**Principal Investigator:**

Univ.-Prof. Dr.-Ing. habil. Michael Breuer

**Affiliation:**

Department of Fluid Mechanics, Helmut-Schmidt-University, Hamburg (Germany)

**Local Project ID:**

pr53ne

**HPC Platform used:**

SuperMUC of LRZ

**Date published:**

**Introduction**

The interaction between fluids and structures is a topic of interest in many fields such as mechanical engineering (e.g. airfoils), civil engineering (e.g. towers) or medicine technique (e.g. artificial heart valves). Beside experimental investigations numerical simulations have become a valuable tool for solving this kind of problems. Numerical predictions based on precise and modern techniques are nowadays able to foresee complex flow phenomena such as vortex shedding, transition and separation or critical stresses in the structure exposed to the flow [1,2]. High loads can lead to severe damages of the structure. These incidents are mostly the consequence of surrounding extreme events. In civil engineering, for instance, lightweight structures are exposed to strong variations of the wind, particularly wind gusts. Ultimately, this can lead to a complete destruction of the structure as visible in Figure 1.

In order to be able to correctly dimension such structures leading to safe constructions, it is of interest to model these gusts and to comprehend their impact on the FSI phenomenon. Two issues have to be handled for this purpose: On the one hand the model of the wind gust itself and their injection into the area of interest and on the other hand the solution of the coupled FSI problem.

**Wind Gust Modeling**

To artificially generate numerical wind gusts, sudden variations of the velocity in time and space are superimposed on the turbulent inflow data. The gusts can have different shapes and amplitudes. Simple shapes such as the Gaussian, 1-cosine or Mexican-hat shape were selected from the literature (Figure 2).

In a first formulation the velocity variations resulting from the superposition of the turbulent inflow data and the gust shapes are imposed at the inlet of the computational domain. This injection of the wind gusts implies a short but brutal change of the total mass inflow, which has to be corrected so that the incompressible solver does not diverge [3]. In the future a source-term formulation will be developed for this purpose, which allows injecting the gusts inside the computational domain.

**Fluid-Structure Interaction Framework**

In order to reach the objective to tackle civil engineering FSI applications exposed to wind gusts, it was decided to use highly advanced solvers for both subtasks of the problem:

The fluid solver FASTEST-3D is a highly parallelized finite-volume 3D CFD solver, written in FORTRAN and relying on MPI. To simulate turbulent flows, an eddy-resolving scheme (large-eddy simulation, LES) is chosen. Since turbulent inflow data play an important role for the results to be achieved by LES, realistic data are synthetically generated and injected at the inlet of the computational domain during the simulation requiring a high amount of IO.

The structure solver Carat++ [4] developed at TU Munich is a 3D C++ solver specialized for the prediction of the deformations of thin structures based on shells or membranes. Form finding procedures, finite-element discretization (FEM) and isogeometric analysis (IGA) are available.

The coupling program EMPIRE, developed at TU Munich, does the required mapping between the non-matching meshes and the exchange of data between both codes using MPI [6].

**Results**

CFD simulations including wind gusts but without FSI and FSI simulations including FEM or IGA structure modeling with turbulent inflow data but without gusts were carried out.

The CFD simulations were conducted on SuperMUC for a rigid wall-mounted cube exposed to a turbulent boundary layer containing wind gusts to investigate the impact of different gust shapes on the flow structures around the bluff body [3].

Figure 3 exemplarily represents the flow around the rigid cube before and after a gust impact: The gust is injected at the entrance of the domain (top left image of Figure 3). Then, it hits the body and its impulse is redistributed (top right image of Figure 3). This sudden additional impulse modifies the surrounding flow and a large vertical structure is shed from the cube (bottom image of Figure 3). This pure CFD simulation was already quite expensive regarding the required CPU time due to a fine grid consisting of more than 30 million cells required to avoid excessive numerical damping of the gust. Moreover, the whole approaching phase of the gust has to be simulated, which increases considerably the duration of the simulation.

Slightly altering the setup by exchanging the rigid top face of the cube by a flexible membrane, coupled FSI simulations were carried out. An instantaneous snapshot of the flow and the deformed roof are shown in Figure 4. Nearly 2D deformations of the roof in form of a wave traveling downstream are visible resulting from the shedding of large symmetrical flow structures at the front top edge. Since the membrane is not very stiff, the smaller vortices also deform the roof delivering a fully 3D deformation pattern.

In order to simulate a more realistic FSI case related to civil engineering, a thin air-inflated structure of hemispherical shape is considered and exposed to a turbulent boundary layer [6,7]. Parallel to the numerical study, experiments are carried out in a wind tunnel [5]. In the coupled simulation the representation of the FSI interface between the structure and fluid domains has an important impact on the quality of the results. Two coupled simulations, one based on the membrane discretized by FEM and one based on IGA, were run in parallel. Both deliver a very good agreement with the experiment. However, the results obtained by IGA fit better to the measurements due to the more realistic representation of the deformed FSI interface [7].

**On-going Research**

Concerning the gust modeling by injection at the inlet, a huge amount of computational time is consumed by solving the approaching phase of the gust, since the inlet boundary is often far away from the zone of interest. Moreover, strong numerical damping is observed during this phase leading to modifications in the shape and amplitude of the modeled wind gusts. To solve this issue, the gusts have to be directly injected within the computational domain near the zone of interest. In the last years turbulent inflow data were successfully injected into the computational domain using source-term formulations [8]. First attempts are made to extend these source-term formulations for the wind gust injection. Finally, the FSI framework extended by the wind gust modeling has to be applied to applications consisting of flexible membranes.

**Research Team**

Dr.-Ing. Andreas Apostolatos^{2}, Univ. Prof. Dr.-Ing. Kai-Uwe Bletzinger^{2}, Univ.-Prof. Dr.-Ing. habil. Michael Breuer (PI)^{1}, Dr.-Ing. Guillaume De Nayer^{1}, Dr.-Ing. Jens Nikolas Wood^{1}, PD Dr.-Ing. Roland Wüchner^{2}

^{1 }Department of Fluid Mechanics, Helmut-Schmidt-University (HSU), Hamburg, Germany^{2} Chair of Structural Analysis, Technical University of Munich, Germany

**Acknowledgement**

The project was financially supported by the Deutsche Forschungsgemeinschaft under the contract numbers BR 1847/12-2 and BL 306/26-2.

**References**

- Breuer, M., De Nayer, G., Münsch, M., Gallinger, T., Wüchner, R.:
*Fluid-structure interaction using a partitioned coupled predictor-corrector scheme for the application of large-eddy simulation*, J. Fluid Struct., 29, 107-130, (2012). - De Nayer, G., Kalmbach, A., Breuer, M., Sicklinger, S., Wüchner, R.:
*Flow past a cylinder with a flexible splitter plate: A complementary experimental-numerical investigation and a new FSI test case (FSI-PfS-1a)*, Comput. Fluids, 99, 18-43, (2014). - De Nayer, G., Breuer, M., Perali, P., Grollmann, K.:
*Modeling of wind gusts for large-eddy simulations related to fluid-structure interactions*, ERCOFTAC Series, vol. 25, 453-459, DLES11, (2019). - Fischer, M., Firl, M., Masching, H., Bletzinger, K.-U.:
*Optimization of nonlinear structures based on object-oriented parallel programming*, ECT2010: 7th Int. Conf. Eng. Comput. Techn., Valencia, Spain, (2010). - Wood, J.N., Breuer, M., De Nayer, G.:
*Experimental studies on the instantaneous fluid-structure interaction of an air-inflated flexible membrane in turbulent flow*,*J. Fluid Struct.*, 80, 405-440, (2018). - De Nayer, G., Apostolatos, A., Wood, J.N., Bletzinger, K., Wüchner, R., Breuer, M.:
*Numerical studies on the instantaneous fluid-structure interaction of an air-inflated flexible membrane in turbulent flow*, J. Fluid Struct., 82, 577-609, (2018). - Apostolatos, A., De Nayer, G., Bletzinger, K., Breuer, M., Wüchner, R.:
*Systematic evaluation of the interface description for fluid-structure interaction simulations using the isogeometric mortar-based mapping*, J. Fluid Struct., 86, 368-399, (2019). - De Nayer, G., Schmidt, S., Wood, J.N., Breuer, M.:
*Enhanced injection method for synthetically generated turbulence within the flow domain of eddy-resolving simulations*, Computer & Mathematics with Applications, 75(7), 2338-2355, (2018).

**Scientific Contact**

Univ.-Prof. Dr.-Ing. habil. Michael Breuer

Faculty of Mechanical Engineering

Department of Fluid Mechanics

Helmut-Schmidt-Universität (HSU) Hamburg

Holstenhofweg 85, D-22043 Hamburg (Germany)

e-mail: breuer [@] hsu-hh.de

http://www.hsu-hh.de/pfs/

*LRZ project ID: pr53ne*

*November 2019*