Computation of unsteady viscous incompressible flow around an obliquely
oscillating cylinder using a parallelized finite difference algorithm
Karl P. Lawrence, M.Sc. Thesis, Memorial University (2004)
Abstract -
The objective of the thesis is to numerically investigate the near
wake structure and fluid forces generated by a circular cylinder
oscillating obliquely in a uniform stream of a viscous
incompressible fluid. A numerical series expansion solution valid
for small values of the time is used to verify the accuracy of the
fully numerical scheme in the initial stages of motion. In this
latter scheme, the governing Navier-Stokes equations in
vorticity-stream function formulation are solved using a
parallelized finite difference algorithm which utilizes global
conditions of an integral character. A non-inertial coordinate
transformation is used to conformally map the unbounded mesh
outside the cylinder to a rectangular mesh which may be
discretized by a set of uniformly spaced grid points. Thus,
implicitly, the equations are solved on a time-dependent adaptive
mesh. The parallel implementation of the algorithm, which is
considered for the first time in this thesis, produces nearly
optimal speedup results on 8 processors of a Silicon Graphics Onyx
shared memory architecture computer. Numerical simulations are
conducted at a Reynolds number of R=200 to first determine
fundamental and super-harmonic lock-on ranges. The effect of the
amplitude and angle of oscillation on the flow characteristics at
several forcing frequencies is then addressed. Whereas inline and
transverse oscillations of a circular cylinder have been the focus
of many articles, previous work on this problem is limited to a
single experimental study by Ongoren and Rockwell (1988b) and
three numerical studies by Kocabiyik and Al-Mdallal (2003a,b) and
Kocabiyik, Mahfouz, and Al-Mdallal (2004). Therefore, the results
of this thesis represent the most comprehensive analysis of the
problem to date. Whenever possible, verifications of the method
with previous experimental and numerical findings are presented
and agreement between the results is excellent.
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Ongoren, A. and Rockwell, D. (1988b). Journal of Fluid Mechanics, 191:225-245.
Kocabiyik, S. and Al-Mdallal, Q. (2003a). Proceedings of the IUTAM Symposium on Fluid
Structure Interactions (Eds: H. Benaroya and T. Wei). Kluwer Academic Publishers, 163-173.
Kocabiyik, S. and Al-Mdallal, Q. (2003b).
Proceedings of the 11th Annual Conference of the
Computational Fluid Dynamics Society of Canada,
Vancouver, British Columbia, 2:191-198.
Kocabiyik, S., Mahfouz, F.M., and Al-Mdallal, Q. (2004).
Advances in Engng. Software, 35:619-631.