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A study of viscous flow past axisymmetric and two-dimensional bodies

Citation

Kang, Sung Phill (1999) A study of viscous flow past axisymmetric and two-dimensional bodies. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-02242008-093110

Abstract

In this thesis, we study the behavior of viscous flow past bodies of different shapes. In Chapter 2, we construct a boundary-fitted, numerical grid around a rigid spheroid of various aspect ratios and solve numerically the Navier-Stokes equations in steady, axisymmetric form at various Reynolds numbers. In addition, we use these steady solutions as a base flow and perform a linear stability analysis to determine the critical Reynolds numbers above which the base flow becomes unstable. We are able to confirm the results of Natarajan and Acrivos [26] and extend them to more generalized body shapes.

In Chapter 3, we solve the Navier-Stokes equations to investigate flows past an oblate ellipsoidal bubble of fixed shape, which is characterized by a free-slip boundary condition. We then compare our results with previous results by Dandy and Leal [6] and Blanco and Magnaudet [4] and use the computed steady solutions as the base flow to perform a linear stability analysis. We show that even with a free-slip boundary condition, if the body is sufficiently oblate, the flow can become unstable in a manner similar to that of flows past rigid bodies.

In Chapter 4, we develop an alternative numerical method to compute steady flows past a deforming, axisymmetric bubble. A newly developed conformal grid generation method is applied. We show that our results are in good agreement with those of Ryskin and Leal [34], [35] and then extend some of their results to higher Reynolds number.

In Chapter 5, we modify the method developed in Chapter 4 to compute steady flows past a symmetric, two-dimensional bubble. We show that the bubble deforms to an elliptical shape and that a wake can develop if the deformation of the bubble is sufficiently large.

Item Type:Thesis (Dissertation (Ph.D.))
Degree Grantor:California Institute of Technology
Major Option:Applied And Computational Mathematics
Thesis Availability:Restricted to Caltech community only
Thesis Committee:
  • Meiron, Daniel I. (chair)
Defense Date:4 November 1998
Record Number:CaltechETD:etd-02242008-093110
Persistent URL:http://resolver.caltech.edu/CaltechETD:etd-02242008-093110
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:743
Collection:CaltechTHESIS
Deposited By: Imported from ETD-db
Deposited On:11 Mar 2008
Last Modified:26 Dec 2012 02:32

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