Improved numerical simulation of bridge deck aeroelasticity by model validation A.Šarkić, R. Höffer Building Aerodynamics Laboratory, Bochum, Germany anina.sarkic@rub.de Abstract In this study, the results of 3D numerical simulations of aerodynamic characteristics of a symmetric bridge deck section using a LES turbulence model are presented. Forced vibration simulations are performed in order to obtain flutter derivatives. The results of the investigated numerical LES model are compared with the results from wind tunnel experiments. Introduction The flow around a bridge deck is characterized by complex physical phenomena such as massive separations, reattachments, shedding of eddies, etc. These interactions between the air flow and the bridge give rise to the pressure fluctuations which create dynamic loads. The complex pressure field generated by these interaction mechanisms is commonly specified by adopting force models. Motioninduced forces are responsible for the occurrence of flutter, an important instability phenomenon, which presents a major criterion in long-span design. Scanlan and Tomko (97) proposed a method in which aerodynamic parameters called flutter derivatives, in Eqn. referred as H i, A i (i=..4), are applied to estimate these forces. L s M = q s 0 = q B B KH 0 KA z& + KH U z& + KA U B & α + K U B & α + K U H α + K 3 A α + K 3 H A 4 4 z B z B Flutter derivatives are functions of the reduced velocity U red =U/(Bf), where U is the undisturbed or mean oncoming wind velocity, B the section width and f the oscillation frequency. The dynamic free stream pressure is expressed as q o, and K represents the reduced frequency K=Bω/u=π/U red. The standard practise for estimating these instationary coefficients of the bridge deck is to undertake specific wind tunnel experiments. In recent years, a new developing approach in the analysis of aeroelasticity is based on the numerics. In this study, a 3D Large Eddy Simulation (LES) is employed as an advanced and computationally demanding method for turbulence modelling. One of the purposes of this paper is to show the applicability of the LES model in predicting the aerodynamic characteristics through the comparison of these simulated results with the experimentally obtained ones. The accuracy improvement with respect to another numerical method, namely the D Unsteady Reynolds-Averaged Navier-Stokes, will be also highlighted. In particular, the focus of this work is on the validation of numerically obtained flutter derivatives, considering a distributive representation of unsteady pressure amplitudes, phases and flutter derivatives. ()
6 th European and African onference on Wind Engineering Identification and Different Representations of Flutter Derivatives As an identification technique, the forced vibration method with prescribed harmonical motions is applied and the forces are measured using force balances. Details regarding this technique can be found in Šarkić et al, 0. Based on the measured aeroelastic lift and for the aeroelastic moment, L x and M x (x = z, α), respectively flutter derivatives can be obtained, related to the vertical (heave) motion: ρk z [ H ( K ) + ih ( K )] = L ( K ) U zˆ 4 and to the torsional (pitch) motion:, z [ A ( K) + ia ( K) ] = M ( K) ρ K U Bzˆ 4 () α [ H ( K ) + ih ( K )] L ( K ), ˆ[ ( ) ( )] α ρ K U B α A K ia K = M ( K) ρ K U B ˆ α 3 = 3 + (3) In addition to aerodynamic forces, simultaneous measurements of pressures are evaluated from the forced vibration tests. This way the flutter derivatives can be also evaluated based on the integrated pressure forces. It is of interest to note, that also other representations exists. In Argentini et al., 0 a distributed representation of flutter derivatives is presented. This approach considers the contribution of each pressure tap to the generation of global forces. Namely, total aeroelastic lift and moment, can be treated as the sum of the contributions of the forces associated to each pressure tap. For example aeroelastic lift under pitch motion can be summed-up as: L α = Ntaps N taps α L j = ρk U ˆ α j= j= [ H 3, j ( K) + ih, j ( K) ] omparing Eqn. 4 and Eqn. the global flutter derivatives can be treated as the sum of its distributed values, for example: N taps H 3 = H 3, j (5) j= Another way of presenting and evaluating pressure flutter derivatives is shown in Haan, 000. It is based on the distributed unsteady pressure amplitude and phase shift. Since pitch measurements are here of special interest, a corresponding unsteady pressure amplitude ˆ = pˆ /( ˆ α ) is introduced by p q o normalizing each pressure amplitude with the dynamic pressure and the amplitude of an angular oscillation. Representation of the distributed flutter derivatives can be derived as: H ( ˆ sinϕ x ), H = ( ˆ cos x ) = ϕ K B K B, j p, j j j 3, j p, j j j (6) where x j is an appropriate influence area. Eqn. 6 is consistent with the integral form of flutter derivatives formulated in Haan, 000. Furthermore, the distributed aeroelastic moment can be interpreted as aeroelastic lift multiplied with the moment arm x j of each pressure tap. This provides following flutter derivatives: A ( ˆ x sinϕ x ), A = ( ˆ x cos x ) = ϕ K B K B, j p, j j j j 3, j p, j j j j (7) The importance of the different representations of flutter derivatives is related to additional information carried by amplitude, phase shift and flutter derivative contributions of each pressure tap. (4)
6 th European and African onference on Wind Engineering 3 It results in deeper insight in the phenomenology of the flow-structure interaction. In addition, these different representations provide a set-up for more detailed validation regarding simulated flutter derivatives. The numerical methodology provides wind forces over the whole deck and pressures at specific locations, leading to both, global and distributed representation. 3 Experimental Approach The wind tunnel tests are performed in the boundary layer wind tunnel of the Ruhr-Universität Bochum. An experimental rig is mounted with a forced vibration mechanism. Detailed explanation of the used experimental rig can be found in Neuhaus, 009. For forced vibration tests a motor and a kinematic mechanism are driving the bridge deck model periodically in two degrees of freedom, applying 4mm amplitudes for vertical displacements and for rotation. The model is instrumented with 40 pressure taps arranged around the cross-section in the middle of the span. The pressure taps are equidistantly placed at each surface of the section. The forced vibration tests are performed using Reynolds numbers in a range of Re= 6 0 4-35 0 4 (with regard to the width of the bridge). A honeycomb grid is located at the inlet of the tunnel, generating a turbulence intensity around 3% and an integral turbulence length around 0.03m. The treated sectional model placed in the experimental rig is shown in Figure (left). Figure : Model of the bridge deck section placed in the experimental rig (left), main part of the computational domain and the hybrid mesh (right) 4 Numerical Methods The open source code OpenFOAM, based on the Finite Volume Method, is used to numerically evaluate the flow field. The 3D turbulent flow around the mentioned bridge deck is modelled by Large Eddy Simulation (LES) approach. The dynamic Smagorinsky model (Germano et al., 99) is adopted as a subgrid model. The computational domain is resolved with a hybrid grid with an overall number of. 0 6 cells. The thickness of the structured grid layer corresponds to 6 cells with the expansion ratio of.05. In the remaining part of the front D plain an unstructured quadriteral grid is used, as shown in Figure (right). The 3D grid is obtained as a projection of mentioned D hybrid grid along the spanwise direction. The spanwise length of the domain is set to L / B =. Periodic boundary conditions are imposed on both lateral sides. Upper and lower surfaces are treated as walls, following corresponding distances from the bridge deck to top and bottom of the wind tunnel. The same mesh is used in the simulations of the fixed tests and in the case of the simulations of the force vibration tests. The incoming flow in present simulations is characterised with maximal Reynolds number around Re = 0 5 (based on the deck width of the bridge) and the incoming flow is treated as smooth (turbulence intensity I = 0% ). The space averaged values of the wall unit y + are around.. The inflow velocity is
6 th European and African onference on Wind Engineering 4 mainly kept constant, where the experimentally reduced velocities are obtained by adopting the frequency of the forced oscillations. In addition, the LES simulations in this work are going to be compared to the results related to the D URANS with k-ω-sst turbulence model (Menter, 993), with details presented in the Šarkić et al., 0. 5 Discussion of the Results 5. Flow around static bridge deck The first considered LES simulation was performed with a fixed bridge deck at 0 of a flow attack. The convergence of the main integral parameters (presented in Table ) is checked following the procedure as presented in Bruno et al., 00. First 50 non-dimensional time units ( t = tu / D ) have been discarded, after which the period of next non-dimensional time units T =400 is selected. This period includes around 95 vortex-shedding periods. Table : omparisons of mean ( D, L,, M ) and RMS ( D, L, M) values of drag, lift and moment coefficients and a Strouhal number (St). Force coefficients are normalized with the bridge deck width (exp. results are obtained out of force measurements with force balances) D L M ' D ' L ' St M Experiments 0.088-0.040 0.0 0.0 0.045 0.00.30±0.03 3-D LES 0.094-0.047 0.034 0.00 0.073 0.05.33 -D URANS 0.074-0.09 0.07 - - -.39 In Table the mean and RMS values of the force coefficients are compared with experimental results. It can be remarked that the results of the LES simulation slightly overestimate the main integral parameters in general, especially the RMS values of lift coefficient. In Šarkić et al., 0 an URANS solution was obtained as nearly steady. The Strouhal number (St) was estimated based on very small oscillations of the computed lift force caused by the wake behind the bridge deck. This flow mechanism slightly overestimates the experimental St value. In contrast, the LES simulation gives well developed unsteady flow (Figure ) with a better fitting prediction of the St number to the experimental range. A deeper insight into the flow mechanism can be obtained comparing the measured and simulated mean and RMS pressure coefficients at 40 pressure taps obtained during tests at the fixed bridge deck section at 0 (Figure 3). From both plots, LES results show the prediction of the separation bubbles on the upside and downside edge of the bridge deck, larger than obtained with the experiments. This could be a result of the smooth inflow condition in LES simulations. URANS results are lacking with the presentation of the separation bubble. From Figure 3 can be observed that the LES model overestimates the RMS values in the vicinity of the reattachment points. 5. Aeroelastic forces Figure 4 compares LES flutter derivatives with two experimental and URANS results. Generally it can be remarked that LES approach is in good accordance. The LES results are showing slightly better
6 th European and African onference on Wind Engineering 5 matching to experimental values. In particular, in region of small reduced velocities, revealing the presence of vortex shedding and lock-in conditions. In addition, more pronounced differences between Figure : 3D instantaneous vorticity magnitude (ω 30) Figure 3: Mean and RMS pressure coefficient distributions for the fixed case at 0 of attack (the provided values in the plots correspond to measurement results) two numerical methods could be observed at higher reduced velocities in case of H flutter derivative. It seems that the LES H coefficients are matching better to the experimental ones, especially to the results based on the pressure measurements. Nevertheless, this improvement of the numerical LES H results has not been followed by the enhancements of numerically obtained A coefficients. Here, both numerical solutions do not show significant deviations. Global flutter derivatives based on pressure measurements are evaluated by two evaluation methods presented in Section : distributed method (Eqn. 5) and method based on total forces (Eqn. and Eqn. 3). Since the results were in good agreement, distributed approach has been enabled. Therefore the approach was used to shed some light at the observed discrepancies between pitch flutter derivatives shown in Figure 4. In Figure 5 distributions of pressure amplitude, pressure phase and distributed flutter derivatives H and A are presented for the case of two reduced velocities U red = 3 and 6.9. Regarding measured pressure amplitude, at upper and down corner of the windward side of the section, a hump shape is evident. This shape is stretched in the downstream direction when reduced velocity increases. This structure was poorly simulated in URANS where the peak value of the pressure amplitudes is placed at the most upstream position at down and upper corners. On the contrary, in LES simulations this typical pattern is present, though it is somehow pushed towards the leading edge. In Haan, 000 similar shift in pressure amplitudes is obtained when smooth inflow conditions are applied compared to the turbulent one. In Haan, 000 experiments with different turbulent inflow conditions were performed on the rectangular cross-section (B/D=6.67). Within measurement phase distributions, similar hump shape as in the case of amplitudes can be observed. Like the amplitude distribution this structure stretches in the downstream direction by an increase in reduced velocity. It is observed that URANS phase distributions disagree with the measured one. For higher reduced velocities, the URANS results provide considerably smaller phase
6 th European and African onference on Wind Engineering 6 values. The absence of the hump shape is also visible. Slightly more comparable results are only obtained in case of U red = 3. Opposite to URANS phase distribution, the LES results are better following measured distribution pattern. Similarly as in case of unsteady pressure amplitudes, phase hump pattern evaluated on the LES results is shifted downstream. This is also consistent with the results presented in Haan, 000 when comparing smooth and turbulent inflow conditions. Figure 4: Examples of flutter derivatives identified from four methods: wind tunnel force measurements, wind tunnel pressure measurements, LES simulations and URANS simulations based on simulated forces As a main source of this typical shape, separation bubbles are recognized by Matsumoto, 996. They are located at upper and down sides of the section. It is interesting that the URANS results in case of U red = 3 showed very small separations leading to slight improvement of the phase distribution, observed in Figure 5. The general form of distributed H flutter derivative is qualitatively similar to the behaviour of the distributed phase angle. This is due to the fact that H is related to the sin(φ(x)) (Haan, 000). In case of U red =6.9 and also for higher reduced velocities related to URANS simulations, hump shape is not properly simulated. This represents a great contribution of experimentally obtained global H flutter derivative, for all test cases. This is further reflected in deviation shown in Figure 4. On the other hand,
6 th European and African onference on Wind Engineering 7 the LES results are showing the same general trend of distributed H derivative compared to the measured values. The only major difference is that the shape seems to be pushed downstream. This downstream shift corresponds to shifts of both pressure amplitudes and phases described earlier. As it is discussed, this could be attributed to the smooth inflow conditions applied in case of LES simulations. Besides the shift, magnitudes of H values are in good agreement with experimental ones. Figure 5: Distributions of pressure amplitude, pressure phase H and A flutter derivatives, evaluated by: wind tunnel pressure measurements, LES simulations and URANS simulations (positive values are outside) This observation is reflected in Figure 4 by good agreement of global H coefficient curves based on LES and pressure measurement results. Despite the high similarity of the LES H results, significant deviation of corresponding A curves is recognized in Figure 4. The reason can be found in Figure 5 where comparison of distributed A results is presented. Due to the shift of the LES H derivative the moment arms are becoming smaller. This leads to the decrease of the peak A values. In other words, the hump shape decreases. This hump shape is recognized in case of measurements as the main contribution to the total A damping coefficient. onsidering the sign of these peak values, the increase of the global LES A flutter derivative in Figure 5 is justified. It is also worth pointing out that the trend of the distributed LES A curves are following the corresponding experimental ones. This was not the case for nearly all URANS simulations, except U red =3, where a similar conclusion as in case of H derivative can be drawn.
6 th European and African onference on Wind Engineering 8 6 onclusions Based on presented extended validation set-up several conclusions regarding numerical results can be drawn. Limitations related to the representation of separation bubbles near the edges using D URANS methodology were identified. These shortcomings are first pointed in case of simulations of the rigid body. Later, they are recognized as a main source of discrepancies related to the distributed unsteady pressure amplitudes and phases leading to the discrepancies in damping coefficients H and A. Validation showed that the LES results are capable of overcoming these deficiencies. In case of LES, separation bubbles were well simulated, also causing adequate changes within pressure amplitudes and phases, reflected later in the derivatives. As the main differences between LES results and pressure measurements, bigger separation bubbles are identified. It is believed that smooth inflow conditions are main factor causing this behaviour. As further development, this research will address numerically turbulence effects regarding flutter derivatives. Acknowledgments Financial support was provided by the German Academic Exchange Service (DAAD) in the framework of a scholarship for a doctorate for author AS during the years 008-0 (scholarship no. A/08/038). This support is gratefully acknowledged. References Argentini, T., Rocchi, D., Muggiasca, S., Zasso, A. 0. ross-sectional distributions versus integrated coefficients of flutter derivatives and aerodynamic admittances identified with surface pressure measurement. Journal of Wind Engineering and Industrial Aerodynamic, 04-06, 5-58. Bruno, L., Fransos, D., oste, N., & Bosco, A., 00. 3D flow around a rectangular cylinder: A computational study. Journal of Wind Engineering and Industrial Aerodynamics, 98, 63-76. Germano, M., Piomelli, U., Moin, P., & abot, W. H. 99. A dynamic subgrid-scale eddy viscosity model. Physics of Fluids A: Fluid Dynamics, 3, 7. Haan, F., 000. The effect of turbulence on the aerodynamics of the long-span bridges. PhD thesis, Department of Aerospace and Mechanical Engineering, University of Notre Dame Matsumoto, M,. Aeodynamic damping of prisms. Journal of Wind Engineering and Industrial Aerodynamic, 59, 59-75. Menter, F.R., 993. Zonal two-equation k-ω turbulence models for aerodynamic flows, AIAA Paper 93-906. Neuhaus,., Rösler, S, Höffer, R., Hortmanns, M., & Zahlten, W., 009. Identification of 8 Flutter Derivatives by Forced Vibration Tests A New Experimental Rig, In: Proceedings of European and African onference on Wind Engineering, Florence Scanlan, R., & Tomko, J., 97. Airfoil and bridge deck flutter derivatives. Journal of Engineering Mechanics Division Proceedings of the ASE 97, 77-737. Šarkić, A., Fisch, R., Höffer, R., & Bletzinger, K. U. 0. Bridge flutter derivatives based on computed, validated pressure fields. Journal of Wind Engineering and Industrial Aerodynamic, 04-06, 4-5.