A fluid-structure interaction benchmark in turbulent flow (FSI-PfS-1a)

A new FSI benchmark case denoted FSI-PfS-1a is proposed. The definition of the test case is driven by the idea to setup a well-defined but nevertheless challenging benchmark for fluid-structure interaction in the turbulent flow regime. A rigid front cylinder and a flexible membranous rubber tail attached to the backside of the cylinder form the structure which is exposed to a uniform inflow at a low turbulence level. Thus three critical issues of precursor benchmarks are circumvented, i.e., an additional degree of freedom of a rotating front cylinder, an extremely thin flexible structure and an additional weight at the end of the membranous structure. The investigations comprise three parts.

First, two dynamic structural tests were carried out experimentally and numerically in order to evaluate an appropriate material model 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 model is sufficient to describe the deflection of the flexible structure.

Second, detailed experimental investigations in a water tunnel using optical measurement techniques for both, the fluid flow and the structure deformation, were carried out. A quasi-periodic oscillating flexible structure in the first swiveling mode with a corresponding Strouhal number of about St = 0.11 is found. A post-processing of the extensive data sets delivered the phase-averaged flow field and the structural deformations.

Third, various simulations relying on a newly developed FSI simulation tool combining a partitioned solution strategy with an eddy-resolving scheme (LES) were performed. A subset case and full case are taken into account. Owing to the wider structure and less constraints of the lateral nodes the deformations in the spanwise direction were found to be larger in the full case reflecting some kind of mild waves in the structure. Nevertheless, in relation to the deformation of the structure in cross-flow direction the spanwise deflections are insignificant, especially for the comparison of the phase-averaged signals.

A study on three parameters for the subset case without structural damping yields that the Young's modulus has a very important influence on the system. It controls in which swiveling mode the flexible structure oscillates. The thickness of the plate h plays a role in the results, too, but not so significant as the Young's modulus. The parameter with the least effect on the FSI simulations is the density of the rubber plate: large variations of the density do not have major influence on the predictions.

As usual for rubber material, a certain level of structural damping has to be expected. To model this phenomenon in a simple and straightforward way, classical Rayleigh damping is used and adjusted based on one of the pure structural test presented. The FSI simulations with and without structural damping are compared with the experiment. It turns out that the structural damping can not be ignored in the present case and significantly affects the deflection of the structure. Without taken the damping into account the structural deflections are overpredicted. Including the simple damping model improves the results. The eddy-resolving FSI simulations are found to be in close agreement with the experiment for every position of the flexible structure. Solely the amplitudes of the deflections are slightly underpredicted with damping. Nevertheless, the shedding phenomenon behind the cylinder/structure and the positions of the vortices convected downstream are correctly predicted. Furthermore, the FSI frequency found in the simulations matches particularly well the measured one.

Evaluation

Comparison of CFD Calculations with Experiments

Discuss how well the CFD calculations of the assessment quantities compare with experiment and with one another. Present some key comparisons in the form of tables or graphical plots and, where possible, provide hyperlinks to the appropriate results database. Results with different turbulence models covering as wide a range as possible should be included in the discussion. However, if too many different calculation results are available (e.g. from workshops) do not present all the comparisons here. A selection should be made showing results only for the most typical and practically important models. Comprehensive comparisons can be made available via a link to the associated databases. Finally, draw conclusions on the ability of the models used to simulate the test case flow.

Contributed by: Michael Breuer — Helmut-Schmidt Universität Hamburg