In this work, unstructured spectral/hp element based direct numerical simulation (DNS) techniques coupled with the Generalized Polynomial Chaos (GPC) method are used to simulate deterministic and stochastic vortex-induced vibrations (VIV) of circular cylinders.; The deterministic flow-structure interaction simulations employ linear structural models and extend to Reynolds number Re = 3000 with uniform or shear inflow conditions. (1) The structural response of a free rigid cylinder with low mass-damping is consistent with the three branch-model documented in experiments. There exists a moderate dependence of the maximum upper-branch amplitude with Re. (2) There also exists a Re-dependent reduced velocity regime within the lock-in region with low cross-correlation but large amplitude response. (3) The existence of a 2P shedding mode in the lower branch and a jump of pi in the total phase between the upper and the lower branch have been confirmed in accordance with experiments. (4) The Independence Principle is not valid in VIV of rigid cylinders with large angle of yaw and large amplitude responses are possible. (5) The existence of a stable 2P-2S hybrid mode in the wake of linearly sheared flows past forced rigid cylinders has been established.; Next, direct and adaptative GPC algorithms for linear and nonlinear random oscillator problems with Gaussian or Non-Gaussian random inputs are presented. (1) Speed-up and limitation of the Karhunen-Loeve (KL) and GPC methods for stochastic ordinary differential equations are discussed. (2) Sharp error bounds for the KL representation of a first-order Markov process and the GPC solution of a linear oscillator subject to it are derived. (3) One-dimensional periodic bi-lateral covariance kernels and their KL representations are derived.; Finally, stochastic flow-structure interaction simulations are studied in the laminar and transitional regimes. Structural response, random-force and random-flow responses are analysed for random inflow and random structural parameters. The effect of noise at the inflow on the stability of the vortex formation behind an oscillating cylinder is also investigated. (1) The dimensionality of the random VIV problem increases in time. Filtering, non-intrusive approach or variable GPC order improve the convergence rate. (2) A noise superimposed to a uniform inflow provokes a shedding-mode switching from a (P+S) pattern to a 2S pattern in the wake of an oscillating cylinder.
展开▼
