URANS Simulations of Turbulence-Induced Vibrations of a Cantilevered Rod With Hemispherical Tip in Axial Flow

Abstract The Flow Induced Vibrations (FIV) of slender cylindrical structures has sparked interest for significant research in the recent decades. Turbulence-induced vibrations of such structures has been a focus for experimental and numerical Fluid Structure Interaction (FSI) simulations owing to its practical engineering applications, one of them being nuclear power plants. In water-cooled reactor cores such as those in a Pressurized Water Reactor (PWR), such vibrations of fuel rods caused by the axial flow of the primary coolant passing through the gaps between fuel rods cause long term damage by fretting wear and mechanical fatigue. The modelling of such vibrations is thus of great importance in order to assess and realize a safe and reliable nuclear power plant. As part of such efforts, NRG PALLAS is partaking in a benchmark as part of the European Collaborative GO-VIKING project where numerical FSI simulations of a cantilever rod with different tips subjected to axial flow is compared to experimental data. In the current study, the rod with a hemispherical tip is considered subjected to water flow at high (40k) and low (21.2k) Reynolds numbers directed from the free end of the rod to the fixed end of the rod. This problem is tackled using the commercial code Simcenter STAR-CCM+ (V2306) that comes with a finite volume Computational Fluid Dynamics (CFD) Solver, a finite element Computational Structural Mechanics (CSM) Solver with the possibility of connecting the two either in a one-way or two-way coupling to carry out FSI simulations. In the current study, the problem is tackled as follows: The fluid governing equations are solved with an Unsteady RANS (URANS) approach, employing the Standard K-Epsilon turbulence model with a cubic constitutive relationship to obtain the forces on the cantilever rod. With the force from the fluid as boundary conditions, the rod displacement is solved for from the solid governing equations. The FSI coupling is selected to be two-way where at every iteration of every time step, the structural displacements are fed back to the fluid solver via a mesh morphing step for calculating the forces on the newly displaced boundary which in turn is fed back to the structural solver. By choosing a medium resolution URANS approach, the aim is to establish the current state of the art and the gap that could be filled with higher resolution and computationally expensive approaches such as Large Eddy Simulations (LES) or hybrid methods. The qualitative numerical results of mean velocity profiles upstream of the rod and mean velocity contours around the rod tip show good agreement with the experimental results. Key quantitative numerical results of dominant vibration frequency and vibration amplitudes reveal good match of the former to the experiments while an underprediction of an order of magnitude for the latter.