# Abstract

The objective of the present contribution is to provide a challenging and well-defined benchmark for fluid-structure interaction (FSI) in turbulent flow to close a gap in the literature. The following list of requirements are taken into account during the definition and setup phase.

• First, the test case should be geometrically simple which is realized by a classical cylinder flow configuration extended by a flexible plate structure attached to the backside of the cylinder (see Fig.1).
• Second, clearly defined operating and boundary conditions are a must and put into practice by a constant inflow velocity and channel walls. The latter are also evaluated against a periodic setup relying on a subset of the computational domain.
• Third, the model to describe the material behavior under load (denoted material model in the following) should be widely used. Although a rubber plate is chosen as the flexible structure, it is demonstrated by additional structural tests that a classical St. Venant-Kirchhoff material model is sufficient to describe the material behavior appropriately.
• Fourth, the flow should be in the turbulent regime. Choosing water as the working fluid and a medium-size water channel, the resulting Reynolds number of Re = 30,470 guarantees a sub-critical cylinder flow with transition taking place in the separated shear layers.
• Fifth, the benchmark results should be underpinned by a detailed validation process.

For this purpose two dynamic structural tests were carried out experimentally and numerically in order to evaluate an appropriate model to describe the material behavior and to check and evaluate the material parameters of the rubber (Young's modulus, damping). This preliminary work has shown that the St. Venant-Kirchhoff material law is sufficient to describe the deflection of the flexible structure.

After these structural tests, complementary numerical and experimental investigations with flow around the cylinder-plate configuration were performed. Based on optical contactless measuring techniques (particle-image velocimetry and laser distance sensor) the phase-averaged flow field and the structural deformations were determined. These data were compared with corresponding numerical predictions relying on large-eddy simulations and a recently developed semi-implicit predictor-corrector FSI coupling scheme. Both results were found to be in close agreement showing a quasi-periodic oscillating flexible structure (see animation of Fig. 1) in the first swiveling FSI mode with a corresponding Strouhal number of about ${\displaystyle {\text{St}}_{\text{FSI}}=0.11}$.

Fig. 1: Flow around the flexible structure of the FSI-PfS-1a Benchmark (Click on the figure to see the animation.).

Contributed by: G. De Nayer, A. Kalmbach, M. Breuer — Helmut-Schmidt Universität Hamburg (with support by S. Sicklinger and R. Wüchner from Technische Universität München)