Best Practice Advice

Key Physics

FSI-PfS-1a consists of a flexible thin structure with a distinct thickness clamped behind a fixed rigid non-rotating cylinder installed in a water channel.

At an inflow velocity of $u_{\text{inflow}}=1.385$ m/s the displacements are quasi two-dimensional, symmetrical, reasonably large and well reproducible. The rubber plate deforms in the first swiveling mode. This FSI phenomenon is dominated by an instability-induced excitation (IIE) (Naudascher and Rockwell (1994)). IIE is provoked by flow instability which gives rise to flow fluctuations if a specific flow velocity is reached. These fluctuations and the resulting forces become well correlated and their frequency is close to a natural frequency of the flexible structure ("lock-in" phenomenon).

Based on the inflow velocity chosen ( $u_{\text{inflow}}=1.385$ m/s) and the cylinder diameter the Reynolds number of the experiment is equal to ${\text{Re}}=30,470$ . Regarding the flow around the front cylinder, at this inflow velocity the flow is in the sub-critical regime. That means the boundary layers are still laminar, but transition to turbulence takes place in the free shear layers evolving from the separated boundary layers behind the apex of the cylinder. Transition to turbulence means that from that point onwards the flow is three-dimensional and chaotic, and consists of a variety of different length and time scales. The low-frequency components of the turbulent flow dominate the coupled FSI problem, whereas the high-frequency contributions are visible in the fluid forces but are filtered out by the flexible structure. That is the reason why the signals for the deflections show the quasi-periodic signals without high-frequency fluctuations.

Numerical Modelling

CFD

Discretization accuracy: In order to perform LES predictions it is required that spatial and temporal discretization are both at least of second-order accuracy. It is also important that the numerical schemes applied possesses low numerical diffusion (and dispersion) properties in order to resolve all the scales and not to dampen them out.

Grid resolution: The second critical issue to perform LES is the grid resolution. The mesh near the wall, in the free-shear layers and also in the interior flow domain has to be enough fine. For wall-resolved LES the recommendations given by Piomelli and Chasnov (1996) should be followed or outperformed, e.g. y+ < 2. In the present investigation two different block-structured grids either for the subset and for the full case are used. In the first case the entire grid consists of about 13.5 million control volumes (CVs). For the full geometry the grid possesses about 22.5 million CVs. The first cell center is positioned at a distance of $\Delta$ y/D=1.7 x 10 $^{-2}$ . For both setups it was found to be sufficient to resolve the flow accurately at walls as well as in the internal flow domain.

Grid quality: The third point is the quality of the grid. Smoothness and orthogonality is a very important issue for LES computations. In order to capture separations and reattachments at the cylinder and on the plate reliably, the orthogonality of the curvilinear grid in the vicinity of the walls has to be high.

CSD

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Physical Modelling

Turbulence modelling
Transition modelling
Near-wall modelling
Other modelling

Application Uncertainties

Application uncertainties can arise due to:

Periodic boundary conditions in spanwise direction:

Top and bottom slip wall boundary conditions:

Phase-averaging method:

Recommendations for Future Work

The described test case FSI-PfS-1a is a part of a series of reference

test cases designed to improve numerical FSI codes. A second test case FSI-PfS-2a is described in Kalmbach and Breuer (2013). The geometry is similar to the first one: A fixed rigid cylinder with a plate clamped behind it. However, this time a rear mass is added at the extremity of the flexible structure and the material (para-rubber) is less stiff. The flexible structure deforms in the second swiveling mode and the structure deflections are completely two-dimensional and larger.

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)