Fluid-structure interaction in turbulent flow past cylinder/plate configuration II (Second swiveling mode)

Flows Around Bodies

Underlying Flow Regime 2-14

Description

Introduction

In this contribution, a thin flexible structure behind a bluff body in the sub-critical Reynolds number regime is considered. Such a geometrically simple fluid-structure interaction (FSI) problem is useful to validate numerical methods and to investigate how they react to different parameter settings. The long-term objective of the present research project is to simulate practically relevant light-weight structural systems in turbulent flows (textile awnings, outdoor tents,...). For this purpose a new numerical FSI simulation methodology using large-eddy simulation (Breuer, 2002) was developed especially for thin flexible structures within turbulent flows (Breuer et al., 2012). The method was validated at first in laminar flows based on the well-known FSI3 benchmark (Turek and Hron, 2006; Turek et al., 2010). The second step was to test it in turbulent flows requiring a geometrically simple reference test case composed of a thin flexible structure within the turbulent flow regime. A deformable splitter plate clamped behind a bluff body represents on the one hand a geometrically manageable setup; on the other hand, complex physical flow features such as separation, transition, and vortex shedding are guaranteed. Hence, it seems to be a good choice. Experimental data are required to evaluate the numerical predictions and to assure their reliability. The final outcome of this study is an interesting benchmark case for FSI in turbulent flow relying on a complementary experimental/numerical investigation results. This is a second test case in addition to UFR 2-13. The main difference is the occurring swiveling mode. Whereas in the first test case the structure deforms in the first swiveling mode, the flexible structure of the present case deforms in the second swiveling mode. Consequently, the deformations are larger than in the previous case leading to a more challenging benchmark.

Review of previous studies

A complete review on the topic of thin structures behind bluff bodies was published by Paıdoussis (2003). Lots of experiments on cantilever plates in axial flow were conducted to investigate the particular instability problem of flutter (Taneda, 1968; Datta and Gottenberg, 1975; Kornecki et al., 1976; Watanabe et al., 2002; Lemaitre et al., 2005; Eloy et al., 2008). Unfortunately, in the experiments presented therein, no flow data are provided. Therefore, these publications cannot be used for a complete validation of FSI codes. More recently, Gomes and Lienhart (2010, 2013) and Gomes (2011) have published several FSI test cases including detailed experimental data based on the following geometry: A very thin metal sheet with an additional weight at the end is attached behind a rotating circular cylinder and mounted inside a water channel. The resulting FSI test case was found to be very challenging from the numerical point of view (combination of two-dimensional elements for the thin structure and three-dimensional elements for the rear weight, rotational degree of freedom of the cylinder). Therefore, an additional experimental FSI investigation was carried out based on a slightly different configuration to provide in a first step a less ambitious test case (De Nayer et al., 2014): a fixed cylinder with a thicker rubber tail and without a rear mass is used (test case denoted FSI-PfS-1a). The Reynolds number was set to Re = 30,470. A complementary numerical investigation of this test case was carried out (De Nayer et al., 2014) to show the capabilities of the present FSI code combining LES and FSI (Breuer et al., 2012). For this first configuration (FSI-PfS-1a) the flexible structure deforms in the first swiveling mode inducing only moderate structural displacements. Good agreement between the experimental and numerical data was achieved. This test case is discussed in UFR 2-13.

Choice of test case

The next step is to take a more challenging test case with large deformations of the plate into account. Similar to the first benchmark FSI-PfS-1a the entire study relies on a complementary experimental/numerical study.

For this purpose the geometry used in the previous test case FSI-PfS-1a is slightly modified: A 2 mm thick flexible plate is clamped behind a fixed cylinder. However, this time a rear mass is added at the extremity of the flexible structure. In contrast to the setup of Gomes and Lienhart (2010, 2013) the rear mass possesses the same thickness as the rubber plate avoiding a jump in the cross-section. Moreover, the material (para-rubber) is less stiff than in FSI-PfS-1a. Consequently, the flexible structure deforms in the second swiveling mode and the structure deflections are larger than for the first case and completely two-dimensional. The Reynolds number is again Re = 30,470. Hence the front cylinder is in the sub-critical regime. The entire experimental investigations of this test case denoted FSI-PfS-2a are presented in Kalmbach and Breuer (2013). The corresponding numerical study is presented in De Nayer and Breuer (2014).

The rear mass and the less stiff material also change completely the governing mechanism responsible for the deformations of the flexible structure. The classification of Naudascher and Rockwell (1994) can be used to distinguish both cases: FSI-PfS-1a is an instability-induced excitation (IIE) (De Nayer et al., 2014). IIE is provoked by a 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). In contrast, FSI-PfS-2a is a movement-induced excitation (MIE). MIE is directly linked to body movements and disappears if the body comes to rest. MIE represents a self-excitation: If a body is accelerated in a flow, fluid forces acting on this body are modified by the unsteady flow induced. If a transfer of energy to the moving body appears, a self-excitation is possible (Naudascher and Rockwell, 1994). This ambitious setup involving large structure deformations and complex flow phenomena is tackled in the present study to provide a second well-defined and challenging FSI benchmark case based on a combined experimental and numerical study.

Note that both cases, FSI-PfS-1a and FSI-PfS-2a, belong to the same series of investigations carried out in order to provide appropriate benchmark test cases for FSI in turbulent flows.

Note that again strong emphasis is put on a precise description of the experimental measurements, a comprehensive discussion of the modeling in the numerical simulation (for the single field solutions as well as for the coupled problem) and the processing of the respective data to guarantee a reliable reproduction of the proposed test case with various suitable methods.

Note that the entire experimental setup and the computational framework is more or less identical to FSI-PfS-1a. Thus in the following those parts are not repeated but links to the corresponding descriptions provided for FSI-PfS-1a are given.

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