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

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~\citep{fsi-les-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~\cite{fsi-les-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.

To propose a new FSI test case supported by experimental data, a brief literature study has to be done. A list of the available FSI benchmarks with simple flexible structures can be divided into two groups: the laminar and the turbulent cases. For the sake of brevity complicated FSI cases are ignored in the following summary.

As laminar, purely numerical FSI test cases one can cite the 2D and 3D modified cavity flows of~\cite{wall1999} and~\cite{mok2001}, taken as example in~\cite{foerster2007a}: this is a modification of the well-known lid-driven cavity CFD benchmark with a flexible membrane at the bottom. The CFD part of the FSI code can be validated at first with the classical lid-driven cavity flow. Then based on a simple modification assuming a flexible instead of a rigid bottom wall, the FSI coupling algorithm can be evaluated. This test is solely numerical and no experimental data are provided.

From the very first, the hemodynamics research domain was interested in FSI to study blood flow in flexible veins and arteries. Therefore, as 2D and 3D numerical laminar test cases the model of a compliant vessel of~\cite{nobile2001} and~\cite{formaggia2001} have to be cited. This unsteady test case is often used to validate FSI codes relying on shells, because of its simplicity and of the 3D structure deformations. Regarding other laminar benchmarks, there are many FSI test cases with elastic plates: a very simple test case is the 2D numerical laminar test case used by~\cite{glueck2001}. A cantilever plate is transversely put into a flow. The solution is stationary and the displacement is small. It is too simple to validate a FSI code, but very useful to debug and evaluate the coupling scheme. In~\cite{glueck2001} another test case is presented: a L-shaped flexible plate is located in a laminar flow and mounted headlong at the bottom wall. This case is 3D and stationary, at least for moderate Reynolds numbers. It is useful for first 3D coupling tests, but no experimental data are provided. More complicated is the 2D numerical laminar benchmark of~\cite{Wall_Ramm_98}, which was later modified by~\cite{Huebner2004}: a thin elastic cantilever plate is attached behind a rigid square cylinder. The geometry is simple, but the deformations of the structure are significant, which implies a good structure model for the great displacements expected and an appropriate remeshing or robust mesh moving procedure for the CFD solver. Moreover, the artificial added-mass effect is strong. Therefore, it represents an appropriate benchmark to test the coupling method~\citep{boyer2011}.

The well-known 2D numerical laminar benchmarks of~\cite{turek2006} and~\cite{turek2010} developed in a collaborative research effort on FSI~\citep{for493} have to be cited here, too: an elastic cantilever plate 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~\citep{fsi-les-2012}. The laminar benchmarks proposed above are all purely numerical, i.e., a cross-comparison between different numerical results is possible, but no rigorous validation against experimental measurements can be carried out.

In order to close this gap, a nominally 2D laminar experimental case was provided by~\cite{gomes2006,gomes2013} and \cite{gomes2011b}: 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. A first comparison between this laminar benchmark and numerical simulations can be found in~\cite{gomes2011}: two configurations with different inflow velocities were taken into account. The FSI code is composed of FASTEST-3D (see Section~\ref{sec:Numerical_Simulation_Methodology_CFD}) for the CFD side and of FEAP~\citep{feap_CSD_solver} for the CSD side. The results show a very good agreement for the configuration with the higher inflow velocity (second swiveling FSI mode). Nevertheless, differences were observed for the low inflow velocity leading to the first swiveling FSI mode. \cite{gomes2011} explained these deviations by the influence of the structural damping: in the high inflow velocity case the relevant frequency for the excitation process is the frequency of the coupled system (motion-induced excitation (MIE), see~\cite{naudascher1994}). In the low inflow velocity case, the relevant frequency for the excitation process is the first natural frequency of the pure structure surrounded by vacuum (instability-induced excitation (IIE), see~\cite{naudascher1994}). Thus as argued by~\cite{gomes2011}, for the first swiveling mode the FSI phenomenon is more sensitive to the structural damping, which was not considered in the numerical model.

The second category in the classification of FSI benchmarks presented here is composed of test cases based on turbulent flows. For example, FSI has early been studied in the submarine research field. Indeed, long underwater cables, called risers, are subjected to the current of the sea and therefore to vortex-induced vibrations (VIV), which reduce their life span. Many studies have been carried out to understand this phenomenon and these can be used as turbulent FSI benchmarks. For example, in~\cite{fujarra2001} a flexible cantilever cylinder is put into a flow. The geometry is quite simple and a variety of Reynolds numbers (7000 $\leq$ Re $\leq$ 47,000) were tested. The VIV phenomenon appears, which means that the structure deformations can be important. So, the FSI model has to be designed for great displacements, which the CSD solver must be capable to handle and a suitable remeshing method or robust mesh moving within the CFD program. In~\cite{yamamoto2004} numerical predictions were carried out and compared with the data of~\cite{fujarra2001}. Furthermore, the well-known Chaplin experiment~\citep{Chaplin_2_05,Chaplin_1_05} has to be cited in this context: a riser is dragged along the long tank "Delta Flume 2" of the institute previously called "Delft Hydraulics", now denoted Deltares{\footnote{http://www.deltares.nl/en/facilities}}. Many different Reynolds numbers (2500 $\leq$ Re $\leq$ 30,000) were tested and lots of experimental data and diverse numerical simulations are available. The displacement and the vibration modes of the riser are highly dependent on the Reynolds number, which makes this experiment useful to validate a multi-physics code.

In the previous test cases the flow is acting outside of the structure. Experiments are also done with aspirating or discharging tubes: Pa\"idoussis is working for years on these problems \citep[cf.][]{paidoussis1998,paidoussis2003}. For example, in~\cite{giacobbi2012} a cantilevered pipe aspirating fluid from the surrounding is presented including experimental, numerical and analytical results. The goal was to investigate its dynamics and to describe whether the flutter phenomenon is possible. However, these FSI test cases are based on a 1D flexible structure and thus are suboptimal for the evaluation of FSI on plane two-dimensional structures targeted on in the present research.

There are also turbulent FSI benchmarks involving 2D structures: in~\cite{stab-fsi-2008} 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~\cite{gomes2010,gomes2013} and \cite{gomes2011b} have to be cited: the same geometry as in~\cite{gomes2006} 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.

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.

The paper is organized as follows: a detailed description of this new test case is given in Section~\ref{sec:Description_of_the_Benchmark_Case}. The measuring techniques used in the experiment are described in Section~\ref{sec:Measuring_Techniques}. Then, the numerical simulation methodology will be presented in Section~\ref{sec:Numerical_Simulation_Methodology} including a brief resume of the theory of the multi-physics code. Afterwards the full numerical setup is explained. Due to cycle-to-cycle variations in the FSI phenomenon observed in the experiment and in the simulation, the results have to be phase-averaged prior to a detailed comparison. The process is described in Section~\ref{sec:Generation_of_phase-resolved_data}. The experimental unsteady raw results are briefly presented in Section~\ref{sec:Experimental_Unsteady_Results}. Finally, numerical and experimental phased-resolved results are compared and discussed in Section~\ref{sec:Phase-resolved_Results_and_Discussion}. All data available for comparison are specified in Section~\ref{sec:Available_Data_for_Comparison}.

Underlying Flow Regime 2-13

Description

Introduction

Give a brief overview of the UFR in question. Describe the main characteristics of the type of flow. In particular, what are the underlying flow physics which characterise this UFR and must be captured by the CFD methods? If the UFR considered here is of special relevance for a particular AC featured in the KB, this should be mentioned.

Review of UFR studies and choice of test case

Provide a brief review of past studies of this UFR which have included test case comparisons of experimental measurements with CFD results. Identify your chosen study (or studies) on which the document will focus. State the test-case underlying the study and briefly explain how well this represents the UFR? Give reasons for this choice (e.g a well constructed test case, a recognised international comparison exercise, accurate measurements, good quality control, a rich variety of turbulence or physical models assessed etc.) . If possible, the study should be taken from established data bases. Indicate whether of not the experiments have been designed for the purpose of CFD validation (desirable but not mandatory)?

Contributed by: Michael Breuer — Helmut-Schmidt Universität Hamburg