthi, Mukesh Kumar and Agrawal, G.S. 2014. Magnetoviscous potential flow analysis of Kelvin–Helmholtz instability with heat and mass transfer. Applied Mathematical Modelling, Vol. 38, Issue. 23, p. 5490.


    Asthana, Rishi Awasthi, Mukesh Kumar and Agrawal, G.S. 2014. Viscous Potential Flow Analysis of Kelvin-Helmholtz Instability of a Cylindrical Flow with Heat and Mass Transfer. Heat Transfer-Asian Research, Vol. 43, Issue. 6, p. 489.


    Awasthi, Mukesh Kumar 2014. Electrohydrodynamic Kelvin–Helmholtz instability with heat and mass transfer: Effect of perpendicular electric field. Ain Shams Engineering Journal, Vol. 5, Issue. 2, p. 605.


    Awasthi, Mukesh Kumar 2014. Viscous potential flow analysis of magnetohydrodynamic Rayleigh–Taylor instability with heat and mass transfer. International Journal of Dynamics and Control, Vol. 2, Issue. 3, p. 254.


    Awasthi, Mukesh Kumar Asthana, Rishi and Agrawal, G.S. 2014. Viscous correction for the viscous potential flow analysis of Kelvin–Helmholtz instability of cylindrical flow with heat and mass transfer. International Journal of Heat and Mass Transfer, Vol. 78, p. 251.


    AWASTHI, Mukesh Kumar 2014. Kelvin-Helmholtz instability with mass transfer through porous media: Effect of irrotational viscous pressure. Journal of Hydrodynamics, Ser. B, Vol. 26, Issue. 4, p. 624.


    Campbell, Bryce K. and Liu, Yuming 2014. Sub-harmonic resonant wave interactions in the presence of a linear interfacial instability. Physics of Fluids, Vol. 26, Issue. 8, p. 082107.


    ×
  • Journal of Fluid Mechanics, Volume 445
  • October 2001, pp. 263-283

Viscous potential flow analysis of Kelvin–Helmholtz instability in a channel

  • T. FUNADA (a1) and D. D. JOSEPH (a2)
  • DOI: http://dx.doi.org/10.1017/S0022112001005572
  • Published online: 16 October 2001
Abstract

We study the stability of stratified gas–liquid flow in a horizontal rectangular channel using viscous potential flow. The analysis leads to an explicit dispersion relation in which the effects of surface tension and viscosity on the normal stress are not neglected but the effect of shear stresses is. Formulas for the growth rates, wave speeds and neutral stability curve are given in general and applied to experiments in air–water flows. The effects of surface tension are always important and determine the stability limits for the cases in which the volume fraction of gas is not too small. The stability criterion for viscous potential flow is expressed by a critical value of the relative velocity. The maximum critical value is when the viscosity ratio is equal to the density ratio; surprisingly the neutral curve for this viscous fluid is the same as the neutral curve for inviscid fluids. The maximum critical value of the velocity of all viscous fluids is given by that for inviscid fluid. For air at 20°C and liquids with density ρ = 1 g cm−3 the liquid viscosity for the critical conditions is 15 cP: the critical velocity for liquids with viscosities larger than 15 cP is only slightly smaller but the critical velocity for liquids with viscosities smaller than 15 cP, like water, can be much lower. The viscosity of the liquid has a strong effect on the growth rate. The viscous potential flow theory fits the experimental data for air and water well when the gas fraction is greater than about 70%.

Copyright
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax