A computational study of fluid-structure interactions: Flow-induced vibrations of a flexible cable

This thesis reports on direct numerical simulations of flows over vibrating cylinders and flexible cables. We study both flow-induced vibrations and forced vibrations at Reynolds numbers 100 and 200. Through a mapping, the moving boundary problem is transformed to a problem with stationary boundaries and time dependent boundary conditions. We solve the incompressible Navier-Stokes equations using the spectral element method.; We start with two-dimensional simulations of flow over a cylinder undergoing forced and flow-induced vibrations. We measure the motion and forces on the cylinder, and examine the flow structures in the wake of the cylinder. A proper orthogonal decomposition analysis identifies the most energetic eigenmodes of these wakes.; The three-dimensional flow-induced vibration simulations start by examining the stability of standing wave and traveling wave cable responses at Re = 100. We investigate the effects of streamwise cable motion, random cable initial conditions, sheared inflow, higher Reynolds number, forced cable vibration and finite cylinder span.; This thesis has a dual focus of both examining the cable dynamics and studying the flow structures in the wake of the moving cable. In summary, we find the following: (1) The two-dimensional forced vibration simulations reproduce lock-in behavior, and the flow-induced vibration simulations reproduce resonant cylinder response. (2) Streamwise-constrained standing wave and traveling wave cable responses are relatively stable and time periodic at Re = 100. (3) A standing wave cable response produces an interwoven pattern of spanwise vorticity, while a traveling wave cable response produces oblique vortex shedding. (4) Without the streamwise motion constraint, a traveling wave is the preferred cable response for an infinitely long cable. (5) A sheared inflow produces a mixed standing wave/traveling wave cable response, and vortex dislocation in the wake. (6) At Re = 200, the cable and wake response are no longer time-periodic, and the motion and forces on the cable are significantly larger. (7) Proper orthogonal decomposition analysis shows that we can capture 99.9% of the wake energy with approximately 10 eigenmodes for locked-in wakes and 30 eigenmodes for non-locked in wakes. (8) An efficient parallel method for computing the flow over a finite-span cylinder spanning a channel shows that for a L/d = 10 cylinder, the channel walls damp the vortex shedding.