DOI QR코드

DOI QR Code

Quasi-steady three-degrees-of-freedom aerodynamic model of inclined/yawed prisms: Formulation and instability for galloping and static divergence

  • Cristoforo Demartino (Zhejiang University - University of Illinois at Urbana Champaign Institute, Zhejiang University) ;
  • Zhen Sun (Construct-ViBest, Faculty of Engineering (FEUP), Univ. of Porto) ;
  • Giulia Matteoni (Arup) ;
  • Christos T. Georgakis (Department of Civil and Architectural Engineering, Aarhus University)
  • 투고 : 2022.10.02
  • 심사 : 2023.03.27
  • 발행 : 2023.07.25

초록

In this study, a generalized three-degree-of-freedom (3-DoF) analytical model is formulated to predict linear aerodynamic instabilities of a prism under quasi-steady (QS) conditions. The prism is assumed to possess a generic cross-section exposed to turbulent wind flow. The 3-DoFs encompass two orthogonal horizontal directions and rotation about the prism body axis. Inertial coupling is considered to account for the non-coincidence of the mass center and the rotation center. The aerodynamic force coefficients-drag, lift, and moment-depend on the Reynolds number based on relative flow velocity, angle of attack, and the angle between the wind and the cable. Aerodynamic forces are linearized with respect to the static equilibrium configuration and mean wind velocity. Routh-Hurwitz and Liénard and Chipart criteria are used in the eigenvalue problem, yielding an analytical solution for instabilities in galloping and static divergence types. Additionally, the minimum structural damping and stiffness required to prevent these instabilities are numerically determined. The proposed 3-DoF instability model is subsequently applied to a conductor with ice accretion and a full-scale dry inclined cable. In comparison to existing models, the developed model demonstrates superior prediction accuracy for unstable regions compared with results in wind tunnel tests.

키워드

과제정보

This research is supported by the National Natural Science Foundation of China (52050410338). This work has been partially supported by the Zhejiang University/University of Illinois at Urbana-Champaign Institute. C. Demartino acknowledges Mr. Hua Zeng for helping in revising this manuscript.

참고문헌

  1. Abdelkefi, A., Hajj, M.R. and Nayfeh, A.H. (2012), "Power harvesting from transverse galloping of square cylinder", Nonlinear Dyna., 70(2), 1355-1363. https://doi.org/10.1007/s11071-012-0538-4.
  2. Blevins, R.D. and Iwan, W.D. (1974), "The galloping response of a two-degree-of-freedom system", J. Appl. Mech., 41(4), 1113-1118. https://doi.org/10.1115/1.3423443
  3. Brennen, C.E. (1982), "A review of added mass and fluid inertial forces", Report No. CR 82.010, Naval Civil Engineering Laboratory.
  4. Carassale, L., Freda, A. and Piccardo, G. (2004), "Quasi-static model for aerodynamic instability of yawed circular cylinders", 5th International Colloquium Bluff Body Aerodynamics and Applications, Ottawa, Canada, July.
  5. Carassale, L., Freda, A. and Piccardo, G. (2005), "Aeroelastic forces on yawed circular cylinders: Quasi-steady modeling and aerodynamic instability", Wind Struct., 8(5), 373-388. https://doi.org/10.12989/was.2005.8.5.373.
  6. Carassale, L. and Kareem, A. (2010), "Modeling nonlinear systems by Volterra series", J. Eng. Mech., 136(6), 801-818. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000113.
  7. Chabart, O. and Lilien, J.L. (1998), "Galloping of electrical lines in wind tunnel facilities", J. Wind Eng. Ind. Aerod., 74-76, 967-976. https://doi.org/10.1016/S0167-6105(98)00088-9.
  8. Chen, X. and Wu, Y. (2021), "Explicit closed-form solutions of the initiation conditions for 3DOF galloping or flutter", J. Wind Eng. Ind. Aerod., 219, 104787. https://doi.org/10.1016/j.jweia.2021.104787
  9. Cheng, S., Larose, G.L., Savage, M.G., Tanaka, H. and Irwin, P.A. (2008), "Experimental study on the wind-induced vibration of a dry inclined cable-Part I: Phenomena", J. Wind Eng. Ind. Aerod., 96(12), 2231-2253. https://doi.org/10.1016/j.jweia.2008.01.008.
  10. de Sa Caetano, E. (2007), Cable Vibrations in Cable-Stayed Bridges, IABSE, Zurich, Switzerland.
  11. Demartino, C., Koss, H.H., Georgakis, C.T. and Ricciardelli, F. (2015), "Effects of ice accretion on the aerodynamics of bridge cables", J. Wind Eng. Ind. Aerod., 138, 98-119. https://doi.org/10.1016/j.jweia.2014.12.010.
  12. Demartino, C. and Ricciardelli, F. (2015), "Aerodynamic stability of ice-accreted bridge cables", J. Fluids Struct., 52, 81-100. https://doi.org/10.1016/j.jfluidstructs.2014.10.003.
  13. Demartino, C. and Ricciardelli, F. (2017), "Aerodynamics of nominally circular cylinders: A review of experimental results for Civil Engineering applications", Eng. Struct., 137, 76-114. https://doi.org/10.1016/j.engstruct.2017.01.023.
  14. Demartino, C. and Ricciardelli, F. (2018), "Assessment of the structural damping required to prevent galloping of dry HDPE stay cables using the quasi-steady approach", J. Bridge Eng., 23(4), 04018004. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001168.
  15. Demartino, C. and Ricciardelli, F. (2019), "Probabilistic versus deterministic assessment of the minimum structural damping required to prevent galloping of dry bridge hangers", J. Struct. Eng., 145(8), 04019078. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002362.
  16. Den Hartog, J.P. (1956), Mechanical Vibrations, Courier Dover Publications, New York, USA.
  17. Denoel, V. and Degee, H. (2006), "Influence of the non-linearity of the aerodynamic coefficients on the skewness of the buffeting drag force", Wind Struct., 9(6), 457-471. https://doi.org/10.12989/was.2006.9.6.457.
  18. Di Nino, S. and Luongo, A. (2020), "Nonlinear aeroelastic behavior of a base-isolated beam under steady wind flow", Int. J. Non-Linear Mech., 119, 103340. https://doi.org/10.1016/j.ijnonlinmec.2019.103340.
  19. Ferretti, M., Zulli, D. and Luongo, A. (2019), "A continuum approach to the nonlinear in-plane galloping of shallow flexible cables", Adv. Math. Phys., 2019, 6865730. https://doi.org/10.1155/2019/6865730.
  20. Gimsing, N.J. and Georgakis, C.T. (2012), Cable Supported Bridges: Concept and Design, John Wiley & Sons, UK.
  21. Gjelstrup, H. and Georgakis, C.T. (2011), "A quasi-steady 3 degree-of-freedom model for the determination of the onset of bluff body galloping instability", J. Fluids Struct., 27(7), 1021-1034. https://doi.org/10.1016/j.jfluidstructs.2011.04.006.
  22. He, M. and Macdonald, J. (2017), "Aeroelastic stability of a 3DOF system based on quasi-steady theory with reference to inertial coupling", J. Wind Eng. Ind. Aerod., 171, 319-329. https://doi.org/0.1016/j.jweia.2017.10.013. 1016/j.jweia.2017.10.013
  23. Hurwitz, A. (1895), "Ueber die bedingungen, unter welchen eine gleichung nur wurzeln mit negativen reellen theilen besitzt", Math. Ann., 46(2), 273-284. https://doi.org/10.1007/BF01446812.
  24. Idelsohn, S.R., Del Pin, F., Rossi, R. and Onate, E. (2009), "Fluid-structure interaction problems with strong added-mass effect", Int. J. Numer. Meth. Eng., 80(10), 1261-1294. https://doi.org/10.1002/nme.2659.
  25. Jones, K.F. (1992), "Coupled vertical and horizontal galloping", J. Eng. Mech., 118(1), 92-107. https://doi.org/10.1061/(ASCE)0733-9399(1992)118:1(92).
  26. Kareem, A. and Wu, T. (2013), "Wind-induced effects on bluff bodies in turbulent flows: Nonstationary, non-Gaussian and nonlinear features", J. Wind Eng. Ind. Aerod., 122, 21-37. https://doi.org/10.1016/j.jweia.2013.06.002.
  27. Lienard, A. and Chipart, M.H. (1914), "Sur le signe de la partie reelle des racines d'une equation algebrique", J. Math. Pures Appl., 10(6), 291-346.
  28. Liu, X., Zou, M., Wu, C., Yan, B. and Cai, M. (2020), "Galloping stability and aerodynamic characteristic of iced transmission line based on 3-DOF", Shock Vibr., 2020, 1-15. https://doi.org/10.1155/2020/8828319.
  29. Liu, Z. and Young, Y.L. (2010), "Static divergence of self-twisting composite rotors", J. Fluids Struct., 26(5), 841-847. https://doi.org/10.1016/j.jfluidstructs.2010.05.002.
  30. Lou, W., Wu, D., Xu, H. and Yu, J. (2020), "Galloping stability criterion for 3-DOF coupled motion of an ice-accreted conductor", J. Struct. Eng., 146(5), 04020071. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002601.
  31. Luongo, A. and Piccardo, G. (2005), "Linear instability mechanisms for coupled translational galloping", J. Sound Vibr., 288(4-5), 1027-1047. https://doi.org/10.1016/j.jsv.2005.01.056.
  32. Macdonald, J.H.G. and Larose, G.L. (2006), "A unified approach to aerodynamic damping and drag/lift instabilities, and its application to dry inclined cable galloping", J. Fluids Struct., 22(2), 229-252. https://doi.org/10.1016/j.jfluidstructs.2005.10.002.
  33. Macdonald, J.H.G. and Larose, G.L. (2008a), "Two-degree-of-freedom inclined cable galloping-Part 1: General formulation and solution for perfectly tuned system", J. Wind Eng. Ind. Aerod., 96(3), 291-307. https://doi.org/10.1016/j.jweia.2007.07.002.
  34. Macdonald, J.H.G. and Larose, G.L. (2008b), "Two-degree-of-freedom inclined cable galloping-Part 2: Analysis and prevention for arbitrary frequency ratio", J. Wind Eng. Ind. Aerod., 96(3), 308-326. https://doi.org/10.1016/j.jweia.2007.07.001.
  35. Mannini, C., Marra, A.M., Massai, T. and Bartoli, G. (2016), "Interference of vortex-induced vibration and transverse galloping for a rectangular cylinder", J. Fluids Struct., 66, 403-423. https://doi.org/10.1016/j.jfluidstructs.2016.08.002.
  36. Martin, W.W., Naudascher, E. and Currie, I.G. (1981), "Streamwise oscillations of cylinders", J. Eng. Mech. Divis., 107(3), 589-607. https://doi.org/10.1061/JMCEA3.0002726.
  37. Matejicka, L. and Georgakis, C.T. (2022), "A review of ice and snow risk mitigation and control measures for bridge cables", Cold Regions Sci. Technol., 193, 103429. https://doi.org/10.1016/j.coldregions.2021.103429.
  38. Matsumiya, H., Yagi, T. and Macdonald, J.H.G. (2021), "Effects of aerodynamic coupling and non-linear behaviour on galloping of ice-accreted conductors", J. Fluids Struct., 106, 103366. https://doi.org/10.1016/j.jfluidstructs.2021.103366.
  39. Nigol, O. and Buchan, P.G. (1981), "Conductor galloping-Part II torsional mechanism", IEEE Trans. Power Appar. Syst., (2), 708-720. https://doi.org/10.1109/TPAS.1981.316922.
  40. Nikitas, N. and Macdonald, J.H.G. (2014), "Misconceptions and generalizations of the Den Hartog galloping criterion", J. Eng. Mech., 140(4), 04013005. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000697.
  41. Nikitas, N. and Macdonald, J.H.G. (2015), "Aerodynamic forcing characteristics of dry cable galloping at critical Reynolds numbers", Eur. J. Mech. B/Fluids, 49, 243-249. https://doi.org/10.1016/j.euromechflu.2014.09.005.
  42. Ohkuma, T., Kagami, J., Nakauchi, H., Kikuchi, T., Takeda, K. and Marukawa, H. (2000), "Numerical analysis of overhead transmission line galloping considering wind turbulence", Electr. Eng. JP., 131(3), 19-33. https://doi.org/10.1002/(SICI)1520-6416(200003)131:3<19::AID-EEJ3>3.0.CO;2-S.
  43. Piccardo, G., Carassale, L. and Freda, A. (2011), "Critical conditions of galloping for inclined square cylinders", J. Wind Eng. Ind. Aerod., 99(6-7), 748-756. https://doi.org/10.1016/j.jweia.2011.03.009.
  44. Piccardo, G., Pagnini, L.C. and Tubino, F. (2015), "Some research perspectives in galloping phenomena: critical conditions and post-critical behavior", Continuum Mech. Thermodyn., 27, 261-285. https://doi.org/10.1007/s00161-014-0374-5.
  45. Raeesi, A., Cheng, S. and Ting, D.S.K. (2013), "Aerodynamic damping of an inclined circular cylinder in unsteady flow and its application to the prediction of dry inclined cable galloping", J. Wind Eng. Ind. Aerod., 113, 12-28. https://doi.org/10.1016/j.jweia.2012.12.003.
  46. Stoyanoff, S. (2001), "A unified approach for 3D stability and time domain response analysis with application of quasi-steady theory", J. Wind Eng. Ind. Aerod., 89(14-15), 1591-1606. https://doi.org/10.1016/S0167-6105(01)00157-X.
  47. Symes, J. and Macdonald, J. (2006), "Quasi-steady" dry-galloping" analysis of inclined cables in turbulent flow", Proceedings of 7th UK Conference on Wind Engineering, Glasgow, September.
  48. Takashi, N. and Hughes, T.J.R. (1992), "An arbitrary Lagrangian-Eulerian finite element method for interaction of fluid and a rigid body", Comput. Meth. Appl. Mech. Eng., 95(1), 115-138. https://doi.org/10.1016/0045-7825(92)90085-X.
  49. Yu, P., Desai, Y.M., Shah, A.H. and Popplewell, N. (1993), "Three-degree-of-freedom model for galloping. Part I: Formulation", J. Eng. Mech., 119(12), 2404-2425. https://doi.org/10.1061/(ASCE)0733-9399(1993)119:12(2404)
  50. Yu, P., Shah, A.H. and Popplewell, N. (1992), "Inertially coupled galloping of iced conductors", J. Appl. Mech., 59(1), 140-145. https://doi.org/10.1115/1.2899419.
  51. Zhao, J., Jacono, D.L., Sheridan, J., Hourigan, K. and Thompson, M.C. (2018), "Experimental investigation of in-line flow-induced vibration of a rotating circular cylinder", J. Fluid Mech., 847, 664-699. https://doi.org/10.1017/jfm.2018.357.
  52. Zulli, D. and Di Egidio, A. (2015), "Galloping of internally resonant towers subjected to turbulent wind", Continuum Mech. Thermodyn., 27(4), 835-849. https://doi.org/10.1007/s00161-014-0384-3.