Nonlinear Interfacial Waves in Inviscid Gas-Liquid Flows
Bontozoglou, Vassilios
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https://hdl.handle.net/2142/69796
Description
Title
Nonlinear Interfacial Waves in Inviscid Gas-Liquid Flows
Author(s)
Bontozoglou, Vassilios
Issue Date
1988
Department of Study
Chemical Engineering
Discipline
Chemical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Chemical
Abstract
This thesis is concerned with understanding and modeling the interfacial waves that exist in stratified gas-liquid flows. The motivation is the central role that interfacial waves are believed to play in flow regime transitions as well as their effect in critical design parameters.
Attention is focused on nonlinear waves generated and sustained by a Kelvin-Helmholtz mechanism, that is pressure variations in phase with the wave height. The nonlinear phenomena are studied both analytically, by second order approximations, and numerically.
Two fundamental studies were carried out, one considering only the effect of gravity as a restoring force and one taking into account the combined effects of gravity and surface tension. For gravity waves, two limits to the existence of progressive solutions of permanent form were investigated; the dynamical limit, encountered when the gas velocity reaches a critical value, was shown to be a decreasing function of the wave height for very thin liquid films. The geometrical limit, encountered when waves reach a critical height, was shown to depend on the gas velocity. Possible inferences for wave breaking under strong wind were discussed.
The study of capillary-gravity waves involved phenomena associated with resonant interactions. The singularity associated with a resonance between the fundamental frequency and the second harmonic was overcome by constructing a uniformly valid second-order expansion. The dynamical limit to steady waves was shown to undergo a fundamental change at the resonant wavelength, going from supercritical for gravity-side waves to subcritical for capillary-side waves.
An interpretation of the resonance as a bifurcation phenomenon leading to wavelength doubling was extended to interfacial waves under wind. The effect of the gas velocity on the occurrence of the bifurcation was investigated and an explanation of slugging in horizontal pipeline flows, based on this phenomenon, was attempted.
The theory developed was finally used to estimate the height of interfacial gas-liquid waves. It was shown that the wave steepness observed scales with the geometrical limit and a design relation was suggested.
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