A Fluid-Structure Interaction Benchmark in Turbulent Flow (FSI-PfS-1a)

Description

Introduction

A flexible structure exposed to a fluid flow is deformed and deflected owing to the fluid forces acting on its surface. These displacements influence the flow field resulting in a coupling process between the fluid and the structure shortly denoted fluid-structure interaction (FSI). Due to its manifold forms of appearance it is a topic of major interest in many fields of engineering. Based on enhanced numerical algorithms and increased computational resources numerical simulations have become an important and valuable tool for solving this kind of problem within the last decade. Today FSI simulations complement additional experimental investigations. A long-lasting vision of the computational engineer is to completely replace or at least strongly reduce expensive experimental investigations in the foreseeable future. However, to attain this goal validated and thus reliable simulation tools are required.

The long-term objective of the present research project is the coupled simulation of big lightweight structures such as thin membranes exposed to turbulent flows (outdoor tents, awnings...). To study these complex FSI problems, a multi-physics code framework was recently developed (Breuer et al., 2012). In order to assure reliable numerical simulations of complex configurations, the whole FSI code needs to be validated at first on simpler test cases with trusted reference data. In Breuer et al. (2012) the verification process of the code developed is detailed. The CFD and CSD solvers were at first checked separately and then, the coupling algorithm was considered in detail based on a laminar benchmark. A 3D turbulent test case was also taken into account to prove the applicability of the newly developed coupling scheme in the context of large-eddy simulations (LES). However, owing to missing reference data a full validation was not possible. The overall goal of the present paper is to present a turbulent FSI test case supported by experimental data and numerical predictions based on the multi-physics code developed. Thus, on the one hand the current FSI methodology involving LES and shell structures undergoing large deformations is validated. On the other hand, a new turbulent FSI benchmark configuration is defined, based on the specific insights into numerical flow simulation, computational structural analysis as well as coupling issues. Hence, the present study should provide a precisely described test case to the FSI community for the technically relevant case of turbulent flows interacting with flexible structures.

Review of previous work

The present study is mainly related to two former investigations of Turek and Hron (2006, 2010) and Gomes et al. (2006, 2012) on vortex-induced fluid-structure interactions. The well-known 2D purely numerical laminar benchmarks of Turek and Hron (2006, 2010) developed in a collaborative research effort on FSI (DFG Forschergruppe 493) consists of an elastic cantilever plate which is clamped behind a rigid circular cylinder. Three different test cases, named FSI1, FSI2 and FSI3 are provided, complemented by additional self-contained CFD and CSD test cases to check both solvers independently. These test cases were also used to validate the solvers applied in the present study (Breuer et al., 2012). In order to close the gap of complementary experimantel and numerical data, a nominally 2D laminar experimental case was provided by Gomes et al. (2006, 2013) and Gomes (2011). Here, a very thin metal sheet with an additional weight at the end is attached behind a rotating circular cylinder and mounted inside a channel filled with a mixture of polyglycol and water to reach a low Reynolds number in the laminar regime. Experimental data are provided for several inflow velocities and two different swiveling motions could be identified depending on the inflow velocity. Owing to the thin metal sheet and the rear mass the accurate prediction of this case is demanding. There are also turbulent FSI benchmarks involving 2D structures: in Gomes et al. (2010) a rigid plate with a single rotational degree of freedom was mounted into a water channel and experimentally studied by particle-image velocimetry (PIV). This study also presents the first comparison between experimental data and predicted results achieved by the present code for a turbulent FSI problem. As another turbulent experimental benchmark, the investigations of Gomes et al. (2010, 2013) and Gomes (2010) have to be cited: the same geometry as in Gomes et al. (2006) was used, but this time with water as the working fluid leading to much higher Reynolds numbers within the turbulent regime. The resulting FSI test case was found to be very challenging from the numerical point of view. Indeed, the prediction of the deformation and motion of the very thin flexible structure requires two-dimensional finite-elements. On the other hand the discretization of the extra weight mounted at the end of the thin metal sheet calls for three-dimensional volume elements. Thus for a reasonable prediction of this test case both element types have to be used concurrently and have to be coupled adequately. Additionally, the rotational degree of freedom of the front cylinder complicates the structural simulation and the grid adaptation of the flow prediction.

Choice of test case

Thus, in the present study a slightly different configuration is considered to provide in a first step a less ambitious test case for the comparison between predictions and measurements focusing the investigations more to the turbulent flow regime and its coupling to a less problematic structural model. For this purpose, a fixed cylinder with a thicker rubber tail and without a rear mass is used. This should open the computation of the proposed benchmark case to a broader spectrum of codes and facilitates its adoption in the community. 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. A detailed description of the present test case is published in De Nayer et al. (2013).

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)