Computation of Wind Structure Interaction on Tension Structures

7/25/2019 Computation of Wind Structure Interaction on Tension Structures

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Journal of Wind Engineering

and Industrial Aerodynamics 89 (2001) 13511368

Computation of fluidstructure interaction on

lightweight structures

M. Gl .ucka,*, M. Breuera, F. Dursta, A. Halfmannb, E. Rankb

a

Lehrstuhl f.ur Str

.omungsmechanik, Universit

.at Erlangen-N

.urnberg, Cauerstrasse 4,D-91058 Erlangen, Germany

b Lehrstuhl f.ur Bauinformatik, Technische Universit .at M.unchen, D-80290 M.unchen, Germany

Abstract

In this paper a numerical approach of a time-dependent fluid-structure coupling for

membrane and thin shell structures with large displacements is presented. The frame algorithm

is partitioned, yet fully implicit because of a predictor-corrector scheme being applied to the

structural displacements within each time step. In order to reach a high modularity, two

powerful codesF

one of them highly adapted to flow simulation and the other one to structuraldynamicsFrun simultaneously and exchange fluid loads and displacements within each fluid-

structure iteration. The finite volume based CFD code is able to compute three-dimensional,

incompressible, turbulent flows. The structural simulations are performed using a finite element

program including algorithms for geometrically and physically non-linear problems.

In this paper the coupled algorithm will first be applied to some geometrically simple test

cases to validate the interaction scheme. Then a real-life textile tent structure of glass-fibre

synthetics with a complex shape is taken into account. This example was investigated under

turbulent flow conditions at a high wind speed leading to a steady deformation state. r 2001

Elsevier Science Ltd. All rights reserved.

1. Introduction

The interaction of fluid and structure plays an important role in many civil

engineering problems. Examples are besides suspension bridges, tall buildings,

towers, oil platforms and power lines also lightweight membrane structures used as

wide area roofage such as awnings, large umbrellas or tent roofs.

*Corresponding author. Tel.: +49-9131-8529501/2; fax: +49-9131-8529503.E-mail addresses:[email protected] (M. Gl.uck), [email protected] (M. Breuer),

[email protected] (F. Durst), [email protected] (A. Halfmann), [email protected]

(E. Rank).

0167-6105/01/$ - see front matter r 2001 Elsevier Science Ltd. All rights reserved.

PII: S 0 1 6 7 - 6 1 0 5 ( 0 1 ) 0 0 1 5 0 - 7


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The lack of knowledge about possible fluid-structure interaction effects led to

heavy catastrophes in the past (e.g., the collapses of the Tay Bridge in Scotland in

1879, of the Tacoma Bridge near Seattle in 1948 and of three tall cooling towers in

Ferrybridge/England in 1965). Today, the basic wind induced effects such asgalloping, buffeting, etc. are well-known. But nowadays, buildings become more and

more wind sensitive because of the trend to lightweight constructions. One of the

most spectacular buildings of this kind is the wired textile dome in Atlanta which

canopies a stadium for 70,000 spectators with a span of 240 m : To determine exactwind loads of such buildingsFespecially for complex geometries or time-dependent

external flowsFexpensive experiments in wind tunnels or semi-empirical methods

can be applied.

In principle there are the following possibilities for fluidstructure interactions:

1. The wind load on the structure causes a steady deformation state.

2. The fluid flow leads to a time-dependent movement of the structure, which is

caused by one of the following effects:

(a) A transient wind field exists even far away from the structure (e.g., change in

wind direction or in strength, sudden gust of wind).

(b) Due to the shape of the structure, the flow becomes time-dependent in the

wake of the building (e.g., generation of a von K !arm!an vortex street past

bluff bodies impigned with a constant wind).

(c) Combination of (a) and (b).

Concerning the constructions mentioned above, a lot of programs are available in

Computational Structure Dynamics (CSD) being able to compute the stresses and

displacements resulting from wind loads. The wind forces on the structure can be

predicted byComputational Fluid Dynamics(CFD). Yet, only a few approaches exist

to simulate coupled fluid-structure problems in civil engineering.

In this paper a partitioned simulation technique for membrane and thin shell

structures is investigated. Fig. 1 shows an example of a textile roof. A similar canopy

was built in front of the entrance to the Max-Planck Institute for Cellular Biology in

Dresden.

In the present study the CFD code FASTEST-3D[1] developed by the Institute ofFluid Mechanics, Erlangen, and the CSD code ASE[2] provided by SOFiSTiK AG

have been modified and coupled by MpCCI [3].

Examples for the cases 1 and 2(a) of possible fluid-structure interactions will be

shown in Section 3.

2. Physical models and numerical approaches

2.1. Fluid dynamics

Viscous fluid flow is governed by the NavierStokes equations expressing the

conservation of mass, momentum and energy. For turbulent flows the Reynolds-

M. Gl.uck et al. / J. Wind Eng. Ind. Aerodyn. 89 (2001) 135113681352


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averaged form of the NavierStokes equations closed by a two-equation turbulence

model is applied in the present investigation.

The general transport equation in a finite volume notation reads as follows:d

dt

ZV

rF dV

ZS

rUUgF GFgrad F n dS

ZV

sFdV: 1

For an incompressible flow with constant fluid properties as assumed in this study

this equation is solved forF 1 (continuity equation),F fU; V; Wg(momentumequations), and forF fk; eg(in case of turbulent flows being treated by a standardke model). For each of these single equations the diffusion coefficient GF and the

source term sF have to be chosen according to F [1].

In case of time-dependent moving meshes, the transport velocity is composed of

the Eulerian or absolute fluid velocity U reduced by the grid velocity Ug: To ensurethe conservation principle, the space conservation law (SCL) has to be fulfilled for

each control volume (CV):

d

dt

ZV

dV

ZS

Ug n dS0: 2

According to Demird$zi!c and Peri!c [4] one can avoid the direct calculation of the

grid velocities by replacing them by the mass fluxes through the CV faces (mesh

fluxes) which result from the motion of the CV faces during the time step. The

convective term in Eq. (1) containing the grid velocity can be discretized as follows:ZS

rFUg n dSEX

c

rcFcdVc

Dt; c fw; e; s; n; b; tg: 3

Fig. 1. Geometry of a tent roof in front of an office building.

M. Gl.uck et al. / J. Wind Eng. Ind. Aerodyn. 89 (2001) 13511368 1353


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This means that the solution of each transport equation is based on the relative

fluxes, which are the differences between the fluxes through a CV face caused by fluid

motion reduced by the mesh fluxes. Based on this formulation the grid velocitiesUg

are no longer required for the internal flow region but they have to be knownexplicitly at moving impermeable walls. This approach is the so-called Arbitrary

Lagrangian Eulerian (ALE) formulation [4]. Furthermore, the time-dependent term

on the left-hand side of Eq. (1) has to be treated in a special way according to first or

second order of accuracy in case of moving grids. It has to be considered, that not

only the transported quantity F but also the cell volume DVis time-dependent.

As mentioned above the CFD calculations were performed with FASTEST-3D.

This is an incompressible, unsteady, three-dimensional finite volume code, which is

able to simulate laminar as well as turbulent flows.

The code is based on non-staggered, block-structured grids and has recently been

adapted to moving meshes. The terms for changing cell volumes, flux corrections and

wall velocities are available for all transported scalars such as temperature,

concentrations, and the turbulent quantities k and e: They are discretized by a fullyimplicit scheme of second-order accuracy in time, consistent with the other time-

dependent terms.

Concerning the spatial discretization, an upwind scheme (UDS) or a central-

difference scheme (CDS) can optionally be used or combined based on a deferred

correction approach. In the present study CDS was applied, if possible.

The ALE extension of FASTEST-3D was verified at several test cases. One

example concerns the flow in a channel with a moving obstacle, which wasexperimentally investigated by Pedley and Stephanoff [5] and calculated by Ralph

and Pedley [6], Demird$zi!c and Peri!c [4], and others. The results coincide very well

with the measurements and the other numerically predicted data.

2.2. Structural dynamics

The characteristics of thin walled structures can be specified by state variables

acting in the middle plane of the structure. The dynamic non-linear response of

membrane and thin shell structures is described by the equation of motion

M.uDuCu Ft; 4

where M is the mass matrix, D the damping matrix representing the inner or

structural damping of the structure and C the stiffness matrix. Ft characterizes

the load acting on the structure caused by the fluid (pressure and shear stress). The

dynamic response is described by the displacement u; the velocity u; and theacceleration .u: It should be noted that any fluid damping is included on the right-hand side of Eq. (4) and not in the damping matrix D:

The structural simulations were performed using the finite element program ASE

[2]. In addition to geometrically non-linear effects such as large displacements/small

deformations, non-linear material properties can be taken into account. The elementformulations are completed by special extensions adapted to the requirements in civil

engineering [2].



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The time-dependent problem is solved by applying a NewmarkWilson approach

[7]. Assuming a linear acceleration within a time step, this scheme is unconditionally

stable and second-order accurate in time for linear and first-order for non-linear

problems [8].

2.3. Fluid-structure coupling

Geometrical modelingandgrid definition: In the design process for civil engineering

constructions the geometrical model of the structure plays an important role.

Therefore, it is also the central point in our software system architecture (see

Fig. 2(a)). All geometrical information is derived directly from given CAD data and

stored in a database describing a b-rep (boundary representation) model completed

by information concerning material properties and boundary conditions.

For membrane structures it is also possible to start from an initial geometry

and to determine the surface geometry under dead load in a so-called form

finding process [9]. In a next step the surface of the structure is discretized

by an unstructured quadrilateral mesh (see Fig. 3) generated by an automatic

mesh generator [10]. The input data for the CFD grid generator, used to create

a three-dimensional block-structured hexahedral grid, is also derived directly

from the geometrical model. Fig. 4 shows an example of the corresponding

surface grid of the tent. The CFD code treats the structure as an infinitely thin

obstacle, whereas the real thickness is taken into account for the structural

simulation.Couplingalgorithm: Both, the CSD code ASEas well as the CFD codeFASTEST-

3D, are highly adapted to their specific field of application providing many special

features. To preserve these advantages and to realize an effective coupling algorithm

apartitionedsolution approach [1114] is performed. The simulation is based on an

iterative frame algorithm integrating both codes developed fully independently from

each other in an implicit time-stepping procedure (see Fig. 2).

Each simulation code runs on its own processor(s) after being spawned by a main

process. The interprocess communication is supported by the MPI Library. Caused

by the large difference in the number of grid points (e.g., 10 6 control volumes for

CFD and 103

finite elements for CSD), the computational effort for the CFD part ismuch higher than for the CSD part. However, the high vectorization rate of

FASTEST-3D allows efficient computations on vector-parallel machines (e.g.,

Fujitsu VPP700, Hitachi SR8000) and the use of multiple processors based on the

domain decomposition approach.

The bilateral data exchange between CSD and CFD is managed using the MpCCI

coupling interface [3]. The exchange of element- and node-based variables between

two non-matching grids (FE vs. FV) is supported by a neutral geometric model.

Although both grids describe the same surface, their nodes do not coincide.

Therefore some mutual interpolation is necessary.

For the transfer of pressure and shear forces from CFD to CSD, a conserva-tive interpolation according to Farhat et al. [15] is used, ensuring that the load

resultants on both grids are exactly the same. The disadvantage of this method is



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Solver

Solver time step

outer FSI iteration

inner iteration

converged final solution

Fluid solution

Structural solution

Fluid Structure

wind loads

displacements

(a)

(b)

Fig. 2. Scheme of the fluidstructure coupling: (a) software system architecture, (b) detailed overview of

the partitioned coupling algorithm.

Fig. 3. Unstructured CSD grid on the tent roof.



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that in case of a coarse source grid and very fine target grid, the loads are distributed

in a non-physical way. However, usually the CFD mesh is finer than the CSD mesh

anyway.

The calculated displacement vectors of the CSD nodes are transferred to the CFD

nodes by using a bilinear interpolation.

The coupling algorithm controlling the time-stepping procedure in the iterative

solution based on Ref. [16] is shown in Fig. 2(b). A similar approach extended by an

optimized relaxation scheme is used by Ramm and Wall [17].

The outer loop describes the time discretization of the problem. Within each

time step outer iterations between the CFD and CSD simulation are performed

until convergence is reached. Thereby, the threshold for the residual structural

displacements is usually 10

4

to 10

3

of the maximum amplitude of oscillationin case of dynamical fluid-structure interactions. The load for the CSD simulation

is computed from the pressure and shear stresses as a result of the CFD compu-

tation and the boundary geometry is modified by the structural displacements

computed by the CSD simulation. Significant structural deformations can be

taken into account by an under relaxation of the boundary geometry. To reduce

the number of outer iterations within each time step of the dynamic

coupling procedure, this strategy is extended by a predictor-corrector scheme.

At the beginning of each time step the boundary geometry is estimated from the

results of previous time steps. Based on this geometry a CFD simulation is

performed followed by a CSD computation which corrects the predicted interfacegeometry used in the next fluid-structure interaction (FSI) iteration as shown in

Fig. 2(b).

Fig. 5 shows the total number of inner CFD iterations needed for the simulation

of the oscillation of a flexible plate (see Section 3.1.1). Compared with the original

formulation, the required number of iterations could be decreased by 25% taking

into account the boundary geometry of the last two time steps (first order in time)

and even by 45% considering the geometry of the last three time steps (second order

in time).

Adaption of the CFD mesh: During each outer fluidstructure iteration the finite

volume mesh of the fluid domain has to be adapted to the new position of theboundaries. This is done in special routines using algebraic methods (linear

distortion in the inner region of a grid block, transfinite interpolation or use of

Fig. 4. Block-structured CFD grid on the tent roof.



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special problem-adapted higher-order polynomials to generate the block faces in the

vicinity of the distorted structure). An example for such a distorted mesh around a

flexible vertical plate is given in Fig. 6.

3. Numerical applications

The coupling procedure presented in the previous sections was applied to several

test cases. Four of them will be discussed here. The first three examples have

relatively simple geometries. They were chosen to do some first time-dependent,

laminar computations. The fourth case represents a real-life civil engineering

application under steady turbulent flow conditions. While the first two cases consider

a quasi 2D flow, the third and fourth example refer to 3D flows and structures.Structural damping was not taken into account in the present study, which

corresponds to D 0 in Eq. (4).

Time step

CFD

iterations

0 10 20 30 40 500

20000

40000

60000

80000

100000

O( t), without estimation

O( t), with estimation

O( t ), without estimation

O( t ), with estimation

Fig. 5. Total number of required inner CFD iterations with and without geometrical estimation.

Fig. 6. 2D-cut through a 3D initial mesh consisting of four blocks (left) and distorted mesh (right) around

a flexible vertical plate using a polynomial of third order to generate the block interface upwardly adjacent

to the plate and linear distortion of the inner grid points inside the blocks.



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3.1. Vertical plate

For the first two test cases the same geometry but different boundary conditions

and different material properties have been used. In Section 3.1.1 a flexible plateexecutes damped oscillations caused by an initial excursion in a closed cavity of

resting fluid. In Section 3.1.2 a plate is suddenly loaded by a constant incoming flow

and oscillates as long as it reaches a steady deformation state.

3.1.1. Oscillations of a plate in resting fluid

Description of the test case: A thin flexible plate with a length ofL 1:0 m and awidth ofW 0:4 m is clamped at the lower boundary. The cross-section of the plateand the ambient fluid domain is depicted in Fig. 7. The coupled simulations were

performed in three dimensions. Yet, because of the symmetry boundary conditions

in z-direction the flow as well as the plate show a two-dimensional behavior.

The flexible plate has a thickness of dS 60 mm; a modulus of elasticity ofE2:5 MPa; a Poissons ratio ofn 0:35; and a density ofrS 2550 kg=m

3: Thefluid has a density of rF 1 kg=m

3: Three different dynamic viscosities(mF;1 0:2 Pa s; mF;2 1:0 Pa s; and mF;3 5:0 Pa s) were examined, resulting in aflow being in the laminar range.

A time increment ofDt 0:1 s was used for the coupled simulations. During thefirst five time steps a constant load was impressed to excite the plate. From the sixth

time step on the plate is loaded by the reacting pressure and shear forces resultingfrom the fluid flow.

Results of the test case: Fig. 8 shows the x-coordinate of the moving free edge of

the flexible plate (point B). The higher the fluid viscosity is, the faster the plate is

damped and reaches its initial state again.

The displacements xB for the case ofmF;1 0:2 Pa s and the resultant of the fluidload in x-direction Fx are depicted in Fig. 9. Fig. 10 shows the results of a fast

Fourier transformation (FFT) applied to these two data sets. One can recognize that

the displacement curve shows almost harmonic behavior, because the influence of the

first eigenfrequency dominates, while the load is also influenced by higher

eigenmodes.

Fig. 7. Geometry of the test case 3:1:1 (not to scale).



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t [s]

xB

[m]

0 10 20 30 40 50-0.2

-0.1

0

0.1

0.2

F= 0.2 Pa s

F= 1.0 Pa s

F= 5.0 Pa s

Fig. 8. Displacements of the free edge of an oscillating flexible plate for three different fluid viscosities.

t [s]

xB

[m],F

x[N]

0 5 10 15 20 25-0.6

-0.4

-0.2

0

0.2

0.4

0.6Displacement x

B

Fluid load Fx

Fig. 9. Displacement of the free edge of the plate and fluid load in x-direction for the case of

mF;1 0:2 Pa s:

f [Hz]

Intensity

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5

0

0.1

0.2

0.3

0.4

Displacement

Fluid load

f4= 1.85 Hz f6= 4.93 Hz

f1= 0.31 Hz

Fig. 10. Results of a FFT concerning the data sets in Fig. 9.



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The same phenomenon is described by Gasch and Knothe [18], who compared the

displacement and the moment of the clamped support of a beam performing bending

oscillations.

The plate is excited at its first, fourth, and sixth eigenfrequency. The eigenmodes inbetween, which have e.g. torsional shape, are not stimulated owing to the quasi 2D

flow with symmetry boundary conditions in the z-direction.

Assuming a simplified model of a clamped beam, the first eigenfrequency can be

obtained analytically according to Ref. [19] as

f1 0:5595 1

L2

ffiffiffiffiffiffiffiffiffiffiEI

m=L

s ; 5

with the polar moment of inertia I and the total mass m: The theoretical value off1 0:30 Hz is approximately equal to the first peak in Fig. 10.

3.1.2. Oscillations of a plate in suddenly starting fluid flow

Description of the test case: A sketch of the test case is shown in Fig. 11. The

geometry is the same as before. However, in contrast to Section 3.1.1, the material of

the plate is not academic but corresponds to polyester according to DIN 16 946 with

a modulus of elasticity ofE3500 MPa;a Poissons ratio ofn 0:32;and a densityof rS 1200 kg=m

3: The thickness of the plate varied between the simulations(dS;1 3 mm; dS;2 4 mm; and dS;3 10 mm). The fluid has a density of rF

1 kg=m3

; and a dynamic viscosity ofmF 0:2 Pa s: The resulting Reynolds numberis Re UNLrF=mF 50:

The fluid domain is open with an inlet (left boundary), an outlet (right boundary),

and a symmetry boundary condition at the top. At the beginning of the coupled

simulation the fluid flow suddenly starts to move and adopts immediately a constant

inflow velocity of UN10 m=s: As a consequence the structural oscillations areinduced by the saltus of the fluid velocity. The response of the plate was investigated

in the present study.

The time increment was Dt 0:01 s in order to reach approximately 30 time stepsper oscillation period, which was found to be a necessary number for good accuracy.

Fig. 11. Geometry of the test case 3:1:2 (not to scale).



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Results of the test case: Fig. 12 indicates a comparison of steady-state and time-

dependent simulations. Due to the low Reynolds number the deformation state of

the plate and also the flow field eventually become time-independent after the sudden

velocity saltus. Therefore, it is possible to do only a steady fluid-structure simulation,

if only the final state of flow and structure is of interest. As a consequence only

several outer FSI iterations but no time steps are performed (according to Fig. 2(b)).

Theoretically, the steady and the unsteady results must coincide after a sufficientlylong simulation time. Three different CFD meshes were examined using 1650, 13200,

and 105,600 cells, respectively. The outcomes were deviations in the displacements of

10.8% for the coarsest, 2.4% for the medium and 0.9% for the finest grid. The

reason for this behavior is given by the specific formulation of the mass fluxes within

the SIMPLE algorithm on non-staggered grids leading to slightly different

approaches for steady and time-dependent simulations.

As a result of this investigation it can be concluded, that good agreement between

the results of stationary and instationary simulations are only obtained on relatively

fine meshes.

A similar study with variable mesh size for the structural simulation showed, thata coarse mesh of only 18 elements on the plate yields sufficient accuracy.

Fig. 13 points out the influence of the thickness dS of the flexible plate. For a

constant outer load the displacement u is inversely proportional to the polar inertia

moment of the cross-section of the plate yielding uBd3S :Yet, concerning the presentcomparison, the outer load is not constant, because the flow resistance decreases,

when the plate is bent more and more caused by decreasing dS: Fig. 6 displays theinitial grid at t 0 s and the distorted grid at t 0:5 s for the case dS 3 mm:

3.2. L-shaped plate

Description of the test case: In contrast to the previous examples a three-

dimensional test case is examined in this section. An L-shaped flexible plate (see

t [s]

xB

[m]

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.01

0.02

0.03

0.04

0.05

0.06steady, 220 x 60 x 8 KV

steady, 110 x 30 x 4 KVsteady, 55 x 15 x 2 KV

unsteady, 220 x 60 x 8 KVunsteady, 110 x 30 x 4 KV

unsteady, 55 x 15 x 2 KV

Fig. 12. Displacements of the free edge of an oscillating flexible plate as results of steady and unsteadycomputations on different CFD grids at Re 50:



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Fig. 14) is clamped at its edge FA:Both, fluid and structure have the same propertiesas mentioned in Section 3.1.2 leading to a Reynolds number of 50. The thickness of

the plate is 10 mm:Again, the inflow velocity performs a saltus at the very beginningof the coupled simulation.

Results of the test case: According to its shape and its clamped support, the plate

was not only bent referring to the y-axis but also referring to the z-axis, yielding a

torsional distortion of the structure. Fig. 15 depicts the state of structural distortionand several selected streamlines of the surrounding fluid flow at t 0:44 s:The time-dependent displacements of the corners B, C, and D are shown in Fig. 16. As

L

L

0.25 L

0.5

L

x

BC

Dy

E

F A

z

U8

solid wall

symmetry outlet

Fig. 14. Geometry of the test case 3:2 (not to scale).

t [s]

xB

[m]

0 0.5 1 1.5 2 2.5 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

dS

= 3 mm

dS

= 4 mm

dS

= 10 mm

Fig. 13. Displacements of the free edge of an oscillating flexible plate for several thicknesses.



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expected, corner C reached the largest displacement in x-direction followed by D

and B.

3.3. Tent roof

Description of the test case: For the tent roof shown in Fig. 1 only computations

leading to steady deformations have been carried out so far. The wind load was

assumed in positive x-direction with a strength of 11 on the Beaufort scale 10 mabove the ground, corresponding to a velocity of 30 m=s and a Reynolds number ofapproximately Re 6 106: The simulations were based on a standard ke model.

XY

Z

X: 0 0.05 0.1 0.15 0.2 0.25 m

t = 0.44 s

Fig. 15. Displacement distribution on a L-shaped flexible plate and selected streamlines at t 0:44 s:

t [s]

x[m]

0 1 2 3 4 5 6 7 8 9 100

0.05

0.1

0.15

0.2

0.25

0.3

xC

xD

xB

Fig. 16. Displacements of the corners B, C, D of a L-shaped flexible plate.



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The computational domain had the dimensions 144 m33 m20 m: Thebottom and the back side behind the tent, which represent the ground and an office

building, were treated as rough walls. The left and right sides were inlet and outlet,

whereas for the two remaining sides symmetry boundary conditions were assumed.Projections of the CSD and the CFD surface grid are depicted in Figs. 3 and 4.

The CFD mesh consists of 1; 024; 000 CV; where 3400 CV are connected to the tentsurface. On the other hand, the CSD grid has only 377 finite elements.

The roof is assumed to be a glass-fibre synthetic material with a thickness of

1:5 mm; a modulus of elasticity of E3000 MPa; and a shear modulus of G1500 MPa: This real-life civil engineering structure is 24 m long and between 3 and8:5 m wide. It is situated between 2.76 and 7:27 m above the ground. Here, thestructural simulation used special membrane elements [9]. This means that in con-

trast to the previously discussed structures, the material cannot resist bending at all.

Results of the test case: An asymptotic behavior of the calculated wind load

and displacement with continuing outer FSI iterations could be observed (see

Table 1). In the present case the calculation was terminated when the incre-

mental maximum displacement fell below the given threshold value for the

tolerance (in this case 2 mm). Three outer FSI iterations were required to reach

this tolerance.

Fig. 17 shows the pressure distribution on the upper and lower side of the tent as

examples for the fluid loads derived from the CFD calculation. Pressure maxima on

Table 1

Example for a coupled computation leading to a steady deformation of the tent structure in Fig. 1

Outer iteration step 1st 2nd 3rd

Number of inner iterations

CFD 1390 369 103

CSD 18 5 3

Total wind force on the 5710 5806 5810

tent structure (N)

Maximum displacement of the 103.6 117.0 118.5

tent structure (mm)

Z X

Y-300 -200 -100 0 100

Z X

Y-300 -200 -100 0 100

(b)(a)

Fig. 17. Computed pressure distribution on the upper (a) and lower side (b) of the tent roof as a result of

the CFD simulation (values in Pa, relative to atmospheric pressure).



16/18

the upper surface correspond with minima on the lower surface yielding to a

relatively high and unevenly distributed load. Pressures and shear stresses on the

upper and the lower tent surface yield the total fluid forces, which have to be

interpolated to the CSD grid. The results of this interpolation are surface forces used

as input for the CSD simulation (see Fig. 18), determining the distribution of the

displacements of the tent (depicted in Fig. 19).

Simulations of the time-dependent behavior of this tent roof being loaded byunsteady wind gusts will be performed in the near future.

4. Conclusions and outlook

In this paper a coupled algorithm for the numerical simulation of fluidstructure

interactions was presented. Both disciplines employ separate codes being coupled by

a neutral coupling interface. A partitionedbut fully implicit coupling algorithm was

set up.

First the ALE extension of the CFD code was verified successfully at a stan-dard test case of a moving obstacle in a channel. Afterwards the coupled code was

applied to several examples of simple geometry, and finally to a real-life lightweight

Z X

Y-0.12 - 0.09 - 0.06 -0.03 0 0.03

Fig. 19. Computed displacements of the tent roof inz-direction as a result of the CSD simulation (valuesin m).

Fig. 18. Computed surface forces as input for the CSD simulation.



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structure from the field of civil engineering. All simulations showed stable

convergent behavior even without any under relaxation in between the outer FSI

iterations.

Because of the great lack of experiments concerning flow-induced oscillations ofsimple structures, a comparison between numerical and measurement data was

unfortunately not possible.

In principle, the algorithm is able to take into account time-dependent fluid

structure interactions, turbulent fluid flow, geometrically non-linear displacements as

well as a non-linear material behavior. However, further developments are necessary

to extend the code to a practical method for problems that civil engineers are really

interested in.

For example, the algorithm of grid adaption in the fluid domain has to be

improved in the sense of universality. Concerning the structural simulation part, the

method should be extended to 3D finite elements to overcome the present constraint

of thin-shell structures.

Finally, time-dependent, three-dimensional problems of complex fluid-structure

interaction are computationally demanding enough that an implementation of the

code on the fastest high-performance hardware is necessary. Therefore, the program

will be ported to the Hitachi SR8000 of the Leibniz Computing Center [20] in the

near future.

Acknowledgements

Financial support by the Bayerische Forschungsstiftung in the Bavarian

Consortium of High-Performance Scientific Computing (FORTWIHR) is gratefully

acknowledged. The authors also want to thank Dr. J. Bellmann and Dr. C. Katz

from SOFiSTiK AG, Munich, for technical support as well as some worthwhile

discussions. The main part of the simulations were carried out on the Fujitsu VPP

700 machine of the Leibniz Computing Center, Munich. This support is also

gratefully acknowledged.

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