A validated numerical methodology for flow-induced vibration of a semi-spherical end cantilever rod in axial flow

This study presents a simulation method for turbulent flow-induced vibrations of cantilever rods with a semi-spherical end exposed to axial flow, a configuration investigated for the first time. This simulation strategy has been developed using solids4Foam, a toolkit for the open-source package OpenFOAM, which uses the finite-volume approach. The fluid and solid domain equations are solved separately. Coupling is achieved with the Interface Quasi-Newton Inverse Least-Squares (IQN-ILS) algorithm. The mean flow is described by the unsteady Reynolds-averaged Navier–Stokes equations. Turbulence is modeled through either the stress-transport model of Launder, Reece, and Rodi or the effective-viscosity k– $ω$ shear stress transport model, both with the wall-function approach accounting for near-wall turbulence. The methodology is validated using experimental data produced during this study. The simulations show good agreement with the measured values of the oscillation amplitude and frequency for both flow directions (toward rod free-end and away from it). Turbulence model comparisons show that (a) Reynolds stress transport models are necessary to reproduce the vibration amplitude and (b) wall functions enable the simulations to be completed in realistic time scales. The significance to the fluid–solid-interaction (FSI) process of a so far overlooked (with the exception of a couple of recent studies) dimensionless number, the ratio of the flow dynamic pressure to the rod's Young's modulus of elasticity, is also explored. Simulations, which decouple the variation of this dimensionless number from that of the Reynolds number, demonstrate this number's strong effect on the vibration amplitude. This finding is important to the contact of further FSI studies and the scaling of FSI data.