Numerical study of the onset of instability in the flow past a sphere.

Persistent Link:
http://hdl.handle.net/10150/184809
Title:
Numerical study of the onset of instability in the flow past a sphere.
Author:
Kim, Inchul.
Issue Date:
1989
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:
Experiment shows that the steady axisymmetric flow past a sphere becomes unstable in the range 120 < Re < 300. The resulting time-dependent nonaxisymmetric flow gives rise to nonaxisymmetric vortex shedding at higher Reynolds numbers. The present work reports a computational investigation of the linear stability of the axisymmetric base flow. When the sphere is towed, fixed, or otherwise constrained, stability is determined solely by the Reynolds number. On the other hand, when the sphere falls due to gravity, the present work shows that a additional parameter, the ratio of fluid density to sphere density (β = ρ(f)/ρ(s)) is involved. We use a spectral technique to compute the steady axisymmetric flow, which is in closer agreement with experiment than previous calculations. We then perform a linear stability analysis of the base flow with respect to axisymmetric and nonaxisymmetric disturbances. A spectral technique similar to that employed in the base flow calculation is used to solve the linear disturbance equations in streamfunction form for axisymmetric disturbances, and in a modified primitive variable form for nonaxisymmetric disturbances. For the density ratio β = 0, which corresponds to a fixed sphere, the analysis shows that the axisymmetric base flow undergoes a Hopf bifurcation at Re = 175.1, with the critical disturbance having azimuthal wavenumber m = 1. The results are favorably compared to previous experimental work.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Unsteady flow (Fluid dynamics) -- Mathematical models.; Vortex-motion -- Mathematical models.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Aerospace and Mechanical Engineering; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Pearlstein, Arne J.

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleNumerical study of the onset of instability in the flow past a sphere.en_US
dc.creatorKim, Inchul.en_US
dc.contributor.authorKim, Inchul.en_US
dc.date.issued1989en_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.abstractExperiment shows that the steady axisymmetric flow past a sphere becomes unstable in the range 120 < Re < 300. The resulting time-dependent nonaxisymmetric flow gives rise to nonaxisymmetric vortex shedding at higher Reynolds numbers. The present work reports a computational investigation of the linear stability of the axisymmetric base flow. When the sphere is towed, fixed, or otherwise constrained, stability is determined solely by the Reynolds number. On the other hand, when the sphere falls due to gravity, the present work shows that a additional parameter, the ratio of fluid density to sphere density (β = ρ(f)/ρ(s)) is involved. We use a spectral technique to compute the steady axisymmetric flow, which is in closer agreement with experiment than previous calculations. We then perform a linear stability analysis of the base flow with respect to axisymmetric and nonaxisymmetric disturbances. A spectral technique similar to that employed in the base flow calculation is used to solve the linear disturbance equations in streamfunction form for axisymmetric disturbances, and in a modified primitive variable form for nonaxisymmetric disturbances. For the density ratio β = 0, which corresponds to a fixed sphere, the analysis shows that the axisymmetric base flow undergoes a Hopf bifurcation at Re = 175.1, with the critical disturbance having azimuthal wavenumber m = 1. The results are favorably compared to previous experimental work.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectUnsteady flow (Fluid dynamics) -- Mathematical models.en_US
dc.subjectVortex-motion -- Mathematical models.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.advisorPearlstein, Arne J.en_US
dc.contributor.committeememberChen, Chuan F.en_US
dc.contributor.committeememberKerschen, Edward J.en_US
dc.contributor.committeememberGreenlee, Wilfred M.en_US
dc.contributor.committeememberBayly, Bruce J.en_US
dc.identifier.proquest9003490en_US
dc.identifier.oclc703255684en_US
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