DOI QR코드

DOI QR Code

Mode analysis and low-order dynamic modelling of the three-dimensional turbulent flow filed around a building

  • Lei Zhou (Department of Civil and Environmental Engineering, The Hong Kong University of Science and Technology) ;
  • Bingchao Zhang (Department of Civil and Environmental Engineering, The Hong Kong University of Science and Technology) ;
  • K.T. Tseb (Department of Civil and Environmental Engineering, The Hong Kong University of Science and Technology)
  • Received : 2023.04.10
  • Accepted : 2024.04.28
  • Published : 2024.05.25

Abstract

This study presents a mode analysis of 3D turbulent velocity data around a square-section building model to identify the dynamic system for Kármán-type vortex shedding. Proper orthogonal decomposition (POD) was first performed to extract the significant 3D modes. Magnitude-squared coherence was then applied to detect the phase consistency between the modes, which were roughly divided into three groups. Group 1 (modes 1-4) depicted the main vortex shedding on the wake of the building, with mode 2 being controlled by the inflow fluctuation. Group 2 exhibited complex wake vortexes and single-sided vortex phenomena, while Group 3 exhibited more complicated phenomena, including flow separation. Subsequently, a third-order polynomial regression model was used to fit the dynamics system of modes 1, 3, and 4, which revealed average trend of the state trajectory. The two limit cycles of the regression model depicted the two rotation directions of Kármán-type vortex. Furthermore, two characteristic periods were identified from the trajectory generated by the regression model, which indicates fast and slow motions of the wake vortex. This study provides valuable insights into 3D mode morphology and dynamics of Kármán-type vortex shedding that helps to improve design and efficiency of structures in turbulent flow.

Keywords

References

  1. Architectural Institute of Japan (2016), AIJ Benchmarks for Validation of CFD Simulations Applied to Pedestrian Wind Environment around Build. Architectural Institute of Japan, Tokyo.
  2. Baker, C.J. (2000), "Aspects of the use of proper orthogonal decomposition of surface pressure fields", Wind Struct., 3, 97-115.
  3. Bendat, J.S. and Piersol, A.G. (2010), Random data : analysis and measurement procedures. John Wiley & Sons, Ltd, Hoboken.
  4. Bhatt, R. and Alam, M.M. (2018), "Vibrations of a square cylinder submerged in a wake", J. Fluid Mech., 853, 301-332.
  5. Bienkiewicz, B. (1996), "New tools in wind engineering", J. Wind Eng. Ind. Aerod., 65, 279-300. https://doi.org/10.1016/S0167-6105(97)00047-0.
  6. Brunton, S.L., Brunton, B.W., Proctor, J.L., Kaiser, E. and Nathan Kutz, J. (2017), "Chaos as an intermittently forced linear system", Nat. Commun. 8, 1-9. https://doi.org/10.1038/s41467-017-00030-8.
  7. Brunton, S.L., Proctor, J.L., Kutz, J.N. and Bialek, W. (2016), "Discovering governing equations from data by sparse identification of nonlinear dynamical systems", Proc. Natl. Acad. Sci., 113, 3932-3937. https://doi.org/10.1073/pnas.1517384113.
  8. Cantwell, B.J. (1981), "Organized motion in turbulent flow", Annu. Rev. Fluid Mech., 13, 457-515. https://doi.org/10.1146/annurev.fl.13.010181.002325.
  9. Carassale, L. and Brunenghi, M.M. (2011), "Statistical analysis of wind-induced pressure fields: A methodological perspective", J. Wind Eng. Ind. Aerod., 99, 700-710.
  10. Carter, G.C., Knapp, C.H. and Nuttall, A.H. (1973), "Estimation of the magnitude-squared coherence function via overlapped fast fourier transform processing", IEEE Trans. Audio Electroacoust. 21, 337-344. https://doi.org/10.1109/TAU.1973.1162496
  11. Cheng, L., Lam, K.M. and Wong, S.Y. (2015), "POD analysis of crosswind forces on a tall building with square and H-shaped cross sections", Wind Struct., 21, 63-84.
  12. Clough, R.W. and Penzien, J. (2010), Dynamics of Structures, Computers and Structures, Berkeley.
  13. Crivellini, A., Nigro, A., Colombo, A., Ghidoni, A., Noventa, G., Cimarelli, A. and Corsini, R. (2022), "Implicit large eddy simulations of a rectangular 5: 1 cylinder with a high-order discontinuous Galerkin method", Wind Struct., 34(1), 59-72.
  14. Galletti, B., Bruneau, C.H., Zannetti, L. and Iollo, A. (2004), "Low-order modelling of laminar flow regimes past a confined square cylinder", J. Fluid Mech., 503, 161-170. https://doi.org/10.1017/S0022112004007906.
  15. Gao, D., Chen, G., Min, X. and Chen, W. (2022), "Wake-vortex evolution behind a fixed circular cylinder with symmetric jets", Exp. Therm. Fluid Sci., 135, 110629.
  16. Guissart, A., Elbaek, E. and Hussong, J. (2022), "PIV study of the flow around a 5: 1 rectangular cylinder at moderate Reynolds numbers and small incidence angles", Wind Struct., 34(1), 15-27.
  17. Hasegawa, K., Fukami, K., Murata, T. and Fukagata, K. (2020), "Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes", Theoretic. Comput. Fluid Dyn., 34, 367-383.
  18. Ikegaya, N., Okaze, T., Kikumoto, H., Imano, M., Ono, H. and Tominaga, Y. (2019), "Effect of the numerical viscosity on reproduction of mean and turbulent flow fields in the case of a 1:1:2 single block model", J. Wind Eng. Ind. Aerod., 191, 279-296. https://doi.org/10.1016/j.jweia.2019.06.013.
  19. Kikitsu, H., Okuda, Y., Ohashi, M. and Kanda, J. (2008), "POD analysis of wind velocity field in the wake region behind vibrating three-dimensional square prism", J. Wind Eng. Ind. Aerod., 96(10-11), 2093-2103.
  20. Kikumoto, H., Ooka, R., Han, M. and Nakajima, K. (2018), "Consistency of mean wind speed in pedestrian wind environment analyses: Mathematical consideration and a case study using large-eddy simulation", J. Wind Eng. Ind. Aerod., 173. https://doi.org/https://doi.org/10.1016/j.jweia.2017.11.021
  21. Lakshmanan, M. and Rajasekar, S. (2003), Nonlinear dynamics : Integrability, chaos and patterns. Springer Berlin Heidelberg.
  22. Lam, K.M., Leung, M.Y.H. and Zhao, J.G. (2008), "Interference effects on wind loading of a row of closely spaced tall buildings", J. Wind Eng. Ind. Aerod., 96, 562-583.
  23. Li, C.Y., Lin, X., Hu, G., Zhou, L., Tse, T.K., and Fu, Y. (2023), "Applied Koopmanistic interpretation of subcritical prism wake physics using the dynamic mode decomposition", Wind Struct., 37(3), 191-209.
  24. Liu, Z., Zhou, L., Tang, H., Wang, Z., Zhao, F., Ji, X. and Zhang, H. (2024), "Primary instability, sensitivity and active control of flow past two tandem circular cylinders", Ocean Eng., 294, 116863.
  25. Loiseau, J.C. and Brunton, S.L. (2018), "Constrained sparse Galerkin regression", J. Fluid Mech., 838, 42-67. https://doi.org/10.1017/jfm.2017.823
  26. Lumley, J.L. (1967), "The structure of inhomogeneous turbulent flows", Atmos. Turbul. Wave Propag., 166-178.
  27. Lumley, J.L. (1970), Stochastic Tools in Turbulence. Academic Press.
  28. Lusch, B., Kutz, J.N. and Brunton, S.L. (2018), "Deep learning for universal linear embeddings of nonlinear dynamics", Nat. Commun. 9, 1-10. https://doi.org/10.1038/s41467-018-07210-0.
  29. Ma, T. and Feng, C. (2022), "Reynolds number and scale effects on aerodynamic properties of streamlined bridge decks", Wind Struct, 34(4), 355-369.
  30. Meng, Y. and Hibi, K. (1998), "Turbulent measurements of the flow field around a high-rise building", Wind Eng. JAWE, 1998, 55-64. https://doi.org/10.5359/jawe.1998.76_55.
  31. Noack, B.R., Afanasiev, K., Morzynski, M., Tadmor, G. and Thiele, F. (2003), "A hierarchy of low-dimensional models for the transient and post-transient cylinder wake", J. Fluid Mech. 497, 335-363. https://doi.org/10.1017/S0022112003006694.
  32. Oberleithner, K., Rukes, L. and Soria, J. (2014), "Mean flow stability analysis of oscillating jet experiments", J. Fluid Mech. 757, 1-32. https://doi.org/10.1017/jfm.2014.472.
  33. Okaze, T., Kikumoto, H., Ono, H., Imano, M., Hasama, T., Kishida, T., Nakao, K., Ikegaya, N., Tabata, Y. and Tominaga, Y. (2017), "Large-eddy simulations of flow around a high-rise building: validation and sensitivity analysis on turbulent statistics", 7th European and African Conference on Wind Engineering. Liege, Belgium.
  34. Pant, P., Doshi, R., Bahl, P. and Barati Farimani, A. (2021), "Deep learning for reduced order modelling and efficient temporal evolution of fluid simulations", Phys. Fluids, 33(10).
  35. Priestley, M.B. (1967), "Power spectral analysis of non-stationary random processes", J. Sound Vib. 6, 86-97. https://doi.org/10.1016/0022-460X(67)90160-5.
  36. Rowley, C.W., Mezi, I., Bagheri, S., Schlatter, P. and Henningson, D.S. (2009), "Spectral analysis of nonlinear flows", J. Fluid Mech., 641, 115-127. https://doi.org/10.1017/S0022112009992059.
  37. Sakamoto, H. and Arie, M. (1983), "Vortex shedding from a rectangular prism and a circular cylinder placed vertically in a turbulent boundary layer", J. Fluid Mech., 126, 147-165. https://doi.org/10.1017/S0022112083000087.
  38. San, O. and Maulik, R. (2018), "Extreme learning machine for reduced order modeling of turbulent geophysical flows", Phys. Rev. E., 97(4), 042322.
  39. Schmid, P.J. (2010), "Dynamic mode decomposition of numerical and experimental data", J. Fluid Mech., 656, 5-28. https://doi.org/10.1017/S0022112010001217.
  40. Sieber, M., Paschereit, C.O. and Oberleithner, K. (2016), "Spectral proper orthogonal decomposition", J. Fluid Mech., 792, 798-828. https://doi.org/10.1017/jfm.2016.103.
  41. Sirisup, S. and Karniadakis, G.E. (2004), "A spectral viscosity method for correcting the long-term behavior of POD models", J. Comput. Phys. 194, 92-116.
  42. Sirovich, L. (1987), "Turbulence and the dynamics of coherent structures", I. Coherent Struct. Q. Appl. Math., 45, 561-571.
  43. Solari, G., Carassale, L. and Tubino, F. (2007), "Proper orthogonal decomposition in wind engineering - Part 1: A state-of-the-art and some prospects", Wind Struct., 10(2), 153-176. https://doi.org/10.12989/was.2007.10.2.153.
  44. Strogatz, S.H. (2014), Nonlinear Dynamics and Chaos : With Applications to Physics, Biology, Chemistry, and Engineering. Westview Press.
  45. Tamura, Y., Suganuma, S., Kikuchi, H. and Hibi, K. (1999), "Proper orthogonal decomposition of ran-dom wind pressure field", J. Fluids Struct., 13, 1069-1095.
  46. Tominaga, Y., Mochida, A., Yoshie, R., Kataoka, H., Nozu, T., Yoshikawa, M. and Shirasawa, T. (2008), "AIJ guidelines for practical applications of CFD to pedestrian wind environment around buildings", J. Wind Eng. Ind. Aerod., 96, 1749-1761. https://doi.org/10.1016/J.JWEIA.2008.02.058.
  47. Towne, A., Schmidt, O.T. and Colonius, T. (2018), "Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis", J. Fluid Mech., 847, 821-867. https://doi.org/10.1017/jfm.2018.283.
  48. Uehara, K., Wakamatsu, S. and Ooka, R. (2003), "Studies on critical Reynolds number indices for wind-tunnel experiments on flow within urban areas", Bound. Layer Meteorol., 107, 353-370. https://doi.org/10.1023/A:1022162807729.
  49. Versteeg, H.K. and Malalasekera, W. (2007), An Introduction to Computational Fluid Dynamics: The Finite Volume Method, Pearson Education Limited, Essex, England.
  50. Wang, F. and Lam, K.M. (2019), "Geometry effects on mean wake topology and large-scale coherent structures of wall-mounted prisms", Phys. Fluids, 31, 125109. https://doi.org/10.1063/1.5126045.
  51. Wang, L., Wang, Y., Li, Z. and Zhang, Y. (2010), "Estimation of the vortex shedding frequency of a 2-D building using correlation and the POD methods", J. Wind Eng. Ind. Aerod., 98(12), 895-902.
  52. Wu, J., Wang, J., Xiao, H. and Ling, J. (2017), "Visualization of high dimensional turbulence simulation data using t-SNE", In: 19th AIAA Non-Deterministic Approaches Conference, 2017. American Institute of Aeronautics and Astronautics Inc, AIAA. https://doi.org/10.2514/6.2017-1770.
  53. Yoshie, R., Mochida, A., Tominaga, Y., Kataoka, H., Harimoto, K., Nozu, T. and Shirasawa, T. (2007), "Cooperative project for CFD prediction of pedestrian wind environment in the Architectural Institute of Japan", J. Wind Eng. Ind. Aerod., 95, 1551-1578. https://doi.org/10.1016/J.JWEIA.2007.02.023.
  54. Zhang, H., Zhang, H., Xin, D., Zhan, J., Wang, R. and Zhou, L. (2022c), "Vortex-induced vibration control of a streamline box girder using the wake perturbation of horizontal axis micro-wind turbines", J. Fluids Struct., 108, 103444.
  55. Zhang, H., Zhou, L. and Tse, K.T. (2022a), "Mode-based energy transfer analysis of flow-induced vibration of two rigidly coupled tandem cylinders", Int. J. Mech. Sci., 228, 107468.
  56. Zhang, H., Zhou, L., Deng, P. and Tse, T.K. (2022d), "Fluid-structure-coupled Koopman mode analysis of free oscillating twin-cylinders", Phys. Fluids, 34(9).
  57. Zhang, H., Zhou, L., Liu, T., Guo, Z. and Golnary, F. (2022b), "Dynamic mode decomposition analysis of the two-dimensional flow past two transversely in-phase oscillating cylinders in a tandem arrangement", Phys. Fluids, 34, 33602.
  58. Zhou, L., Tse, K.T. and Hu, G. (2022), "Aerodynamic correlation and flow pattern of high-rise building with side ratio of 3:1 under twisted wind profile: A computational study", J. Wind Eng. Ind. Aerod., 228, 105087.
  59. Zhou, L., Zhu, Q., Tse, K. T., Ning, X., Ai, Y., & Zhang, H. 2024. Flow pattern-and forces-susceptibility to small attack angles for a rectangular cylinder. Ocean Eng. 300, 117376.
  60. Zhu, Q., Zhou, L., Wen, J., Liu, T., Zhang, J., Tang, H. and Zhang, H. (2023), "Laminar flow over a rectangular cylinder experiencing torsional flutter: Dynamic response, forces and coherence modes", Phys. Fluids, 35(9).
  61. Zhu, Q., Zhou, L., Zhang, H., Tse, K.T., Tang, H. and Noack, B.R. (2024), "A zero-net-mass-flux wake stabilization method for blunt bodies via global linear instability", Phys. Fluids, 36(4).
  62. Zu, G.B. and Lam, K.M. (2018a), "Across-wind excitation mechanism for interference of twin tall buildings in tandem arrangement", Wind Struct., 26, 397-413.