Skip to main content
SpringerLink
Log in

Evaluation of numerical techniques for modeling flutter phenomenon into two geometries: the 1:4.9 rectangle and the Great Belt East Bridge in scale 1:7

  • Technical Paper
  • Published:
Journal of the Brazilian Society of Mechanical Sciences and Engineering Aims and scope Submit manuscript

Abstract

The flutter phenomenon must be carefully evaluated, as it can lead structures to collapse. This study presents a methodology based on computational fluid dynamics to obtain the flutter derivatives and the critical flutter velocity, through forced vibrations in bodies immersed in a fluid medium. Two approaches were analyzed. In the first (8COEF), torsion and flexural movements were imposed. In the second, simulations were carried out in torsion mode, and through linear equations (LE), the complete set of eight coefficients was obtained. While the first can be seen as the most robust, as all coefficients are obtained from computer simulations, the second is less computationally expensive. The study was applied to a 1:4.9 rectangle and to the cross-section of the Great Belt East Bridge (GBEB). The simulations were submitted to turbulent flow with Reynolds number equal to 10\(^{5}\), using k–\(\omega \) SST and k–\(\omega \) SSTLM turbulence models. For the static case, simulations were performed to obtain the average values of the aerodynamic coefficients. OpenFOAM® was used to solve the Navier–Stokes equations for an incompressible fluid. The critical flutter velocity for the GBEB was estimated using the 8COEF and the LE approaches. It was noticed that the results estimated with the LE were effective and with a good approximation with those of the 8COEF but at a lower computational cost. All results were validated with numerical and experimental studies available in the literature. Finally, this research stands out in presenting an assertive and pragmatic CFD methodology to obtain critical flutter velocity on structures.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23

Similar content being viewed by others

References

  1. Menter FR (1994) Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J 32(8):1598–1605. https://doi.org/10.2514/3.12149

    Article  Google Scholar 

  2. Menter FR, Langtry R, Völker S (2006) Transition modelling for general purpose CFD codes. Flow Turbul Combust 77(1):277–303

    Article  MATH  Google Scholar 

  3. Le Maitre OP, Scanlan RH, Knio OM (2003) Estimation of the flutter derivatives of an NACA airfoil by means of Navier–Stokes simulation. J Fluids Struct 17(1):1–28

    Article  Google Scholar 

  4. Matsumoto M (1996) Aerodynamic damping of prisms. J Wind Eng Ind Aerodyn 59(2):159–175

    Article  Google Scholar 

  5. Leonard BP (1979) A stable and accurate convective modelling procedure based on quadratic upstream interpolation. Comput Methods Appl Mech Eng 19(1):59–98

    Article  MATH  Google Scholar 

  6. Warming RF, Beam RM (1976) Upwind second-order difference schemes and applications in aerodynamic flows. AIAA J 14(9):1241–1249. https://doi.org/10.2514/3.61457

    Article  MathSciNet  MATH  Google Scholar 

  7. Nieto F, Owen JS, Hargreaves DM, Hernández S (2015) Bridge deck flutter derivatives: efficient numerical evaluation exploiting their interdependence. J Wind Eng Ind Aerodyn 136:138–150

    Article  Google Scholar 

  8. Scanlan RH, Tomko JJ (1971) Airfoil and bridge deck flutter derivatives. J Eng Mech Div 97(6):1717–1737

    Article  Google Scholar 

  9. Larsen A (1993) Aerodynamic aspects of the final design of the 1624 m suspension bridge across the great belt. J Wind Eng Ind Aerodyn 48(2):261–285. https://doi.org/10.1016/0167-6105(93)90141-A

    Article  Google Scholar 

  10. Scanlan RH, Jones NP, Singh L (1997) Inter-relations among flutter derivatives. J Wind Eng Ind Aerodyn 69–71:829–837. https://doi.org/10.1016/S0167-6105(97)00209-2 (Proceedings of the 3rd international colloqium on bluff body aerodynamics and applications)

    Article  Google Scholar 

  11. Larsen A, Walther JH (1998) Discrete vortex simulation of flow around five generic bridge deck sections. J Wind Eng Ind Aerodyn 77(1–3):591–602

    Article  Google Scholar 

  12. Honoré Walther J, Larsen A (1997) Two dimensional discrete vortex method for application to bluff body aerodynamics. J Wind Eng Ind Aerodyn 67:183–193

    Article  Google Scholar 

  13. Huang L, Liao H, Wang B, Li Y (2009) Numerical simulation for aerodynamic derivatives of bridge deck. Simul Model Pract Theory 17(4):719–729. https://doi.org/10.1016/j.simpat.2008.12.004

    Article  Google Scholar 

  14. Bai Y, Sun D, Lin J (2010) Three dimensional numerical simulations of long-span bridge aerodynamics, using block-iterative coupling and des. Comput Fluids 39(9):1549–1561

    Article  MATH  Google Scholar 

  15. Jurado JA, Hermandez S, Nieto F, Mosquera A (2011) Bridge aeroelasticity: sensitivity analysis and optimal design. WIT PRESS, Printed in Great Britain by MPG Books Group, Bodmin and King’s Lynn, Southampton

    Google Scholar 

  16. de Miranda S, Patruno L, Ubertini F, Vairo G (2014) On the identification of flutter derivatives of bridge decks via RANS turbulence models: benchmarking on rectangular prisms. Eng Struct 76:359–370. https://doi.org/10.1016/j.engstruct.2014.07.027

    Article  Google Scholar 

  17. Farsani HY, Valentine DT, Arena A, Lacarbonara W, Marzocca P (2014) Indicial functions in the aeroelasticity of bridge decks. J Fluids Struct 48:203–215

    Article  Google Scholar 

  18. Tubino F (2005) Relationships among aerodynamic admittance functions, flutter derivatives and static coefficients for long-span bridges. J Wind Eng Ind Aerodyn 93(12):929–950

    Article  Google Scholar 

  19. Bakis KN, Massaro M, Williams MS, Limebeer DJN (2016) Aeroelastic control of long-span suspension bridges with controllable winglets. Struct Control Health Monit 23(12):1417–1441

    Article  Google Scholar 

  20. Cid Montoya M, Nieto F, Hernández S, Kusano I, Álvarez AJ, Jurado JA (2018) Cfd-based aeroelastic characterization of streamlined bridge deck cross-sections subject to shape modifications using surrogate models. J Wind Eng Ind Aerodyn 177:405–428

    Article  Google Scholar 

  21. Zamiri G, Sabbagh-Yazdi S-R (2021) A numerical technique for determining aerodynamic derivatives of a suspension bridge deck. Iran J Sci Technol Trans Civ Eng 45(4):2283–2296

    Article  Google Scholar 

  22. Costa LMF, Montiel JES, Corrêa L, Lofrano FC, Nakao OS, Kurokawa FA (2022) Influence of standard \(\kappa \)-\(epsilon\), sst \(\kappa \)-\(omega\) and les turbulence models on the numerical assessment of a suspension bridge deck aerodynamic behavior. J Braz Soc Mech Sci Eng 44(8):350

    Article  Google Scholar 

  23. Launder BE, Spalding DB (1974) The numerical computation of turbulent flows. Comput Methods Appl Mech Eng 3(2):269–289

    Article  MATH  Google Scholar 

  24. Yakhot V, Thangam S, Gatski TB, Orszag SA, Speziale CG (1991) Development of turbulence models for shear flows by a double expansion technique, legacy CDMS

  25. Menter F, Kuntz M, Langtry R (2003) Ten years of industrial experience with the SST turbulence model. Heat Mass Transf 4:625–632

    Google Scholar 

  26. Langtry R (2006) A correlation-based transition model using local variables for unstructured parallelized CFD codes. Master’s thesis, Universität Stuttgart, Germany

  27. Simiu E, Scanlan RH (1978) Wind effects on structures: an introduction to wind engineering. Wiley, New York

    Google Scholar 

  28. Wilcox DC (2008) Formulation of the k–\(\omega \) turbulence model revisited. AIAA J 46(11):2823–2838. https://doi.org/10.2514/1.36541

    Article  Google Scholar 

  29. Patankar S (1988) Recent developments in computational heat transfer

  30. Issa RI, Gosman A, Watkins A (1986) The computation of compressible and incompressible recirculating flows by a non-iterative implicit scheme. J Comput Phys 62(1):66–82

    Article  MathSciNet  MATH  Google Scholar 

  31. Kusano I, Baldomir A, Ángel Jurado J, Hernández S (2018) The importance of correlation among flutter derivatives for the reliability based optimum design of suspension bridges. Eng Struct 173:416–428. https://doi.org/10.1016/j.engstruct.2018.06.091

    Article  Google Scholar 

  32. Spalding DB (1972) A novel finite difference formulation for differential expressions involving both first and second derivatives. Int J Numer Methods Eng 4(4):551–559. https://doi.org/10.1002/nme.1620040409

    Article  Google Scholar 

  33. Sweby PK (1984) High resolution schemes using flux limiters for hyperbolic conservation laws. SIAM J Numer Anal 21(5):995–1011

    Article  MathSciNet  MATH  Google Scholar 

  34. Araújo AMS, Fronczak J, Flores GAM, Cury AA, Hallak PH (2022) Comparison of divergence schemes applied to the static case of the Great Belt East Bridge. Paper presented at the XLIII Ibero-Latin-American congress on computational methods in engineering (CILAMCE 2022), 21–25 November

  35. Versteeg HK, Malalasekera W (2007) An introduction to computational fluid dynamics: the finite volume method. Pearson Education Ltd., Harlow

    Google Scholar 

  36. Šarkić A, Fisch R, Höffer R, Bletzinger K-U (2012) Bridge flutter derivatives based on computed, validated pressure fields. J Wind Eng Ind Aerodyn 104–106:141–151. https://doi.org/10.1016/j.jweia.2012.02.033 (13th international conference on wind engineering)

    Article  Google Scholar 

  37. Dowell EH (2014) A modern course in aeroelasticity. Springer, London

    MATH  Google Scholar 

Download references

Acknowledgements

The authors wish to thank the Graduate Program in Civil Engineering of the UFJF and CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Finance Code 001)

Co-author Alexandre A. Cury acknowledges the financial support by CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico - Grant 303982/2022-5) and FAPEMIG (Fundação de Amparo à Pesquisa do Estado de Minas Gerais - Grant PPM-00001-18).

Co-author Patricia H. Hallak acknowledges the financial support by CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico - Grant 303221/2022-4) and FAPEMIG (Fundação de Amparo à Pesquisa do Estado de Minas - Grant APQ-00869-22).

Author information

Author notes

  1. Alexandre Miguel Silva Araújo, Juliema Fronczak, Alexandre Abrahão Cury and Patricia Habib Hallak have contributed equally to this work.

Authors and Affiliations

  1. Postgraduate Program in Civil Engineering, Federal University of Juiz de Fora, José Lourenço Kelmer Street, Juiz de Fora, Minas Gerais, 36036-900, Brazil

    Alexandre Miguel Silva Araújo, Juliema Fronczak, Gabriel Antonio Mendes das Flores, Lucas Lucinda de Sá, Alexandre Abrahão Cury & Patricia Habib Hallak

  2. Department of Computational and Applied Mechanics, Federal University of Juiz de Fora, José Lourenço Kelmer Street, Juiz de Fora, Minas Gerais, 36036-900, Brazil

    Alexandre Abrahão Cury & Patricia Habib Hallak

Authors
  1. Alexandre Miguel Silva Araújo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Juliema Fronczak
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Gabriel Antonio Mendes das Flores
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Lucas Lucinda de Sá
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Alexandre Abrahão Cury
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Patricia Habib Hallak
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Patricia Habib Hallak.

Ethics declarations

Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Technical Editor: Savio Souza Venancio Vianna.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix A Vibration modes from Table 5

Appendix A Vibration modes from Table 5

See Table 6.

Table 6 Vibration modes
Full size table

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Araújo, A.M.S., Fronczak, J., das Flores, G.A.M. et al. Evaluation of numerical techniques for modeling flutter phenomenon into two geometries: the 1:4.9 rectangle and the Great Belt East Bridge in scale 1:7. J Braz. Soc. Mech. Sci. Eng. 45, 641 (2023). https://doi.org/10.1007/s40430-023-04545-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40430-023-04545-8

Keywords

Search

Navigation