wind effects on the cross section of a suspension bridge

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14th International Conference on Wind Engineering – Porto Alegre, Brazil – June 21-26, 2015

Wind Effects on the Cross Section of a Suspension Bridge by CFD Analysis

Leandro Malveira1, Fernando Akira Kurokawa1, Osvaldo Shigueru Nakao 2

1Department of Construction Engineering, Escola Politécnica of the University of São Paulo, Brazil 2Department of Engineering Structures and Geotechnical, Escola Politécnica of the University of São Paulo, Brazil

email: [email protected], [email protected], [email protected]

ABSTRACT: This work presents a brief contribution to the complex and important issue discussed by fluid dynamics that is the interaction fluid structure, which in the example treated by this work is the interaction between wind flow and the cross section

of a suspended bridge deck. The aerodynamic behavior is investigated for the Great Belt East Bridge and when the fluid flow

across the bridge deck, it gives rise to wind loads. One of the most important parameter for this type of load is the aerodynamic

forces for drag, lift and torsional moment. Related to these forces, the aerodynamic coefficients dimensionless for drag, lift and

moment were obtained for different wind flow angles of incidence. The vortex shedding was also analyzed in this fluid structure

interaction and the Strouhal number was calculated. This dimensionless parameter is dependent on the geometry of the cross

section of the bridge and the Reynolds number. The technique used in this study for evaluating the fluid structure interaction is

the numerical simulation that is aided by the use digital computers and called Computational Fluid Dynamics (CFD). The CFD

study allows analyzing the moving air behavior in the contour of the cross section of the bridge. The basic features of the fluid

flow for this computational simulation are incompressible and transient. The turbulence model adopted in this work is the k-ε

model. The results of aerodynamic coefficients obtained in this study were compared with the experimental and numerical data existing in the literature and the results proved to be consistent.

KEY WORDS: Wind Effects; Suspension Bridges; Computational Fluid Dynamics; Aerodynamic Coefficients; Strouhal

Number, Vortex Shedding.

1 INTRODUCTION

The knowledge about the interaction phenomenon caused by the wind in bridges with slender features and flexible structural

model raises studies in wind engineering field with a view to producing reliable information on the aerodynamic and aeroelastic

behavior of this type of structure. It is the case of suspension and cable-stayed bridges.

The aerodynamic forces, which are caused by the interaction between the wind loads on structures, can lead to catastrophic

events or even total collapse of a building. RASMUSSEN (2011) indicated that strong winds may cause great destruction

through powerful forces but more subtle phenomena may lead to structural failure even at relatively low wind speeds.

According BRAUN (2007) apud SIMIU and SCANLAN (1996) these phenomena of interaction between wind actions and

structures present the main task of this area known as wind engineering, that is to provide information about the structural

performance and environmental conditions in the contours of structures subjected to wind loads. The study of wind effects on civil engineering structures began to receive relevant highlight from 1940, with the event which

caused the collapse of the Tacoma Narrows Bridge located on United States. It was destroyed after undergoing wind flows

around the speed of 70 km/h (LIMAS, 2007), presenting divergent oscillations and with significantly large amplitudes, as shown

in Figure 1 and Figure 2.

In lightweight and long constructions, the dynamic wind effects should be considered, especially those with low natural

vibration frequencies (f < 1.0 Hz). The primary concern in the long span suspension bridges project is the action of wind,

however the study of wind behavior in bridges still need more extensive studies and research. The analysis of a dynamic

instabilities demand attention in the design process of a suspension bridge and the designer should spend a lot of time to

research (PFEIL, 1993). Over the years, science has developed physical experiments to increase knowledge and understanding

of a particular phenomenon. HALLAK (2002) points out that with the growing advancement of computational tools used in the

projects there is a tendency to build more and more light and slender structures. Although the experimental tests in the wind tunnel has become the most important method for determining the wind actions on structures, in recent years, the Computational

Fluid Dynamics (CFD) has been established as an alternative and complement to the laboratory tests.

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Figure 1. Tacoma Narrows Bridge during the oscillations.

Source: HALLAK (2002).

Figure 2. Tacoma Narrows Bridge in the instant of collapse.

Source: HALLAK (2002).

The CFD is represented by the tests in the wind tunnel, consolidated and widely regarded as an important and reliable tool for

obtaining data from wind structure interaction. It has made significant advances in the fields of digital computing and

programming and its methodology complements analytical approaches and experimental tests. The purpose of CFD is to

minimize the need for experimental tests and research events cannot be studied in the laboratory because of cost, time and

complexity of assembly or even a more detailed characterization of the actual element structure (HIRSCH, 1988; FOX e

MCDONALD, 1995).

This work presents a computational analysis of the wind action on the cross section of a suspension bridge, in order to

investigate its behavior under wind action. The objective was to determine the aerodynamic coefficients of drag, lift and

moment of the model subjected to a wind flow with a given speed and different values of wind’s angle of attack. The Strouhal

number was also obtained and the vortex shedding in the wake of flow was analyzed.

The present computational simulation was performed using the Fluent® software, developed by ANSYS Inc., and the sectional model analyzed in this simulation is similar to the Great Belt East Bridge, located on Denmark.

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2 FLOW AROUND A BLUNT BODY

2.1 Wind Effects

In the design of structures submitted to wind actions, should be contemplated the studies and the checks of both static and

dynamics effects. According to LIMAS (2003) apud KOLOUSEK et al. (1984), theoretically any wind action is dynamic

because the true wind speed varies with time and it may be subdivided into a constant component and a fluctuation component.

However, when the average period of separation component of fluctuation is equal to or greater than one hundred times the

period of vibration of the structure, one can consider the effect of wind as static. The issues related to static behavior can be

checked by the aerodynamic force components like drag force, lift force and pitching moment. The static issues are taken care of

by the plot of the coefficients of drag, lift and moment against the angle of incidence of wind. Dynamic behavior includes the responses due to vortex shedding excitation, self-excited oscillations and buffeting by wind

turbulence (SELVAM, 2008). SACHS (1978) states that suspension bridges could oscillate in two natural modes, vertical and

torsional. In the vertical mode, all joints at any cross-section move the same distance in the vertical plane, while in the torsional

mode every cross-section rotates about a longitudinal axis parallel to the roadway.

2.2 Flow Parameters

2.2.1 Reynolds Number

The Reynolds number (Re) is one of non-dimension hydrodynamic number that is used to describe the regime of the flow. The

Reynolds number represents the ratio of the inertia forces to viscous forces and is formulated as:

(1)

in wich D is a reference body dimension, U is the undisturbed velocity, is the kinematic viscosity, is the specific mass and

is the dynamic viscosity of the fluid. This concept was developed by Osborne Reynolds in 1883 and the Reynolds numbers

frequently arise when performing scaling of fluid dynamics problems, and as such can be used to determine dynamic similitude

between two different cases of fluid flow.

2.2.2 Strouhal Number

According to MANNINI (2006), an experimental study of Vincenc Strouhal at end of the nineteenth century showed that there

is a linear relation between the frequency of vortex shedding ( ) and the undisturbed flow velocity (U). This linear relation is

the definition of a non-dimensional quantity known as Strouhal number (St):

(2)

where D is a reference body dimension and is the undisturbed velocity. The Strouhal number is dependent on the body

geometry and Reynolds number and is typically about 0.2 for bridge deck (RIGHI, 2003). Also according to RIGHI (2003), an

analytical study concerning the stability of the vortex patterns in a wake of a stationary cylindrical body was carried out by Von

Kármán and Rubach in 1911. Based on two-dimensional potential flow theory and assuming that the fluid is irrotational except

in concentrated vortices, it was shown, that the vortex pattern is stable, if the vortices are organized in unsymmetrical double

row pattern, showed on Figure 3.

Figure 3. A sketch of unsymmetrical double row pattern of vortices known as the von Kármán vortex trail.

Source: RIGHI (2003).

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2.2.3 Aerodynamic Coefficients

As the result of the periodic change of the vortex shedding, the pressure distribution of the body due to the flow will also

change periodically, generating a periodic variation in the force components (ASYIKIN, 2012). The force components can be

divided into cross-flow and in-line directions. The force of the in-line direction is commonly named as the drag force ( ) while

the force of the cross-flow is named as the lift force ( ). The lift force appears when the vortex shedding starts to occur and it

fluctuates at the vortex shedding frequency. There is also the appearance of a torsional forces, due to the position difference

between the elastic center and the center of mass of the body and this is the torsional moment ( ).

The aerodynamic coefficients are dimensionless coefficients that depend on the shape of the cross section and the angle of

wind incidence. Also depend on the flow characteristics of turbulence and Reynolds number. They are given by:

(3)

(4)

(5)

in which , and are the coefficients of drag, lift and moment, respectively. and are the mean drag and lift force,

respectively and is the mean torsional moment, is the specific mass, is the mean wind speed in the oncoming flow at the

deck elevation and is the width of the cross-section bridge deck.

2.3 Vortex Shedding

According to BLESSMANN (2005), in blunt bodies, i.e. with no aerodynamic shape, immersed in flows with low number of

Reynolds, appears an alternate shedding vortex, with a defined frequency. These aeroelastic phenomena are known as von

Kármán vortices, giving rise to periodic and oblique forces in relation to wind direction. The components of these forces tend to

produce oscillations that occur in the frequency of shedding of each pair of vortices (LIMAS 2007). A von Kármán vortex sheet

is a repeating pattern of swirling vortices caused by the unsteady of flow of a fluid around a blunt body. Figure 4 is showing the vortex shedding models on a bluff body.

(a)

(b)

(c)

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(d)

Figure 4. Flow past a bluff body at: (a) , (b) , (c) and (d) .

Source: SIMIU and SCANLAN (1996).

As mentioned above, vortex shedding occurs at a certain frequency, which is called as vortex shedding frequency ( ). This

frequency normalized with the flow velocity and is a reference dimension, can basically be seen as a function of the

Reynolds number (ASYIKIN, 2012).

2.4 Numerical Methods for Computer Simulation

Numerical methods had its beginning with the work of RICHARDSON (1910), who found solution to the Laplace equation in

two-dimensional plane (MARCHI, 2001; ROACHE, 1972). They aim to mathematical representation of a real phenomenon, i.e.

seek to find the mathematical model for an event that involves physical behavior, such as the case of a moving fluid.

Furthermore, they can get solution from more general problems to more specific phenomena, problems with boundary conditions and complex geometry and discrete numerical solutions. Therefore, a phenomenon related to the flow of a fluid

around a solid body is of such complexity that only with the aid of a numerical solution method would be possible to get some

response.

The interaction between a fluid in motion and a body immersed in it is the object of study of an important mechanical area of

fluid called fluid dynamics. The evolution of computers and information technology in recent years has allowed the union

between the numerical solution methods and fluid dynamics, emerging a new area of knowledge CFD.

The CFD is the area of scientific computing that studies computational methods for simulation phenomena involving moving

fluid with or without heat exchanges (FORTUNA, 2012). The common responses from an analysis of the fluid structure

interaction are distributions velocities, pressures and temperatures in the outflow region.

2.4.1 Governing Equations

The governing equations of fluid motion have a mathematical model for fluid flow solution, which represents physical

principles that may be compressible or incompressible, laminar or turbulent, stationary or transient. The mathematical

complexity of these equations does not allow finding analytical solutions to the general case. The governing equations for a

transient Newtonian incompressible fluid flow are given by (WHITE, 2011):

Conservation of Mass

(6)

Conservation of Momentum

(7)

where is the velocity vector, t is time, is the fluid density, P is the pressure, is the viscosity coefficient, is the external

force.

2.4.2 Turbulence model

Turbulent flow can be defined as a chaotic, fluctuating and randomly condition of flow (ASYIKIN, 2012). These fluctuations

mix transported quantities such as momentum, energy and mix species transportation and cause the transported quantities to

fluctuate as well. Turbulent flows are highly unstable, three-dimensional and also are a time-dependent process. According to WILCOX (1993) there are many methods that can be used to predict turbulence flow. Some of them are DNS (Direct Numerical

Simution), RANS (Reynolds Average Navier-Stokes) and LES (Large Eddy Simulation). In this work, the turbulence model to be

adopted is the - model (YAKHOT and ORSZAG, 1986; YAKHOT et al. 1992), which is one of the many solution forms at

RANS method, where is turbulent kinect energy and is dissipation rate.

The transport equation of the turbulent kinetic energy is:

( ) ((

) ) (8)

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and the equation of the dissipation rate of turbulent kinetic energy is:

( ) ((

) )

(9)

where is the turbulent viscosity, is the term of turbulent kinetic average energy production, and are the turbulent

diffusion coefficients, and e are empirical constants. The turbulent viscosity is calculated as follows:

(10)

in which is an empirical constant.

The constants and assume the numerical values given in Table 1.

Table 1. Constants of the - turbulence model equations.

1,44 1,92 0,09 1,0 1,3

3 SIMULATION METHODOLOGY

3.1 Numerical Simulation Software

The computational tool used for the simulations in this work is the ANSYS Fluent®, which is software for modeling and numerical simulation that allows the development of complex models to fluid dynamics analysis. This software solves the

simulation of any kind of flows, applying laws governing the movement of fluids through the volume element method. The

software has a pre-processor, a mesh generator to determine the boundary conditions and physical models. From their

geometries, this code is capable of generating structured and unstructured meshes combined with the boundary conditions. In

addition, you can define the type of analysis (static, modal, transient, etc.), applied loads and movement restrictions. The tool

also has a post-processor that allows viewing and analysis of simulation results, such as stress diagram, strain and deflection,

presentation of critical points, list of nodal displacements, stresses or any other variable.

3.2 Long Span Suspension Bridge

Storebaeltforbindelsen is the road and railway link between the Danish Islands Funen and Zealand. It connects Copenhagen

with the mainland of central Europe. An important part of this link is the Great Belt East Bridge, one of the longest suspension

bridges in the world. It is located on the east side of the link, as showed in Figure 5, the construction of the bridge began in 1988

and its inauguration and full opening to traffic occurred on June 14, 1998 (WEIGHT, 2009).

Figure 5. Plan a location of the Great Belt East Bridge.

Source: WEIGHT (2009).

The complete east bridge has 2.7 kilometers with a central span of 1624 meters (Figure 6). The pylons from which the main

span is suspended will rise to a height of 254 meters. Actually, the Great Belt East Bridge has the third longest main span in the

world, staying behind only to the Xihoumen Bridge in China, which central span has 1650 meters and the Akashi-Kaikyo Bridge in Japan, with the longest central span of any suspension bridge of the world, at 1991 meters.

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Figure 6. View of Great Belt East Bridge.

Source: http://www.hochtief-construction.at/en/pdf/Great_Belt_East_Bridge.pdf.

3.2.1 Cross Section of the Bridge Deck

The cross section of the bridge deck has a box girder format, which contributes to the aerodynamic performance of the

assembly. The cross section shape and other geometric characteristics of the bridge are displayed in Figure 7.

Figure 7. Elevation and cross section of the Great Belt East Bridge.

Source: WEIGHT (2009).

3.3 Assembly of Computer Simulation

For numerical simulation using the ANSYS Fluent® software, the three basic steps of a CFD method were performed, in

which the first is preprocessing, in sequence the solver and finally the post processing. In the pre-processing the type of analysis

are defined and builds up the model geometry. At this stage are inserted the properties of material, fluid and solid. Sets up the

model characteristics to be studied and their respective domain of analysis, flow regime (laminar, turbulent, compressible,

incompressible, adiabatic, Newtonian, non-Newtonian, among others), and then create the mesh model. In the solution are

defined analysis parameters (static, harmonic, transient, etc.) and their options, degrees of freedom, loads, load steps, and

performed the resolution of the system of equations. In the post processing is performed reading of results such as stress, nodal

displacements, axial forces, speed, among others.

3.3.1 Geometry and Computational Domain

It was used the domain of the model presented in work of BRAUN and AWRUCH (2002), illustrated in Figure 8, indicating

its dimensions and boundary conditions. The model was created in ANSYS Fluent® (Figure 9) using its application for

computer-aided-design (CAD) known as Design Modeler, which is the gateway to geometry handling for analysis in the

Workbench Platform for ANSYS.

The computational domain created for this paper repeated the geometric property of the reference work. The solution domain

is a rectangular box shape and its dimensions are based on the width of the bridge deck cross section of the Great Belt East. The

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width of the bridge deck is 31 meters, so the computational domain length is 279 meters and the height is 62 meters. The position of the bridge deck within the domain is also a function of its width, as shown in Figure 8.

Figure 8. Schematic illustration of the solution domain similar at the reference model.

Source: authors.

Figure 9. Solution domain created by ANSYS Fluent® software.

Source: authors.

3.3.2 Mesh Generation

The meshing process performed in this step had kept the structured mesh characteristics of the reference model presented in

BRAUN and AWRUCH (2002), as illustrated in Figure 10. The mesh created by ANSYS Fluent® used the mesh generator

software from Workbench Platform known as ANSYS ICEM CFD, which is a powerful tool for meshing, with advanced

controls. For the present simulation had used a structured mesh with 150000 nodes.

Figure 10. Meshing created by ANSYS Fluent® software.

Source: authors.

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3.3.3 Fluid Properties and Physical Modeling Parameters

In present simulation the fluid is considered as atmospheric air and their characteristics as well as the data of fluid flow are

shown in Table 2 and were obtained from the reference work (BRAUN and AWRUCH, 2002).

Table 2. Data used in the computational simulation.

Constants Value Unit

Specific mass ( ) 1.32 ⁄

Kinematic viscosity ( ) 5.78x10-4 ⁄ Reference inflow velocity ( ) 40.0 ⁄

Charact. dimension/cross section ( ) 31.0

The Reynolds number adopted in this work is 3x105 and the time step is . Both values were extracted from

work of BRAUN and AWRUCH (2002). The analysis was developed in transient flow and total simulation time of 50 seconds.

3.3.4 Initial and Boundary Conditions

As indicated in Figure 8 (section 3.3.1), the boundary conditions for this simulation were made in accordance with the terms of

reference work. In the solution domain, that it was represented by a rectangular box shape, the vertical left edge is the inlet and

the initial velocity is 40 m/s. The inlet were established in four different inclinations to the wind’s angle of attack ( ): -10°, -5°, 0°, and +5°. The vertical right edge is the outlet, where the fluid flow out of the solution domain. The conditions assumed for

this boundary is the atmospheric pressure, setting the pressure 0 (zero) in the software.

The horizontal edges (top and bottom) of the rectangular box shape are characterized as wall boundary condition, however it

was established no slip and an initial speed condition for this walls, in relation to initial velocity and the wind angle of attack.

The free-slip boundary condition was used to correctly model the flow at the cross section of the bridge deck walls.

4 NUMERICAL RESULTS

The numerical results obtained in the simulations are visualized in the post-processing step from de ANSYS Fluent®, where

the results of some parameters are obtained, as well as graphics and illustrations on simulated phenomena.

Table 3. Comparison of aerodynamic coefficients with the reference results for = -10º.

Test CD CL CM

Present simulation 0.76 -0.60 -0.10 BRAUN and AWRUCH (2002) 0.74 -0.62 -0.11

REINHOLD et al. (1992) 0.74 -0.71 -0.19

KURODA (1997) 0.80 -1.16 -0.19

Table 4. Comparison of aerodynamic coefficients with the reference results for = -5º.

Test CD CL CM

Present simulation 0.67 -0.42 -0.06

BRAUN and AWRUCH (2002) 0.65 -0.43 -0.07

REINHOLD et al. (1992) 0.58 -0.42 -0.09

KURODA (1997) 0.86 -0.86 -0.07

Table 5. Comparison of aerodynamic coefficients with the reference results for = 0º.

Test CD CL CM

Present simulation 0.63 0.05 0.04

BRAUN and AWRUCH (2002) 0.63 0.05 0.05

REINHOLD et al. (1992) 0.58 0.05 0.05

KURODA (1997) 0.49 -0.17 0.05

Table 6. Comparison of aerodynamic coefficients with the reference results for = +5º.

Test CD CL CM

Present simulation 0.67 0.31 0.11 BRAUN and AWRUCH (2002) 0.68 0.32 0.12

REINHOLD et al. (1992) 0.65 0.35 0.12

KURODA (1997) 0.60 0.47 0.16

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One of this parameters is the aerodynamic coefficient for drag, lift and torsional momente, which were obtained for wind’s

angles of attack ( ): -10 °, -5 °, 0 and +5º. Tables 3 to 6 show comparisons of the results obtained with the results of BRAUN

and AWRUCH (2002), REINHOLD et al. (1992) and KURODA (1997).

Table 7 shows comparison between the present numerical simulation and numerical simulation reference of BRAUN and

AWRUCH (2002), as well as the relative percentage error. It is observed in this table, the numerical values of this simulation are

in good agreement with the values, with relative errors in general small (around 3%) for drag and lift coefficients. For the

coefficient torsional momente, the relative error was around 15% ( ). Only for , the error was around

20%.

Table 7. Comparison between the present computer simulation and numerical

simulation reference identifying the relative percentage error.

Results for = -10°, -5°, 0° and +5°.

CD CL CM

Present simulation 0.76 -0.60 -0.10

BRAUN and AWRUCH (2002) 0.74 -0.62 -0.11

Relative error (%) 2.63 3.22 9.09

CD CL CM

Present simulation 0.67 -0.42 -0.06 BRAUN and AWRUCH (2002) 0.65 -0.43 -0.07

Relative error (%) 3.07 2.33 14.3

CD CL CM


BRAUN and AWRUCH (2002) 0.63 0.05 0.05

Relative error (%) 0 0 20.0

CD CL CM


BRAUN and AWRUCH (2002) 0.68 0.32 0.12

Relative error (%) 1.47 3.13 8.33

The results obtained in the post processing tool Workbench Platform from ANSYS Fluent® are presented below. In Figure 11

it is presented the computed velocity flow field corresponding to the instant of time 50 seconds. It can clearly show the

formation of the alternating vortex shedding flow in the wake upstream of the bridge deck.

Figure 11. Computed velocity field obtained by ANSYS Fluent® software.

Source: authors.

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Figure 12 shows the pressure contours around the cross-section of the bridge deck for the flow developed in the time 50 seconds.

Figure 12. Computed pressure field obtained by ANSYS Fluent® software.

Source: authors.

The Strouhal number was obtained through the application of the FFT method (Fast Fourier Transform). The FFT was applied

from each speed range in the wake of the flow, which is the same region where BRAUN and AWRUCH (2002) got the Strouhal

number. The values of the Strouhal number for a wind’s angle of attack ( 0°) are showed in Table 8 and compared with reference works. One can see from this table that the value of the Strouhal number is consistent with the reference results.

Table 8. Comparison of the Strouhal number for the Great Belt East Bridge.

Reference St

Present simulation 0,189

BRAUN and AWRUCH (2002) 0.180

Numerical approach by LARSEN et al. (1998) 0.170

Wind tunnel tests by LARSEN et al. (1998) 0.160

Also, it were obtained the configuration of the streamlines for the fluid flow with wind’s angles of attack ( ) 10°, -5°, 0° and

+5° and compared with reference results, respectively, as showed in Figures 13 to 18.

Figure 13. Great Belt East Bridge streamlines for = -10° by

ANSYS Fluent®. Source: authors.

Figure 14. Great Belt East Bridge reference results for

streamlines ( = -10°). Source: BRAUN and AWRUCH. (2002).

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Figure 13. Great Belt East Bridge streamlines for = -5° by



streamlines ( = -5°). Source: BRAUN and AWRUCH. (2002).

Figure 13. Great Belt East Bridge streamlines for = 0° by



streamlines ( = 0°). Source: BRAUN and AWRUCH. (2002).

Figure 13. Great Belt East Bridge streamlines for = 5° by



streamlines ( = 5°). Source: BRAUN and AWRUCH. (2002).

5 GENERAL CONCLUSIONS

The phenomenon of interaction between wind flow and the cross section of suspension bridge was simulated successfully in

Ansys Fluent® software. It was possible to clearly see through the responses in the velocity field the characteristic alternate

vortex shedding, assigned to the parameters of the flow and the turbulence model adopted. The comparison of this response with

the reference model of vortex shedding presented wake of von Kármán (RIGHI, 2003), validates the computer simulation.

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The values obtained for the aerodynamic coefficients, presented in Tables 3 to 6, show small deviations from the reference results, presented in the work of BRAUN and AWRUCH (2002). These deviations, which are summarized as shown in Table 7

above show that there adherence on the results obtained in this computer simulation results with numerical simulation from the

reference work. However, improvements can be achieved in the responses with mesh refinement in the contours of the bridge

deck section or even the adoption of a turbulence model that features more accurately the wall call functions, as in this work the

boundary conditions at the board the bridge is established as without slipping. Measurements of elastic center and center of mass

of the cross section of the bridge deck should be reviewed in the equation for best accuracy the moment coefficient.

Likewise, the analysis of the Strouhal number ( ) showed values close to the reference results, validating the numerical method

applied in this simulation work.

The streamlines obtained by ANSYS Fluent® software showed in Figures 13, 15, 17 and 19, demonstrate slight difference

compared to the result of reference, indicating that to approach the vortex shedding of the reference model. However, the

simulation results can be improved by adopting the measures already presented above, as a larger mesh refinement, in both the contour of the deck of the bridge and in the wake of the flow, that are best captured the streamlines. Other turbulence models

can also be tested, as a model that captures the least scales of turbulence.

Finally, it is understood that computer simulation was featured in an appropriate and similar to the numerical approach tests

presented in the results of reference. Therefore the validation of this modeling computed by ANSYS Fluent® allows

incorporating new studies of the phenomenon of fluid structure interaction, such as torsional and vertical displacements of the

cross-section of the bridge deck, self-excited aeroelastic efforts, such as flutter and buffeting, or even the oscillations originated

by vortices induced vibrations.

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