Computational engineering for wind-exposed thin-walled structures

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Computational engineering for wind-exposed thin-walled structures 3 sentation) model completed by information concerning material properties and boundary conditions [9]. For the structural part of the analysis system this project database represents a central module. All programs used for the structural simulation have access to the information stored in the database. The geometric model for the uid 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 nite volume technique. Due to extremely high computational requirements, the numerical simulation of the dynamic uid-structure interaction is performed on a high-performance computer [8] in the next step. Thereby the data transfer between the two simulation codes, each running on dierent nodes/processors, is performed via a common geometric model using a suitable coupling interface [1]. Finally, the results can be evaluated and visualized by powerful postprocessors on a workstation or on a PC. 3 Coupling algorithm The uid-structure interaction is described by the structural deformations as response to wind forces, resulting in a modication of the uid ow domain. The coupling is performed by a partitioned solution approach [3]. The Computational Fluid Dynamics (CFD) simulations are performed by a nite volume based code [4] solving the Reynolds-Averaged-Navier-Stokes (RANS) equations using a two-equation k- model. It is adapted to moving grids by an Arbitrary Lagrangian Eulerian (ALE) formulation. For the Computational Structure Dynamics (CSD) the dynamic non-linear structural response (large displacements/small deformations) is described by the equations of motion based on a nite element approach and an implicit time-stepping procedure [11]. For more details concerning the simulation codes we refer to [6]. The time-dependent simulation process is controlled by the coupling algorithm shown in Fig. 3. The solution is based on an iteration Fluid Structure procedure between the CFD and CSD simulation until convergence is reached within each Solver inner iteration time-step. Thereby the nodal loads as input for the CSD Fluid solution outer FSI iteration simulation are computed from wind loads the results of the CFD simulation Solver time step (pressure and wall shear Structural solution stresses). The updated boundary displacements geometry is based on the structural displacements as a result of converged final solution the CSD simulation. In cases of large structural deformations an Fig. 3. Coupling algorithm
4 Ansgar Halfmann et al. under-relaxation of the update of the boundary geometry was found to improve the convergence signicantly. A reduction of the number of iterations within each time-step can be obtained by a predictor-corrector scheme [6]. Informations concerning the data transfer between the dierent numerical grids can be found in [7]. 4 Numerical examples The coupling procedure presented in the previous section was applied to several test cases. In the following the results of two elementary systems will be discussed with respect to dierent parameters for spatial and temporal discretization. Based on this, the coupled application was used to simulate the uid-structure interaction of a complex membrane structure. 4.1 Vertical plate in a resting uid The rst example describes a temporarily loaded rectangular plate clamped at the lower boundary in a closed cavity of a resting uid. The dimensions of the exible plate pictured in Fig. 4 are length/width/thickness = 1.0/0.4/0.06 m. For the material properties a polyester with a modulus of elasticity of E = 2.5 MPa, a Poisson's ratio of =0:35 and a density of S = 2550 kg/m 3 is assumed. The density and dynamic viscosity of the uid are F = 1kg/m 3 and F =0:2 Pa. Using these parameters, a laminar ow is expected. During the rst ve time-steps a constant load is applied in x-direction. After removing the Fig. 4. System conguration load the plate executes oscillations induced by the initial deection damped by the surrounding uid ow. In a rst simulation the inuence of the time-step size was investigated. The uid domain was discretized by 1650 hexaeder elements, yielding 10 quadrilateral elements to describe the interface. For the structural simulation a surface mesh of 8 elements was chosen. Both surface discretizations are shown in Fig. 5. Due to the boundary conditions for the uid simulation the results of the coupled three-dimensional simulation shows a quasi twodimensional behavior. Fig. 6 points out the computed displacement of the upper boundary of the plate for simulations with three dierent time-step sizes. The amplitude of the plate oscillation is damped by theambient uid. For the dierent time-step sizes only small deviations could be identied. Therefore, t 1 =0:025 s was chosen for the following simulations. The dependence of the displacement on dierent spatial discretizations is depicted in Fig. 8. Starting again from a discretization of 1650 hexaeder elements for the uid domain (10 quadrilaterals on the interface, Fig. 7) a
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Computational engineering for wind-exposed thin-walled structures

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