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Journal of Environmental Accounting and Management
António Mendes Lopes (editor), Jiazhong Zhang(editor)
António Mendes Lopes (editor)

University of Porto, Portugal


Jiazhong Zhang (editor)

School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi Province 710049, China

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Analysis of Pollutant Transport Around a Circular Cylinder in Subcritical Regime Using Lagrangian Coherent Structures

Journal of Environmental Accounting and Management 10(3) (2022) 321--333 | DOI:10.5890/JEAM.2022.09.009

Xinyao Zheng${}^{1,2}$, Zhizhe Chen${}^{2}$, Zhiyu Chen${}^{2}$, Lianjie Chai${}^{1}$, Jiazhong Zhang${}^{2}$

$^{1}$ State Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Mianyang, 621000,

P. R. China

$^{2}$ School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an 710049, P. R. China

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Lagrangian coherence structures (LCSs) are introduced to study the pollutant transport process in detail, more powerful than traditional Eulerian method in describing the mass transport in transient flow. First, pollutant transport in air around a circular cylinder in the subcritical regime with Reynolds number of 140000 is numerically simulated using DES Turbulence Model. Then, the complex turbulent flow and the accompanying transport process in the cylinder wake are revealed from Lagrangian viewpoint, through the analysis of LCSs which are extracted utilizing the ridges in the finite-time Lyapunov exponent fields. Further, a comparison between flow in the laminar and subcritical regime is carried out, and the factors for the intense mixing and quasi-periodical characteristic of the subcritical regime are discovered. Finally, based on lobe dynamics, the flow field is partitioned into several regions with different physical properties, so the mass and energy transport and mixing between those regions can be precisely described and captured. The results show the application of LCSs in uncovering the structures of complex turbulent flow in environmental problems, as well as the potential of LCSs to quantitatively analyze the pollutant transport process, could provide an efficient way for the optimal control of the pollutant.


  1. [1]  Ahmad, K., Khare, M., and Chaudhry, K.K. (2005), Wind tunnel simulation studies on dispersion at urban street canyons and intersections-a review, Journal of Wind Engineering and Industrial Aerodynamics, 93(9), 697-717.
  2. [2]  Beaudan, P.B. (1995), Numerical experiments on the flow past a circular cylinder at sub-critical Reynolds number, (Doctoral dissertation, Stanford University).
  3. [3]  Beron‐Vera, F.J., Olascoaga, M.J., and Goni, G.J. (2008), Oceanic mesoscale eddies as revealed by Lagrangian coherent structures, Geophysical Research Letters, 35(12).
  4. [4]  BozorgMagham, A.E., Ross, S.D., and Schmale III, D.G. (2013), Real-time prediction of atmospheric Lagrangian coherent structures based on forecast data: An application and error analysis, Physica D: Nonlinear Phenomena, 258, 47-60.
  5. [5]  Breuer, M. (1998), Large eddy simulation of the subcritical flow past a circular cylinder: numerical and modeling aspects, International journal for numerical methods in fluids, 28(9), 1281-1302.
  6. [6]  Breuer, M. (2000), A challenging test case for large eddy simulation: high Reynolds number circular cylinder flow, International journal of heat and fluid flow, 21(5), 648-654.
  7. [7]  Cantwell, B. and Coles, D. (1983), An experimental study of entrainment and transport in the turbulent near wake of a circular cylinder, Journal of fluid mechanics, 136, 321-374.
  8. [8]  Cao, S., Dang, N., Ren, Z., Zhang, J., and Deguchi, Y. (2020), Lagrangian analysis on routes to lift enhancement of airfoil by synthetic jet and their relationships with jet parameters, Aerospace Science and Technology, 104, 105947.
  9. [9]  Cao, S., Sun, X., Zhang, J.Z., and Zhang, Y.X. (2021), Forced convection heat transfer around a circular cylinder in laminar flow: An insight from Lagrangian coherent structures, Physics of Fluids, 33(6), 067104.
  10. [10]  Casalino, D. and Jacob, M. (2003), Prediction of aerodynamic sound from circular rods via spanwise statistical modelling, Journal of Sound and Vibration, 262(4), 815-844.
  11. [11]  Choi, S.D., Eum, T.S., Shin, E.T., and Song, C.G. (2021), Numerical investigation of flow around a structure using Navier-slip boundary conditions, World Journal of Engineering. %
  12. [12]  % Govardhan, R. and Williamson, C.H.K. (2001), Mean and fluctuating velocity fields in the wake of a freely-vibrating cylinder, Journal of Fluids and Structures, 15(3-4), 489-501.
  13. [13]  Guo, L., Zhang, X., and He, G. (2016), Large-eddy simulation of circular cylinder flow at subcritical Reynolds number: Turbulent wake and sound radiation, Acta mechanica sinica, 32(1), 1-11.
  14. [14]  Haller, G. and Poje, A.C. (1998), Finite time transport in aperiodic flows, Physica D: Nonlinear Phenomena, 119(3-4), 352-380.
  15. [15]  Haller, G. (2000), Finding finite-time invariant manifolds in two-dimensional velocity fields, Chaos: An Interdisciplinary Journal of Nonlinear Science, 10(1), 99-108.
  16. [16]  Haller, G. and Yuan, G. (2000), Lagrangian coherent structures and mixing in two-dimensional turbulence, Physica D: Nonlinear Phenomena, 147(3-4), 352-370.
  17. [17]  Haller, G. (2002), Lagrangian coherent structures from approximate velocity data, Physics of fluids, 14(6), 1851-1861.
  18. [18]  Haller, G. (2015), Lagrangian coherent structures, Annual Review of Fluid Mechanics, 47, 137-162.
  19. [19]  Hofman, J., Castanheiro, A., Nuyts, G., Joosen, S., Spassov, S., Blust, R., ... and Samson, R. (2020), Impact of urban street canyon architecture on local atmospheric pollutant levels and magneto-chemical PM10 composition: An experimental study in Antwerp, Belgium, Science of The Total Environment, 712, 135534.
  20. [20]  Kasten, J., Petz, C., Hotz, I., Hege, H.C., Noack, B.R., and Tadmor, G. (2010), Lagrangian feature extraction of the cylinder wake, Physics of fluids, 22(9), 091108.
  21. [21]  Kim, S.E. (2006), Large eddy simulation of turbulent flow past a circular cylinder in subcritical regime, In 44th AIAA Aerospace Sciences Meeting and Exhibit (p. 1418).
  22. [22]  Mathur, M., Haller, G., Peacock, T., Ruppert-Felsot, J.E., and Swinney, H.L. (2007), Uncovering the Lagrangian skeleton of turbulence, Physical Review Letters, 98(14), 144502.
  23. [23]  Mittal, R. and Moin, P. (1997), Suitability of upwind-biased finite difference schemes for large-eddy simulation of turbulent flows, AIAA journal, 35(8), 1415-1417.
  24. [24]  Norberg, C. (2003), Fluctuating lift on a circular cylinder: review and new measurements, Journal of Fluids and Structures, 17(1), 57-96.
  25. [25]  Ong, L. and Wallace, J. (1996), The velocity field of the turbulent very near wake of a circular cylinder, Experiments in fluids, 20(6), 441-453.
  26. [26]  Orselli, R., Meneghini, J., and Saltara, F. (2009, May), Two and three-dimensional simulation of sound generated by flow around a circular cylinder, In 15th AIAA/CEAS aeroacoustics conference (30th AIAA aeroacoustics conference) (p. 3270).
  27. [27]  Ouvrard, H., Koobus, B., Salvetti, M.V., Camarri, S., and Dervieux, A. (2008), Variational Multiscale LES and Hybrid RANS/LES Parallel Simulation of Complex Unsteady Flows, In International Conference on High Performance Computing for Computational Science (pp. 465-478). Springer, Berlin, Heidelberg.
  28. [28]  Peng-Fei, L., Jia-Zhong, Z., Zhuo-Pu, W., and Jia-Hui, C. (2014), Lagrangian coherent structure and transport in unsteady transient flow, Acta Physica Sinica, 63(8).
  29. [29]  Perrin, R., Braza, M., Cid, E., Cazin, S., Chassaing, P., Mockett, C., ... and Thiele, F. (2008), Coherent and turbulent process analysis in the flow past a circular cylinder at high Reynolds number, Journal of fluids and structures, 24(8), 1313-1325.
  30. [30]  Rockwood, M.P., Taira, K., and Green, M.A. (2017), Detecting vortex formation and shedding in cylinder wakes using Lagrangian coherent structures, AIAA journal, 55(1), 15-23.
  31. [31]  Roshko, A. (1993), Perspectives on bluff body aerodynamics, Journal of Wind Engineering and Industrial Aerodynamics, 49(1-3), 79-100.
  32. [32]  Shadden, S.C., Lekien, F., and Marsden, J.E. (2005), Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows, Physica D: Nonlinear Phenomena, 212(3-4), 271-304.
  33. [33]  Shuckburgh, E.F. (2012), Mapping unstable manifolds using drifters/floats in a Southern Ocean field campaign. In AIP Conference Proceedings (Vol. 1479, No. 1, pp. 650-653), American Institute of Physics.
  34. [34]  Tang, W., Chan, P.W., and Haller, G. (2011), Lagrangian coherent structure analysis of terminal winds detected by lidar. Part I: Turbulence structures, Journal of Applied Meteorology and Climatology, 50(2), 325-338.
  35. [35]  Wang, W., Prants, S.V., Zhang, J., and Wang, L. (2018), A Lagrangian analysis of vortex formation in the wake behind a transversely oscillating cylinder, Regular and Chaotic Dynamics, 23(5), 583-594.
  36. [36]  Wania, A., Bruse, M., Blond, N., and Weber, C. (2012), Analysing the influence of different street vegetation on traffic-induced particle dispersion using microscale simulations, Journal of environmental management, 94(1), 91-101.
  37. [37]  Wiggins, S. (1992), Chaotic transport in dynamical systems, NASA STI/Recon Technical Report A, 92, 28228.
  38. [38]  Williamson, C.H. (1996), Vortex dynamics in the cylinder wake, Annual review of fluid mechanics, 28(1), 477-539.