The phenomena of vortex shedding around a cylinder oscillating harmonically in a fluid at rest are investigated by a two-dimensional numerical simulation of the Navier-Stokes equations. The simulation is based on a vorticity-velocity integro-differential formulation dealing with vorticity, velocity and pressure variables. Three combinations of Reynolds number(Re) and Keulegan-Carpenter number(KC) were taken to investigate the associated vortex development around the cylinder in the different flow regimes.
The motion of circular cylinders in a fluid at rest is especially of interest in fields of offshore and civil engineering, such as marine risers, subsurface pipelines, etc. Such flows have been investigated by many researchers, e.g., Sarpkaya(1975,1986), Williamson(1985), Bearman et al.(1985), Obasaju et al.(1988), Tatsuno and Bearman(1990), Justesen (1991) and Dütsch et al. (1998). An overall review is given by Williamson (1996) and by Sumer and Fredsøe (1997).
The present calculation provides solutions obtained by the Eulerian FVM method for the problem of the oscillating cylinder. It is expected to provide the simulations of vortex shedding from the cylinder. The simulation is based on a vorticity-velocity integro-differential formulation. This formulation deals with vorticity, velocity and pressure variables. The brief explanation about the formulation is given in the next section. In the following sections, we investigate the flow characteristics such as the number of shedding vortex and the shedding direction, with the variety of the flow regimes with each other KC and Re (or β) numbers. In addition, drag and lift forces of the cylinder are computed. Through the Fourier transform of these coefficients, we describe their dominant frequency modulation which is related to the vortex shedding and to the harmonic motion of the cylinder. In comparison of the experimental researches and the present calculation, we validate the numerical simulation of the flow around an oscillating circular cylinder.