Wind and Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Aerostatic pressure of streamlined box girder based on conformal mapping method and its application

  • Wu, Lianhuo (Department of Bridge Engineering, Southwest Jiaotong University) ;
  • Ju, J. Woody (Department of Civil and Environmental Engineering, University of California) ;
  • Zhang, Mingjin (Department of Bridge Engineering, Southwest Jiaotong University) ;
  • Li, Yongle (Department of Bridge Engineering, Southwest Jiaotong University) ;
  • Qin, Jingxi (Department of Civil and Environmental Engineering, University of California)
  • Received : 2022.04.27
  • Accepted : 2022.09.06
  • Published : 2022.10.25
⟨ Previous Next ⟩

Abstract

The conformal mapping method (CMM) has been broadly exploited in the study of fluid flows over airfoils and other research areas, yet it's hard to find relevant research in bridge engineering. This paper explores the feasibility of CMM in streamlined box girder bridges. Firstly, the mapping function transforming a unit circle to the streamlined box girder was solved by CMM. Subsequently, the potential flow solution of aerostatic pressure on the streamlined box girder was obtained and was compared with numerical simulation results. Finally, the aerostatic pressure attained by CMM was utilized to estimate the aerostatic coefficient and flutter performance of the streamlined box girder. The results indicate that the solution of the aerostatic pressure by CMM on the windward side is satisfactory within a small angle of attack. Considering the windward aerostatic pressure and coefficient of correction, CMM can be employed to estimate the rate of change of the lift and moment coefficients with angle of attack and the influence of the geometric shape of the streamlined box girder on flutter performance.

Keywords

Acknowledgement

This work was supported by a grant from the National Natural Science Foundation of China (No. U21A20154).

References

  1. Adanur, S., Gunaydin, M., Altunisik, A.C. and Sevim, B. (2012), "Construction stage analysis of Humber Suspension Bridge", Appl. Math. Model., 36(11), 5492-5505. https://doi.org/10.1016/j.apm.2012.01.011.
  2. Chen, H. and Jaworski, J.W. (2020), "Aeroelastic interactions and trajectory selection of vortex gusts impinging upon Joukowski airfoils", J. Fluid. Struct., 96, 103026. https://doi.org/10.1016/j.jfluidstructs.2020.103026.
  3. Chen, S.R. and Cai, C.S. (2003), "Evolution of long-span bridge response to wind-numerical simulation and discussion", Comput. Struct., 81(21), 2055-2066. https://doi.org/10.1016/S0045-7949(03)00261-X.
  4. Chen, X. and Kareem, A. (2002), "Advances in modeling of aerodynamic forces on bridge decks", J. Eng. Mech., 128(11), 1193-1205. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:11(1193).
  5. Chen, X. and Kareem, A. (2006), "Revisiting multimode coupled bridge flutter: Some new insights", J. Eng. Mech., 132(10), 1115-1123. https://doi.org/10.1061/(ASCE)0733-9399(2006)132:10(1115).
  6. Chen, Z., Tang, H., Li, Y. and Wang, B. (2019), "Wake effects of an upstream bridge on aerodynamic characteristics of a downstream bridge", Wind Struct., 29(6), 417-430. https://doi.org/10.12989/was.2019.29.6.417.
  7. Cheng, J., Jiang, J.J. and Xiao, R.C. (2003), "Aerostatic stability analysis of suspension bridges under parametric uncertainty", Eng. Struct., 25(13), 1675-1684. https://doi.org/10.1016/S0141-0296(03)00146-9.
  8. Chui, S.T., Chen, X., Liu, M., Lin, Z. and Zi, J. (2018), "Scattering of electromagnetic waves from a cone with conformal mapping: Application to scanning near-field optical microscope", Phys. Rev. B, 97(8), 081406. https://doi.org/10.1103/PhysRevB.97.081406.
  9. DeLillo, T.K. and Sahraei, S. (2019), "Computation of plane potential flow past multi-element airfoils using conformal mapping, revisited", J. Comput. Appl. Math., 362, 246-261. https://doi.org/10.1016/j.cam.2018.08.031.
  10. Dyachenko, A.I., Lushnikov, P.M. and Zakharov, V.E. (2019), "Non-canonical Hamiltonian structure and Poisson bracket for two-dimensional hydrodynamics with free surface", J. Fluid Mech., 869, 526-552. https://doi.org/10.1017/jfm.2019.219.
  11. Fujino, Y., Iwamoto, M., Ito, M. and Hikami, Y. (1992), "Wind tunnel experiments using 3D models and response prediction for a long-span suspension bridge", J. Wind Eng. Ind. Aerod., 42(1-3), 1333-1344. https://doi.org/10.1016/0167-6105(92)90141-V.
  12. Jiang, B., Zhou, Z., Yan, K. and Hu, C. (2021), "Effect of web inclination of streamlined flat box Ddeck on aerostatic performance of a bridge", J. Bridge Eng., 26(2), 04020126. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001663.
  13. Krishnamurty, K. (1966), Principles of Ideal-fluid Aerodynamics, New York: John Wiley & Sons Inc.
  14. Kuroda, S. (1997), "Numerical simulation of flow around a box girder of a long span suspension bridge", J. Wind Eng. Ind. Aerod., 67, 239-252. https://doi.org/10.1016/S0167-6105(97)00076-7.
  15. Lee, N., Lee, H., Baek, C. and Lee, S. (2016), "Aeroelastic analysis of bridge deck flutter with modified implicit coupling method", J. Wind Eng. Ind. Aerod., 155, 11-22. https://doi.org/10.1016/j.jweia.2016.04.010.
  16. Li, H., Zhang, L., Wu, B., Ni, Z. and Yang, Y. (2021), "Effects of the angle of attack on the aerodynamic characteristics of a streamlined box girder", Adv. Struct. Eng., 24(10), 2090-2104. https://doi.org/10.1177/1369433221992490.
  17. Li, S., Li, M., Zeng, J. and Liao, H., (2016), "Aerostatic load on the deck of cable-stayed bridge in erection stage under skew wind", Wind Struct., 22(1), 43-63. https://doi.org/10.12989/was.2016.22.1.043.
  18. Li, Y. and Zheng, K. (2021), "Stress intensity factor analysis of kinked and hole crack in an infinite plate using numerical conformal mapping", Theor. Appl. Fract. Mech., 114, 103022. https://doi.org/10.1016/j.tafmec.2021.103022.
  19. Li, Y.L., Chen, X.Y., Yu, C.J., Togbenou, K., Wang, B. and Zhu, L.D. (2018), "Effects of wind fairing angle on aerodynamic characteristics and dynamic responses of a streamlined trapezoidal box girder", J. Wind Eng. Ind. Aerod., 177, 69-78. https://doi.org/10.1016/j.jweia.2018.04.006.
  20. Liao, H., Mei, H., Hu, G., Wu, B. and Wang, Q. (2021), "Machine learning strategy for predicting flutter performance of streamlined box girders", J. Wind Eng. Ind. Aerod., 209, 104493. https://doi.org/10.1016/j.jweia.2020.104493.
  21. Ma, C., Wang, J., Li, Q.S. and Liao, H. (2019), "3D aerodynamic admittances of streamlined box bridge decks", Eng. Struct., 179, 321-331. https://doi.org/10.1016/j.engstruct.2018.11.007.
  22. Ma, R., Zhou, Q. and Li, M., (2020), "Effect of countermeasures on the galloping instability of a long-span suspension footbridge", Wind Struct., 30(5), 499-509. https://doi.org/10.12989/was.2020.30.5.499.
  23. Ma, T., Zhao, L., Shen, X. and Ge, Y. (2021), "Case study of three-dimensional aeroelastic effect on critical flutter wind speed of long-span bridges", J. Wind Eng. Ind. Aerod., 212, 104614. https://doi.org/10.1016/j.jweia.2021.104614.
  24. Mei, H. (2020), "Improvement of flutter performance of a streamlined box girder by using an upper central stabilizer", J. Bridge Eng., 25(8), 04020053. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001584.
  25. Oiseth, O., Ronnquist, A. and Sigbjornsson, R. (2010), "Simplified prediction of wind-induced response and stability limit of slender long-span suspension bridges, based on modified quasisteady theory: A case study", J. Wind Eng. Ind. Aerod., 98, 730-741. https://doi.org/10.1016/j.jweia.2010.06.009.
  26. Poozesh, A. and Mirzaei, M., (2017), "Flow simulation around cambered airfoil by using conformal mapping and intermediate domain in lattice boltzmann method", J. Stat. Phys., 166, 354-367. https://doi.org/10.1007/s10955-016-1657-y.
  27. Qi, H., Keshan, C., Wanhua, S. and Hengjun, Z. (2007), "Vertical curve analysis of extruding die cavity and conformal mapping", J. Rare Earths, 25, 375-378. https://doi.org/10.1016/S1002-0721(07)60509-2.
  28. Scanlan, R.H. and Tomko, J.J. (1971), "Airfoil and bridge deck flutter derivatives", J. Eng. Mech., 97(6), 1717-1737. https://doi.org/10.1061/JMCEA3.0001526.
  29. Selig, M.S. and Maughmer, M.D. (1992), "Multipoint inverse airfoil design method based on conformal mapping", AIAA J., 30(5), 1162-1170. https://doi.org/10.2514/3.11046.
  30. Simiu, E. and Scanlan, R.H. (1996), Wind effects on structures: fundamentals and applications to design (Vol. 688). New York: John Wiley.
  31. Song, K., Yin, D., Dai, M. and Schiavone, P. (2021), "Design of non-circular nanoinhomogeneities with uniform heat flux in two-dimensional heat conduction", Int. J. Heat Mass Transf., 166, 120789. https://doi.org/10.1016/j.ijheatmasstransfer.2020.120789.
  32. Walsh, J.L. (1973), "History of the riemann mapping theorem", Am. Math. Mon., 80(3), 270-276. https://doi.org/10.1080/00029890.1973.11993266.
  33. Wang, Z., Tang, H., Li, Y., Guo, J. and Liu, Z. (2021), "Windproof ability of aerodynamic measures to improve the wind environment above a truss girder", Wind Struct., 32(5), 423-437. https://doi.org/10.12989/was.2021.32.5.423.
  34. Wu, T. and Kareem, A. (2013), "Bridge aerodynamics and aeroelasticity: A comparison of modeling schemes", J. Fluid. Struct., 43, 347-370. https://doi.org/10.1016/j.jfluidstructs.2013.09.015.
  35. Xu, F.Y., Li, B.B., Cai, C.S. and Zhang, Z. (2014), "Experimental investigations on aerostatic characteristics of bridge decks under various conditions", J. Bridge Eng., 19(7), 04014024. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000601.
  36. Xu, L. and Chen, H. (2015), "Conformal transformation optics", Nat. Photonics, 9(1), 15-23. https://doi.org/10.1038/nphoton.2014.307.
  37. Zhang, X. (2007), "Influence of some factors on the aerodynamic behavior of long-span suspension bridges", J. Wind Eng. Ind. Aerod., 95, 149-164. https://doi.org/10.1016/j.jweia.2006.08.003.