Department of Mechanical Engineering, Indian Institute of Technology (ISM) Dhanbad Dhanbad - 826004, Jharkhand, India
Two-dimensional space-time finite-element simulations are carried out to study the free vibrations of a rigid elliptic cylinder of aspect ratio 1.11 and low non-dimensional mass of unity. Undamped transverse-only as well as two-degrees-of-freedom oscillations are considered. The effect of damping is investigated on transverse-only motion. For all three cases, results for cylinder response are presented for 50≤Re≤180. In the absence of damping, transverse oscillations are mostly periodic except for a very narrow region near the end of lock-in. In contrast, a damping of 0.044 removes quasi-periodicity as well as secondary hysteresis from flow and body motion. For undamped motion, inclusion of in-line oscillations excites high amplitude oscillations, widens the range of synchronization and delays phase shift between lift and cross-stream response. In each case, synchronization between cylinder oscillations and vortex-shedding is 1:1. In addition, drag-lift phase plots are symmetric about mean lift (= 0) line. Thus, symmetrical shedding of two equally strong alternate vortices per oscillation cycle forms 2S, CNW(2S) or C(2S) modes. For each case, the lower branch initiates at Re = 65 where the oscillation or shedding frequency is found to be locally maximum.