In this study, we conducted numerical simulations to compute the hydrodynamic forces acting on a circular cylinder undergoing bidirectional oscillations in still fluid. The simulations correspond to the regime of attached laminar two-dimensional flow at low values of the Keulegan-Carpenter number (KC ≤ 5) and Reynolds numbers from 35 to 1000 based on the primary motion of the cylinder. The effect of a secondary motion transverse to the primary motion having twice the frequency and a fifth of the amplitude of the latter is investigated and the results are compared with the corresponding case of unidirectional motion and theoretical predictions from Stokes–Wang theory. The results for unidirectional motion show that the computed force in-line with the motion agree well with theory for KC < 1 and KCRe > 100. The agreement between computations and theory improves as KC decreases and Re increases. The addition of a secondary motion with different phase angles with respect to the primary motion did not have any observable effect on the force acting along the direction of the primary motion compared to that for the same unidirectional motion, although it had a marked effect on the distribution of vorticity around the cylinder. The forces on the cylinder undergoing bidirectional oscillations could be well predicted from Stokes–Wang theory applied in each individual direction for the range of parameters examined in this study. The present study provides insight into the relationship between the generation of vorticity around an oscillating cylinder and the fluid forces acting on it.

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