This paper reports computational results of forces and wake structure in two-dimensional flow past a circular cylinder forced to vibrate both transversely and inline to a uniform stream, following a figure-eight trajectory. For a flow stream from left to right, we distinguish between a counterclockwise mode and a clockwise mode, if the upper part of the trajectory is traversed counterclockwise or clockwise, respectively. The present computations correspond to a range of transverse oscillation frequencies close to the natural frequency of the Kármán vortex street and several oscillation amplitudes, both for counterclockwise motion and clockwise motion. The nondimensional forces and nondimensional power transfer from the fluid to the body are calculated. The results demonstrate a strong dependence of the forces and power transfer on the direction in which the figure-eight is traversed. In general, counterclockwise motion maintains positive power transfer at higher oscillation amplitudes. Flow visualizations show that the wakes are characterized by the presence of two single (2S) vortex shedding mode at low oscillation amplitudes and can attain more complex structures at higher amplitudes.

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