RANS Simulations of Premixed Turbulent Flames

  • Andrei N. LipatnikovEmail author
Part of the Energy, Environment, and Sustainability book series (ENENSU)


While Reynolds-Averaged Navier-Stokes (RANS) simulations are widely used in applied research into premixed turbulent burning in spark ignition piston engines and gas-turbine combustors, fundamental challenges associated with modeling various unclosed terms in the RANS transport equations that describe premixed flames have not yet been solved. These challenges stem from two kinds of phenomena. First, thermal expansion due to heat release in combustion reactions affects turbulent flow and turbulent transport. Such effects manifest themselves in the so-called counter gradient turbulent transport, flame-generated turbulence, hydrodynamic instability of premixed combustion, etc. Second, turbulent eddies wrinkle and stretch reaction zones, thus, increasing their surface area and changing their local structure. Both the former effects, i.e. the influence of combustion on turbulence, and the latter effects, i.e. the influence of turbulence on combustion, are localized to small scales unresolved in RANS simulations and, therefore, require modeling. In the present chapter, the former effects, their physical mechanisms and manifestations, and approaches to modeling them are briefly overviewed, while discussion of the latter effects is more detailed. More specifically, the state-of-the-art of RANS modeling of the influence of turbulence on premixed combustion is considered, including widely used approaches such as models that deal with a transport equation for the mean Flame Surface Density or the mean Scalar Dissipation Rate. Subsequently, the focus of discussion is placed on phenomenological foundations, closed equations, qualitative features, quantitative validation, and applications of the so-called Turbulent Flame Closure (TFC) model and its extension known as Flame Speed Closure (FSC) model.


Turbulent combustion Premixed turbulent flames Modelling RANS simulations validation 



This work was supported by Swedish Research Council (VR), Swedish Energy Agency (EM), Swedish Gas Turbine Center (GTC), Chalmers Areas of Advance Transport and Energy, and Combustion Engine Research Center (CERC). The author is grateful to Profs. Chomiak, Karpov, Sabelnikov, and Zimont for valuable discussions.


  1. Abdel-Gayed RG, Al-Khishali KJ, Bradley D (1984) Turbulent burning velocities and flame straining in explosions. Proc R Soc Lond A 391:391–414CrossRefGoogle Scholar
  2. Atashkari K, Lawes M, Sheppard CGW, Woolley R (1999) Towards a general correlation of turbulent premixed flame wrinkling. In: Rodi W, Laurence D (eds) Engineering turbulence modelling and measurements 4. In: Proceedings of 4th International Symposium on Engineering Turbulence Modelling and Measurements, Ajaccio, Corsica, France, 24–26 May, 1999, pp 805–814Google Scholar
  3. Bailly P, Champion M, Garreton D (1997) Counter-gradient diffusion in a confined turbulent premixed flame. Phys Fluids 9:766–775CrossRefGoogle Scholar
  4. Bilger RW, Pope SB, Bray KNC, Driscoll JF (2005) Paradigms in turbulent combustion research. Proc Combust Inst 30:21–42CrossRefGoogle Scholar
  5. Borghi R (1990) Turbulent premixed combustion: further discussions of the scales of fluctuations. Combust Flame 80:304–312CrossRefGoogle Scholar
  6. Boudier P, Henriot S, Poinsot T, Baritaud T (1992) A model for turbulent flame ignition and propagation in spark ignition engines. Proc Combust Inst 24:503–510CrossRefGoogle Scholar
  7. Boughanem H, Trouvé A (1998) The domain of influence of flame instabilities in turbulent premixed combustion. Proc Combust Inst 27:971–978CrossRefGoogle Scholar
  8. Bradley D (1992) How fast can we burn? Proc Combust Inst 24:247–262CrossRefGoogle Scholar
  9. Bradley D (2002) Problems of predicting turbulent burning rates. Combust Theory Model 6:361–382CrossRefGoogle Scholar
  10. Bradley D, Lau AKC, Lawes M (1992) Flame stretch rate as a determinant of turbulent burning velocity. Philos Trans R Soc Lond A 338:359–387CrossRefGoogle Scholar
  11. Bradley D, Lawes M, Sheppard CGW (1994a) Study of turbulence and combustion interaction: measurement and prediction of the rate of turbulent burning. Report, University of LeedsGoogle Scholar
  12. Bradley D, Lawes M, Scott MJ, Mushi EMJ (1994b) Afterburning in spherical premixed turbulent explosions. Combust Flame 99:581–590Google Scholar
  13. Bradley D, Gaskell PH, Gu XJ, Sedaghat A (2005) Premixed flamelet modelling: factors influencing the turbulent heat release rate source term and the turbulent burning velocity. Combust Flame 143:227–245CrossRefGoogle Scholar
  14. Bray KNC (1979) The interaction between turbulence and combustion. Proc Combust Inst 17:223–233CrossRefGoogle Scholar
  15. Bray KNC (1980) Turbulent flows with premixed reactants. In: Libby PA, Williams FA (eds) Turbulent reacting flows. Springer, BerlinGoogle Scholar
  16. Bray KNC (1987) Methods of including realistic chemical reaction mechanisms in turbulent combustion models. In: Warnatz J, Jager W (ed) Complex chemical reaction systems. Mathematical modelling and simulation. Springer, HeidelbergGoogle Scholar
  17. Bray KNC (1990) Studies of the turbulent burning velocity. Proc R Soc Lond A 431:315–335CrossRefGoogle Scholar
  18. Bray KNC (1995) Turbulent transport in flames. Proc R Soc Lond A 451:231–256MathSciNetzbMATHCrossRefGoogle Scholar
  19. Bray KNC (1996) The challenge of turbulent combustion. Proc Combust Inst 26:1–26CrossRefGoogle Scholar
  20. Bray KNC, Moss JB (1977) A unified statistical model for the premixed turbulent flame. Acta Astronaut 4:291–319CrossRefGoogle Scholar
  21. Bray KNC, Cant RS (1991) Some applications of Kolmogorov’s turbulence research in the field of combustion. Proc R Soc Lond A 434:217–240zbMATHCrossRefGoogle Scholar
  22. Bray KNC, Libby PA, Moss JB (1985) Unified modeling approach for premixed turbulent combustion—Part I: General formulation. Combust Flame 61:87–102CrossRefGoogle Scholar
  23. Bray KNC, Champion M, Libby PA, Swaminathan N (2006) Finite rate chemistry and presumed PDF models for premixed turbulent combustion. Combust Flame 146:665–667CrossRefGoogle Scholar
  24. Brodkey RS (1967) The phenomena of fluid motions. Addison-Wesley Publishing Company, LondonGoogle Scholar
  25. Burluka AA, Griffiths JF, Liu K, Orms M (2009) Experimental studies of the role of chemical kinetics in turbulent flames. Combust Explos Shock Waves 45:383–391CrossRefGoogle Scholar
  26. Candel S, Poinsot T (1990) Flame stretch and the balance equation for the flame area. Combust Sci Technol 170:1–15CrossRefGoogle Scholar
  27. Candel S, Veynante D, Lacas F, Maistret E, Darabiha N, Poinsot T (1990) Coherent flame model: applications and recent extensions. In: Larrouturou BE (ed) Advances in combustion modeling. World Scientific, SingaporeGoogle Scholar
  28. Cant RS, Pope SB, Bray KNC (1990) Modelling of flamelet surface-to-volume ratio in turbulent premixed combustion. Proc Combust Inst 23:809–815CrossRefGoogle Scholar
  29. Chakraborty N, Champion M, Mura A, Swaminathan N (2011) Scalar-dissipation-rate approach. In: Swaminathan N, Bray KNC (eds) Turbulent premixed flames. Cambridge University Press, CambridgeGoogle Scholar
  30. Chaudhuri S, Akkerman V, Law CK (2011) Spectral formulation of turbulent flame speed with consideration of hydrodynamic instability. Phys Rev E 84:026322CrossRefGoogle Scholar
  31. Cheng RK, Shepherd IG (1991) The influence of burner geometry on premixed turbulent flame propagation. Combust Flame 85:7–26CrossRefGoogle Scholar
  32. Cheng WK, Diringer JA (1991) Numerical modelling of SI engine combustion with a flame sheet model. SAE Paper 910268Google Scholar
  33. Cho P, Law CK, Cheng RK, Shepherd IG (1988) Velocity and scalar fields of turbulent premixed flames in stagnation flow. Proc Combust Inst 22:739–745CrossRefGoogle Scholar
  34. Choi CR, Huh KY (1998) Development of a coherent flamelet model for spark-ignited turbulent premixed flame in a closed vessel. Combust Flame 114:336–348CrossRefGoogle Scholar
  35. Chowdhury BR, Cetegen BM (2017) Experimental study of the effects of free stream turbulence on characteristics and flame structure of bluff-body stabilized conical lean premixed flames. Combust Flame 178:311–328CrossRefGoogle Scholar
  36. Clavin P (1985) Dynamical behavior of premixed flame fronts in laminar and turbulent flows. Prog Energy Combust Sci 11:1–59CrossRefGoogle Scholar
  37. Clavin P, Williams FA (1979) Theory of premixed-flame propagation in large-scale turbulence. J Fluid Mech 90:589–604zbMATHCrossRefGoogle Scholar
  38. Cohé C, Chauveau C, Gökalp I, Kurtuluş DF (2009) CO\(_2\) addition and pressure effects on laminar and turbulent lean premixed CH\(_4\) air flames. Proc Combust Inst 32:1803–1810CrossRefGoogle Scholar
  39. Damköhler G (1940) Der einfuss der turbulenz auf die flammengeschwindigkeit in gasgemischen. Z Electrochem 46:601–652Google Scholar
  40. Darrieus G (1938) Propagation d’un front de flamme. Presented at La Technique Moderne (Paris) and in 1945 at Congrés de Mećanique Appliqueé (Paris)Google Scholar
  41. Dasgupta D, Sun W, Day M, Lieuwen T (2017) Effect of turbulence-chemistry interactions on chemical pathways for turbulent hydrogen-air premixed flames. Combust Flame 176:191–201CrossRefGoogle Scholar
  42. Dinkelacker F (2002) Numerical calculation of turbulent premixed flames with an efficient turbulent flame speed closure model. In: Breuer M, Durst F, Zenger C (eds) High-performance scientific and engineering computing. Lecture notes in computational science and engineering, vol 21, pp 81–88Google Scholar
  43. Dinkelacker F, Hölzler S (2000) Investigation of a turbulent flame speed closure approach for premixed flame calculations. Combust Sci Technol 158:321–340CrossRefGoogle Scholar
  44. Duclos JM, Veynante D, Poinsot T (1993) A comparison of flamelet models for premixed turbulent combustion. Combust Flame 95:101–117CrossRefGoogle Scholar
  45. Fichot F, Lacas F, Veynante D, Candel S (1993) One-dimensional propagation of a premixed turbulent flame with a balance equation for the flame surface density. Combust Sci Technol 90:35–60CrossRefGoogle Scholar
  46. Fogla N, Creta F, Matalon M (2017) The turbulent flame speed for low-to-moderate turbulence intensities: Hydrodynamic theory vs. experiments. Combust Flame 175:155–169CrossRefGoogle Scholar
  47. Frank JH, Kalt PAM, Bilger RW (1999) Measurements of conditional velocities in turbulent premixed flames by simultaneous OH PLIF and PIV. Combust Flame 116:220–232CrossRefGoogle Scholar
  48. Ghirelli F (2011) Turbulent premixed flame model based on a recent dispersion model. Comput Fluids 44:369–376MathSciNetzbMATHCrossRefGoogle Scholar
  49. Giovangigli V (1999) Multicomponent flow modeling. Springer, BerlinzbMATHCrossRefGoogle Scholar
  50. Goix P, Paranthoen P, Trinité M (1990) A tomographic study of measurements in a V-shaped H\(_2\)-air flame and a Lagrangian interpretation of the turbulent flame brush thickness. Combust Flame 81:229–241CrossRefGoogle Scholar
  51. Gouldin FC, Miles PC (1995) Chemical closure and burning rates in premixed turbulent flames. Combust Flame 100:202–210CrossRefGoogle Scholar
  52. Goulier J, Comandini A, Halter F, Chaumeix N (2017) Experimental study on turbulent expanding flames of lean hydrogen/air mixtures. Proc Combust Inst 36:2823–2832CrossRefGoogle Scholar
  53. Griebel P, Siewert P, Jansohn P (2007) Flame characteristics of turbulent lean premixed methane/air flames at high-pressure: turbulent flame speed and flame brush thickness. Proc Combust Inst 31:3083–3090CrossRefGoogle Scholar
  54. Hinze JO (1975) Turbulence, 2nd edn. McGraw Hill, New YorkGoogle Scholar
  55. Hirschfelder JO, Curtiss CF, Bird RB (1954) Molecular theory of gases and liquids. Wiley, New YorkzbMATHGoogle Scholar
  56. Huang C, Yasari E, Johansen LCR, Hemdal S, Lipatnikov AN (2016) Application of flame speed closure model to RANS simulations of stratified turbulent combustion in a gasoline direct-injection spark-ignition engine. Combust Sci Technol 188:98–131CrossRefGoogle Scholar
  57. Karlovitz B, Denniston DW, Wells FE (1951) Investigation of turbulent flames. J Chem Phys 19:541–547CrossRefGoogle Scholar
  58. Karpov VP, Severin ES (1980) Effects of molecular-transport coefficients on the rate of turbulent combustion. Combust Explos Shock Waves 16:41–46CrossRefGoogle Scholar
  59. Karpov VP, Lipatnikov AN (1995) An effect of molecular thermal conductivity and diffusion on premixed combustion. Doklady Phys Chemistry 341:83–85Google Scholar
  60. Karpov VP, Lipatnikov AN, Zimont, (1996) A test of an engineering model of premixed turbulent combustion. Proc Combust Inst 26:249–257Google Scholar
  61. Karpov VP, Lipatnikov AN, Zimont (1997) Flame curvature as a determinant of preferential diffusion effects in premixed turbulent combustion. In: Sirignano WA, Merzhanov AG, De Luca L (eds) Advances in combustion science: In honor of Ya.B. Zel’dovich. Prog Astronaut Aeronaut 173:235-250Google Scholar
  62. Kha KQN, Robin V, Mura A, Champion M (2016) Implications of laminar flame finite thickness on the structure of turbulent premixed flames. J Fluid Mech 787:116–147MathSciNetzbMATHCrossRefGoogle Scholar
  63. Kheirkhah S, Gülder ÖL (2013) Turbulent premixed combustion in V-shaped flames: characteristics of flame front. Phys Fluids 25:055107CrossRefGoogle Scholar
  64. Kheirkhah S, Gülder ÖL (2014) Influence of edge velocity on flame front position and displacement speed in turbulent premixed combustion. Combust Flame 161:2614–2626CrossRefGoogle Scholar
  65. Kheirkhah S, Gülder ÖL (2015) Consumption speed and burning velocity in counter-gradient and gradient diffusion regimes of turbulent premixed combustion. Combust Flame 162:1422–1439CrossRefGoogle Scholar
  66. Kim SH (2017) Leading points and heat release effects in turbulent premixed flames. Proc Combust Inst 36:2017–2024CrossRefMathSciNetGoogle Scholar
  67. 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 26:389–396CrossRefGoogle Scholar
  68. Kuznetsov VR (1975) Certain peculiarities of movement of a flame front in a turbulent flow of homogeneous fuel mixtures. Combust Explos Shock Waves 11:487–493CrossRefGoogle Scholar
  69. Kuznetsov VR, Sabelnikov VA (1990) Turbulence and combustion. Hemisphere Publ Corp, New YorkGoogle Scholar
  70. Landau LD (1944) On the theory of slow combustion. Acta Psysicochim USSR 19:77–85Google Scholar
  71. Lapointe S, Blanquart G (2016) Fuel and chemistry effects in high Karlovitz premixed turbulent flames. Combust Flame 167:294–307CrossRefGoogle Scholar
  72. Launder BE, Spalding DB (1972) Mathematical models of turbulence. Academic Press, LondonzbMATHGoogle Scholar
  73. Law CK (2006) Combustion physics. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  74. Lee B, Choi CR, Huh KY (1998) Application of the coherent flamelet model to counterflow turbulent premixed combustion and extinction. Combust Sci Technol 138:1–25CrossRefGoogle Scholar
  75. Li SC, Libby PA, Williams FA (1994) Experimental investigation of a premixed flame in an impinging turbulent stream. Proc Combust Inst 25:1207–1214CrossRefGoogle Scholar
  76. Libby PA (1975) On the prediction of intermittent turbulent flows. J Fluid Mech 68:273–295CrossRefGoogle Scholar
  77. Libby PA, Bray KNC (1977) Variable density effects in premixed turbulent flames. AIAA J 15:1186–1193CrossRefGoogle Scholar
  78. Libby PA, Bray KNC (1981) Countergradient diffusion in premixed turbulent flames. AIAA J 19:205–213CrossRefGoogle Scholar
  79. Libby PA, Williams FA (1994) Fundamental aspects and a review. In: Libby PA, Williams FA (eds) Turbulent reactive flows. Academic Press, LondonGoogle Scholar
  80. Lindstedt RP, Váos EM (1999) Modeling of premixed turbulent flames with second moment methods. Combust Flame 116:461–485CrossRefGoogle Scholar
  81. Lipatnikov AN (2009a) Can we characterize turbulence in premixed flames? Combust Flame 156:1242–1247Google Scholar
  82. Lipatnikov AN (2009b) Testing premixed turbulent combustion models by studying flame dynamics. Int J Spray Combust Dyn 1:39–66Google Scholar
  83. Lipatnikov AN (2011a) Conditioned moments in premixed turbulent reacting flows. Proc Combust Inst 33:1489–1496Google Scholar
  84. Lipatnikov AN (2011b) Transient behavior of turbulent scalar transport in premixed flames. Flow Turbul Combust 86:609–637Google Scholar
  85. Lipatnikov AN (2012) Fundamentals of premixed turbulent combustion. CRC Press, Boca-Raton, FloridaCrossRefGoogle Scholar
  86. Lipatnikov AN, Chomiak J (1997) A simple model of unsteady turbulent flame propagation. SAE Paper 972993Google Scholar
  87. Lipatnikov AN, Chomiak J (2000a) Transient and geometrical effects in expanding turbulent flames. Combust Sci Technol 154:75–117Google Scholar
  88. Lipatnikov AN, Chomiak J (2000b) Dependence of heat release on the progress variable in premixed turbulent combustion. Proc Combust Inst 28:227–234Google Scholar
  89. Lipatnikov AN, Chomiak J (2001) Developing premixed turbulent flames: Part I. A self-similar regime of flame propagation. Combust Sci Technol 162:85–112CrossRefGoogle Scholar
  90. Lipatnikov AN, Chomiak J (2002) Turbulent flame speed and thickness: phenomenology, evaluation, and application in multi-dimensional simulations. Prog Energy Combust Sci 28:1–74CrossRefGoogle Scholar
  91. Lipatnikov AN, Chomiak J (2004) Comment on “Turbulent burning velocity, burned gas distribution, and associated flame surface definition” Bradley D, Haq MZ, Hicks RA, Kitagawa T, Lawes M, Sheppard CGW, Woolley R, Combust Flame, 133:415 (2003). Combust Flame 137:261–263Google Scholar
  92. Lipatnikov AN, Chomiak J (2005a) A theoretical study of premixed turbulent flame development. Proc Combust Inst 30:843–850Google Scholar
  93. Lipatnikov AN, Chomiak J (2005b) Self-similarly developing, premixed, turbulent flames: a theoretical study. Phys Fluids 17:065105Google Scholar
  94. Lipatnikov AN, Chomiak J (2005c) Molecular transport effects on turbulent flame propagation and structure. Prog Energy Combust Sci 31:1–73Google Scholar
  95. Lipatnikov AN, Sathiah P (2005) Effects of turbulent flame development on thermoacoustic oscillations. Combust Flame 142:130–139CrossRefGoogle Scholar
  96. Lipatnikov AN, Chomiak J (2010) Effects of premixed flames on turbulence and turbulent scalar transport. Prog Energy Combust Sci 36:1–102CrossRefGoogle Scholar
  97. Lipatnikov AN, Wallesten J, Nisbet J (1998) Testing of a model for multi-dimensional computations of turbulent combustion in spark ignition engines. In: Proc Fourth Int Symp Diagnostics and modeling of combustion in internal combustion engines—COMODIA98. JSME, Kyoto, pp 239–44Google Scholar
  98. Lipatnikov AN, Nishiki S, Hasegawa T (2015a) DNS assessment of relation between mean reaction and scalar dissipation rates in the flamelet regime of premixed turbulent combustion. Combust Theory Model 19:309–328Google Scholar
  99. Lipatnikov AN, Chomiak J, Sabelnikov VA, Nishiki S, Hasegawa T (2015b) Unburned mixture fingers in premixed turbulent flames. Proc Combust Inst 35:1401–1408Google Scholar
  100. 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 94:513–526Google Scholar
  101. Lipatnikov AN, Sabelnikov VA, Nishiki S, Hasegawa T (2017) Flamelet perturbations and flame surface density transport in weakly turbulent premixed combustion. Combust Theory Model 21:205–227MathSciNetCrossRefGoogle Scholar
  102. Majda A, Sethian J (1985) The derivation and numerical solution of the equations for zero Mach number combustion. Combust Sci Technol 42:185–205CrossRefGoogle Scholar
  103. Meneveau C, Poinsot T (1991) Stretching and quenching of flamelets in premixed turbulent combustion. Combust Flame 86:311–332CrossRefGoogle Scholar
  104. Moreau P (1977) Turbulent flame development in a high velocity premixed flow. AIAA paper 77/49Google Scholar
  105. Moreau V (2009) A self-similar premixed turbulent flame model. Appl Math Model 33:835–851zbMATHCrossRefGoogle Scholar
  106. Moss JB (1980) Simultaneous measurements of concentration and velocity in an open premixed turbulent flame. Combust Sci Technol 22:119–129CrossRefGoogle Scholar
  107. Mouqallid M, Lecordier B, Trinité M (1994) High speed laser tomography analysis of flame propagation in a simulated internal combustion engine—applications to nonuniform mixture. SAE paper 941990Google Scholar
  108. Muppala SRP, Dinkelacker F (2004) Numerical modelling of the pressure dependent reaction source term for turbulent premixed methane-air flames. Prog Comp Fluid Dyn 4:328–336CrossRefGoogle Scholar
  109. Namazian M, Shepherd IG, Talbot L (1986) Characterization of the density fluctuations in turbulent V-shaped premixed flames. Combust Flame 64:299–308CrossRefGoogle Scholar
  110. van Oijen JA, Donini A, Bastiaans RJM, ten Thije Boonkkamp JHM, de Goey LPH (2016) State-of-the-art in premixed combustion modeling using flamelet generated manifolds. Prog Energy Combust Sci 57:30–74CrossRefGoogle Scholar
  111. Peters N (2000) Turbulent combustion. The University Press, CambridgezbMATHCrossRefGoogle Scholar
  112. Pfadler S, Leipertz A, Dinkelacker F (2008) Systematic experiments on turbulent premixed Bunsen flames including turbulent flux measurements. Combust Flame 152:616–631CrossRefGoogle Scholar
  113. Poinsot T, Veynante D (2005) Theoretical and numerical combustion, 2nd edn. Edwards, PhiladelphiaGoogle Scholar
  114. Poinsot T, Veynante D, Candel S (1991) Quenching processes and premixed turbulent combustion diagrams. J Fluid Mech 228:561–606Google Scholar
  115. Polifke W, Flohr P, Brandt M (2002) Modeling of inhomogeneously premixed combustion with an extended TFC model. ASME J Eng Gas Turbines Power 124:58–65CrossRefGoogle Scholar
  116. Poludnenko AY, Oran ES (2011) The interaction of high-speed turbulence with flames: turbulent flame speed. Combust Flame 158:301–326CrossRefGoogle Scholar
  117. Pope SB (1988) The evolution of surface in turbulence. Int J Eng Sci 26:445–469MathSciNetzbMATHCrossRefGoogle Scholar
  118. Pope SB (2000) Turbulent flows. The University Press, CambridgezbMATHCrossRefGoogle Scholar
  119. Prudnikov AG (1960) Hydrodynamics equations in turbulent flames. In: Prudnikov AG (ed) Combustion in a turbulent flow. Oborongiz, Moscow (in Russian)Google Scholar
  120. Prudnikov AG (1964) Burning of homogeneous fuel-air mixtures in a turbulent flow. In: Raushenbakh BV (ed) Physical principles of the working process in combustion chambers of jet engines. Mashinostroenie, Moscow (in Russian; translated from Russian by the Translation Division, Foreign and Technology Division, Wright Patterson AFB, Clearing House for Federal Scientific & Technical Information, Ohio, 1967, pp 244–336)Google Scholar
  121. Renou B, Mura A, Samson E, Boukhalfa A (2002) Characterization of the local flame structure and flame surface density for freely-propagating premixed flames at various Lewis numbers. Combust Sci Technol 174:143–179CrossRefGoogle Scholar
  122. Roberts WL, Driscoll JF, Drake MC, Goss LP (1993) Images of the quenching of a flame by a vortex—to quantify regimes of turbulent combustion. Combust Flame 94:58–69CrossRefGoogle Scholar
  123. Sabelnikov VA, Lipatnikov AN (2011) A simple model for evaluating conditioned velocities in premixed turbulent flames. Combust Sci Technol 183:588–613CrossRefGoogle Scholar
  124. Sabelnikov VA, Lipatnikov AN (2013) Transition from pulled to pushed premixed turbulent flames due to countergradient transport. Combust Theory Model 17:1154–1175MathSciNetCrossRefGoogle Scholar
  125. Sabelnikov VA, Lipatnikov AN (2015) Transition from pulled to pushed fronts in premixed turbulent combustion: theoretical and numerical study. Combust Flame 162:2893–2903CrossRefGoogle Scholar
  126. Sabelnikov VA, Lipatnikov AN (2017) Recent advances in understanding of thermal expansion effects in premixed turbulent flames. Annu Rev Fluid Mech 49:91–117MathSciNetzbMATHCrossRefGoogle Scholar
  127. Sabelnikov VA, Lipatnikov AN, Chakraborty N, Nishiki S, Hasegawa T (2016) A transport equation for reaction rate in turbulent flows. Phys Fluids 28:081701CrossRefGoogle Scholar
  128. Sabelnikov VA, Lipatnikov AN, Chakraborty N, Nishiki S, Hasegawa T (2017) A balance equation for the mean rate of product creation in premixed turbulent flames. Proc Combust Inst 36:1893–1901CrossRefGoogle Scholar
  129. Sathiah P, Lipatnikov AN (2007) Effects of flame development on stationary premixed turbulent combustion. Proc Combust Inst 31:3115–3122CrossRefGoogle Scholar
  130. Schmidt HP, Habisreuther P, Leuckel W (1998) A model for calculating heat release in premixed turbulent flames. Combust Flame 113:79–91CrossRefGoogle Scholar
  131. Scurlock AC, Grover JH (1953) Propagation of turbulent flames. Proc Combust Inst 4:645–658CrossRefGoogle Scholar
  132. Shelkin KI (1943) On combustion in a turbulent flow. J Tech Phys 13:520–530. Transl NACA, 1967, in NACA TM 1110:1–18 (from Russian)Google Scholar
  133. Siewert P (2006) Flame front characteristics of turbulent lean premixed methane/air flames at high-pressure. PhD thesis, ETHZ ZürichGoogle Scholar
  134. Sjunnesson A, Henrikson, Löfström C (1992) CARS measurements and visualization of reacting flows in a bluff body stabilized flame. AIAA paper 92/3650Google Scholar
  135. Sponfeldner T, Soulopoulos N, Beyrau F, Hardalupas Y, Taylor AMKP, Vassilicos JC (2015) The structure of turbulent flames in fractal- and regular-grid-generated turbulence. Combust Flame 162:3379–3393zbMATHCrossRefGoogle Scholar
  136. Stevens EJ, Bray KNC, Lecordier B (1998) Velocity and scalar statistics for premixed turbulent stagnation flames using PIV. Proc Combust Inst 27:949–955CrossRefGoogle Scholar
  137. Swaminathan N, Bray KNC (2005) Effect of dilatation on scalar dissipation in turbulent premixed flames. Combust Flame 143:549–565CrossRefGoogle Scholar
  138. Taylor GI (1935) Statistical theory of turbulence. IV. Diffusion in a turbulent air stream. Proc R Soc Lond A 151:465–478CrossRefGoogle Scholar
  139. Tamadonfar P, Gülder ÖL (2014) Flame brush characteristics and burning velocities of premixed turbulent methane/air Bunsen flames. Combust Flame 161:3154–3165CrossRefGoogle Scholar
  140. Tamadonfar P, Gülder ÖL (2015) Effects of mixture composition and turbulence intensity on flame front structure and burning velocities of premixed turbulent hydrocarbon/air Bunsen flames. Combust Flame 162:4417–4441CrossRefGoogle Scholar
  141. Townsend AA (1976) The structure of turbulent shear flow, 2nd edn. Cambridge University Press, CambridgezbMATHGoogle Scholar
  142. Trouvé A, Poinsot T (1994) Evolution equation for flame surface density in turbulent premixed combustion. J Fluid Mech 278:1–31MathSciNetzbMATHCrossRefGoogle Scholar
  143. Venkateswaran P, Marshall A, Shin DH, Noble D, Seitzman J, Lieuwen T (2011) Measurements and analysis of turbulent consumption speeds of H\(_2\)/CO mixtures. Combust Flame 158:1602–1614CrossRefGoogle Scholar
  144. Venkateswaran P, Marshall A, Seitzman J, Lieuwen T (2013) Pressure and fuel effects on turbulent consumption speeds of H\(_2\)/CO blends. Proc Combust Inst 34:1527–1535CrossRefGoogle Scholar
  145. Venkateswaran P, Marshall A, Seitzman J, Lieuwen T (2015) Scaling turbulent flame speeds of negative Markstein length fuel blends using leading points concepts. Combust Flame 162:375–387CrossRefGoogle Scholar
  146. Verma S, Lipatnikov AN (2016) Does sensitivity of measured scaling exponents for turbulent burning velocity to flame configuration prove lack of generality of notion of turbulent burning velocity? Combust Flame 173:77–88CrossRefGoogle Scholar
  147. Vervisch L, Bidaux E, Bray KNC, Kollmann W (1995) Surface densiuty function in premixed turbulent combustion modeling, similarities between probability density function and flame surface approaches. Phys Fluids 7:2496–2503zbMATHCrossRefGoogle Scholar
  148. Veynante D, Vervisch L (2002) Turbulent combustion modeling. Prog Energy Combust Sci 28:193–266CrossRefGoogle Scholar
  149. Wallesten J, Lipatnikov AN, Chomiak J (2002) Modeling of stratified combustion in a DI SI engine using detailed chemistry pre-processing. Proc Combust Inst 29:703–709CrossRefGoogle Scholar
  150. Wang Z, Magi V, Abraham J (2017) Turbulent flame speed dependencies of lean methane-air mixtures under engine relevant conditions. Combust Flame 180:53–62CrossRefGoogle Scholar
  151. Williams FA (1985) Combustion theory, 2nd edn. Benjamin/Cummings, Menlo Park, CaliforniaGoogle Scholar
  152. Wu MS, Kwon A, Driscoll G, Faeth GM (1990) Turbulent premixed hydrogen/air flames at high Reynolds numbers. Combust Sci Technol 73:327–350CrossRefGoogle Scholar
  153. Yanagi T, Mimura Y (1981) Velocity-temperature correlation in premixed flame. Proc Combust Inst 18:1031–1039CrossRefGoogle Scholar
  154. Yasari E, Lipatnikov AN (2015) Assessment of a recent model of turbulent scalar flux in RANS simulations of premixed Bunsen flames. In: Hanjalic K, Miyauchi T, Borello D, Had\(\breve{\rm z}\)iabdi\(\acute{\rm c}\) M, Venturini P (eds) THMT15, Proceedings of the International Symposium Turbulence, Heat and Mass Transfer 8, Sarajevo, Bosnia and Herzegovina, September 15–18, 2015. ICHMTGoogle Scholar
  155. Yasari E, Verma S, Lipatnikov AN (2015) RANS simulations of statistically stationary premixed turbulent combustion using flame speed closure model. Flow Turbul Combust 94:381–414CrossRefGoogle Scholar
  156. Yu R, Lipatnikov AN (2017a) A direct numerical simulation study of statistically stationary propagation of reaction wave in homogeneous turbulence. Phys Rev E 95:063101Google Scholar
  157. Yu R, Lipatnikov AN (2017b) DNS study of dependence of bulk consumption velocity in a constant-density reacting flow on turbulence and mixture characteristics. Phys Fluids 29:065116Google Scholar
  158. 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 26:085104CrossRefGoogle Scholar
  159. Yu R, Bay XS, Lipatnikov AN (2015) A direct numerical simulation study of interface propagation in homogeneous turbulence. J Fluid Mech 772:127–164CrossRefGoogle Scholar
  160. Zel’dovich YaB, Barenblatt GI, Librovich VB, Makhviladze GM (1985) The mathematical theory of combustion and explosions. Consultants Bureau, New YorkCrossRefGoogle Scholar
  161. Zimont VL (1979) Theory of turbulent combustion of a homogeneous fuel mixture at high Reynolds number. Combust Explos Shock Waves 15:305–311CrossRefGoogle Scholar
  162. Zimont VL (2000) Gas premixed combustion at high turbulence. Turbulent flame closure combustion model. Exp Thermal Fluid Sci 21:179–186CrossRefGoogle Scholar
  163. Zimont VL (2015) Unclosed Favre-averaged equation for the chemical source and an analytical formulation of the problem of turbulent premixed combustion in the flamelet regime. Combust Flame 162:874–875CrossRefGoogle Scholar
  164. Zimont VL, Lipatnikov AN (1993) Calculation of the rate of heat release in a turbulent flame. Doklady Phys Chem 332:440–443Google Scholar
  165. Zimont VL, Lipatnikov AN (1995) A numerical model of premixed turbulent combustion. Chem Phys Rep 14:993–1025Google Scholar
  166. Zimont VL, Biagioli F, Syed K (2001) Modelling turbulent premixed combustion in the intermediate steady propagation regime. Prog Comput Fluid Dyn 1:14–28CrossRefGoogle Scholar
  167. Zimont VL, Polifke W, Bettelini M, Weisenstein W (1998) An efficient computational model for premixed turbulent combustion at high Reynolds number based on a turbulent flame speed closure. J Eng Gas Turbines Power 120:526–532CrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Chalmers University of TechnologyGothenburgSweden

Personalised recommendations