Large eddy simulation and proper orthogonality decomposition of turbulent flow around a vibrissa-shaped cylinder

The flow dynamics over a vibrissa-shaped cylinder at the sub-critical Reynolds number of 1.8 × 104 are comparatively investigated using the large eddy simulation (LES) approach, with particular emphasis on the wake structure and self-induced force. Three reference configurations with the same hydrodynamic diameters, i.e., a circular cylinder, an elliptical cylinder and a wavy cylinder, are compared with the vibrissa-shaped cylinder configuration. The results demonstrate that the fluctuation of lift force for the vibrissa-shaped cylinder is reduced by approximately 79.2% compared with that for the circular cylinder, and the predicted RMS magnitudes for the four configurations agree reasonably well with the experimental data. For the vibrissa-shaped cylinder, only one sharp peak with relatively low magnitude is observed at the characteristic frequency fD/U0=0.20, and the wake shedding does not dominate the dynamics, while the vortex structures show significantly three-dimensional features. Meanwhile, the separation line of the recirculation zone shows a remarkable wavy structure that corresponds to the trailing geometrical surface with a spanwise shift of approximately a half-period of undulation. A proper orthogonal decomposition (POD) analysis is performed to explore the three-dimensional structures in the wake behind the vibrissa-shaped cylinder. The POD modes reveal a completely three-dimensional and periodically staggered arrangement along both the spanwise and streamwise directions. The spectra of the first two time coefficients reveal that the wake shedding processes on the nodal and saddle planes are not synchronous. Finally, the phase-averaging results show sequential processes of vortex shedding in the wake behind the vibrissa-shaped cylinder, and demonstrate marked differences between this and the other cylinders. Two symmetrical vortices are attached closely to the backward side of the vibrissa-shaped cylinder, resulting in smaller fluctuations of velocity and wall pressure, which in turn contribute to reducing the vortex-induced force and suppressing its vibrations.