BBAA VI International Colloquium on:Bluff Bodies Aerodynamics & Applications

Milano, Italy, July, 20–24 2008

INVESTIGATION ON THE DEPENDENCE OF BRIDGE DECKFLUTTER DERIVATIVES ON STEADY ANGLE OF ATTACK

Claudio Mannini? and Gianni Bartoli?

?CRIACIV/Department of Civil EngineeringUniversity of Florence, Via S. Marta 3, 50139 Firenze, Italy

e-mails: claudio.mannini@dicea.unifi.it, gbartoli@dicea.unifi.it

Keywords: Bridges, Aeroelasticity, Wind-Tunnel Tests, Flutter Derivatives, Particle Image Ve-locimetry

1 INTRODUCTION

In order to prevent bridge deck flutter instability, it is very important to accurately measurein the wind tunnel the flutter derivatives, i.e. the nondimensional coefficients which expressthe assumed proportionality between unsteady forces and deck motion. These aerodynamiccoefficients are functions of the reduced frequency of oscillation but, in view of the fact thatbridge decks are more-or-less bluff bodies, they also depend on the mean angle of attack (e.g.Ref. [1]). It was also shown in Ref. [2] that the influence of this additional parameter can bedramatic in some cases.

This fact represents a relevant problem in case of free-vibration experimental set-ups, wherethe steady angle of attack varies with the mean wind speed, due to the section-model rotation.Bridge decks characterized by positive values and positive gradients of the mean aerodynamicmoment coefficient around zero angle of attack are particularly critical, as it is for the single-box girder deck with lateral cantilevers, very similar to the Sunshine Skyway Bridge, Florida,whose experimental study is reported in Refs. [2, 3] and which is also the reference geometryfor this work.

In the present paper, a method is proposed to determine the flutter derivatives from free-vibration tests as continuous functions of both reduced wind speed and mean angle of attack. Inaddition, the very peculiar behaviour of the section model for a certain range of angles of attackis discussed and partially explained from the physical point of view by means of Particle ImageVelocimetry.

2 EXPERIMENTAL RESULTS

Using the aeroelastic set-up extensively described in Ref. [2], flutter derivatives are extractedfrom heaving-pitching free-decay time histories through the Modified Unifying Least-Squaresmethod (Ref. [4]), imposing several initial angles of attack (namely -3.72◦, -1.70◦, 0◦, +1.24◦,+2.61◦, +4.32◦), increasing for each configuration the wind speed until the flutter limit andrecording at each measuring step the steady angle of attack. Measures are repeated many times,

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Claudio Mannini and Gianni Bartoli

in order to be able to give a probabilistic description to the flutter derivatives and perform aprobabilistic calculation of the flutter boundaries (Refs. [2, 5]). After the identification, thestatistical moments of the aeroelastic coefficients can be calculated for each association of re-duced wind speed UR and initial angle of attack α0. These values can be then approximated bymeans of Generalized Regression Neural Networks so that, once a steady angle of attack hasbeen fixed, the intersection of the corresponding vertical plane with the surface gives the flutterderivative function relative to a constant mean angle of attack, which can be correctly used ina bridge prototype flutter prediction. Examples of these flutter derivative surfaces are shown inFig. 1.

05

10−4 −2 0 2 4 6

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UR [−]

α0 [°]

H1* [

−]

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460

1

2

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UR [−]α

0 [°]

H1*

RM

S [

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UR [−]

α0 [°]

A2* [

−]

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−4−202460

0.02

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0.1

UR [−]

α0 [°]

A2*

RM

S [

−]

Figure 1: Surfaces approximating the mean values and the RMS values of the flutter derivatives H∗1 and A∗2. The

circles denote the experimental points.

From the analysis of these pictures it can be remarked that the flutter derivative H∗1 presents

an evident dip in correspondence of small negative angles of attack, as well as a significant in-crease in the variance of the measured values. In the same range the A∗

2 function is characterizedby an anomalous slow decrease, suggesting that less aerodynamic damping in pitch is pumpedinto the system. These remarks are confirmed by the observation of the peculiar behaviour ofthe section model for small negative angles of attack: as it is shown in Ref. [2], for relativelylow wind speed the system continuously switches between a stable and an unstable flutter-likeconfiguration, changing at the same time the mean angle of attack. This strange behaviour can

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also be related to the static aerodynamic coefficients which show that, for angles of attack in therange roughly −2.5◦ < α < 0◦, drag anomalously increases while lift and moment suddenlylose their linear pattern (Fig. 2).

In order to explain these results from a physical point of view, the flow features in the nearwake of the fixed profile are measured through Particle Image Velocimetry (PIV) technique.A selection of the results are reported in Fig. 3. It can be noted that for α = −2◦ the meanrecirculation area immediately behind the body is definitely larger not only than for α = 0◦

and α = +5◦ but also than for α = −5◦. Conversely, the flow on the extrados of the model isattached until stall, that is for angles of attack smaller than α ∼= +7◦. The larger wake explainsthe increase in the drag coefficient and suggests a different type of separation of the flow, per-haps occurring in correspondence of the upstream lower corner instead of the downstream one.Further PIV measurements at these locations are necessary to fully understand the phenomenonbut it is clear that suddenly, for small negative angles of attack, the flow field around the bodyqualitatively changes, while the main flow configuration becomes stable again for α < −2.5◦,with evident effects on both the steady and unsteady behaviour of the section model.

3 CONCLUSIONS

In this paper the issue of dependence of bridge deck flutter derivatives on steady angle ofattack is dealt with, showing the results of a vast wind-tunnel test campaign on a single-boxgirder section model. A new procedure to express the flutter derivatives, particularly thoughtfor free-vibration set-ups, is proposed. The analysis of these experimental results shows a verypeculiar static and aeroelastic behaviour of the studied profile for a certain range of anglesof attack. Therefore, PIV measurements are employed in order to characterize the details ofthe flow around the body, thus trying to explain from the physical point of view the observedbehaviour of the section model.

4 ACKNOWLEDGEMENT

Eng. Lorenzo Procino, technical responsible of the CRIACIV Boundary Layer Wind Tunnel,is gratefully thanked for his help and advice during the wind-tunnel tests.

−12 −10 −8 −6 −4 −2 0 2 4 6 8 10 120

0.05

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0.25

Mean DRAG

α [°]

CD [

−]

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−0.05

0

0.05

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α [°]

CM

[−]

Mean MOMENT

Figure 2: Static aerodynamic drag and moment coefficients at various angles of attack (Re = 5.8e05).

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Claudio Mannini and Gianni Bartoli

−100 −50 0 50 100 150 2000

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100

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250α = −5°

x [mm]

z [m

m]

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x [mm]

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x [mm]

z [m

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x [mm]

z [m

m]

Figure 3: Streamlines of the time-averaged flow in the near wake of the bridge deck model at various angles ofattack, measured through the PIV technique (Re = 4.5e05).

REFERENCES

[1] G. Diana, F. Resta, A. Zasso, M. Belloli and D. Rocchi. Forced motion and free motionaeroelastic tests on a new concept dynamometric section model of the Messina suspensionbridge. Journal of Wind Engineering and Industrial Aerodynamics, 92(6), 441–462, 2004.

[2] C. Mannini. Flutter vulnerability assessment of flexible bridges. Ph.D. Thesis, Universityof Florence, Italy - TU Braunschweig, Germany, 2006.

[3] C. Mannini and G. Bartoli. Analisi del comportamento aeroelastico di un impalcato daponte a cassone unicellulare. Proceedings of the 9th Italian National Conference on WindEngineering IN-VENTO, pp. 439–448, Pescara, Italy, June 18-21, 2006.

[4] G. Bartoli, S. Contri, C. Mannini and M. Righi. Improvement of existing methods forthe identification of bridge deck flutter derivatives. Journal of Engineering Mechanics(submitted).

[5] C. Mannini and G. Bartoli. A probabilistic approach to bridge deck flutter. Proceedings ofthe 12th International Conference on Wind Engineering, pp. 2351–2358, Cairns, Australia,July 1-6, 2007.

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