G. Diana, D. Rocchi, T. Argentini and S. Muggiasca

BBAA VI International Colloquium on: Bluff Bodies Aerodynamics & Applications

Milano, Italy, July, 20-24 2008

AERODYNAMIC INSTABILITY OF A DECK SECTION MODEL: LINEAR AND NON-LINEAR APPROACH TO FORCE MODELLING

Giorgio Diana∗, Daniele Rocchi∗, Tommaso Argentini∗, and Sara Muggiasca∗

∗ Politecnico di Milano, Campus Bovisa, Via La Masa 1, 20156 Milano, Italy Dipartimento di Ingegneria Meccanica

e-mail: giorgio.diana@polimi.it, daniele.rocchi@polimi.it, tomma-so.argentini@polimi.it, sara.muggiasca@polimi.it

Keywords: Aerodynamic instability, non linearities, numerical model, pressure distribution.

1 INTRODUCTION A wind tunnel campaign on a deck sectional model with a simple single box shape was

performed in the wind tunnel at the Politecnico di Milano to investigate the aerodynamic tor-sional instability. The instability that arises, for the considered deck shape, at large nose-up angles of attack, shows important non linear effects and represents an interesting case to de-velop and validate non linear numerical models to deal with the aeroelastic problem. Large fluctuations of the instantaneous angle of attack, that can be induced by large deck motion components and/or large wind velocity turbulence components, may lead the deck to work between stable and unstable conditions. Only fully non linear numerical models are able to simulate the deck response under these particular operating conditions and may provide the estimation of the instability onset. The wind tunnel results will be therefore used to validate a non linear numerical approach for the modeling of the aerodynamic forces and to study the aeroelastic conditions close to the instability by means of pressure distribution measurements.

To this purpose, the deck sectional model was equipped with both an internal force balance and 94 pressure tabs, and a new measurement system to record the deck motion, during free motion tests, is adopted. The wind tunnel tests allowed to define all the static and dynamic coefficients that are required by linear and non linear numerical modeling of the problem by means of forced motion tests [1]. Furthermore, the tests allowed to measure the aeroelastic response to turbulent wind when the deck sectional model is excited to vibrate under actively generated turbulent conditions during free motion tests [1]. In these tests both the forces, the displacements and the accelerations of the elastically suspended model are contemporary re-corded for the different wind turbulent conditions. The contemporary knowledge of the in-coming wind condition (input) and of the deck motion (output) represents the minimum requirement to validate the numerical approaches used to simulate the deck response to turbu-lent wind. The control of the incoming wind allowed also to investigate specific operating conditions where the deck is working close to instability and the small changes in the wind turbulence content may drive the deck behavior to cross the stability threshold. The investiga-tion of these operating conditions will be the topic of the present research and will be per-formed by analyzing the experimental data gathered during the wind tunnel tests both in terms

G. Diana, D. Rocchi, T. Argentini and S. Muggiasca

of global forces and pressure distribution and the results obtained using a linear [2] and a non linear [3] numerical model.

2 WIND TUNNEL TESTS The wind tunnel tests were performed at the Politecnico di Milano on a single box deck

sectional model whose geometry is reported in Figure 1 together with its main dimensions. The deck shape is taken from a real highway bridge without considering the barriers on the upper surface. This simplification makes the measure of the aerodynamic force through the integration of the pressure distribution easier. The sectional model is equipped by a 6 compo-nent internal balance measuring all the forces acting on the central dynamometric part (0.91 m wide), in a local reference system that is moving together with the model. Pressure is meas-ured on a ring of 78 pressure tabs around the middle section of the dynamometric part at a sample frequency equal to 100 Hz. The pressure measurement is contemporary performed with the global force obtained by the internal balance. The distribution of the pressure tabs was studied to refine the measure where strong pressure gradient are expected. 16 pressure tabs are distributes along 4 lines aligned with the deck axis, 2 in the upper part and 2 in the lower part, to measure the pressure distribution correlation in the axial direction. 2 laser trans-ducers measure the deck vertical and torsional displacement when the model is linked to the oil dynamic actuators during the forced motion tests. A system of 3 infrared cameras allows the measurement of the deck displacement during the free motion tests. The model displace-ment is reconstructed by measuring the position of 10 markers that are located on the upper surface of the deck model, and specifically reflecting the light that is emitted by specific stroboscopic lamps triggered with the camera sample frequency in the infrared field. The marker position reconstruction is defined by the triangulation of the images recorded by a couple of cameras after a calibration procedure allowing for the correction of the prospective and geometric aberrations.

The deck aerodynamics was characterized in terms of static coefficients, flutter derivatives and admittance functions. Furthermore, aerodynamic hysteresis loops were also measured to identify the non linear numerical model parameters [3][4] and some free motion tests on the elastically suspended deck sectional model were performed to study the model behavior close to instability.

1 m

0.128 m 20 °

V z

y

ϑ

Figure 1: Deck shape and wind tunnel set-up.

3 AERODYNAMIC INSTABILITY Looking at the trend of the static aerodynamic coefficients reported in Figure 2 according

to the sign convention of Figure 1, positive slopes of the lift and moment coefficient are kept respectively up to 9 and 6 deg. The torsional instability may occur even at low reduced veloc-

IR cameras

Laser

G. Diana, D. Rocchi, T. Argentini and S. Muggiasca

ity as highlighted by the negative values of the a2* flutter derivatives coefficient reported in

Figure 2 for different mean angles of attack according to the following formulation:

2 2 * * * *1 2 3 4 *2

12 2

z B zF V B a a a aV V V Bθ

ω

ϑ πρ ϑ ⋅

= ⋅ ⋅ − ⋅ − ⋅ + ⋅ + ⋅ ⋅ ⋅

�� (1)

where B is the deck chord, V the mean wind speed, * *2VV Vf B ωπ= = the reduced velocity

and z and θ are the vertical and torsional model degrees of freedom.

-10 -5 0 5 10-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

CL

-10 -5 0 5 10-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

θ [deg]

CM

/CD

CL

CD

CM

0 10 20 30 40 50 60-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

V*

a 2*-3 deg 0 deg3 deg6 deg

Figure 2: Static coefficients (left) and a2* coefficient vs reduced velocity (right).

The torsional instability is experienced also when the instantaneous angle of attack reaches large oscillation amplitudes around the static value. Results of wind tunnel tests performed on the deck sectional model elastically suspended on stays and run over by a wind with a vertical turbulent component that is able to make the wind instantaneous angle of attack w/V to oscil-late with an amplitude of 0.5 deg and 1 deg are reported in Figure 3. In the figure the time his-tories of the torsional displacement are also plotted. Being the moment coefficient positive at 0 deg, the deck model starts rotating counterclockwise when it is run over by the wind with a mean speed of 8 m/s, until to reach a static position with positive mean angle of attack (3 deg) that is less than the moment coefficient stall. Two different conditions are reported: in the case on the left the turbulent wind component is not sufficiently high to make the instantane-ous angle of attack to cross the instability threshold and the model oscillates with small ampli-tudes around the static angle of attack. In the case on the right the amplitude of the variation of the instantaneous angle of attack is large enough to drive the deck in and out from the in-stability range of the angles of attack resulting in very large torsional oscillation amplitudes. The considered situation represents therefore a possible real operating condition where the amplitude of the angle of attack fluctuation may lead to stable or unstable behaviors, high-lighting the strong non linearity of the aeroelastic problem. The problem will be deeply ana-lyzed in the full paper comparing the aerodynamic hysteresis loops at different amplitudes and the pressure distribution in different operating conditions.

A comparison between the results of a linear numerical approach and a non linear approach [4] will be also included in the full paper.

G. Diana, D. Rocchi, T. Argentini and S. Muggiasca

0 10 20 30 40 50 60-2

-1

0

1

2wind angle

s

w/V

[deg

]

0 10 20 30 40 50 60-20

-10

0

10

20

s

θ[d

eg]

deck angle0 10 20 30 40 50 60

-2

-1

0

1

2wind angle

s

w/V

[deg

]

0 10 20 30 40 50 60-20

-10

0

10

20

s

θ[d

eg]

deck angle

Figure 3: Torsional displacements of the aeroelastic model under 2 different turbulent wind conditions.

The comparison shows how the linear approach based on the flutter derivatives and admit-tance function formulation is not able to predict the instability condition since the aerody-namic coefficients, for this approach, are considered at the static mean angle of attack and assume values leading to stable behavior.

The non linear approach, that is based on the aerodynamic hysteresis loops definition, con-tains also the information related to the effects induced by large variation of the angle of at-tack and is therefore able to simulate the instability onset.

4 CONCLUSIONS The torsional aerodynamic instability was studied on a deck sectional model by specific

tests performed in wind tunnel and by numerical simulations. The instability driven by the stall of the moment coefficient at an angle of attack equal to 6 deg may be reached instantane-ously because of the fluctuation of the angle of attack due to the deck motion and the turbu-lent wind components. Under this condition, the deck works between stable and unstable conditions and damp or increase its energy depending if the part of the oscillation is per-formed before or after the stability threshold. This amplitude driven instability represents an interesting example of the strong non linearity that may be present in the aeroelastic behavior and that requires necessarily non linear numerical formulations to be predicted.

REFERENCES [1] G. Diana, F. Resta, A. Zasso, M. Belloli and D. Rocchi. Forced motion and free motion

aeroelastic tests on a new concept dynamometric section model of the Messina suspen-sion bridge. J. of Wind Engineering and Industrial Aerodynamics, 92, 441–462, 2004.

[2] G. Diana, S. Bruni and D. Rocchi. A numerical and experimental investigation on aero-dynamic non linearities in bridge response to turbulent wind, Proceedings of the EACWE 4, Prague CR, 2005.

[3] G. Diana, F. Resta and D. Rocchi. A new approach to model the aeroelastic response of bridges in time domain by means of a rheological model, Proceedings of the ICWE 12, Cairns Australia, 2007.

[4] G. Diana, F. Resta, D. Rocchi and T. Argentini. Aerodynamic hysteresis: wind tunnel tests and numerical implementation of a fully non linear model for the bridge aeroelastic forces, Proceedings of the AWAS’08, Jeju, Korea, 2008.