A numerical study of flow-structure interactions with application to flow past a pair of cylinders

Flow-structure interaction is a generic problem for many engineering applications, such as flow-induced oscillations of marine risers and cables. In this thesis a Direct Numerical Simulation (DNS) approach based on spectral/hp elements is employed. Structural motion implies changes on the boundaries of the flow domain. An Arbitrary Lagrangian Eulerian (ALE) scheme is incorporated to efficiently move the mesh without remeshing. Efficient three-dimensional simulations with periodicity in at least one space direction are achieved using Hybrid Fourier-Jacobi expansions. Both 2D and 3D formulations can treat an arbitrary number of oscillating bodies. Due to the large computational demands of the resulting systems parallel computing is used with MPI. Numerical experiments are run and systematic data sets are obtained for flow around two cylinders. Stationary cylinders in tandem and side-by-side arrangements are examined parametrically over spacing and Reynolds number. Parametric studies of tandem cylinders in prescribed motion and free oscillation are also conducted. For tandem cylinders, sudden changes in the forces occur at a critical spacing where a transition from reattachment to binary vortex regime occurs. A hysteresis effect is observed for spacings near the nominal critical, where for given Reynolds number there are two possible solutions depending on the initial conditions. Discrepancies in the prediction of the critical spacing using 2D and 3D simulations are identified and explained. The three-dimensional effects are found to cause a weakening of the strength of the primary vortices and a delay in the inception to binary vortex regime. When the cylinders oscillate in prescribed motion, the phase angle of the oscillations can alter significantly the hydrodynamic work on the downstream cylinder. For spacings smaller than the critical spacing, the lock-on range of frequencies is wider than that of a single cylinder. As the oscillations amplitude increases however, pockets of non-lock-on regions are found within the Arnold synchronization regions. A shift towards higher frequencies in the synchronization range is found for the in-phase oscillations compared to the anti-phase oscillations. A consistent change is found in the spanwise correlations. For the elastically mounted two-degree of freedom tandem cylinders it is found that the synchronization range of the upstream cylinder is wider when its latest shed pair of vortices intercepts the downstream cylinder. A shifting of the synchronization curve on the reduced velocity axis is observed and explained in terms of the natural shedding frequency of the corresponding stationary system of cylinders. Thesis Supervisor: Dick K.P. Yue Title: Professor of Hydrodynamics and Ocean Engineering Thesis Supervisor: Michael Triantafyllou Title: Professor of Ocean Engineering Thesis Committee Member: George Em. Karniadakis Title: Professor of Applied Mathematics, Brown University Thesis Committee Member: Franz Hover Title: Principal Research Engineer