Flow past a cylinder with a flexible splitter plate: A complementary experimental–numerical investigation and a new FSI test case (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, etc.). To study these complex FSI problems, a multi-physics code framework was recently developed [11]. 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. [11] the verification process of the code developed is detailed. The computational fluid dynamics (CFD) and computational structural dynamics (CSD) solvers were at first checked separately and then, the coupling algorithm was considered in detail based on a laminar benchmark. A 3D turbulent example 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 validation test case is defined based on detailed measurements and with specific insights into numerical flow simulations, 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 thin structures. To propose a new FSI test case supported by experimental data a brief literature study of the available FSI test cases with simple flexible thin structures has to be done. These validation test cases 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 Wall [56] and Mok [44], taken as example in Förster et al. [27]: 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 purely 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 Nobile [46] and Formaggia et al. [26] 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 Glück et al. [29]. 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 Glück et al. [29] another test case is presented: a L-shaped flexible body 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. Balint and Lucey [2] carried out a 2D cantilever plate in axial flow in order to describe human snoring caused by flutter of the soft palate. Two Reynolds numbers are tested with large deflections of the plate and numerical flow results are provided. More complicated is the 2D numerical laminar benchmark of Wall and Ramm [57], which was later modified by Hübner et al. [38]: 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 [9].
The well-known 2D numerical laminar benchmarks of Turek and Hron [54] and Turek et al. [55] developed in a collaborative research effort on FSI [14] 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 [11]. 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 Gomes and Lienhart [31], [33] and Gomes [30]: 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 Gomes et al. [35]: two configurations with different inflow velocities were taken into account. The FSI code is composed of FASTEST-3D (see Section 4.1) for the CFD side and of FEAP [52] 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. Gomes et al. [35] 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 Naudascher and Rockwell [45]). 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 Naudascher and Rockwell [45]). Thus as argued by Gomes et al. [35], 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 involving 2D structures: In Gomes et al. [34] 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 and Lienhart [32], [33] and Gomes [30] have to be cited: the same geometry as in Gomes and Lienhart [31] 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 2. The measuring techniques used in the experiment are described in Section 3. Then, the numerical simulation methodology will be presented in Section 4 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 5. The experimental unsteady raw results are briefly presented in Section 6. Finally, numerical and experimental phased-resolved results are compared and discussed in Section 7. All data available for comparison are specified in Section 8. For the sake of clarity, the investigations on the material and on the structural model have been relegated to Appendices at the end of the paper.
Section snippets
Description of the geometrical model and the test section
The proposed benchmark case, denoted FSI-PfS-1a, is derived from the turbulent benchmark of Gomes and Lienhart [32], [33]. In their test case a very thin metal sheet with an additional weight at the end was attached behind a rotating cylinder. The case was found to be very challenging from the point of view of modeling and simulation. Therefore, the idea of the present paper is to propose a simpler FSI benchmark avoiding the aforementioned complicated features and being similar to the recently
Measuring techniques for the experimental investigations
Experimental FSI investigations need to contain fluid and structure measurements for a full description of the coupling process. Under certain conditions, the same technique for both disciplines can be used. The measurements performed by Gomes and Lienhart [31], [32], [33] used the same camera system for the simultaneous acquisition of the velocity fields and the structural deflections. This procedure works well for FSI cases involving laminar flows and 2D structure deflections. In the present
Numerical simulation methodology
The applied numerical method relies on an efficient partitioned coupling scheme developed for dynamic fluid–structure interaction problems in turbulent flows [11]. The fluid flow is predicted by an eddy-resolving scheme, i.e., the large-eddy simulation technique. FSI problems very often encounter instantaneous non-equilibrium flows with large-scale flow structures such as separation, reattachment and vortex shedding. For this kind of flows the LES technique is obviously the best choice [10].
Generation of phase-resolved data
Each flow characteristic of a quasi-periodic FSI problem can be written as a function , where describes the global mean part, the quasi-periodic part and a random turbulence-related part [50], [15]. This splitting can also be written in the form , where is the phase-averaged part, i.e., the mean at constant phase. In order to be able to compare numerical results and experimental measurements, the irregular turbulent part has to be averaged out. This measure is
Unsteady results
In order to comprehend the real structure deformation and the turbulent flow field found in the present test case, experimentally and numerically obtained unsteady results are presented in this section.
Fig. 11 shows experimental raw signals of dimensionless displacements from a point located at a distance of 9 mm from the shell extremity in the midplane of the test section. In Fig. 11(a) the history of the y-displacement obtained in the experiment is plotted. The signal shows
Phase-resolved results and discussion
The following part is divided into two different sections: in the first one numerical phased-resolved results obtained for the two configurations (full and subset case) are compared. Based on this evaluation one case is chosen for a parameter study. Then, in the second subsection the numerical phased-averaged results chosen are juxtaposed to the experimental ones in order to verify their quality.
In both simulations (subset and full case) the flow is initialized by assuming the entire structure
Available data for comparison
The described benchmark FSI-PfS-1a is supposed to test, evaluate and improve numerical FSI codes. Therefore, the authors support all interested groups by the experimental and numerical data presented in this paper. For this purpose the data are made available on the ERCOFTAC Knowledge Base Wiki in the category ’Flow around Bodies’ accessible as case 2–13 under
http://qnet-ercoftac.cfms.org.uk/w/index.php/UFR_2-13.Available for comparison are:
- •
The data for the structural test cases described in
Conclusions
A new FSI validation test 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 validation test case 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
Acknowledgments
The project is financially supported by the Deutsche Forschungsgemeinschaft under the Contract Numbers BR 1847/12-1 and BL 306/26-1. The computations were partially carried out on the German Federal Top-Level Computer SuperMUC/SuperMIG at LRZ Munich under the contract number pr47me. We would like to thank the Draftex Automotive GmbH in Grefrath for providing the rubber material and the corresponding measurements of its characteristic properties. Special thanks goes also to H. Lienhart (LSTM
References (59)
- et al.
Instability of a cantilevered flexible plate in viscous channel flow
J Fluids Struct
(2005) - et al.
On the physical significance of higher-order kinematic and static variables in a three-dimensional shell formulation
Int J Solids Struct
(2000) - et al.
Computational methods for form finding and optimization of shells and membranes
Comput Methods Appl Mech Eng
(2005) - et al.
Fluid–structure interaction using a partitioned semi-implicit predictor–corrector coupling scheme for the application of large-eddy simulation
J Fluids Struct
(2012) - et al.
Load and motion transfer algorithms for fluid–structure interaction problems with non-matching discrete interfaces: momentum and energy conservation, optimal discretization and application to aeroelasticity
Comput Methods Appl Mech Eng
(1998) - et al.
Optimization of non-linear structures based on object-oriented parallel programming
- et al.
On the coupling of 3D and 1D Navier–Stokes equations for flow problems in compliant vessels
Comput Methods Appl Mech Eng
(2001) - et al.
Artificial added mass instabilities in sequential staggered coupling of non-linear structures and incompressible viscous flows
Comput Methods Appl Mech Eng
(2007) - et al.
Computation of fluid–structure interaction on lightweight structures
J Wind Eng Ind Aerodynam
(2001) - et al.
Experimental and numerical study on a laminar fluid–structure interaction reference test case
J Fluids Struct
(2011)
A monolithic approach to fluid–structure interaction using space–time finite elements
Comput Methods Appl Mech Eng
Experimental PIV/V3V measurements of vortex–induced fluid–structure interaction in turbulent flow—a new benchmark FSI–PfS-2a
J Fluids Struct
Geometric conservation laws for flow problems with moving boundaries and deformable meshes, and their impact on aeroelastic computations
Comput Methods Appl Mech Eng
Particle-imaging techniques for experimental fluid mechanics
Annu Rev Fluid Mech
Shear deformable shell elements for large strains and rotations
Int J Numer Methods Eng
Models and finite elements for thin-walled structures
Algorithmic treatment of shells and free form-membranes in FSI
Geometrically exact Kirchhoff beam theory: application to cable dynamics
J Comput Nonlin Dynam
Shell theory versus degeneration – a comparison in large rotation finite element analysis
Int J Numer Methods Eng
Three-dimensional extension of non-linear shell formulation based on the enhanced assumed strain concept
Int J Numer Methods Eng
An experimental study of entrainment and transport in the turbulent near wake of a circular cylinder
J Fluid Mech
A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized- method
J Appl Mech
Dynamics of structures
Space conservation law in finite-volume calculations of fluid flow
Int J Numer Methods Fluids
Finite-volume method for prediction of fluid flow in arbitrarily shaped domains with moving boundaries
Int J Numer Methods Fluids
Cited by (63)
Surrogate-based optimization for the worst-case prediction regarding a flexible structure impacted by wind gusts
2023, Journal of Wind Engineering and Industrial AerodynamicsDesign of a high fidelity Fluid–Structure Interaction solver using LES on unstructured grid
2023, Computers and FluidsFluid-Structure-Acoustic coupling analysis for external laminar and turbulent fluid flows
2023, Results in PhysicsAeroelastic response of an elastically mounted 2-DOF airfoil and its gust-induced oscillations
2023, Journal of Fluids and StructuresExperimental and numerical study on heat transfer enhancement by Flow-induced vibration in pulsating flow
2022, Applied Thermal Engineering