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CAMS/SCMA Doctoral Dissertation Award 89
Winner and Abstract
1989
Peter J. S. Young (S. C. R. Dennis), Department of Applied Mathematics,
University of Western Ontario
Steady Asymmetric Flow of a Viscous Fluid Past a Cylinder.
The steady flow of viscous incompressible fluid past a cylinder is
considered. In particular, asymmetric flows, which involves a lift force in
addition to the drag, are investigated. The Navier-Stokes equations and the
equation of continuity are formulated in terms of the stream function and
vorticity. The work may be divided into two parts, an asymptotic solution
of the governing equations of motion at far distances from the cylinder,
and a numerical solution of these equations near the cylinder. An
asymptotic solution to the vorticity is obtained in the form of a Hermite
polynomial expansion. This solution is in perfect agreement with
Imai (1953). The asymptotic solution involves unknown constants (namely the
lift and drag coefficients) which must be obtained from a numerical
solution valid near the cylinder. Leading terms of this solution are then
used as the boundary condition at far distances in the numerical
calculations.
A study of the asymptotic solution illustrates the difficulty in obtaining a
numerical solution in the far wake. This is especially prevalent in
asymmetric flow calculations as an errors occurring here may not be damped
out. To ensure that the numerical solution properly matches the asymptotic
solution the is transformed and the grid size in the angular direction is
reduced in the far wake. This s is done in a manner so as to minimize the
total number of grid points but allowing a fine enough angular grid size in
the far wake to be used. A numerical solution is then obtained from which
the asymptotic boundary condition is continuously updated.
Numerical results are given for the flows past a rotating circular cylinder
and an inclined elliptic cylinder for Reynolds number 5 and 20. The influence
of the asymptotic solution and grid size upon the numerical solutions is
investigated. In the case of the rotating circular cylinder, results are
given that are in agreement with unsteady results that are taken to a limit
in large time (Badr et al., (1998)). The flow past an elliptic cylinder
with ratio of minot to major axes of 0.2 is investigated for various angles
of incidence. Results of the symmetric problem are compared to Dennis and
Chang (1969). The dependence of the life, drag and moment upon the Reynolds
number and angle of incidence is studied. For both types of cylinder,
surface pressure and vorticity distributions given. In addition, plots of
streamlines and lines of equivorticity for the flow past the cylinder are
presented.
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