Abstract

The objective of the present contribution is to provide a second well-defined benchmark case for fluid-structure interaction as a growing branch of research in science and industry. Similar to the previous case UFR 2-13 (denoted FSI-PfS-1a in Kalmbach (2014) and De Nayer et al. (2014); Note that the PhD thesis of Kalmbach (2014) comprises further test cases for FSI-PfS-1x and FSI-PfS-2x denoted by lower case appendages x=b or x=c not considered here) the entire study relies on a complementary experimental and numerical investigation. The same measuring techniques (planar particle image velocimetry (PIV), volumetric three-component velocimetry (V3V),multiple-point laser triangulation sensor) and the same numerical methodology (partitioned FSI coupling scheme based on large-eddy simulation (LES)) is applied and will thus only partially repeated here for the sake of brevity. However, all details are available at UFR 2-13.

What are the differences between the previous case and the present one? For the previous configuration (FSI-PfS-1a, UFR 2-13) the flexible structure deforms in the first swiveling mode inducing only moderate structural displacements by an instability-induced excitation. In contrast, the new case denoted FSI-PfS-2a is

• a movement-induced excitation
• with significantly larger deformations of the flexible structure
• in the second swiveling mode.

In order to achieve these more challenging features of the flow and the structure, the previous test case UFR 2-13 (FSI-PfS-1a) is slightly modified: A 2 mm thick flexible plate is clamped behind the fixed cylinder. However, this time a rear mass is added at the extremity of the flexible structure. Moreover, the material (para-rubber) is less stiff than in FSI-PfS-1a. The Reynolds number is again Re = 30,470.

The three-dimensional fluid velocity results show shedding vortices behind the structure, which reaches the second swiveling mode with a frequency of about 11.25 Hz corresponding to a Strouhal number of St = 0.179 (see Fig. 1). Providing phase-averaged flow and structure measurements, precise experimental data for coupled computational fluid dynamics (CFD) and computational structure dynamics (CSD) validations are available for this new benchmark case. The test case possesses four main advantages:

• (i) The geometry is rather simple;
• (ii) Kinematically, the rotation of the front cylinder is avoided;
• (iii) The boundary conditions are well defined;
• (iv) Nevertheless, the resulting flow features and structure displacements are challenging from the computational point of view.

Besides these experimental investigations detailed predictions based on LES are available. Particular attention has been paid to the computational model and the numerical set-up. Special seven-parameters shell elements are applied to precisely model the flexible structure. Structural tests are carried out to approximate the optimal structural parameters. A fine and smooth mesh for the flow calculation has been generated in order to correctly predict the wide range of different flow structures presents near and behind the flexible rubber plate. In accordance with the measurements, phase-averaging is applied to the numerical results allowing a detailed comparison with the phase-averaged experimental data. Both are found to be in close agreement exhibiting a structure deformation in the second swiveling mode with similar frequencies and amplitudes. Finally, a sensitivity study is carried out to show the influence of different physical parameters (e.g. Young’s modulus) and modeling aspects (e.g. subgrid-scale model) on the FSI phenomenon.

Fig. 1: Flow around the flexible structure of the FSI-PfS-2a benchmark (Iso-surfaces of the velocity magnitude of ${\displaystyle u/u_{inflow}\,\operatorname {=} \,0.79}$. The contours on the iso-surfaces depict the instantaneous spanwise velocity component).

Fig. 2: Flow around the flexible structure of the FSI-PfS-2a benchmark (Vorticity magnitude) (Click on the figure to see the animation).

Contributed by: Andreas Kalmbach, Guillaume De Nayer, Michael Breuer — Helmut-Schmidt Universität Hamburg