Gravity modulation and cross-diffusion effects on the onset of multicomponent convection.

Persistent Link:
http://hdl.handle.net/10150/185643
Title:
Gravity modulation and cross-diffusion effects on the onset of multicomponent convection.
Author:
Terrones, Guillermo.
Issue Date:
1991
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
A linear stability analysis is undertaken to investigate the effects of cross-diffusion and gravity modulation on the onset of convective instability in horizontally unbounded multiply diffusive fluid layers. We consider layers of incompressible Boussinesq fluid in which all thermophysical properties are constant except for the density insofar as it contributes to a buoyant force. It is assumed that the density is a linear function of the various components present and the fluxes are linear combinations of all the gradients of those components. We begin with a study of the effects of coupled molecular diffusion in a triply diffusive fluid layer under a constant gravity field. The bounding surfaces are perfectly conducting, perfectly permeable, and free of stresses. Stability is determined by way of temporal eigenvalues of a linear system of ODE's. We find that the off-diagonal elements of the diffusivity matrix may strongly affect the linear stability criteria, regardless of their relative value (as long as they do not vanish) as compared to the main-diagonal elements. We also investigate the combined effects of a sinusoidally varying gravity field and cross-diffusion in several doubly diffusive configurations. In particular, we consider: (1) stress-free and rigid boundaries with imposed gradients, and (2) stress-free and rigid boundaries when a solute gradient is induced by Soret separation. Stability is determined by way of Floquet multipliers of a linear system of ODE's with periodic coefficients. The topology of neutral curves and stability boundaries exhibits features not found in the modulated singly diffusive or unmodulated multiply diffusive fluid layers. In a gravity modulated doubly diffusive layer with cross-diffusion, when one Rayleigh number, say R₂, is fixed or induced, neutral curves spanned by the other Rayleigh number (R₁) and the horizontal wavenumber are in general multivalued. In addition, finite as well as semi-infinite R₁ stability ranges can be found. A notable feature is the occurrence of double minima, each one corresponding to a different asymptotically stable neutral response. A temporally and spatially quasi-periodic bifurcation from the basic state is possible when the Rayleigh numbers of the double extrema coincide. In this situation, there are two incommensurate critical wavenumbers at two incommensurate onset frequencies at the same Rayleigh number.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Dissertations, Academic; Mechanical engineering; Fluid dynamics.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Aerospace and Mechanical Engineering; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Chen, Chaun F.

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleGravity modulation and cross-diffusion effects on the onset of multicomponent convection.en_US
dc.creatorTerrones, Guillermo.en_US
dc.contributor.authorTerrones, Guillermo.en_US
dc.date.issued1991en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractA linear stability analysis is undertaken to investigate the effects of cross-diffusion and gravity modulation on the onset of convective instability in horizontally unbounded multiply diffusive fluid layers. We consider layers of incompressible Boussinesq fluid in which all thermophysical properties are constant except for the density insofar as it contributes to a buoyant force. It is assumed that the density is a linear function of the various components present and the fluxes are linear combinations of all the gradients of those components. We begin with a study of the effects of coupled molecular diffusion in a triply diffusive fluid layer under a constant gravity field. The bounding surfaces are perfectly conducting, perfectly permeable, and free of stresses. Stability is determined by way of temporal eigenvalues of a linear system of ODE's. We find that the off-diagonal elements of the diffusivity matrix may strongly affect the linear stability criteria, regardless of their relative value (as long as they do not vanish) as compared to the main-diagonal elements. We also investigate the combined effects of a sinusoidally varying gravity field and cross-diffusion in several doubly diffusive configurations. In particular, we consider: (1) stress-free and rigid boundaries with imposed gradients, and (2) stress-free and rigid boundaries when a solute gradient is induced by Soret separation. Stability is determined by way of Floquet multipliers of a linear system of ODE's with periodic coefficients. The topology of neutral curves and stability boundaries exhibits features not found in the modulated singly diffusive or unmodulated multiply diffusive fluid layers. In a gravity modulated doubly diffusive layer with cross-diffusion, when one Rayleigh number, say R₂, is fixed or induced, neutral curves spanned by the other Rayleigh number (R₁) and the horizontal wavenumber are in general multivalued. In addition, finite as well as semi-infinite R₁ stability ranges can be found. A notable feature is the occurrence of double minima, each one corresponding to a different asymptotically stable neutral response. A temporally and spatially quasi-periodic bifurcation from the basic state is possible when the Rayleigh numbers of the double extrema coincide. In this situation, there are two incommensurate critical wavenumbers at two incommensurate onset frequencies at the same Rayleigh number.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectDissertations, Academicen_US
dc.subjectMechanical engineeringen_US
dc.subjectFluid dynamics.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineAerospace and Mechanical Engineeringen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorChen, Chaun F.en_US
dc.contributor.committeememberChan, Choliken_US
dc.contributor.committeememberHeinrich, Juan C.en_US
dc.contributor.committeememberBayly, Bruce J.en_US
dc.contributor.committeememberLamb, George L.en_US
dc.identifier.proquest9208042en_US
dc.identifier.oclc711874995en_US
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