Simultaneous streamwise and cross-stream oscillations of a diamond oscillator at low Reynolds numbers

A two-dimensional stabilized space-time finite-element-based in-house solver is used to explore flow around an elastically mounted rigid diamond oscillator undergoing undamped vortex-induced vibrations in transverse and stream-wise directions simultaneously. The computations are carried over a reduced velocity ( U*) range of 1-12 keeping the Reynolds number (Re) and the mass ratio (m*) fixed at 100 and 10, respectively. In the current investigation, a five-branch response behavior with the presence of an "upper branch " is identified, which is absent for transverse-only oscillations. A shift in normalized time-averaged phase difference (phi/ pi) from 0 to 1 is related to the transition from the upper to the lower branch. The non-dimensional oscillation frequencies in both streamwise and cross-stream directions (F-x and F-y, respectively) collapse on the upper branch, matching the oscillator's non-dimensional natural frequency (F-N). This leads to periodic single-looped "raindrop-shaped " cylinder trajectories. On this branch, the vortex-shedding mode is asymmetric, and the mean lift is non-zero (C-lavg &NOTEQUexpressionL; 0). For all other response branches, C-lavg asymptotic to 0 and the vortex-shedding modes are symmetric. The presence of multiple frequencies in the in-line oscillations makes the initial branch quasi-periodic, whereas all other response branches are periodic. The addition of in-line motion modifies the fluid loading on the oscillator significantly.