**Principal Investigator:**

Michael Breuer

**Affiliation:**

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

**Local Project ID:**

pr84na

**HPC Platform used:**

SuperMUC of LRZ

**Date published:**

The interaction between a turbulent flow field and light-weight structural systems such as a membranous structures (tents, awnings, roofings, ...) is the main topic of the present research project financially supported by the Deutsche Forschungsgemeinschaft under the contract number BR 1847/12-2. The idea is to develop advanced computational methodologies for this kind of multi-physics problem denoted fluid-structure interaction (FSI). That should allow to predict these complex coupled problems more reliably and to get closer to reality. For this purpose, a cooperation between the Helmut-Schmidt University Hamburg and the University of Technology Munich was established. An original computational methodology based on advanced techniques on the fluid and the structure side has been developed especially for thin flexible structures in turbulent flows. Presently, this methodology is applied to the flow around a flexible, air-inflated hemisphere.

In order to reach the final objective to tackle civil engineering FSI applications involving light-weight structures, it was decided to use highly advanced solvers for both sub-tasks of the problem:

- The fluid solver FASTEST-3D is a highly parallelized finite-volume 3D CFD solver. To simulate turbulent flows, an eddy-resolving scheme relying on a large-eddy simulation (LES) with different subgrid-scale models is applied.
- The structure solver Carat++ [5] developed at TU Munich is a 3D finite-element solver specialized for the prediction of deformations of thin structures.
- The coupling program EMPIRE [7], developed at TU Munich, does the required mapping between the non-matching meshes and the exchange of the data between both codes using MPI.

For the partitioned solution algorithms applied, a strong coupling procedure is recommended in order to guarantee a stable FSI simulation. Thus, a sub-iteration process is required in order to guarantee dynamic equilibrium between the fluid and the structure at each time-step [1].

One of the big challenges of this research project are the CPU-time requirements. To reduce the CPU-time consumption a special coupling procedure for eddy-resolving schemes was developed, which on the one hand guarantees a strong coupling between the flow and the structure and on the other hand maintains the advantageous properties of explicit time-marching schemes typically used for LES [1].

In order to assure reliable numerical simulations for complex configurations, the present methodology was successfully validated on different benchmark cases, i.e., for laminar flows [1] and for turbulent flows using the complementary experimental and numerical benchmark cases FSI-PfS-1a and FSI-PfS-2a [3,4,9,10]. The next step is to evaluate the FSI framework on a more complex geometry to get stronger three-dimensional FSI effects. For this purpose, a real structure from civil engineering is considered, i.e., a wall-mounted air-inflated membranous hemisphere in a turbulent boundary layer.

In a first step, LES predictions were carried out for a rigid wall-mounted hemisphere exposed to a turbulent boundary layer to investigate the turbulent flow without any structural deformations [2,8,11]. Figure 1 depicts a snapshot of the instantaneous flow field including the arising complex flow structures in the wake. A good agreement with corresponding measurements was found.

In order to simulate the FSI case of the air-inflated hemisphere, the structure is considered as a flexible thin pre-stressed membrane with a constant inner pressure. The FSI framework mentioned above combined with synthetically generated inflow turbulence for LES and with a novel hybrid mesh adaption procedure [6] is applied. First numerical results are very encouraging with respect to corresponding experimental measurements [8] carried out in the wind tunnel at PfS Hamburg.

Figure 2 depicts an instantaneous snapshot of the deformed membrane and the corresponding flow field at Re = 50,000. In order to visualize the rather small deformations, the displacement values are magnified by a factor of 15. The largest deformations are found at the stagnation region. In this area, distinct impacts of incoming turbulent vortices on the flexible structure are clearly visible. Strong wave-like deformations are observed on the leeward side of the hemisphere, resulting from the interaction of vortical structures such as the Kelvin-Helmholtz vortices with the membrane.

In the on-going work, these oscillations of the FSI interface will be compared with the different characteristic frequencies of the coupled problem (vortex shedding frequencies and eigenfrequencies of the membranous structure) in order to better understand the interaction between the fluid flow and the structural deformations.

**References:**

[1] 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).

[2] Breuer, M., De Nayer, G., Wood, J.N.: Complementary experimental-numerical investigation of the flow past a rigid and a flexible hemisphere in turbulent flow: Part II: Numerical simulations. Proc. 24. Gala-Fachtagung “Lasermethoden in der Strömungsmesstechnik”, BTU Cottbus-Senftenberg, Sept. 6-8, (2016).

[3] 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), Computer & Fluids, 99, 18-43, (2014).

[4] De Nayer, G., Breuer, M.: Numerical FSI investigation based on LES: Flow past a cylinder with a flexible splitter plate involving large deformations (FSI-PfS-2a), Int. J. Heat Fluid Flow, 50, 300-315, (2014).

[5] 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).

[6] Sen, S., De Nayer, G., Breuer, M.: A fast and robust hybrid method for block-structured mesh deformation with emphasis on FSI-LES applications, Int. J. Numer. Meth. Eng., accepted, (2016).

[7] Sicklinger, S., Belsky, V., Engelmann, B., Elmqvist, H., Olsson, H., Wüchner, R., Bletzinger, K.-U.: Interface Jacobian-based co-simulation, Int. J. Numer. Meth. Eng., 98 (6), 418-444, (2014).

[8] Wood, J.N., De Nayer, G., Schmidt, S., Breuer, M.: Experimental investigation and large-eddy simulation of the turbulent flow past a smooth and rigid hemisphere, Flow Turbul. Combust., 97 (1), 79-119, (2016).

[9] http://qnet-ercoftac.cfms.org.uk/w/index.php/UFR_2-13

[10] http://qnet-ercoftac.cfms.org.uk/w/index.php/UFR_2-14

[11] http://qnet-ercoftac.cfms.org.uk/w/index.php/UFR_3-33

**Scientific Contact:**

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

Professur fuer Stroemungsmechanik (PfS)

Institut fuer Mechanik, Helmut-Schmidt-Universitaet Hamburg

Holstenhofweg 85, D-22043 Hamburg (Germany)

e-mail: breuer@hsu-hh.de

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