Nonlinear effects on interfacial wave growth into slug flow

It is known that when two fluids flow through a horizontal channel, depending on the relative velocity between the two fluids, two different instability mechanisms can create initial wave disturbances on the interface: the classic Kelvin-Helmholtz instability or shear induced instability. These instability mechanisms, which affect the initial growth of the disturbances on the interface, are well understood; however, the subsequent nonlinear evolution and the effects of wave resonances on the interface remain a subject of interest and will be the focus of this study. The Kelvin-Helmholtz (KH) instability is the traditional model for predicting interfacial instability in stratified flows. This linear instability occurs when the lower phase inertia and the pressure from the upper phase overcome the stabilizing effects of gravity and surface tension. This mechanism is most unstable to short waves and does not allow for modal interactions. When nonlinearity is included, additional second order sum- and difference-wavenumber modes as well as higher harmonics must be accounted for. Given an initial spectrum of stable modes, sum-wavenumber modes and higher harmonics are generated due to nonlinear wave-wave interactions, which can be unstable to KH. The generated second-order difference-wavenumber modes are stable to KH. For certain combinations of wave modes, we found that there exist simultaneous coupled second-harmonic (overtone) and triad resonances. Due to the second harmonic resonance, energy from the KH unstable second harmonic is transferred to the first harmonic. Meanwhile, this first harmonic, which is involved in a triad resonance, transfers its energy to the other two (stable) wave modes.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Mechanical Engineering.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2009

Author dc:creator

• Campbell, Bryce K

Advisor dc:contributor.advisor

• Yuming Liu.

• Mechanical Engineering.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/55268

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/55268