Parallel simulations of vortex-induced vibrations in turbulent flow: Linear and nonlinear models

In this work unstructured spectral/hp element based direct numerical simulation (DNS) techniques are used to simulate vortex-induced vibrations (VIV) of flexible cylinders.; Linear structural models are employed for tension-dominated structures (cables) and bending stiffness-dominated structures (beams). Flow-structure interactions are studied in transitional (200–300) and turbulent (1000) Reynolds numbers. Structural responses as well as hydrodynamic forces are analyzed and their relationship with the near wake flow structures is examined. The following conclusions were reached: (1) A Reynolds number effect exists for the observed oscillation amplitude. (2) The phase relationship between cross-flow displacement and coefficient of lift is correlated with both the magnitudes of lift forces and displacement. (3) Cables enhance transition to turbulent flow, while beams (and rigidly vibrating cylinders) delay it. In the transition regime beams oscillate with 70% of the amplitude of cables. (4) Oblique and parallel shedding appear to coexist in the turbulent wake of cables and beams with a traveling wave structural response. The corresponding wake structure behind a cylinder with pinned ends vibrating as a standing wave, displays lambda-type vortices similar to those seen at lower (laminar) Reynolds numbers. (5) Cables and beams at a Reynolds number of 1000 give: (a) extremely similar velocity spectra, (b) differing autocorrelation profiles and large flow structures, and (c) differing structural responses. (6) The empirical formula for the coefficient of drag due to Skop et al. (1977) is shown to be in disagreement with the experimental data; a modified formula fits the results much better.; A non-linear set of equations for the finite amplitude vibrations of a string are also derived and investigated. It is combined with an Arbitrary Lagrangian-Eulerian (ALE) flow solver and applied to model simulations of low Reynolds number (100) flow past flexible cylinders with pinned ends. It is noted that: (1) The string tension shows considerable variability with time and to a lesser extent along the span, giving rise to non-classical lock-in phenomena. (2) The coupled flow-structure system is very sensitive to large tension variations in the initial conditions. (3) The hydrodynamic forces in the spanwise direction are non-negligible.