Skip to main content
×
Home
    • Aa
    • Aa

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

  • T. FUNADA (a1) and D. D. JOSEPH (a2)
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

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 156 *
Loading metrics...

Abstract views

Total abstract views: 310 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 24th September 2017. This data will be updated every 24 hours.