Computation of unsteady viscous incompressible flow around an obliquely oscillating circular cylinder using a parallelized finite difference algorithm

Lawrence, Karl P. (2004) Computation of unsteady viscous incompressible flow around an obliquely oscillating circular cylinder using a parallelized finite difference algorithm. Masters thesis, Memorial University of Newfoundland.

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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 domain outside the cylinder to a rectangular domain 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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