a geometric model for fluid-structure interaction of wind-exposed structures

BAUINGENIEUR− UND VERMESSUNGSWESENTECHNISCHE UNIVERSITÄT MÜNCHEN

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A Geometric Model forFluid-Structure Interaction of

Wind-Exposed Structures

Ansgar Halfmann, Ernst RankLehrstuhl fur Bauinformatik, TU Munchen

Markus Gluck, Michael Breuer, Franz DurstLehrstuhl fur Stromungsmechanik,

Universitat Erlangen-Nurnberg

October 2001

TECHNISCHEUNIVERSITÄTM Ü N C H E N

Prof.Dr.rer.nat. Ernst RankLehrstuhl fur Bauinformatik

Fakultat fur Bauingenieur- und VermessungswesenTechnische Universitat Munchen

Arcisstr. 21D-80290 Munchen

email: [email protected] Telefon: int++49 (89) 289 23048www: http://www.inf.bauwesen.tu-muenchen.de/ Telefax: int++49 (89) 289 25051

A Geometric Model forFluid-Structure Interaction of

Wind-Exposed Structures

Ansgar Halfmann, Ernst RankLehrstuhl fur Bauinformatik, TU Munchen

Markus Gluck, Michael Breuer, Franz DurstLehrstuhl fur Stromungsmechanik,

Universitat Erlangen-Nurnberg

October 2001

The Ninth International Conference on Computing in Civil and Building Engineering April 3-5, 2002, Taipei, Taiwan

Halfmann, Rank, Glück, Breuer and Durst

A GEOMETRIC MODEL FOR FLUID-STRUCTURE INTERACTION OF WIND-EXPOSED STRUCTURES

A. Halfmann1, E. Rank1, M. Glück2, M. Breuer2 and F. Durst2 1Lehrstuhl für Bauinformatik, Technische Universität München, München, Germany

{halfmann, rank}@bv.tum.de 2Lehrstuhl für Strömungsmechanik, Universität Erlangen-Nürnberg, Erlangen, Germany

{glueck, breuer, durst}@lstm.uni-erlangen.de

Abstract

In this paper a computer aided simulation approach for fluid-structure-interaction of wind-exposed structures is presented. In the center of our software architecture is the geometrical model, from which a finite element mesh for the structure and a finite volume mesh for the fluid are derived. The interaction of fluid and structure is effected by wind-induced vibrations and causes large deformations of the structure. A powerful simulation tool is provided by coupling two codes developed for flow simulation and structural dynamics by an fully implicit coupling algorithm. Results of three-dimensional simulation of fluid-structure-interaction for real-life problems will be presented.

Introduction

During the last few years much progress has been achieved to integrate analysis and design in civil engineering. The computer aided design process starts by setting up a geometric model being used for the definition of all structural properties as well as for the loads on the construction. From this geometric model a computational model is derived as the basis for the following dimensioning of the construction. This computer aided engineering process has to efficiently support the primary goals of any civil engineering design, i.e. the development of constructions satisfying the requirements of safety during their whole lifetime, resisting all expected influences they might be exposed to. Considering for example light textile structures, the most demanding engineering task is to dimension the construction so that it will resist wind loads. If simplified, conservative load assumptions for this pressure distribution are made the structures may be strongly over-designed. Yet, also an under-design with the danger of a collapse of the structure may result from this simplified procedure, as the mutual influence of neighboring constructions could change the wind pressure field dramatically. Therefore todays standard of practice are time-consuming and costly experiments in wind tunnels. A model of the construction is considered and wind pressure fields on its surface are measured to be used for later numerical structural analysis. One of the major drawbacks of this mixed computational and experimental approach is the difficulty to quickly change the geometry of the model construction for the wind tunnel experiment. Therefore it would be highly desirable to have available a 'numerical wind tunnel', being directly integrated in the civil engineering design and analysis process, and making it possible, to investigate a structure also under the influence of neighboring constructions. Several steps in this direction have been performed by the authors in a joint research project during the past years, Glück et. al. (2000), Halfmann et al. (2001).


System Architecture

The determination of wind loads for lightweight structures leads to a coupled problem. Thereby the interaction of structural (CSD) and fluid (CFD) simulation is described by the structural deformation as response to wind forces, resulting in a modification of the fluid flow domain. Powerful numerical simulation techniques have been established in structural engineering as well as in fluid mechanics so that the software structure shown in Figure 1 is influenced by the idea of a loose coupling strategy based on highly specialized and well evaluated simulation codes, each developed for the special field of the interacting system.The simulation process starts from a structural model defined using a classical CAD en-vironment on a PC (Rank, 2000). All geometric information is stored in a database describing a b-rep (boundary representation) model completed by information concerning material properties and boundary conditions. The geometric model for the fluid dynamic part is also derived from the CAD model completed by boundary conditions and discretized as a block-structured three-dimensional grid being adequate to the finite volume technique. Due to the extremely unbalanced computational requirements the CFD part of the numerical simulation of the dynamic fluid-structure interaction is performed on a high-performance computer where-as the CSD simulation can also be carried out on a workstation. The data

Fig. 1: Software structure of the coupled application

transfer between the two simulation codes is performed via a neutral geometric model using a suitable coupling interface (Ahrem et al., 2000). Finally, the results can be evaluated and visualized by powerful postprocessors on a workstation or PC.

Coupling Algorithm

The coupling of the two simulation codes is performed by a partitioned solution approach. Therefore the finite volume based CFD code (Durst and Schäfer, 1996) solving the Reynolds-Averaged-Navier-Stokes (RANS) equations is adapted to moving grids by an Arbitrary Lagrangian Eulerian (ALE) formu- lation. The non- linear structural response is described by the equations of motion based on a finite element approach for thin walled structures and an implicit time-stepping procedure (ASE, 2001). The coupling algorithm controlling the iterative solution is shown in Figure 2. Thereby the solution is based on an iterative procedure between the CFD and CSD simulation subdivided in iter-

Fig. 2: Coupling algorithm


ations for the fluid structure interaction (FSI) and the time discretization. Within the FSI iterations the nodal loads as input for the CSD simulation are computed from the results of the CFD simulation and the updated boundary geometry is based on the structural displacements as a result of the CSD simulation. The FSI iterations are proceeded until convergence is reached within each time-step of a dynamic simulation. A reduction of the number of required FSI iterations can be obtained by a predictor-corrector scheme. For more detailed information concerning the simulation codes, the coupling algorithm and the data transfer between different numerical grids see Glück et al. (2000) and Halfmann et al. (2000).

Quasi Static Simulations

Dynamic simulations of fluid-structure interaction require extremely high computational resources. Due to this the practical use of such simulations is still very limited. Reducing the coupling algorithm to the FSI iterations only, as it is marked by the light gray area in Figure 2, leads to a simplified quasi static simulation which takes into account the structural response onto the fluid domain. The integration of geometric model and numerical simulation as it isdescribed in our system architecture makes it possible to combine these quasi static simulations with an adaptive cycle (Figure 3). Based on the results of a first simulation on a coarse mesh the discretization error of the structural problem can be estimated by a ZZ-error estimator (Zienkiewicz and Zhu, 1991). The knowledge about the size and distribution of the discretization error leads to a mesh density function as input for the mesh gene-

Fig. 3: Adaptive cycle

rator creating a finite element mesh adapted to the desired element sizes. Performing these steps in a loop describes the adaptive cycle for generating optimized meshes. It should be noted, that in each cycle the complete quasi static fluid-structure- interaction and not only the structural problem is solved.

Numerical Results

Geometric Model

Figure 4 shows a screenshot of the CAD-environ-ment representing the geometric model of a real-life structure as a starting point for a simulation. The shape of the structure is a result of a form-finding process as described in Bellmann (1998) and specifies a prestressed textile roof being positioned in front of an office building. The structure is 24 m long, shows a width between 3 m and 8.5 m and a height of 5.76 m – 10.28 m. The fiberglass synthetics has a thickness of 1.5 mm, a modulus of elasticity of E = 3000 MPa and a shear modulus of G = 1000 MPa.

Fig. 4: Geometric model of a tent roof


Quasi Static Simulations

Based on this geometric model the first example shows the results of a quasi static simulation as described in the previous section. Thereby the tent roof is loaded by a uniform wind load of 40 m/s in positive x-direction. The coarse mesh used for the first simulation is pictured in Figure 5. Equivalent nodal loads as input and the membrane forces as a result of the structural simulation are pictured in Figure 6 and Figure 7.

Fig. 5: Initial mesh (167 nodes, 87 elements)

Fig. 6: Nodal loads

Fig. 7: Membrane forces

The results of the error estimation in terms of equivalent error forces are shown in Figure 8 and point out regions where mesh refinement is reasonable. Whereas the results based on the initial mesh (Figure 5) shows a estimated error of 2 % in energy norm the refined mesh pictured in Figure 9 as a result of a few cycles in the adaptive loop reduces it to 0.05%.

Fig. 8: Error forces

Fig. 9: Adaptively refined mesh (3149 nodes, 2961 elements)

Dynamic simulations

Taking now into account the time discretization, as marked by the dark gray area in Figure 2, the quasi static simulation can be extended to a real dynamic simulation. The structure is loaded by a complex approaching flow composed of the superposition of a uniform flow and a time variable wind gust as shown in Figure 10. In addition to the structural response of the tent roof in terms of the maximal displacement shown in Figure 11 the damping of the surrounding fluid is pictured in Figure 13, when considering the displacement in z-direction of the points of evaluation (see Figure 12).


Fig. 10: Wind gust

Fig. 11: Max. displacement of the tent roof

Fig. 12: CSD mesh (1409 nodes, 1311elements)

Fig. 13: Displacement in z-direction of several points

Reducing now the prestressing in the membrane from 3 kN/m2 to 2 kN/m2 effects no significant change in the maximal displacement of the tent roof. For time step 62, i.e. shortly before maximum deflection of the construction, the relative difference of the displacement in z-direction, refer- ring to the maximal displacement of Figure 11, is below 0.5 %. This shows that the lower prestressing level is already suffi- cient for a stable construction.

Fig. 14: Difference of displacement in z-direction


Conclusions

The simulation of fluid-structure interaction for wind-exposed lightweight structures based on a system architecture attaching great importance to the geometric model of the structure is presented in this paper. Embedding the partitioned solution approach in the civil engineering design process offers a lot of possibilities indicated by the examples. Thereby investigations whether a structure is also stable using a lower prestressing level or not, require only minor modifications of the numerical model. Further developments with regard to more elaborated turbulence modeling and verification with experimental wind tunnel data are necessary to advance the simulation environment to a practically used engineering tool.

Acknowledgements

The authors gratefully acknowledge the support by the Bayerische Forschungsstiftung in the Bavarian Consortium of High-Performance Scientific Computing, FORTWIHR III, and the funding of FLUSIB by the Bavarian State Ministery of Education, Religion, Science and Arts in the Competence Network for Technical, Scientific High Performance Computing in Bavaria, KONWIHR

References

Ahrem, R., M.G. Hackenberg, P. Post, R. Redler and J. Roggenbuck (2000), “MpCCI – Mesh Based Parallel Code Coupling Interface”. Institute for Algorithms and Scientific Computing (SCAI), GMD, http://www.mpcci.org/.

ASE (2001), “ASE Manual”, SOFiSTiK AG, München.

Bellmann, J. (1998), “Membrantragwerke und Seifenhaut – Unterschiede in der Formfindung”, Bauingenieur, 3/98, 118-123.

Durst, F., M. Schäfer (1996), “A Parallel Block-Structured Multigrid Method for the Prediction of Incompressible Flows”, International Journal of Numerical Methods for Fluids, 22, 549-565.

Glück, M., M. Breuer, F. Durst, A. Halfmann and E. Rank (2000), “Computation of Fluid-Structure Interaction on Lightweight Structures”, Proceedings of the 4th International Colloquium on Bluff Body Aerodynamics & Applications, Bochum, Germany, September 11-14, 2000. To appear in Journal of Wind Engineering and Industrial Aerodynamics

Halfmann, A., E. Rank, M. Glück, M. Breuer and F. Durst (2000), “A Partitioned Solution Approach for the Fluid-Structure Interaction of Wind and Thin-Walled Structures“, Proceedings of IKM 2000, Weimar, Germany, June 22-24, 2000.

Halfmann, A., E. Rank, M. Glück, M. Breuer, F. Durst, J. Bellmann and C. Katz (2001), “Computational Engneering for Wind-Exposed Thin-Walled Structures“, Proceedings of the 3rd International FORTWIHR Conference 2001 , Erlangen, Germany, March 12-14, 2001. Will be published in High-Performance Scientific and Computing Engineering, Erlangen 2001, Lecture Notes on Computational Science and Engineering, Springer Verlag, Germany.

Rank, E., A. Halfmann, M. Rücker, C. Katz and S. Gebhard (2000), “Integrierte Modellierungs- und Berechnungssoftware für den konstruktiven Ingenierbau: Systemarchitektur und Netzgenerierung”, Bauingenieur, Februar 2000, 60-66.

Zienkiewicz, O.C. and J.Z. Zhu (1991), “Adaptivity and mesh generation”, International Journal of Numerical Methods in Engineering, 32, 783-810.

a geometric model for fluid-structure interaction of wind-exposed structures

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