Date of Award
1993
Degree Type
Dissertation
Degree Name
Doctor of Philosophy
Abstract
Three steady state models for determining the flow of a viscous incompressible Newtonian isothermal fluid past a two-dimensional cylindrical object are proposed. These models offer numerical methods of solving the governing Navier-Stokes equations as well as a mathematical understanding of the nature of the flow.;In the first model, the behaviour of the vorticity is patterned for both large and small distances by expressing the vorticity as {dollar}\zeta\ =\ \Phi\rm e\sp{lcub}\rm F{rcub}{dollar} with F chosen to accommodate both boundary-layer and wake theory. The resulting equations are then solved by finite differences and by the method of Dennis and Chang (1970).;The second model presented involves a method of implementing the velocity-vorticity formulation of the Navier-Stokes equations. In this technique the vorticity transport equation is solved by finite differences while the continuity equation is integrated using the method of lines. The remaining equation is reduced to a system of ordinary differential equations by assuming a Fourier series expansion. These differential equations can then be solved analytically and involve the evaluation of integrals.;The last model introduces a numerical method employing domain decomposition to address the behaviour of the vorticity. Here, the flow field is divided into an inner boundary-layer region and an outer wake region. The boundary separating these two regions is permitted to move with Reynolds number to provide grid reduction. In the outer region a change of variables is introduced. The equations of motion are solved in each region with a matching condition used at the boundary.;Numerical solutions to the governing equations have been obtained for the trial case of a circular cylinder. The results are in close agreement with existing ones in the literature. The first model was extended to deal with a general cylinder with illustrative calculations carried our for the elliptic cylinder. This is presented in Appendix III. The solutions obtained for the asymmetric cases of flow past a rotating circular cylinder and flow past an inclined elliptic cylinder are in good agreement with the recent works of Badr, Dennis and Young (1989), Ingham and Tang (1990), and Dennis and Young (1992).
Recommended Citation
D'Alessio, Sergio J., "Models For Steady State Flow Past A Cylinder" (1993). Digitized Theses. 2222.
https://ir.lib.uwo.ca/digitizedtheses/2222