Direct Numerical Simulations for Combustion Science: Past, Present, and Future

Part of the Energy, Environment, and Sustainability book series (ENENSU)


Direct numerical simulations (DNS) of turbulent combustion have evolved tremendously in the past decades, thanks to the rapid advances in high performance computing technology. Today’s DNS is capable of incorporating detailed reaction mechanisms and transport properties, with physical parameter ranges approaching laboratory scale flames, thereby allowing direct comparison and cross-validation against laser diagnostic measurements. While these developments have led to significantly improved understanding of fundamental turbulent flame characteristics, there are increasing demands to explore combustion regimes at higher levels of turbulent Reynolds (Re) and Karlovitz (Ka) numbers, with a practical interest in new combustion engines driving towards higher efficiencies and lower emissions. This chapter attempts to provide a brief historical review of the progress in DNS of turbulent combustion during the past decades. Major scientific accomplishments and contributions towards fundamental understanding of turbulent combustion will be summarized and future challenges and research needs will be proposed.


Direct numerical simulations Turbulent combustion High performance computing Flame-flow interaction Extreme combustion 



The author was sponsored by King Abdullah University of Science and Technology (KAUST).


  1. Abdel-Gayed RG, Bradley D, Lawes M (1987) Turbulent burning velocities: a general correlation in terms of straining rates. Proc R Soc London A 1847:389–413CrossRefGoogle Scholar
  2. Alshaalan TM, Rutland CJ (1998) Turbulence, scalar transport, and reaction rates in flame-wall interaction. Proc Combust Inst 27:793–799CrossRefGoogle Scholar
  3. Arias PG, Im HG, Narayanan P, Trouvé A (2011) A Computational study of nonpremixed flame extinction by water spray. Proc Combust Inst 33:2591–2597CrossRefGoogle Scholar
  4. Ashurst WT, Kerstein AR, Kerr RM, Gibson CH (1987) Alignment of vorticity and scalar gradient with strain in simulated Navier-Stokes turbulence. Phys Fluids 30:2343–2353Google Scholar
  5. Aspden AJ, Bell JB, Day MS, Woosley SE, Zingale M (2008) Turbulence-flame interactions in type Ia supernovae. Astrophys J 689(2)Google Scholar
  6. Aspden AJ, Day MS, Bell JB (2011a) Characterization of low Lewis number flames. Proc Combust Inst 33:1463–1471CrossRefGoogle Scholar
  7. Aspden AJ, Day MS, Bell JB (2011b) Turbulence–flame interactions in lean premixed hydrogen: transition to the distributed burning regime. J Fluid Mech 680:287–320CrossRefzbMATHGoogle Scholar
  8. Aspden AJ, Day MS, Bell JB (2011c) Lewis number effects in distributed flames. Proc Combust Inst 33:1473–1480CrossRefGoogle Scholar
  9. Aspden AJ, Day MS, Bell JB (2015) Turbulence-chemistry interaction in lean premixed hydrogen combustion. Proc Combust Inst 35:1321–1329CrossRefGoogle Scholar
  10. Baum M, Poinsot T, Haworth D, Darabiha N (1994) Using direct numerical simulations to study H2/O2/N2 flames with complex chemistry in turbulent flows. J Fluid Mech 281:1–32Google Scholar
  11. Bedat B, Egolfopoulos F, Poinsot T (1999) Direct numerical simulation of heat release and NOx formation in turbulent non premixed flames. Combust Flame 119:69–83CrossRefGoogle Scholar
  12. Bell JB, Collela P, Glaz HM (1989) A second-order projection method for the incompressible Navier-Stokes equations. J Comput Phys 85:257–283Google Scholar
  13. Bell JB, Day MS, Grcar JF, Lijewski MJ, Driscoll JF, Filatyev SA (2007) Numerical simulation of a laboratory-scale turbulent slot flame. Proc Combust Inst 27:1299–1307CrossRefGoogle Scholar
  14. Bennett JC, Abbasi H, Bremer P-T, Grout R, Gyulassy A, Jin T, Klasky S, Kolla H, Parashar M, Pascucci V, Pebay P, Thompson D, Yu H, Zhang F, Chen JH (2012) Combining in-situ and in-transit processing to enable extreme-scale scientific analysis. In: Proceedings of the international conference on high performance computing, networking, storage and analysis, SC ’12, pp 49:1–49:9, Los Alamitos, CA, USA. IEEE Computer Society PressGoogle Scholar
  15. Bobbitt B, Blanquart G (2016) Vorticity isotropy in high Karlovitz number premixed flames. Phys Fluids 28:105101CrossRefGoogle Scholar
  16. Bradley D (1992) How fast can we burn? Proc Combust Inst 24:247–262CrossRefGoogle Scholar
  17. Bradley D (2002) Problems of predicting turbulent burning rates. Combust Theory Model 6(2):361–382CrossRefGoogle Scholar
  18. Bradley D, Lawes M, Mansour MS (2011) The problems of the turbulent burning velocity. Flow Turbul Combust 87:191–204CrossRefzbMATHGoogle Scholar
  19. Bruneaux G, Akselvoll K, Poinsot T, Ferziger JH (1996) Flame-wall interaction simulation in a turbulent channel flow. Combust Flame 107:27–44CrossRefGoogle Scholar
  20. Buckmaster J (2002) Edge flames. Prog Energy Combust Sci 28:435–475Google Scholar
  21. Carlsson H, Yu R, Bai XS (2014) Direct numerical simulation of lean premixed CH4/air and H2/air flames at high Karlovitz numbers. Int J Hydrogen Energy 39:20216–20232CrossRefGoogle Scholar
  22. Carlsson H, Yu R, Bai XS (2015) Flame structure analysis for categorization of lean premixed CH4/air and H2/air flames at high Karlovitz numbers: direct numerical simulation studies. Proc Combust Inst 35:1425–1432CrossRefGoogle Scholar
  23. Chatakonda O, Hawkes ER, Aspden AJ, Kerstein AR, Kolla H, Chen JH (2013) On the fractal characteristics of low Damköhler number flames. Combust Flame 160:2422–2433CrossRefGoogle Scholar
  24. Chaudhuri S, Wu F, Zhu D, Law CK (2012) Flame speed and self-similar propagation of expanding turbulent premixed flames. Phys Rev Lett 108:044503CrossRefGoogle Scholar
  25. Chen JH (2011) Petascale direct numerical simulation of turbulent combustion—fundamental insights towards predictive models. Proc Combust Inst 33:99–123CrossRefGoogle Scholar
  26. Chen JH, Echekki T, Kollman W (1998) The mechanism of two-dimensional pocket formation in lean premixed methane air flames with implications for turbulent combustion. Combust Flame 116:15–48CrossRefGoogle Scholar
  27. Chen JH, Im HG (1998) Correlation of flame speed with stretch in turbulent premixed methane/air flames. In: 27th international symposium on combustion, vol 27, The Combustion Institute, pp 819–826Google Scholar
  28. Chen JH, Im HG (2000) Stretch effects on the burning velocity of turbulent premixed hydrogen-air flames. Proc Combust Inst 28:211–218CrossRefGoogle Scholar
  29. Coppola G, Coriton B, Gomez A (2009) Highly turbulent counterflow flames: a laboratory scale benchmark for practical systems. Combust Flame 156:1834–1843CrossRefGoogle Scholar
  30. Cuenot B, Poinsot T (1994) Effects of curvature and unsteadiness in diffusion flames. Implications for turbulent diffusion combustion. In: 25th proceedings of the symposium (international) on combustion, Irvine, pp 1383–1390Google Scholar
  31. Dabireau F, Cuenot B, Vermorel O, Poinsot T (2003) Interaction of flames of H2 + O2 with inert walls. Combust Flame 135:123–133CrossRefGoogle Scholar
  32. Desjardins O, Moureau V, Pitsch H (2008) An accurate conservative level set/ghost fluid method for simulating turbulent atomization. J Comput Phys 18:8395–8416MathSciNetCrossRefzbMATHGoogle Scholar
  33. Domingo P, Vervisch L (1996) Triple flames and partially premixed combustion in autoignition of non-premixed mixtures. In: 26th symposium (international) on combustion, The Combustion Institute, Pittsburgh, pp 233–240Google Scholar
  34. Driscoll JF (2008) Turbulent premixed combustion: flamelet structure and its effect on turbulent burning velocities. Prog Energy Combust Sci 34:91–134CrossRefGoogle Scholar
  35. Echekki T, Chen JH (1996) Unsteady strain rate and curvature effects in turbulent premixed methane-air flames. Combust Flame 106:184–202CrossRefGoogle Scholar
  36. Echekki T, Chen JH (1998) Structure and propagation of methanol-air triple flames. Combust Flame 114:231–245CrossRefGoogle Scholar
  37. Egolfopoulos FN, Campbell CS (1996) Unsteady counterflowing strained diffusion flames: diffusion-limited frequency response. J Fluid Mech 318:1–29CrossRefzbMATHGoogle Scholar
  38. Eswaran V, Pope S (1988) An examination of forcing in direct numerical simulations of turbulence. Comput Fluids 16(3):257–278CrossRefzbMATHGoogle Scholar
  39. Favier V, Vervisch L (2001) Edge flames and partially premixed combustion in diffusion flame quenching. Combust Flame 125:788–803CrossRefGoogle Scholar
  40. Grout RW, Gruber A, Kolla H, Bremer P-T, Bennett JC, Gyulassy A, Chen JH (2012) A direct numerical simulation study of turbulence and flame structure in transverse jets analysed in jet-trajectory based coordinates. J Fluid Mech 706(10):351–383CrossRefzbMATHGoogle Scholar
  41. Gruber A, Sankaran R, Hawkes ER, Chen JH (2010) Turbulent flame-wall interaction: a direct numerical simulation study. J Fluid Mech 658:5–32CrossRefzbMATHGoogle Scholar
  42. Gruber A, Chen JH, Valiev D, Law CK (2012) Direct numerical simulation of premixed flame boundary layer flashback in turbulent channel flow. J Fluid Mech 709:516–542CrossRefzbMATHGoogle Scholar
  43. Hamlington PE, Poludnenko AY, Oran ES (2011) Interactions between turbulence and flames in premixed reacting flows. Phys Fluids 23:125111CrossRefGoogle Scholar
  44. Hamlington PE, Poludnenko AY, Oran ES (2012) Intermittency in premixed turbulent reacting flows. Phys Fluids 24:075111CrossRefGoogle Scholar
  45. Hawkes ER, Chatakonda O, Kolla H, Kerstein AR, Chen JH (2012) A petascale direct numerical simulation study of the modelling of flame wrinkling for large-eddy simulations in intense turbulence. Combust Flame 159:2690–2703CrossRefGoogle Scholar
  46. Hawkes ER, Sankaran R, Chen JH, Kaiser SA, Frank JH (2009) An analysis of lower-dimensional approximations to the scalar dissipation rate using direct numerical simulations of plane jet flames. Proc Combust Inst 32:1455–1463CrossRefGoogle Scholar
  47. Haworth D, Cuenot B, Poinsot T, Blint R (2000) Numerical Simulation of turbulent propane-air combustion with non homogeneous reactants. Combust Flame 121:395–417CrossRefGoogle Scholar
  48. Hilbert R, Thevenin D (2002) Autoignition of turbulent non-premixed flames investigated using direct numerical simulations. Combust Flame 128:22–37CrossRefGoogle Scholar
  49. Hilbert R, Tap F, El-Rabii H, Thévenin D (2004) Impact of detailed chemistry and transport models on turbulent combustion simulations. Prog Energy Combust Sci 30:61–117CrossRefGoogle Scholar
  50. Huan X, Marzouk YM (2013) Simulation-based optimal Bayesian experimental design for nonlinear systems. J Comput Phys 232(1):288–317MathSciNetCrossRefGoogle Scholar
  51. Im HG, Arias PG, Chaudhuri S, Uranakara H (2016) Direct numerical simulations of statistically stationary turbulent premixed flames. Combust Sci Technol 188(8):1182–1198CrossRefGoogle Scholar
  52. Im HG, Bechtold JK, Law CK (1995) Counterflow diffusion flames with unsteady strain rates. Combust Sci Technol 106:345–361CrossRefGoogle Scholar
  53. Im HG, Chen JH, Law CK (1998) Ignition of hydrogen/air mixing layer in turbulent flows. In: 27th international symposium on combustion, The Combustion Institute, vol 27, pp 1047–1056Google Scholar
  54. Im HG, Chen JH (1999) Structure and propagation of triple flames in partially premixed hydrogen/air mixtures. Combust Flame 119:436–454CrossRefGoogle Scholar
  55. Im HG, Chen JH (2001) Effects of flow strain on triple flame propagation. Combust Flame 126:1384–1392CrossRefGoogle Scholar
  56. Jenkins KW, Cant RS (2002) Curvature effects on flame kernels in a turbulent environment. Proc Combust Inst 29:2023–2029CrossRefGoogle Scholar
  57. Jenkins KW, Klein M, Chakraborty N, Cant RS (2006) Effects of strain rate and curvature on the propagation of a spherical flame kernel in the thin-reaction-zones regime. Combust Flame 145:415–434CrossRefGoogle Scholar
  58. Jimenez C, Cuenot B, Poinsot T, Haworth D (2002) Numerical simulation and modeling for lean 
stratified propane-air flames. Combust Flame 128:1–21Google Scholar
  59. Kee RJ, Rupley FM, Miller JA (1989) Chemkin-II: a Fortran chemical kinetics package for the analysis of gas-phase chemical kinetics, Sandia Report SAND-89-8009Google Scholar
  60. Kim J, Moin P, Moser RD (1987) Turbulence statistics in fully-developed channel flow at low Reynolds number. J Fluid Mech 177:133–166CrossRefzbMATHGoogle Scholar
  61. Kim, Y.J., Lee, B.J., Im, H.G. 2017. Scale effect on dynamics of meso-scale bluff-body-stabilized flames in lean premixed hydrogen-air and syngas-air mixtures. In: Fourteenth international conference on flow dynamics, Sendai, Japan, 1–3 Nov, 2017Google Scholar
  62. Lapointe S, Savard B, Blanquart G (2015) Differential diffusion effects, distributed burning, and local extinctions in high Karlovitz premixed flames. Combust Flame 162(9):3341–3355CrossRefGoogle Scholar
  63. Le Maître OP, Knio OM (2010) Spectral methods for uncertainty quantification: with applications to computational fluid dynamics. SpringerGoogle Scholar
  64. Lebas R, Menard T, Beau PA, Berlemont A, Demoulin FX (2009) Numerical simulation of primary break-up and atomization: DNS and modelling study. Int J Multiph Flow 35:247–260CrossRefGoogle Scholar
  65. Lee ED, Yoo CS, Chen JH, Frank JH (2010) Effect of NO on extinction and re-ignition of vortex-perturbed hydrogen flames. Combust Flame 157:217–229CrossRefGoogle Scholar
  66. Lee S, Lele SK, Moin P (1991) Simulations of spatially decaying compressible turbulence. Center for Turbulence Research, NASA Ames/Stanford University, Manuscript 126Google Scholar
  67. Lignell DO, Chen JH, Smith PJ, Lu T, Law CK (2007) The effect of flame structure on soot formation and transport in turbulent nonpremixed flames using direct numerical simulation. Combust Flame 151:2–28CrossRefGoogle Scholar
  68. Lignell DO, Chen JH, Smith PJ (2008) Three-dimensional direct numerical simulation of soot formation and transport in a temporally evolving nonpremixed ethylene jet flame. Combust Flame 155:316–333CrossRefGoogle Scholar
  69. 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
  70. Lipatnikov AN, Chomiak J (2005) Molecular transport effects on turbulent flame propagation and structure. Prog Energy Combust Sci 31:1–73CrossRefzbMATHGoogle Scholar
  71. Lipatnikov AN, Chomiak J (2010) Effects of premixed flames on turbulence and turbulent scalar transport. Prog Energy Combust Sci 36:1–102CrossRefGoogle Scholar
  72. Liu CC, Shy SS, Peng MW, Chiu CW, Dong Y-C (2012) High-pressure burning velocities measurements for centrally-ignited premixed methane/air flames interacting with intense near-isotropic turbulence at constant Reynolds numbers. Combust Flame 159:2608–2619CrossRefGoogle Scholar
  73. Lu TF, Yoo CS, Chen JH, Law CK (2010) Three-dimensional direct numerical simulation of a turbulent lifted hydrogen jet flame in a heated coflow: a chemical explosive mode analysis. J Fluid Mech 652:45–64CrossRefzbMATHGoogle Scholar
  74. Mahalingam S, Chen JH, Vervisch L (1995) Finite-rate chemistry and transient effects in simulations of turbulent non-premixed flames. Combust Flame 102:285CrossRefGoogle Scholar
  75. Mastorakos E, Baritaud TA, Poinsot TJ (1997) Numerical simulations of autoignition in turbulent mixing flows. Combust Flame 109:198–223Google Scholar
  76. Matalon M (1983) On flame stretch. Combust Sci Technol 31:169–181CrossRefGoogle Scholar
  77. Mashayek F (1998) Droplet-turbulence interactions in low Mach number homogeneous shear two-phase flows. J Fluid Mech 367:163–203CrossRefzbMATHGoogle Scholar
  78. Minamoto Y, Fukushima N, Tanahashi M, Miyauchi T, Dunstan TD, Swaminathan N (2011) Effect of flow-geometry on turbulence-scalar interaction in premixed flames. Phys Fluids 23:125107CrossRefGoogle Scholar
  79. Minamoto Y, Swaminathan N, Cant RS, Leung T (2014) Reaction zones and their structure in MILD combustion. Combust Sci Technol 186(8):1075–1096CrossRefGoogle Scholar
  80. Mizobuchi Y, Tachibana S, Shinjo J, Ogawa S, Takeno T (2002) A numerical analysis of the structure of a turbulent hydrogen jet lifted flame. Proc Combust Inst 29:2009–2015CrossRefGoogle Scholar
  81. Mizobuchi Y, Shinjo J, Ogawa S, Takeno T (2005) A numerical study on the formation of diffusion flame islands in a turbulent hydrogen jet lifted flame. Proc Combust Inst 30:611–619CrossRefGoogle Scholar
  82. Modest MF (2013) Radiative heat transfer, 3rd edn. Academic PressGoogle Scholar
  83. Moin P, Mahesh K (1998) Direct numerical simulation: a tool in turbulence research. Annu Rev Fluid Mech 40:539–578MathSciNetCrossRefGoogle Scholar
  84. Mueller ME, Blanquart G, Pitsch H (2009) Hybrid method of moments for modeling soot formation and growth. Combust Flame 156:1143–1155CrossRefGoogle Scholar
  85. Najm HN, Knio OM, Paul PH, Wyckoff PS (1998) A study of flame observables in premixed methane-air flames. Combust Sci Technol 140:369–403CrossRefGoogle Scholar
  86. Nikolaou ZM, Swaminathan N (2015) Direct numerical simulation of complex fuel combustion with detailed chemistry: physical insight and mean reaction rate modeling. Combust Sci Technol 187:1759–1789CrossRefGoogle Scholar
  87. O’Brien J, Towery CAZ, Hamlington PE, Ihme M, Poludnenko AY, Urzay J (2017) The cross-scale physical-space transfer of kinetic energy in turbulent premixed flames. Proc Combust Inst 36:1967–1975CrossRefGoogle Scholar
  88. Pascucci V, Scorzelli G, Summa B, Bremer PT, Gyulassy A, Christensen C, Philip S, Kumar S (2012) The ViSUS visualization framework, Chapter 19. Chapman & Hall/CRC Computational Science, pp 401–414Google Scholar
  89. Peters N (2000) Turbulent combustion. Cambridge University PressGoogle Scholar
  90. Poinsot T (1996) Using direct numerical simulations to understand premixed turbulent combustion. Proc Combust Inst 26:219–232CrossRefGoogle Scholar
  91. Poinsot T, Candel S, Trouvé A (1995) Applications of direct numerical simulation to premixed turbulent combustion. Prog Energy Combust Sci 21:531–576CrossRefGoogle Scholar
  92. Poinsot T, Veynante D (2005) Theoretical and numerical combustion. 2nd edn. RT Edwards, Inc.Google Scholar
  93. Poinsot T, Veynante D, Candel S (1991) Quenching processes and premixed turbulent combustion diagrams. J Fluid Mech 228:561–606Google Scholar
  94. Poinsot T, Haworth DC, Bruneaux G (1993) Direct simulation and modeling of flame-wall interaction for premixed turbulent combustion. Combust Flame 95:118–132CrossRefGoogle Scholar
  95. Pope SB (1987) Turbulent premixed flames. Annu Rev Fluid Mech 19:237–270CrossRefGoogle Scholar
  96. Rogallo RS (1981) Numerical experiments in homogeneous turbulence. NASA TM-81315Google Scholar
  97. Rogallo RS, Moin P (1984) Numerical simulation of turbulent flows. Annu Rev Fluid Mech 16:99–137Google Scholar
  98. Ronney PD (1995) Modeling in combustion science. Lect Notes Phys 449:1–22CrossRefGoogle Scholar
  99. Rutland CJ, Ferziger JH (1991) Simulations of flame-vortex interactions. Combust Flame 84:343–360CrossRefGoogle Scholar
  100. Rutland CJ, Cant RS (1994) Turbulent transport in premixed flames. In Proceedings of the summer program center for turbulence research, NASA Ames/Stanford UniversityGoogle Scholar
  101. Salenbauch S, Sirignano M, Marchisio D, Pollack M, D’Anna A, Hasse C (2017) Detailed particle nucleation modeling in a sooting ethylene flame using a conditional quadrature method of moments (CQMOM). Proc Combust Inst 36:771–779CrossRefGoogle Scholar
  102. Sankaran R, Hawkes ER, Chen JH, Lu TF, Law CK (2007) Structure of a spatially developing turbulent lean methane-air Bunsen flame. Proc Combust Inst 27:1291–1298CrossRefGoogle Scholar
  103. Sankaran R, Hawkes ER, Yoo CS, Chen JH (2015) Response of flame thickness and propagation speed under intense turbulence in spatially developing lean premixed methane-air jet flames. Combust Flame 162:3294–3306CrossRefGoogle Scholar
  104. Sarkar S, Erlebacher G, Hussaini MY (1991) Direct simulation of compressible turbulence in a shear flow. Theor Comput Fluid Dyn 2:291–305CrossRefzbMATHGoogle Scholar
  105. Savard B, Blanquart G (2015) Broken reaction zone and differential diffusion effects in high Karlovitz n-C7H16 premixed turbulent flames. Combust Flame 162:2020–2033CrossRefGoogle Scholar
  106. Savard B, Bobbitt B, Blanquart G (2015) Structure of a high Karlovitz n-C7H16 premixed turbulent flame. Proc Combust Inst 35:1377–1384CrossRefGoogle Scholar
  107. Shim YS, Fukushima N, Shimura M, Nada Y, Tanahashi M, Miyauchi T (2013) Radical fingering in turbulent premixed flame classified into thin reaction zones. Proc Combust Inst 34:1383–1391CrossRefGoogle Scholar
  108. Tanahashi M, Nada Y, Ito Y, Miyauchi T (2002) Local flame structure in the well-stirred reactor regime. Proc Combust Inst 29:2041–2049CrossRefGoogle Scholar
  109. Taylor GI (1938) The spectrum of turbulence. Proc R Soc London 164(919):476–490CrossRefzbMATHGoogle Scholar
  110. Tomboulides A (2013) DNS of Flame Propagation Phenomena, ERCOFTAC Spring Festival, ToulonGoogle Scholar
  111. Trouve A, Poinsot T (1994) The evolution equation for the flame surface density in turbulent premixed combustion. J Fluid Mech 278:1–31MathSciNetCrossRefzbMATHGoogle Scholar
  112. Vervisch L, Hauguel R, Domingo P, Rullaud M (2004) Three facets of turbulent combustion modelling: DNS of premixed V-flame, LES of lifted nonpremixed flame and RANS of jet-flame. J Turbul 5:004CrossRefGoogle Scholar
  113. Wabel TM, Skiba AW, Temme JE, Driscoll JF (2017) Measurements to determine the regimes of premixed flames in extreme turbulence. Proc Combust Inst 36:1809–1816CrossRefGoogle Scholar
  114. Wacks DH, Chakraborty N, Klein M, Arias PG, Im HG (2016) Flow topologies in different regimes of premixed turbulent combustion: a direct numerical simulation analysis. Phys Rev Fluids 1:083401CrossRefGoogle Scholar
  115. Wang H, Hawkes ER, Chen JH (2017) A direct numerical simulaiton study of flame structure and stabilization of an experimental high Ka CH4/air premixed jet flame. Combust Flame 180:110–123CrossRefGoogle Scholar
  116. Williams FA (1985) Combustion theory, 2nd edn. Westview PressGoogle Scholar
  117. Yoo CS, Im HG (2005) Transient dynamics of edge flames in a laminar nonpremixed hydrogen-air counterflow. Proc Combust Inst 30:349–356CrossRefGoogle Scholar
  118. Yoo CS, Im HG (2007) Transient soot dynamics in turbulent nonpremixed ethylene-air counterflow flames. Proc Combust Inst 31:701–708CrossRefGoogle Scholar
  119. Yoo CS, Richardson ES, Sankaran R, Chen JH (2011) A DNS study on the stabilization mechanism of a turbulent lifted ethylene jet flame in highly heated coflow. Proc Combust Inst 33:1619–1627CrossRefGoogle Scholar

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© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Clean Combustion Research Center, King Abdullah University of Science and TechnologyThuwalSaudi Arabia

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