Simulation of a low-reynolds number flow around a cylinder following a figure-8-path

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Abstract
This numerical study investigates a circular cylinder placed in a uniform stream and moving along a slender figure-8-path, using a 2D computational method based on the finite difference method. The effects of in-line amplitude of oscillation and of frequency ratio are investigated. Computations for varying amplitude values were carried out at Re = 150, 200 and 250 for a clockwise orbit (in the upper loop). Time-mean and rms values of force coefficients yielded smooth curves and tended to increase with amplitude. The effect of frequency ratio was investigated at Re = 200, 250 and 300 in the lock-in domain for both clockwise (CW) and anticlockwise (ACW) orientation. Results differ substantially depending on the direction of orientation. Mechanical energy transfer was always positive in ACW direction, which may lead to vortex-induced vibration, and always negative for CW orientation. The time-mean of drag was much lower for CW over the whole frequency ratio domain investigated. For the CW orbit vortex switches were found at specific frequency ratios at Re = 250 and 300. Limit cycle curves for the CW orbit before and after a jump were symmetric, mirror images, and quite complex, while vorticity contours were close to symmetry. These results indicate the possibility of symmetry-breaking bifurcation.

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