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Modeling and simulation of aerodynamic in a long span suspensionbridge

F. PetriniStructural Engineer, Rome, Italy

F. GiulianoDepartment of Structural Mechanics, University of Pavia, Italy

F. BontempiDepartment of Structural and Geotechnical Engineering, University of Rome La Sapienza, Rome, Italy

Keywords: bridge design, bridge aerodynamic, CFD, large eddy simulation, turbulence

ABSTRACT: Some aspects pertaining the modeling of the aerodynamic behavior of bridge deck sections are pre-sented. The analyses have been conducted by Computational Fluid Dynamic (CFD) codes (ANSYS and ADINA), with

Finite Element Method (FEM) and Large Eddy Simulation (LES) based approaches respectively.The calibration of turbulence mathematical models, the robustness of the overall computational model and the behavior

changes due to deck geometry or presence of traffic, are investigated by sensitivity analyses.

1 INTRODUCTION

When a fluid flow impacts on a rigid body, aerody-namic forces (D drag, L lift, M moment) gener-ate themselves on the body (Fig.1). The forces de-pend from the shape of the body and from therelative angle of attack between the flow and the

body. They are identified by non-dimensional coef-ficients Mdl ccc ,, which represent, respectively, thenon-dimensional forces of lift, drag and moment act-ing on the body. Furthermore, a diagram which de-scribes the variation of an aerodynamic force withthe angle of attack is called polar.

Figure 1. Aerodynamics forces

Aerodynamics of suspension bridge is usually in-vestigated by wind-tunnel tests. In the last decadecomputational applications of fluid dynamic (CFD)have became an important resource to complete theexperimental tests which are very expensive both intime and money. Especially during the designphases, there is the necessity to explore different andalternative deck configurations: thats where CFDare more appreciable.

2 UNCERTAINTIES AND APPROXIMATIONS

The main causes of errors in the investigation ofsuspension bridge aerodynamic are connected to thefollowing aspects:a. Model similitude in wind-tunnel tests. In

wind-tunnel tests, it is impossible to obtain a to-

tal similitude between the real structure and itsreduced scale model. Therefore, specially in re-stricted flow-way (like near-traffic barriersplaces), the Reynolds number investigated bywind-tunnel tests is not equal to the real one; justbecause in restricted way there is not a completeformation of the boundary layer, the non-similitude effect increases with the reduced scalesize of the model. CFD could be able to solvethis problem because its results doesnt dependfrom the reduced scale size of the model.

b. Turbulence of flow. In CFD approaches of theaerodynamic problem, the turbulent character of

the flow induces uncertainties and unquantifiableterms in the governing equations.

c. Model approximations. The models which areused in CFD approaches solve the problem usingsome approximation (interpolation of unknownfunctions, viscosity models, turbulence models,etc.). An important (and usual) approximationhas been used in this paper: the incident flow hasbeen considered like laminar; doing so, only theturbulence due to the impact of flow on thestructure has been considered while the naturalflow turbulence has been neglected.

d. Analysis results sensibility. Because of previ-

ous points, the results of the CFD analyses are

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usually very sensible to the analysis parameters.Therefore, the analyses need an optimization ofthe parameters.

3 OBJECTIVES OF THIS PAPER

In this paper some applications of CFD on a suspen-sion bridge deck section are presented: the referenceis the Great Belt East Bridge (GBEB) located inDenmark (Fradsen, 2002).

The analyses have been conducted by ANSYScode, with Finite Element Method approaches andRng turbulent model (results are indicated belowwith FEM legend), and by ADINA code, with LargeEddy Simulation approaches (results are indicatedbelow with LES legend).

The following objectives are pursued:1) modeling techniques optimization, for the simu-

lation of physical phenomena (vortex shedding,

temporal fluctuations of aerodynamics forces,punctual pressure values around the deck), in or-

der to compare computational results with wind-tunnel data;

2) definition of the influence of deck details (traffic

barriers) and traffic vehicles on most importantaerodynamic design data: the aerodynamics po-lar.

4 CFD GOVERNING EQUATIONS

In aerodynamic design of suspension bridges, be-

cause of low relative wind velocities (usually lessthan 80 m/s) one can consider the fluid incompressi-ble. Also using Newtons approximation on fluidviscosity, in CFD problems there are four scalar un-known functions in time t: pressure p and velocitycomponents in a Cartesian coordinate sys-tem zyx vvv ,, . The four governing equations are:- scalar continuity equation

0vdiv

(1)

- vectorial Navier-Stokes equation

v

Dt

Dvpgradf 2

(2)

where is the fluid viscosity, is the fluid densityand DtD is the total derivate operator.

Equations (1) and (2) should be solved after fix-ing adeguate boundary and initial conditions.

4.1 Aspect of turbulence

In turbulent motion, one considers temporal meansof local-instantaneous functions values. Every func-tion ),,,( tzyxb will be a sum of two parts:

)('),,(),,,( tbzyxbtzyxb (3)

where b is the mean time value component of thefunction and 'b is the fluctuant value component ofthe function. Mean value is calculated in a period Tso short that b is constant in T, and long enough thatmean value of 'b is equal to zero.

bdtb

T

Tt

t

1; 0'

1

Tt

t

dtb

T

(4)

4.1.1 RNG turbulent modelWith reference to a planar motion problem, adoptingequation (3) for the component of velocity xv :

)('),(),,( tvyxvtyxv xxx (5)

and making an average on the Navier-Stokes equa-tion for opportune periods T (removing fluctuantcomponent of functions), the x component of equa-tion (2) becomes

y

vv

x

vv

t

v

vvyvvxy

v

x

v

x

p

f

xy

xx

x

yxxxxx

x

''''2

2

2

2

(6)

In equation (6) there are turbulent Reynolds stressterms:

''jiji xx

i

R

xx vvx

T

(7)

By introducing a new scalar entity T (turbulentviscosity) such as

jx

Txxx

vvv iji

'' (8)

so that

Te (9)

equation (6) becomes

y

vv

x

vv

t

v

y

v

x

v

x

pf

xy

xx

x

xxex

2

2

2

2

(10)

Several models of turbulent motion are based on

T expression. RNG model fixes

2kCT (11)

where Cis a constant, k is the turbulent kinetic en-ergy and is its dissipation velocity; kand val-ues are obtained by a system of two differentialequations.

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4.1.2 Large Eddy Simulation (LES)LES basic concept is the following: making a com-putational grid with minimum sizeA, LES computesfluids vortexes which have a size bigger than A andmodels vortexes which have a size smaller than A(sub grid vortexes). In LES approaches, any functionf is divisible in two parts: a calculable part f and asub grid part f . Taking into account equation (6),written in indicial form

ji

i

i

ji

j

i

xx

v

x

pvv

xt

v

2

11

(12)

and applying a spatial filter tothe equation (12), oneobtains

j

ij

ji

i

i

ji

j

i

xxx

v

x

pvv

xt

v

211

(13)

where online elements are filtered. In equation (13)

there are terms in the form:

jijiij vvvv (14)

which represent the sub grid Reynolds stresses, thatare related to energy dissipations due to sub gridvortexes. There are many models for these stresses.The most used is the Smagorinsky model; it fixes:

ijSGSij S 2 (15)

where

jiijSGSSGS SSC 22

(16)

is the sub grid viscosity, SGSC is the Smagorinskyconstant, which changes with stream configurationand shape of the invested body, is the grid size(and filter parameter) and ijS is given by:

i

j

j

i

ijx

v

x

vS

2

1

LES method is very suitable for the investigation ofthe aerodynamic of structures since the fluctuationof the forces is mainly due to big vortexes. The mainproblem of LES method is to determine the optimalvalue of the constant

SGSC in equation (16).

5 CFD APPLICATION

The GBEB and its deck section are shown in Fig. 2,being the central suspension span of the bridge 1624m long. Wind-tunnel tests show that, when wind im-pacts on the bridge, there are aerodynamics force os-cillations and some vortexes structures are generatedaround the deck. Previous studies (Bruno-Khris2002) attributed these fluctuations to the relative po-sitions of these vortexes (Fig. 3). Furthermore, when

vortexes loose themselves in the wake, there is avortex shedding phenomenon.

Applications of this paper are summarized in Ta-ble 1

6,07 18,93

27

6,07

4

Figure 2. The GBEB and its deck section (meters)

Figure 3. Flow screenshot (Bruno-Khris 2002)

Table 1. Analyses

Type of section (paragraph) Type of analyses

parameters optimizationNude deck section (5.1)

forces analysis

Deck+traffic barriers(5.2) forces analysis

Deck+traffic barriers+vehicles(5.3) forces analysis

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5.1 Nude section

For the computational analysis, a fluid domain withopportune boundary and initial conditions has beendefined. Deck section contour has been defined witha wall inside the domain; the domain has been dis-cretized by different size grids (Fig. 4) described be-

low:1. FEM - coarse ( 2103 By ), medium

( 3104,2 By ), fine ( 4108 By );2. LES - medium ( 3102,1 By );where y is the orthogonal grid size from deck con-tour and B is the geometric reference size of thedeck (31m).

(a)

(b)

Figure 4. Grid size: fine FEM (a), medium LES (b)

Analysis results show that FEM computes anaerodynamic force oscillation only by fine grid

(Fig.5). The flow screenshots (when Cl(t) is station-ary) (Fig. 6) clarify the reasons: using the coarsegrid, two static vortexes are generated behind thedeck, while using the fine grid, the same vortexesare generated, but they arent static, since they havea relative motion which generates a wake fluctua-tions that causes aerodynamic forces fluctuations.

Comparing Fig. 3 with Fig. 6, one can see thatFEM doesnt simulate the lower deck boundarylayer separation bubble; furthermore FEM does notsimulates the vortex shedding phenomenon: in factthe vortexes dissolve themselves before loosing inthe wake.

-0,025

-0,02

-0,015

-0,01

-0,005

0

0,005

0,01

0,015

0,02

10 15 20 25 30 35 40

t (sec)

Cl

fine medium coarse

Figure 5. FEM: lift coefficient function Cl(t) for zero angle ofattack

Coarse grid: t=t0, t1, ........, tn

Fine grid: t=t0

Fine grid: t=t1

Figure 6. FEM: flow screenshots for zero angle of attack

Because of the mentioned sensibility to SGSC (kdin ADINA code) constant values, the LES approachneeds a calibration/optimization process. When kdchanges its value (always smaller than 1), also the Cltemporal value changes (Fig. 7). Optimized parame-ters had been chosen according to these points:1. the Cl(t) function regularity (one wants to obtain

a function with only one dominant frequencyvalue) (Fig. 8),

2. mean Cl(t) value,3. good physical phenomena simulation (one can

compare the computed flow with the experimen-

tal flow) (Fig. 9)

-0,30

-0,20

-0,10

0,00

0,10

0,20

0,30

0,40

2,0 4,0 6,0 8,0 10,0 12,0 14,0 16,0

t'=t*U/B

Cl

kd=0,1 kd=0,2 kd=0,3 kd=0,4 kd=0,5 kd=0,7 kd=0,9

Figure 7. LES: Cl(t) functions (zero angle of attack)

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0

0,25

0,5

0,75

1

1,25

1,5

0 0,5 1 1,5 2

freq

F

0

0,03

0,06

0,09

0,12

0,15

0,18

0 0,5 1 1,5 2

freq

F

(a) (b)Figure 8. Cl(t) Fourier transform: kd=0.3 (a), kd=0.5 (b)

(a)

(b)

(c)

(d)

Figure 9. LES: flow screenshots (zero angle of attack). kd=0.2 (a); 0.3 (b); 0.4 (c); 0.5 (d)

Following these parameters, the value 0.3 resultsthe optimum value for the constant kd. Adopting thisvalue, the function Cl(t) appears regular, with mean

value inside the range of literature values. One cansee from the flow screenshot (Fig. 9) the physical

phenomena like vortex shedding; the lower deckboundary layer separation bubble is computed withits size. In fact, the physical phenomena importancedecreases when the kd value increases, so they areoverestimated when kd =0.2 and they are underesti-mated when kd=0.5.

Comparing LES and FEM, one sees that the meanvalue of Cl(t) and his oscillation amplitude com-

puted by LES are bigger than the correspondent onescomputed by FEM, while for the Strouhal numberone has an opposite situation: the FEM Strouhal

number is bigger than the LES one; anyway, bothFEM and LES Strouhal numbers are within the lit-erature computed values range (Fig. 10). On thedeck, aerodynamic actions output values have beencompared to:1. the distribution of the mean pressure coefficient

values Cp on deck surfaces (upper and lower)

(Fig. 11),2. the lift Polar (Fig. 12).

About the Cp values (Fig. 11), on the upper sur-face, both FEM and LES values have good agree-ment with experimental data while on the lower sur-face both methods led to underestimate the

depression for 0.2< Bx


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-1

-0,8

-0,6

-0,4

-0,2

0

0,2

0,4

0,6

0,8

1

-15 -10 -5 0 5 10 15

a (deg)

Cl

FEM (Ans ys ) LES (Adina) Sperimental

Figure 12. FEM-LES: lift polar lines

About the polar line (Fig. 12), the most importantdesign output, both methods have a good agreementwith experimental data. One wants to highlight that,

due to the large computational time required by finegrid computations, the Fig. 10 and the Fig. 11 areobtained by medium grid.

5.2 Aerodynamic influence of traffic barriers

To evaluate the influence of particulars in bridgedeck aerodynamic (traffic barriers) they have beenmodeled (Fig. 12).

Viewing the near barriers stream flow (zero angleof attack) (Fig. 14), following the singular particleflow way, one can see that the flow deviations due tothe barriers in LES are bigger than in FEM.

Figure 13. Deck section modeling

(a)-1 (b)-1

(a)-2 (b)-2

(a)-3 (b)-3

Figure 14. Near barriers flow (zero angle of attack). FEM (a),LES (b); left front (1), central barrier (2), right front (3).

About the polar line (Fig. 15), at low angle of at-tack ( 5 ) both methods had computed a lower-ing of the lift line due to the barriers, while at highangle of attack ( 10 ) the used methods are notin agreement. At negative angles, the outputs ofmethods about the barriers effect on the polar valueshave an opposite sign.

-1

-0,8

-0,6

-0,4

-0,2

0

0,2

0,4

0,6

0,8

1

1,2

-15 -10 -5 0 5 10 15

a (deg)

Cl

FEM(Ansys) without barriers FEM(Ansys) with barriers

(a)

-1

-0,8

-0,6

-0,4

-0,2

0

0,2

0,4

0,6

0,8

1

1,2

-15 -10 -5 0 5 10 15

a (deg)

Cl

LES (Adina) without barriers LES (Adina) with barriers

(b)

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-0,6

-0,5

-0,4

-0,3

-0,2

-0,1

0

0,1

0,2

0,3

0,4

-15 -10 -5 0 5 10 15

a (deg)

Cy

FEM (Ansys) with vehicles LES (Adina) with vehicles

Figure 19. FEM-LES: lift polar lines with vehicles

6 CONCLUSIONS

In this paper two kinds of aspects about aerody-namic of suspension bridge deck section have beeninvestigated:1. Computational aspects. With a computational

fluid dynamic application on an existing bridge

section, two of the more used solver methods

have been compared: FEM (Finite Element

Method with classic model of turbulence) using

ANSYS code, and LES (Large Eddy Simulation)

using ADINA code.

2. Structural aspects. Aerodynamic influence of:

a. Deck particulars like traffic barriers

b. Traffic vehicles presenceAbout the computational aspects, the authors con-clusions are:

FEM has not a good computing of physical phe-

nomena like vortex shedding and (by coarse

grids) aerodynamics forces temporal fluctua-

tions. On the other side, FEM has a very good

computing of the mean numerical design values

(polar lines and pressure coefficients). This

method denotes a high robustness with regards to

problem configuration and analysis parameters.

LES has a good computing of both physical phe-

nomena and mean numerical design values;however, it denotes a low robustness with re-

gards to problem configuration and analysis pa-

rameters. So, LES need optimization (which is

difficult without having experimental data).About the structural and aerodynamics aspects, theauthors conclusions are:

Especially at positive angles of attack, the traffic

barriers downed the polar numerical values and

the polar slope. At negative angles of attack, the

barriers influence on the polar numerical values

is better than at positive angles.

The vehicles presence on the deck changes the

flow configuration around the body; it generates

a complex flow, especially behind the vehicles.

At positive angles of attack, the lift polar values

moved down. Because of this great aerodynamic

influence, the authors think it will be important

to study the relative vehicles position influencein future applications.

ACKNOWLEDGEMENTS

The financial contribution of University of Rome LaSapienza, COFIN 2004 and the support of professorsG. Augusti and M. Ciampoli is acknowledged.

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