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
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  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  and Blanco and Magnaudet  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 ,  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|
|Defense Date:||4 November 1998|
|Default Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Imported from ETD-db|
|Deposited On:||11 Mar 2008|
|Last Modified:||26 Dec 2012 02:32|
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