1932

Abstract

When a premixed flame propagates in a turbulent flow, not only does turbulence affect the burning rate (e.g., by wrinkling the flame and increasing its surface area), but also the heat release in the flame perturbs the pressure field, and these pressure perturbations affect the turbulent flow and scalar transport. For instance, the latter effects manifest themselves in the so-called countergradient turbulent scalar flux, which has been documented in various flames and has challenged the combustion community for approximately 35 years. Over the past decade, substantial progress has been made in investigating () the influence of thermal expansion in a premixed flame on the turbulent flow and turbulent scalar transport within the flame brush, as well as () the feedback influence of countergradient scalar transport on the turbulent burning rate. The present article reviews recent developments in this field and outlines issues to be solved in future research.

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2017-01-03
2024-04-19
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Literature Cited

  1. Ashurst WT, Kerstein AR, Kerr RM, Gibson CH. 1987. Alignment of vorticity and scalar gradient with strain rate in simulated Navier-Stokes turbulence. Phys. Fluids 30:2343–53 [Google Scholar]
  2. Batchelor GK. 1952. The effect of homogeneous turbulence on material lines and surfaces. Proc. R. Soc. Lond. A 213:349–66 [Google Scholar]
  3. Bell JB, Day MS, Grcar JF, Lijewski MJ. 2006. Active control for statistically stationary turbulent premixed flame simulations. Commun. Appl. Math. Comput. Sci. 1:29–51 [Google Scholar]
  4. Besson M, Bruel P, Champion JL, Deshaies B. 2000. Experimental analysis of combusting flows developing over a plane-symmetric expansion. J. Thermophys. Heat Transfer 14:59–67 [Google Scholar]
  5. Biagioli F, Zimont VL. 2002. Gasdynamics modelling of counter-gradient transport in open and impinging turbulent premixed flames. Proc. Combust. Inst. 29:2087–95 [Google Scholar]
  6. Bobbitt B, Lapointe S, Blanquart G. 2016. Vorticity transformation in high Karlovitz number premixed flames. Phys. Fluids 28:015101 [Google Scholar]
  7. Borghi R. 1988. Turbulent combustion modeling. Prog. Energy Combust. Sci. 14:245–92 [Google Scholar]
  8. Bray KNC. 1995. Turbulent transport in flames. Proc. R. Soc. Lond. A 451:231–56 [Google Scholar]
  9. Bray KNC, Champion M, Libby PA. 2000. Premixed flames in stagnating turbulence. Part IV: a new theory for the Reynolds stresses and Reynolds fluxes applied to impinging flows. Combust. Flame 120:1–18 [Google Scholar]
  10. Bray KNC, Libby PA. 1976. Interaction effects in turbulent premixed flames. Phys Fluids 19:1687–701 [Google Scholar]
  11. Bray KNC, Moss JB. 1977. A unified statistical model for the premixed turbulent flame. Acta Astronaut. 4:291–319 [Google Scholar]
  12. Buckmaster JD. 1993. The structure and stability of laminar flames. Annu. Rev. Fluid Mech. 25:21–53 [Google Scholar]
  13. Buschmann A, Dinkelacker F, Schäfer T, Schäfer M, Wolfrum J. 1996. Measurement of the instantaneous detailed flame structure in turbulent premixed combustion. Proc. Combust. Inst. 26:437–45 [Google Scholar]
  14. Bychkov V. 2003. Importance of the Darrieus-Landau instability for strongly corrugated turbulent flames. Phys. Rev. E 68:066304 [Google Scholar]
  15. Chakraborty N. 2014. Statistics of vorticity alignment with local strain rates in turbulent premixed flames. Eur. J. Mech. B 46:201–20 [Google Scholar]
  16. Chakraborty N, Cant RS. 2009. Effects of Lewis number on scalar transport in turbulent premixed flames. Phys. Fluids 21:035110 [Google Scholar]
  17. Chakraborty N, Katragadda M, Cant RS. 2011. Effects of Lewis number on turbulent kinetic energy transport in premixed flames. Phys. Fluids 23:075109 [Google Scholar]
  18. Chakraborty N, Klein M, Swaminathan N. 2009. Effects of Lewis number on the reactive scalar gradient alignment with local strain rate in turbulent premixed flames. Proc. Combust. Inst. 32:1409–17 [Google Scholar]
  19. Chakraborty N, Konstantinou I, Lipatnikov AN. 2016. Effects of Lewis number on vorticity and enstrophy transport in turbulent premixed flames. Phys. Fluids 28:015109 [Google Scholar]
  20. Chakraborty N, Lipatnikov AN. 2013. Effects of Lewis number on conditional fluid velocity statistics in low Damköhler number turbulent premixed combustion: a direct numerical simulation analysis. Phys. Fluids 25:045101 [Google Scholar]
  21. Chakraborty N, Swaminathan N. 2007. Influence of the Damköhler number on turbulence-scalar interaction in premixed flames. I. Physical insight. Phys. Fluids 19:045103 [Google Scholar]
  22. Chaudhuri S, Akkerman V, Law CK. 2011. Spectral formulation of turbulent flame speed with consideration of hydrodynamic instability. Phys. Rev. E 84:026322 [Google Scholar]
  23. Chen JH, Lumley JL, Gouldin FC. 1986. Modeling of wrinkled laminar flames with intermittency and conditional statistics. Proc. Combust. Inst. 21:1483–91 [Google Scholar]
  24. Cheng RK, Shepherd IG. 1986. Interpretation of conditional statistics in open oblique premixed turbulent flames. Combust. Sci. Technol. 49:17–40 [Google Scholar]
  25. Cheng RK, Shepherd IG. 1991. The influence of burner geometry on premixed turbulent flame propagation. Combust. Flame 85:7–26 [Google Scholar]
  26. Cho P, Law CK, Cheng RK, Shepherd IG. 1988. Velocity and scalar fields of turbulent premixed flames in stagnation flow. Proc. Combust. Inst. 22:739–45 [Google Scholar]
  27. Chomiak J. 1990. Combustion: A Study in Theory, Fact and Application New York: Gordon & Breach
  28. Chomiak J, Nisbet JR. 1995. Modeling variable density effects in turbulent flames—some basic considerations. Combust. Flame 102:371–86 [Google Scholar]
  29. Clavin P. 1994. Premixed combustion and gas dynamics. Annu. Rev. Fluid Mech. 26:321–52 [Google Scholar]
  30. Clavin P, Williams FA. 1979. Theory of premixed-flame propagation in large-scale turbulence. J. Fluid Mech. 90:589–604 [Google Scholar]
  31. Creta F, Matalon M. 2011. Propagation of wrinkled turbulent flames in the context of hydrodynamic theory. J. Fluid Mech. 680:225–64 [Google Scholar]
  32. Damköhler G. 1940. Der Einfuss der Turbulenz auf die Flammengeschwindigkeit in Gasgemischen. Z. Electrochem. 46:601–52 [Google Scholar]
  33. Darrieus G. 1938. Propagation d'un front de flamme Presented at Tech. Mod., Paris
  34. Dong HQ, Robin V, Mura A, Champion M. 2013. Analysis of algebraic closures of the mean scalar dissipation rate of the progress variable applied to stagnating turbulent flames. Flow Turbul. Combust. 90:301–23 [Google Scholar]
  35. Dopazo C, Cifuentes L, Martin J, Jimenez C. 2015. Strain rates normal to approaching iso-scalar surfaces in a turbulent premixed flame. Combust. Flame 162:1729–36 [Google Scholar]
  36. Driscoll JF. 2008. Turbulent premixed combustion: flamelet structure and its effect on turbulent burning velocities. Prog. Energy Combust. Sci. 34:91–134 [Google Scholar]
  37. Ebert U, van Saarlos W. 2000. Front propagation into unstable states: universal algebraic convergence towards uniformly translating pulled fronts. Physica D 146:1–99 [Google Scholar]
  38. Echekki T, Mastorakos E. 2011. Turbulent Combustion Modeling Berlin: Springer
  39. Fogla N, Creta F, Matalon M. 2015. Effect of folds and pockets on the topology and propagation of premixed turbulent flames. Combust. Flame 162:2758–77 [Google Scholar]
  40. Frank JH, Kalt PAM, Bilger RW. 1999. Measurements of conditional velocities in turbulent premixed flames by simultaneous OH PLIF and PIV. Combust. Flame 116:220–32 [Google Scholar]
  41. Furukawa J, Noguchi Y, Hirano T, Williams FA. 2002. Anisotropic enhancement of turbulence in large-scale, low-intensity turbulent premixed propane-air flames. J. Fluid Mech. 462:209–43 [Google Scholar]
  42. Günther R. 1983. Turbulence properties of flames and their measurement. Prog. Energy Combust. Sci. 9:105–54 [Google Scholar]
  43. Hamlington PE, Poludnenko AY, Oran ES. 2011. Interactions between turbulence and flames in premixed reacting flows. Phys. Fluids 23:125111 [Google Scholar]
  44. Hartung G, Hult J, Kaminski CF, Rogerson JW, Swaminathan N. 2008. Effect of heat release on turbulence and scalar-turbulence interaction in premixed combustion. Phys. Fluids 20:035110 [Google Scholar]
  45. Hinze JO. 1975. Turbulence New York: McGraw Hill, 2nd ed..
  46. Im YH, Huh KY, Nishiki S, Hasegawa T. 2004. Zone conditional assessment of flame-generated turbulence with DNS database of a turbulent premixed flame. Combust. Flame 137:478–88 [Google Scholar]
  47. Kalt PAM, Frank JH, Bilger RW. 1998. Laser imaging of conditional velocities in premixed propane-air flames by simultaneous OH PLIF and PIV. Proc. Combust. Inst. 27:751–58 [Google Scholar]
  48. Karlovitz B, Denniston DW, Wells FE. 1951. Investigation of turbulent flames. J. Chem. Phys. 19:541–47 [Google Scholar]
  49. Kataoka I. 1986. Local instant formulation of two-phase flow. Int. J. Multiphase Flow 12:745–58 [Google Scholar]
  50. Kheirkhah S, Gülder ÖL. 2013. Turbulent premixed combustion in V-shaped flames: characteristics of flame front. Phys. Fluids 25:055107 [Google Scholar]
  51. Klimenko AY. 1998. Examining the cascade hypothesis for turbulent premixed combustion. Combust. Sci. Technol. 139:15–40 [Google Scholar]
  52. Kobayashi H, Tamura T, Maruta K, Niioka T, Williams FA. 1996. Burning velocity of turbulent premixed flames in a high-pressure environment. Proc. Combust. Inst. 26:389–96 [Google Scholar]
  53. Kolla H, Hawkes ER, Kerstein AR, Swaminathan N, Chen JH. 2014. On velocity and reactive scalar spectra in turbulent premixed flames. J. Fluid Mech. 754:456–87 [Google Scholar]
  54. Kuznetsov VR. 1979. Estimate of the correlation between pressure pulsations and the divergence of the velocity in subsonic flows of variable density. Fluid Dyn. 14:328–34 [Google Scholar]
  55. Kuznetsov VR, Sabelnikov VA. 1990. Turbulence and Combustion New York: Hemisphere
  56. Landau LD. 1944. On the theory of slow combustion. Acta Psysicochim. USSR 19:77–85 [Google Scholar]
  57. Lecocq G, Richard S, Colin O, Vervisch L. 2010. Gradient and counter-gradient modeling in premixed flames: theoretical study and application to the LES of a lean premixed turbulent swirl burner. Combust. Sci. Technol. 182:465–79 [Google Scholar]
  58. Lee E, Huh KY. 2004. Zone conditional modeling of premixed turbulent flames at a high Damköhler number. Combust. Flame 138:211–24 [Google Scholar]
  59. Lee E, Im YH, Huh KY. 2005. Zone conditional analysis of a freely propagating one-dimensional turbulent premixed flame. Proc. Combust. Inst. 30:851–57 [Google Scholar]
  60. Li SC, Libby PA, Williams FA. 1994. Experimental investigation of a premixed flame in an impinging turbulent stream. Proc. Combust. Inst. 25:1207–14 [Google Scholar]
  61. Libby PA. 1975. On the prediction of intermittent turbulent flows. J. Fluid Mech. 68:273–95 [Google Scholar]
  62. Libby PA, Bray KNC. 1977. Variable density effects in premixed turbulent flames. AIAA J. 15:1186–93 [Google Scholar]
  63. Libby PA, Bray KNC. 1981. Countergradient diffusion in premixed turbulent flames. AIAA J. 19:205–13 [Google Scholar]
  64. Librovich VB, Lisitzyn VI. 1977. Interaction of flow pulsations and chemical reaction in turbulent flames. AIAA J. 15:227–33 [Google Scholar]
  65. Lipatnikov AN. 2008. Conditionally averaged balance equations for modeling premixed turbulent combustion in flamelet regime. Combust. Flame 152:529–47 [Google Scholar]
  66. Lipatnikov AN. 2009. Can we characterize turbulence in premixed flames?. Combust. Flame 156:1242–47 [Google Scholar]
  67. Lipatnikov AN. 2011a. Conditioned moments in premixed turbulent reacting flows. Proc. Combust. Inst. 33:1489–96 [Google Scholar]
  68. Lipatnikov AN. 2011b. A test of conditioned balance equation approach. Proc. Combust. Inst. 33:1497–504 [Google Scholar]
  69. Lipatnikov AN. 2011c. Transient behavior of turbulent scalar transport in premixed flames. Flow Turbul. Combust. 86:609–37 [Google Scholar]
  70. Lipatnikov AN. 2012. Fundamentals of Premixed Turbulent Combustion Boca Raton, FL: CRC
  71. Lipatnikov AN, Chomiak J. 2002. Turbulent flame speed and thickness: phenomenology, evaluation, and application in multi-dimensional simulations. Prog. Energy Combust. Sci. 28:1–74 [Google Scholar]
  72. Lipatnikov AN, Chomiak J. 2005. Molecular transport effects on turbulent flame propagation and structure. Prog. Energy Combust. Sci. 31:1–73 [Google Scholar]
  73. Lipatnikov AN, Chomiak J. 2010. Effects of premixed flames on turbulence and turbulent scalar transport. Prog. Energy Combust. Sci. 36:1–102 [Google Scholar]
  74. Lipatnikov AN, Chomiak J, Sabelnikov VA, Nishiki S, Hasegawa T. 2015a. Influence of heat release in a premixed flame on weakly turbulent flow of unburned gas: a DNS study. Proc. 25th Int. Colloq. Dyn. Explos. Reactive Syst. MI Radulescu, Pap. 74. http://www.engineering.leeds.ac.uk/short-courses/ICDERS/documents/ICDERS074.pdf
  75. Lipatnikov AN, Chomiak J, Sabelnikov VA, Nishiki S, Hasegawa T. 2015b. Unburned mixture fingers in premixed turbulent flames. Proc. Combust. Inst. 35:1401–8 [Google Scholar]
  76. Lipatnikov AN, Nishiki S, Hasegawa T. 2014. A direct numerical simulation study of vorticity transformation in weakly turbulent premixed flames. Phys. Fluids 26:105104 [Google Scholar]
  77. Lipatnikov AN, Sabelnikov VA. 2013. Transition from countergradient to gradient scalar transport in developing premixed turbulent flames. Flow Turbul. Combust. 90:401–18 [Google Scholar]
  78. Lipatnikov AN, Sabelnikov VA, Nishiki S, Hasegawa T, Chakraborty N. 2015c. DNS assessment of a simple model for evaluating velocity conditioned to unburned gas in premixed turbulent flames. Flow Turbul. Combust. 94:513–26 [Google Scholar]
  79. Majda A, Sethian J. 1985. The derivation and numerical solution of the equations for zero Mach number combustion. Combust. Sci. Technol. 42:185–205 [Google Scholar]
  80. Markstein GH. 1951. Experimental and theoretical studies of flame front stability. J. Aeronaut. Sci. 18:199–220 [Google Scholar]
  81. Matalon M. 2007. Intrinsic flame instabilities in premixed and nonpremixed combustion. Annu. Rev. Fluid Mech. 39:163–91 [Google Scholar]
  82. Moss JB. 1980. Simultaneous measurements of concentration and velocity in an open premixed turbulent flame. Combust. Sci. Techol. 22:119–29 [Google Scholar]
  83. Mura A, Champion M. 2009. Relevance of the Bray number in the small-scale modeling of turbulent premixed flames. Combust. Flame 156:729–33 [Google Scholar]
  84. Nishiki S, Hasegawa T, Borghi R, Himeno R. 2002. Modeling of flame-generated turbulence based on direct numerical simulation databases. Proc. Combust. Inst. 29:2017–22 [Google Scholar]
  85. Nishiki S, Hasegawa T, Borghi R, Himeno R. 2006. Modelling of turbulent scalar flux in turbulent premixed flames based on DNS databases. Combust. Theory Model. 10:39–55 [Google Scholar]
  86. Nivarti GB, Cant RS. 2015. Aerodynamic quenching and burning velocity of turbulent premixed methane-air flames Presented at ASME Turbo Expo 2015, Montreal, ASME Pap. GT2015-43416
  87. Paul RN, Bray. 1996. Study of premixed turbulent combustion including Landau-Darrieus instability effects. Proc. Combust. Inst. 26:259–66 [Google Scholar]
  88. Peters N. 2000. Turbulent Combustion Cambridge, UK: Cambridge Univ. Press
  89. Pfadler S, Leipertz A, Dinkelacker F. 2008. Systematic experiments on turbulent premixed Bunsen flames including turbulent flux measurements. Combust. Flame 152:616–31 [Google Scholar]
  90. Pitsch H. 2006. Large-eddy simulation of turbulent combustion. Annu. Rev. Fluid Mech. 38:453–82 [Google Scholar]
  91. Poinsot T, Veynante D. 2005. Theoretical and Numerical Combustion Philadelphia: Edwards, 2nd ed..
  92. Poludnenko AY. 2015. Pulsating instability and self-acceleration of fast turbulent flames. Phys. Fluids 27:014106 [Google Scholar]
  93. Poludnenko AY, Oran ES. 2010. The interaction of high-speed turbulence with flames: global properties and internal flame structure. Combust. Flame 157:995–1011 [Google Scholar]
  94. Poludnenko AY, Oran ES. 2011. The interaction of high-speed turbulence with flames: turbulent flame speed. Combust. Flame 158:301–26 [Google Scholar]
  95. Prudnikov AG. 1960. Hydrodynamics equations in turbulent flames. Combustion in a Turbulent Flow AG Prudnikov 7–29 Moscow: Oborongiz (In Russian) [Google Scholar]
  96. Robin V, Mura A, Champion M. 2011. Direct and indirect thermal expansion effects in turbulent premixed flames. J. Fluid Mech. 689:149–82 [Google Scholar]
  97. Robin V, Mura A, Champion M. 2012. Algebraic models for turbulent transports in premixed flames. Combust. Sci. Technol. 184:1718–42 [Google Scholar]
  98. Robin V, Mura A, Champion M, Hasegawa T. 2010. Modeling of the effects of thermal expansion on scalar turbulent fluxes in turbulent premixed flames. Combust. Sci. Technol. 182:449–64 [Google Scholar]
  99. Sabelnikov VA, Lipatnikov AN. 2011. A simple model for evaluating conditioned velocities in premixed turbulent flames. Combust. Sci. Technol. 183:588–613 [Google Scholar]
  100. Sabelnikov VA, Lipatnikov AN. 2013a. Towards an extension of TFC model of premixed turbulent combustion. Flow Turbul. Combust. 90:387–400 [Google Scholar]
  101. Sabelnikov VA, Lipatnikov AN. 2013b. Transition from pulled to pushed premixed turbulent flames due to countergradient transport. Combust. Theory Model. 17:1154–75 [Google Scholar]
  102. Sabelnikov VA, Lipatnikov AN. 2014. Speed selection for traveling-wave solutions to the diffusion-reaction equation with cubic reaction term and Burgers nonlinear convection. Phys. Rev. E 90:033004 [Google Scholar]
  103. Sabelnikov VA, Lipatnikov AN. 2015. Transition from pulled to pushed fronts in premixed turbulent combustion: theoretical and numerical study. Combust. Flame 162:2893–903 [Google Scholar]
  104. Scurlock AC, Grover JH. 1953. Propagation of turbulent flames. Proc. Combust. Inst. 4:645–58 [Google Scholar]
  105. Shchelkin KI. 1947. On combustion in a turbulent flow Tech. Memo 1110, Natl. Advis. Comm. Aeronaut., Washington, DC
  106. Shepherd IG, Cheng RK. 2001. The burning rate of premixed flames in moderate and intense turbulence. Combust. Flame 127:2066–75 [Google Scholar]
  107. Sivashinsky GI. 1983. Instabilities, pattern formation, and turbulence in flames. Annu. Rev. Fluid. Mech. 15:179–99 [Google Scholar]
  108. Sponfeldner T, Boxx I, Beyrau F, Hardalupas Y, Meier W, Taylor AMKP. 2015. On the alignment of fluid-dynamic principal strain-rates with the 3D flamelet-normal in a premixed turbulent V-flame. Proc. Combust. Inst. 35:1269–76 [Google Scholar]
  109. Steinberg AM, Coriton B, Frank JH. 2015. Influence of combustion on principal strain-rate transport in turbulent premixed flames. Proc. Combust. Inst. 35:1287–94 [Google Scholar]
  110. Steinberg AM, Driscoll JF. 2009. Straining and wrinkling processes during turbulence-premixed flame interaction measured using temporally-resolved diagnostics. Combust. Flame 156:2285–306 [Google Scholar]
  111. Steinberg AM, Driscoll JF, Ceccio SL. 2009. Temporal evolution of flame stretch due to turbulence and the hydrodynamic instability. Proc. Combust. Inst. 32:1713–21 [Google Scholar]
  112. Steinberg AM, Driscoll JF, Swaminathan N. 2012. Statistics and dynamics of turbulence-flame alignment in premixed combustion. Combust. Flame 159:2576–88 [Google Scholar]
  113. Stevens EJ, Bray KNC, Lecordier B. 1998. Velocity and scalar statistics for premixed turbulent stagnation flames using PIV. Proc. Combust. Inst. 27:949–55 [Google Scholar]
  114. Swaminathan N, Bray KNC. 2011. Turbulent Premixed Flames Cambridge, UK: Cambridge Univ. Press
  115. Swaminathan N, Grout RW. 2006. Interaction of turbulence and scalar fields in premixed flames. Phys. Fluids 18:045102 [Google Scholar]
  116. Townsend AA. 1976. The Structure of Turbulent Shear Flow Cambridge, UK: Cambridge Univ. Press, 2nd ed..
  117. Treurniet TC, Nieuwstadt FTM, Boersma BJ. 2006. Direct numerical simulation of homogeneous turbulence in combination with premixed combustion at low Mach number modelled by the G-equation. J. Fluid Mech. 565:25–62 [Google Scholar]
  118. Troiani G, Creta F, Matalon M. 2015. Experimental investigation of Darrieus-Landau instability effects on turbulent premixed flames. Proc. Combust. Inst. 35:1451–59 [Google Scholar]
  119. Troiani G, Marrocco M, Giammartini S, Casciola CM. 2009. Counter-gradient transport in the combustion of a premixed CH4/air annular jet by combined PIV/OH-LIF. Combust. Flame 156:608–20 [Google Scholar]
  120. Tsinober A. 2009. An Informal Conceptual Introduction to Turbulence Heidelberg: Springer
  121. Veynante D, Poinsot T. 1997. Effects of pressure gradients on turbulent premixed flames. J. Fluid Mech. 353:83–114 [Google Scholar]
  122. Veynante D, Trouvé A, Bray KNC, Mantel T. 1997. Gradient and counter-gradient scalar transport in turbulent premixed flames. J. Fluid Mech. 332:263–93 [Google Scholar]
  123. Videto BD, Santavicca DA. 1990. Flame-turbulence interactions in a freely-propagating, premixed flame. Combust. Sci. Technol. 70:47–73 [Google Scholar]
  124. Yanagi T, Mimura Y. 1981. Velocity-temperature correlation in premixed flame. Proc. Combust. Inst. 18:1031–39 [Google Scholar]
  125. Yasari E, Lipatnikov AN. 2015. Assessment of a recent model of turbulent scalar flux in RANS simulations of premixed Bunsen flames. Proc. 8th Int. Symp. Turbul. Heat Mass Transfer. Sarajevo: Begell House (CD-ROM) [Google Scholar]
  126. Yu R, Bai XS, Bychkov V. 2015a. Fractal flame structure due to the hydrodynamic Darrieus-Landau instability. Phys. Rev. E 92:063028 [Google Scholar]
  127. Yu R, Bay XS, Lipatnikov AN. 2015b. A direct numerical simulation study of interface propagation in homogeneous turbulence. J. Fluid Mech. 772:127–64 [Google Scholar]
  128. Yu R, Lipatnikov AN, Bay XS. 2014. Three-dimensional direct numerical simulation study of conditioned moments associated with front propagation in turbulent flows. Phys. Fluids 26:085104 [Google Scholar]
  129. Zel'dovich YB, Barenblatt GI, Librovich VB, Makhviladze GM. 1985. The Mathematical Theory of Combustion and Explosions New York: Plenum
  130. Zimont VL, Biagioli F. 2002. Gradient, counter-gradient transport and their transition in turbulent premixed flames. Combust. Theory Model. 6:79–101 [Google Scholar]
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