Direct Numerical Simulations of the Flow Past a Cylinder Moving With Sinusoidal and Nonsinusoidal Profiles

We perform direct numerical simulations of the flow past a circular cylinder undergoing a one-degree-of-freedom transverse oscillation. The displacement follows a sine function raised to an arbitrary integer power ranging from 1 to 8. When the displacement power is above 2, we have multifrequency oscillation, and the number of Fourier components in the oscillation increases with the power, but they are either odd or even multiples of the input (argument) frequency of the displacement function. We study the responses of the nondimensional lift and drag under these different oscillation profiles and the transfer of nondimensional mechanical energy due to the oscillation, and their trends as the power (hence the number of Fourier components in the oscillation) increases. For odd powers, the energy is transferred to the cylinder; whereas for even powers, it is transferred to the flow. A unity power (harmonic oscillation) corresponds to the maximum energy transfer to the cylinder, which can explain the occurrence of this profile in the case when the cylinder is free to oscillate due to the vortex-induced vibration (VIV) phenomenon. The lift exhibits a mean value only with even powers above 2. The results show that the lift is driven to a large extent by the acceleration of the oscillation rather than its velocity. This should be considered when modeling the fluid-structure coupling in reduced-order VIV models.