Skip Navigation Links
Journal of Vibration Testing and System Dynamics

C. Steve Suh (editor), Pawel Olejnik (editor),

Xianguo Tuo (editor)

Pawel Olejnik (editor)

Lodz University of Technology, Poland


C. Steve Suh (editor)

Texas A&M University, USA


Xiangguo Tuo (editor)

Sichuan University of Science and Engineering, China


Analysis of Mass Transport in a Turbulent Flame Using Lagrangian Coherent Structures

Journal of Vcibration Testing and System Dynamics 4(1) (2020) 79--93 | DOI:10.5890/JVTSD.2020.03.005

Shengli Cao$^{1}$,$^{2}$, Jiazhong Zhang$^{1}$, Yoshihiro Deguchi$^{2}$, Nannan Dang$^{1}$,$^{2}$, Shaohua Tian$^{1}$

$^{1}$ School of Power and Energy Engineering, Xi'an Jiaotong University, Xi'an, 710049, P. R. China

$^{2}$ Advanced Technology and Science, Tokushima University, Tokushima 770-8501, Japan

Download Full Text PDF



The premixed piloted turbulent flame is studied numerically using Lagrangian coherent structures (LCS) to study and analyze the masstransport process from the viewpoint of nonlinear dynamic systems. The mass transport is shown to demonstrate a rich dynamical behavior. Firstly, the numerical simulation results show that the boundaries in the combustion field are delineated by the Lagrangian Coherent Structures. Secondly, the distribution of the attracting LCSs and the OH radical are compared to study the surface of the flame. Finally, the evolution of the LCS was tracked to analyze the vortexes and mass transport near the burner. The results show that the attracting LCS can be considered as a surface of the turbulent flame near the burner. The serial vortexes are regularly generated near the piloted jet, and they are gradually stretched and folded. These vortexes are attracted by the main jet as they move downward in the flow. The main jet goes into the flow field following an attracting LCS and moves forward attracting the piloted jet and the co-flow. However, fluid in the mainstream region has never entered into the piloted jet region, and this region does not exchange substance with the co-flow region. If the flow speed increases, air from the co-flow may pass through the LCS to mix with the material from the piloted jet region. Application of the LCS technique to study mass transport processes provides a new viewpoint for analyzing premixed piloted turbulent flames.


The research is supported by the Key Research and Development Program of Shaanxi Province (No.2017ZDCXL-GY-02-02), the Key Laboratory of Compressor of China (No. SKL-YSJ201802) and the World-Class Universities(Disciplines) and the Characteristic Development Guidance Funds for the Central Universities ( No. PY3A056).


  1. [1]  Amani, E. and Nobari, M. (2010), An efficient PDF calculation of flame temperature and major species in turbulent non-premixed flames, Applied Mathematical Modelling, 34(8), 2223-2241.
  2. [2]  Lilleberg, B., Christ, D., Ertesv˚ag, I.S., Rian, K.E., and Kneer, R. (2013), Numerical simulation with an extinction database for use with the eddy dissipation concept for turbulent combustion, Flow, Turbulence and Combustion, 91(2), 319-346.
  3. [3]  Xu, X., Chen, Y., and Wang, H. (2006), Numerical investigation of influences of thermal radiation in Sandia flame D, Journal of Engineering Thermophysics, 27(4), 649.
  4. [4]  Yi-Liang, W.H.F.C. and Liu, M.H. (2005), Numerical investigations of turbulent nonpremixed combustion: performance of PDF method and flamelet models, Journal of Engineering Thermophysics, S1.
  5. [5]  Mustata, R., Vali no, L., Jiménez, C., Jones,W., and Bondi, S. (2006), A probability density function Eulerian Monte Carlo field method for large eddy simulations: application to a turbulent piloted methane/air diffusion flame (Sandia D), Combustion and Flame, 145(1-2), 88-104.
  6. [6]  Lysenko, D.A., Ertesvåg, I.S., and Rian, K.E. (2014), Numerical simulations of the Sandia flame D using the eddy dissipation concept, Flow, Turbulence and Combustion, 93(4), 665-687.
  7. [7]  Wang, F., Zhou, L.X., and Xu, C.X. (2006), Large-eddy simulation of a jet flame using a SOM-SGS combustion model, Journal of Combustion Science & Technology, 12(3), 221-225.
  8. [8]  Ihme, M. and Pitsch, H. (2008), Prediction of extinction and reignition in nonpremixed turbulent flames using a flamelet/progress variable model: 2. Application in LES of Sandia flames D and E, Combustion and Flame, 155(1-2), 90-107.
  9. [9]  Chen, Y. and Ihme, M. (2013), Large-eddy simulation of a piloted premixed jet burner, Combustion and Flame, 160(12), 2896-2910.
  10. [10]  Ferraris, S. and Wen, J. (2008), LES of the Sandia flame D using laminar flamelet decomposition for conditional source-term estimation, Flow, Turbulence and Combustion, 81(4), 609-639.
  11. [11]  Pitsch, H. and Steiner, H. (2000), Large-eddy simulation of a turbulent piloted methane/air diffusion flame (Sandia flame D), Physics of Fluids, 12(10), 2541-2554.
  12. [12]  Garmory, A. and Mastorakos, E. (2013), Sensitivity analysis of LES-CMC predictions of piloted jet flames, International Journal of Heat and Fluid Flow, 39, 53-63.
  13. [13]  Coelho, P. and Peters, N. (2001), Unsteady modelling of a piloted methane/air jet flame based on the Eulerian particle flamelet model, Combustion and Flame, 124(3), 444-465.
  14. [14]  Tang, Q., Xu, J., and Pope, S.B. (2000), Probability density function calculations of local extinction and NO production in piloted-jet turbulent methane/air flames, Proceedings of the Combustion Institute, 28(1), 133-139.
  15. [15]  Kemenov, K.A. and Pope, S.B. (2011), Molecular diffusion effects in LES of a piloted methane-air flame, Combustion and Flame, 158(2), 240-254.
  16. [16]  Kempf, A., Flemming, F., and Janicka, J. (2005), Investigation of lengthscales, scalar dissipation, and flame orientation in a piloted diffusion flame by LES, Proceedings of the Combustion Institute, 30(1), 557-565.
  17. [17]  Cao, R.R. and Pope, S.B. (2005), The influence of chemical mechanisms on PDF calculations of nonpremixed piloted jet flames, Combustion and Flame, 143(4), 450-470.
  18. [18]  Barlow, R.S. and Karpetis, A.N. (2005), Scalar length scales and spatial averaging effects in turbulent piloted methane/air jet flames, Proceedings of the Combustion Institute, 30(1), 673-680.
  19. [19]  Zhou, B., Brackmann, C., Li, Q., Wang, Z., Petersson, P., Li, Z., Aldén, M., and Bai, X.S. (2015), Distributed reactions in highly turbulent premixed methane/air flames: part I. flame structure characterization, Combustion and Flame, 162(7), 2937-2953.
  20. [20]  Meares, S. and Masri, A.R. (2014), A modified piloted burner for stabilizing turbulent flames of inhomogeneous mixtures, Combustion and Flame, 161(2), 484-495.
  21. [21]  Barlow, R., Meares, S., Magnotti, G., Cutcher, H., and Masri, A. (2015), Local extinction and near-field structure in piloted turbulent CH4/air jet flames with inhomogeneous inlets, Combustion and Flame, 162(10), 3516-3540.
  22. [22]  Karpetis, A. and Barlow, R. (2002), Measurements of scalar dissipation in a turbulent piloted methane/air jet flame, Proceedings of the Combustion Institute, 29(2), 1929-1936.
  23. [23]  Li, Z., Li, B., Sun, Z., Bai, X.S., and Aldén, M. (2010), Turbulence and combustion interaction: High resolution local flame front structure visualization using simultaneous single-shot PLIF imaging of CH, OH, and CH2O in a piloted premixed jet flame, Combustion and Flame, 157(6), 1087-1096.
  24. [24]  Haller, G. (2000), Finding finite-time invariant manifolds in two-dimensional velocity fields, Chaos: An Interdisciplinary, Journal of Nonlinear Science, 10(1), 99-108.
  25. [25]  Haller, G. (2002), Lagrangian coherent structures from approximate velocity data, Physics of Fluids, 14(6), 1851-1861.
  26. [26]  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.
  27. [27]  Rockwood, M., Huang, Y., and Green, M. (2018), Tracking coherent structures in massively-separated and turbulent flows, Physical Review Fluids, 3(1), 014702.
  28. [28]  Chen, J., Zhang, J., and Cao, S. (2016), Using lagrangian coherent structure to understand vortex dynamics in flow around plunging airfoil, Journal of Fluids and Structures, 67, 142-155.
  29. [29]  S. Prants, M. Budyansky, M. Y. Uleysky, Identifying lagrangian fronts with favourable fishery conditions, Deep Sea Research Part I: Oceanographic Research Papers 90 (2014) 27-35.
  30. [30]  Budyansky, M., Goryachev, V., Kaplunenko, D., Lobanov, V., Prants, S., Sergeev, A., Shlyk, N., and Uleysky, M.Y. (2015), Role of mesoscale eddies in transport of fukushima-derived cesium isotopes in the ocean, Deep Sea Research Part I: Oceanographic Research Papers, 96, 15-27.
  31. [31]  Prants, S.V., Uleysky, M.Y., and Budyansky, M.V. (2017), Lagrangian oceanography: large-scale transport and mixing in the ocean, Springer.
  32. [32]  Garaboa-Paz, D., Eiras-Barca, J., Huhn, F., Pérez-Mu nuzuri, V. (2015), Lagrangian coherent structures along atmospheric rivers, Chaos: An Interdisciplinary, Journal of Nonlinear Science, 25(6), 063105.
  33. [33]  Curbelo, J., Garc´ıa-Garrido, V.J., Mechoso, C.R., Mancho, A.M., Wiggins, S., and Niang, C. (2017), Insights into the three-dimensional lagrangian geometry of the antarctic polar vortex, Nonlinear Processes in Geophysics, 24(3), 379-392.
  34. [34]  Sampath, R., Mathur, M., and Chakravarthy, S.R. (2016), Lagrangian coherent structures during combustion instability in a premixed-flame backward-step combustor, Physical Review E, 94(6), 062209.