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Articles

Transported PDF simulation of auto-ignition of a turbulent methane jet in a hot, vitiated coflow

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Pages 326-361 | Received 24 Jan 2019, Accepted 10 Oct 2019, Published online: 23 Oct 2019

References

  • T. Kamimoto and H. Kobayashi, Combustion processes in diesel engines, Prog. Energy Combust. Sci. 17 (1991), pp. 163–189. doi: 10.1016/0360-1285(91)90019-J
  • C. Lechner and J. Seume, Stationäre Gasturbinen, Springer-Verlag, Berlin Heidelberg, 2003.
  • E. Mastorakos, Ignition of turbulent non-premixed flames, Prog. Energy Combust. Sci. 35 (2009), pp. 57–97. doi: 10.1016/j.pecs.2008.07.002
  • A.Y. Klimenko and R.W. Bilger, Conditional moment closure for turbulent combustion, Prog. Energy Combust. Sci. 25 (1999), pp. 595–687. doi: 10.1016/S0360-1285(99)00006-4
  • O. Colin and J.-B. Michel, A simplified CMC approach based on tabulated reaction rates applied to a lifted methane-air jet flame, Proc. Combust. Inst. 35 (2015), pp. 1393–1399. doi: 10.1016/j.proci.2014.07.033
  • A. Tyliszczak, LES–CMC study of an excited hydrogen flame, Combust. Flame 162 (2015), pp. 3864–3883. doi: 10.1016/j.combustflame.2015.07.024
  • I. Stankovic, E. Mastorakos, and B. Merci, LES-CMC simulations of different auto-ignition regimes of hydrogen in a hot turbulent air co-flow, Flow Turbul. Combust. 90 (2013), pp. 583–604. doi: 10.1007/s10494-013-9443-2
  • I. Stankovic and B. Merci, LES-CMC simulations of a turbulent lifted hydrogen flame in vitiated co-flow, Thermal Sci. 17 (2013), pp. 763–772. doi: 10.2298/TSCI120704035S
  • A. Tyliszczak, Assessment of implementation variants of conditional scalar dissipation rate in LES–CMC simulation of auto-ignition of hydrogen jet, Arch. Mech. 65 (2013), pp. 97–129.
  • S. Navarro-Martinez and S. Rigopoulos, Large eddy simulation of a turbulent lifted flame using conditional moment closure and rate-controlled constrained equilibrium, Flow Turbul. Combust. 87 (2011), pp. 407–423. doi: 10.1007/s10494-011-9324-5
  • S. Navarro-Martinez and A. Kronenburg, Flame stabilization mechanisms in lifted flames, Flow Turbul. Combust. 87 (2011), pp. 377–406. doi: 10.1007/s10494-010-9320-1
  • I. Stankovic, A. Triantafyllidis, E. Mastorakos, C. Lacor, and B. Merci, Simulation of hydrogen auto-ignition in a turbulent co-flow of heated air with LES and CMC approach, Flow Turbul. Combust. 86 (2011), pp. 689–710. doi: 10.1007/s10494-010-9277-0
  • S. Navarro-Martinez and A. Kronenburg, Analysis of stabilization mechanisms in lifted flames, AIP Conf. Proc. 1190 (2009), pp. 13–38. doi: 10.1063/1.3290166
  • G. De Paola, I.S. Kim, and E. Mastorakos, Second-order conditional moment closure simulations of autoignition of an n-heptane plume in a turbulent coflow of heated air, Flow Turbul. Combust. 82 (2009), pp. 455–475. doi: 10.1007/s10494-008-9183-x
  • S.S. Patwardhan, De Santanu, K.N. Lakshmisha, and B.N. Raghunandan, CMC simulations of lifted turbulent jet flame in a vitiated coflow, Proc. Combust. Inst. 32 (2009), pp. 1705–1712. doi: 10.1016/j.proci.2008.06.031
  • A.J.M. Buckrell and C.B. Devaud, Investigation of mixing models and conditional moment closure applied to autoignition of hydrogen jets, Flow Turbul. Combust. 90 (2013), pp. 621–644. doi: 10.1007/s10494-013-9445-0
  • S.H. Kim, K.Y. Huh, and R.A. Fraser, Numerical prediction of the autoignition delay in a diesel-like environment by the conditional moment closure model, SAE Technical Papers, 2000.
  • M. Bolla, D. Farrace, Y.M. Wright, K. Boulouchos, and E. Mastorakos, Influence of turbulence-chemistry interaction for n-heptane spray combustion under diesel engine conditions with emphasis on soot formation and oxidation, Combust. Theory Model. 18 (2014), pp. 330–360. doi: 10.1080/13647830.2014.898795
  • F. Bottone, A. Kronenburg, D. Gosman, and A. Marquis, The numerical simulation of diesel spray combustion with LES-CMC, Flow Turbul. Combust. 89 (2012), pp. 651–673. doi: 10.1007/s10494-012-9415-y
  • Y.M. Wright, O.-N. Margari, K. Boulouchos, G. De Paola, and E. Mastorakos, Experiments and simulations of n-heptane spray auto-ignition in a closed combustion chamber at diesel engine conditions, Flow Turbul. Combust. 84 (2010), pp. 49–78. doi: 10.1007/s10494-009-9224-0
  • J. Behzadi, M. Bolla, M. Talei, E.R. Hawkes, T. Lucchini, G. D'Errico, and S. Kook, Assessment of conditional moment closure for ignition in compositionally and thermally stratified mixtures, Proceedings of the 10th Asia-Pacific Conference on Combustion, 2015.
  • N. Peters, Turbulent Combustion, Cambridge Monographs on Mechanics, Cambridge, 2006.
  • B. Naud, R. Novella, J.M. Pastor, and J.F. Winklinger, RANS modelling of a lifted H2/N2 flame using an unsteady flamelet progress variable approach with presumed PDF, Combust. Flame 162 (2015), pp. 893–906. doi: 10.1016/j.combustflame.2014.09.014
  • C. Han, P. Zhang, T.H. Ye, and Y.L. Chen, Numerical study of methane/air jet flame in vitiated co-flow using tabulated detailed chemistry, Sci. China Technol. Sci. 57 (2014), pp. 1750–1760. doi: 10.1007/s11431-014-5604-3
  • C. Bajaj, M. Ameen, and J. Abraham, Evaluation of an unsteady flamelet progress variable model for autoignition and flame lift-off in diesel jets, Combust. Sci. Technol. 185 (2013), pp. 454–472. doi: 10.1080/00102202.2012.726667
  • M. Ihme and Y.C. See, Prediction of autoignition in a lifted methane/air flame using an unsteady flamelet/progress variable model, Combust. Flame 157 (2010), pp. 1850–1862. doi: 10.1016/j.combustflame.2010.07.015
  • M. Ihme and Y.C. See, LES flamelet modeling of a three-stream MILD combustor: Analysis of flame sensitivity to scalar inflow conditions, Proc. Combust. Inst. 33 (2011), pp. 1309–1317. doi: 10.1016/j.proci.2010.05.019
  • S.-K. Kim, Y. Yu, J. Ahn, and Y.-M. Kim, Numerical investigation of the autoignition of turbulent gaseous jets in a high-pressure environment using the multiple-RIF model, Fuel 83 (2004), pp. 375–386. doi: 10.1016/j.fuel.2003.01.001
  • I. Stankovic and B. Merci, Analysis of auto-ignition of heated hydrogen-air mixtures with different detailed reaction mechanisms, Combust. Theory Model. 15 (2011), pp. 409–436. doi: 10.1080/13647830.2010.542830
  • P. Kundu, T. Echekki, Y. Pei, and S. Som, An equivalent dissipation rate model for capturing history effects in non-premixed flames, Combust. Flame 176 (2017), pp. 202–212. doi: 10.1016/j.combustflame.2016.10.001
  • P. Pal, S. Keum, and H.G. Im, Assessment of flamelet versus multi-zone combustion modeling approaches for stratified-charge compression ignition engines, Int. J. Engine Res. 17 (2016), pp. 280–290. doi: 10.1177/1468087415571006
  • J. Tillou, J.-B. Michel, C. Angelberger, and D. Veynante, Assessing LES models based on tabulated chemistry for the simulation of diesel spray combustion, Combust. Flame 161 (2014), pp. 525–540. doi: 10.1016/j.combustflame.2013.09.006
  • G. D'Errico, T. Lucchini, F. Contino, M. Jangi, and X.-S. Bai, Comparison of well-mixed and multiple representative interactive flamelet approaches for diesel spray combustion modelling, Combust. Theory Model. 18 (2014), pp. 65–88. doi: 10.1080/13647830.2013.860238
  • I. Dhuchakallaya, P. Rattanadecho, and P. Watkins, Auto-ignition and combustion of diesel spray using unsteady laminar flamelet model, Appl. Therm. Eng. 52(2) (2013), pp. 420–427. doi: 10.1016/j.applthermaleng.2012.12.016
  • U. Egüz, S. Ayyapureddi, C. Bekdemir, B. Somers, and P. De Goey, Modeling fuel spray auto-ignition using the FGM approach: Effect of tabulation method, SAE Technical Papers, 2012.
  • J. Lim, Y. Kim, S. Lee, J. Chung, W. Kang, and K. Min, 3-D simulation of the combustion process for di-methyl ether-fueled diesel engine, J. Mech. Sci. Technol. 24 (2010), pp. 2597–2604. doi: 10.1007/s12206-010-0915-1
  • H. Lehtiniemi, F. Mauss, M. Balthasar, and I. Magnusson, Modeling diesel spray ignition using detailed chemistry with a progress variable approach, Combust. Sci. Technol. 178 (2006), pp. 1977–1997. doi: 10.1080/00102200600793148
  • Y. Yu, S.-K. Kim, and Y.-M. Kim, Numerical modeling for auto-ignition and combustion processes of fuel sprays in high-pressure environment, Combust. Sci. Technol. 168 (2001), pp. 85–112. doi: 10.1080/00102200108907832
  • E. Abtahizadeh, P. de Goey, and J. van Oijen, LES of Delft jet-in-hot coflow burner to investigate the effect of preferential diffusion on autoignition of CH4/H2 flames, Fuel 191 (2017), pp. 36–45. doi: 10.1016/j.fuel.2016.11.054
  • M.U. Göktolga, J.A. Van Oijen, and L.P.H. De Goey, Modeling MILD combustion using a novel multistage FGM method, Proc. Combust. Inst. 36 (2017), pp. 4269–4277. doi: 10.1016/j.proci.2016.06.004
  • E. Abtahizadeh, P. De Goey, and J. Van Oijen, Development of a novel flamelet-based model to include preferential diffusion effects in autoignition of CH4/H2 flames, Combust. Flame 162 (2015), pp. 4358–4369. doi: 10.1016/j.combustflame.2015.06.015
  • C. Bekdemir, B. Somers, and P. de Goey, DNS with detailed and tabulated chemistry of engine relevant igniting systems, Combust. Flame 161 (2014), pp. 210–221. doi: 10.1016/j.combustflame.2013.08.022
  • Z. Hu, L.M.T. Somers, T. Davies, A. McDougall, and R.F. Cracknell, A study of liquid fuel injection and combustion in a constant volume vessel at diesel engine conditions, Fuel 107 (2013), pp. 63–73. doi: 10.1016/j.fuel.2013.01.043
  • C. Bekdemir, L.M.T. Somers, and L.P.H. De Goey, Modeling diesel engine combustion using pressure dependent flamelet generated manifolds, Proc. Combust. Inst. 33 (2011), pp. 2887–2894. doi: 10.1016/j.proci.2010.07.091
  • P. Domingo, L. Vervisch, and D. Veynante, Large-eddy simulation of a lifted methane jet flame in a vitiated coflow, Combust. Flame 152 (2008), pp. 415–432. doi: 10.1016/j.combustflame.2007.09.002
  • J.-B. Michel and O. Colin, A tabulated diffusion flame model applied to diesel engine simulations, Int. J. Engine Res. 15 (2014), pp. 346–369. doi: 10.1177/1468087413488590
  • Z. Chen, S. Ruan, and N. Swaminathan, Simulation of turbulent lifted methane jet flames: Effects of air-dilution and transient flame propagation, Combust. Flame 162 (2015), pp. 703–716. doi: 10.1016/j.combustflame.2014.09.010
  • H. Zhou, S. Li, Z. Ren, and D.H. Rowinski, Investigation of mixing model performance in transported PDF calculations of turbulent lean premixed jet flames through lagrangian statistics and sensitivity analysis, Combust. Flame 181 (2017), pp. 136–148. doi: 10.1016/j.combustflame.2017.03.011
  • W. Han, V. Raman, and Z. Chen, LES/PDF modeling of autoignition in a lifted turbulent flame: Analysis of flame sensitivity to differential diffusion and scalar mixing time-scale, Combust. Flame 171 (2016), pp. 69–86. doi: 10.1016/j.combustflame.2016.05.027
  • C. Heye, V. Raman, and A.R. Masri, Influence of spray/combustion interactions on auto-ignition of methanol spray flames, Proc. Combust. Inst. 35 (2015), pp. 1639–1648. doi: 10.1016/j.proci.2014.06.087
  • M. Jangi, T. Lucchini, C. Gong, and X.-S. Bai, Effects of fuel cetane number on the structure of diesel spray combustion: An accelerated Eulerian stochastic fields method, Combust. Theory Model. 19 (2015), pp. 549–567. doi: 10.1080/13647830.2015.1057234
  • S. Bhattacharjee and D.C. Haworth, Simulations of transient n-heptane and n-dodecane spray flames under engine-relevant conditions using a transported PDF method, Combust. Flame 160 (2013), pp. 2083–2102. doi: 10.1016/j.combustflame.2013.05.003
  • S.M. Mir Najafizadeh, M.T. Sadeghi, R. Sotudeh-Gharebagh, and D.J.E.M. Roekaerts, Chemical structure of autoignition in a turbulent lifted H2/N2 jet flame issuing into a vitiated coflow, Combust. Flame 160 (2013), pp. 2928–2940. doi: 10.1016/j.combustflame.2013.06.021
  • W.P. Jones and S. Navarro-Martinez, Numerical study of n-heptane auto-ignition using LES-PDF methods, Flow Turbul. Combust. 83 (2009), pp. 407–423. doi: 10.1007/s10494-009-9228-9
  • K. Gkagkas and R.P. Lindstedt, The impact of reduced chemistry on auto-ignition of H2 in turbulent flows, Combust. Theory Model. 13 (2009), pp. 607–643. doi: 10.1080/13647830902928524
  • C.W. Lee and E. Mastorakos, Transported scalar PDF calculations of autoignition of a hydrogen jet in a heated turbulent co-flow, Combust. Theory Model. 12 (2008), pp. 1153–1178. doi: 10.1080/13647830802283095
  • H. Wang and S. Pope, Lagrangian investigation of local extinction, re-ignition and auto-ignition in turbulent flames, Combust. Theory Model. 12 (2008), pp. 857–882. doi: 10.1080/13647830802056137
  • K. Gkagkas and R.P. Lindstedt, Transported PDF modelling with detailed chemistry of pre- and auto-ignition in CH4/air mixtures, Proc. Combust. Inst. 31(I) (2007), pp. 1559–1566. doi: 10.1016/j.proci.2006.08.078
  • W.P. Jones, S. Navarro-Martinez, and O. Röhl, Large eddy simulation of hydrogen auto-ignition with a probability density function method, Proc. Combust. Inst. 31(II) (2007), pp. 1765–1771. doi: 10.1016/j.proci.2006.07.041
  • R.L. Gordon, A.R. Masri, S.B. Pope, and G.M. Goldin, A numerical study of auto-ignition in turbulent lifted flames issuing into a vitiated co-flow, Combust. Theory Model. 11 (2007), pp. 351–376. doi: 10.1080/13647830600903472
  • V. Sabel'nikov, M. Gorokhovski, and N. Baricault, The extended IEM mixing model in the framework of the composition PDF approach: Applications to diesel spray combustion, Combust. Theory Model. 10 (2006), pp. 155–169. doi: 10.1080/13647830500348109
  • R.R. Cao, S.B. Pope, and A.R. Masri, Turbulent lifted flames in a vitiated coflow investigated using joint PDF calculations, Combust. Flame 142 (2005), pp. 438–453. doi: 10.1016/j.combustflame.2005.04.005
  • A.R. Masri, R. Cao, S.B. Pope, and G.M. Goldin, PDF calculations of turbulent lifted flames of H2/N2 fuel issuing into a vitiated co-flow, Combust. Theory Model. 8 (2004), pp. 1–22. doi: 10.1088/1364-7830/8/1/001
  • J. Prause, C.M. Arndt, B. Noll, and M. Aigner, Large-eddy-simulation of auto-ignition in a turbulent jet in hot coflow, Thirteenth International Workshop on Measurement & Computation of Turbulent Flames, 2016.
  • C.M. Arndt, J.D. Gounder, W. Meier, and M. Aigner, Auto-ignition and flame stabilization of pulsed methane jets in a hot vitiated coflow studied with high-speed laser and imaging techniques, Appl. Phys. B 108 (2012), pp. 407–417. doi: 10.1007/s00340-012-4945-5
  • C.M. Arndt and W. Meier, Quantitative OH measurements in turbulent flames using laser-diagnostics with high spatio-temporal resolution, Proceedings of the OSA Imaging and Applied Optics Congress – Laser Applications to Chemical, Security and Environmental Analysis, number LTu2C.3, 2018.
  • C.M. Arndt, M.J. Papageorge, F. Fuest, J.A. Sutton, W. Meier, and M. Aigner, The role of temperature, mixture fraction, and scalar dissipation rate on transient methane injection and auto-ignition in a jet in hot coflow burner, Combust. Flame 167 (2016), pp. 60–71. doi: 10.1016/j.combustflame.2016.02.027
  • C.M. Arndt, R. Schießl, J.D. Gounder, W. Meier, and M. Aigner, Flame stabilization and auto-ignition of pulsed methane jets in a hot coflow: Influence of temperature, Proc. Combust. Inst. 34 (2013), pp. 1483–1490. doi: 10.1016/j.proci.2012.05.082
  • C.M. Arndt, M.J. Papageorge, F. Fuest, J.A. Sutton, and W. Meier, Experimental investigation of the auto-ignition of a transient propane jet-in-hot-coflow, Proc. Combust. Inst. 37 (2019), pp. 2117–2124. doi: 10.1016/j.proci.2018.06.195
  • C.M. Arndt and W. Meier, Influence of boundary conditions on the flame stabilization mechanism and on transient auto-ignition in the DLR jet-in-hot-coflow burner. Flow Turbul. Combust. 102 (2019), pp. 973–993. doi: 10.1007/s10494-018-9991-6
  • M.J. Papageorge, C. Arndt, F. Fuest, W. Meier, and J.A. Sutton, High-speed mixture fraction and temperature imaging of pulsed, turbulent fuel jets auto-igniting in high-temperature, vitiated co-flows, Exp. Fluids 55 (2014), p. 1763. doi: 10.1007/s00348-014-1763-z
  • C.M. Arndt, R. Schießel, and W. Meier, OH planar laser-induced fluorescence measurements with high spatio-temporal resolution for the study of auto-ignition, Appl. Opt. 58 (2019), pp. C14–C22. doi: 10.1364/AO.58.000C14
  • F. Fuest, M.J. Papageorge, W.R. Lempert, and J.A Sutton, Ultrahigh laser pulse energy and power generation at 10  kHz. Opt. Lett. 37 (2012), pp. 3231–3233. doi: 10.1364/OL.37.003231
  • M.J. Papageorge, T.A. McManus, F. Fuest, and J.A. Sutton, Recent advances in high-speed planar rayleigh scattering in turbulent jets and flames: increased record lengths, acquisition rates, and image quality. Appl. Phys. B 115 (2014), pp. 197–213. doi: 10.1007/s00340-013-5591-2
  • S.B. Pope, PDF methods for turbulent reactive flows, Prog. Energy Combust. Sci. 11 (1985), pp. 119–192. doi: 10.1016/0360-1285(85)90002-4
  • S.B. Pope, The probability approach to the modelling of turbulent reacting flows, Combust. Flame 27 (1976), pp. 299–312. doi: 10.1016/0010-2180(76)90035-3
  • J. Villermaux and J.C. Devillon, Representation de la coalescence et de la redispersion des domaines de segregation dans un fluide par un modele d' interaction phenomenologique, Second International Symposium on Chemical Reaction Engineering, Elsevier, New York, 1972, pp. 1–13.
  • H. Möbus, P. Gerlinger, and D. Brüggemann, Comparison of Eulerian and Lagrangian monte carlo PDF methods for turbulent diffusion flames, Combust. Flame 124 (2001), pp. 519–534. doi: 10.1016/S0010-2180(00)00207-8
  • J. Löwe, A. Probst, T. Knopp, and R. Kessler, Low-dissipation low-dispersion second-order scheme for unstructured finite volume flow solvers, AIAA J. 54 (2016), pp. 2961–2971. doi: 10.2514/1.J054956
  • G. Reichling, B. Noll, and M. Aigner, Development of a projection-based method for the numerical calculation of compressible reactive flows, Proceedings of the 51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, Number AIAA 2013-1003, 2013.
  • A. Fiolitakis, P.R. Ess, P. Gerlinger, and M. Aigner, Modeling of heat transfer and differential diffusion in transported PDF methods, Combust. Flame 161 (2014), pp. 2107–2119. doi: 10.1016/j.combustflame.2014.01.021
  • A. Fiolitakis, P.R. Ess, P. Gerlinger, and M. Aigner, Development and application of a transported probability density function methond on unstructured three-dimensional grids for the prediction of nitric oxides, J. Eng. Gas Turbine. Power 136 (2013), pp. 031506 031506–01–031506–10.
  • R.O. Fox, Computational Models for Turbulent Reacting Flows, Cambridge University Press, Cambridge, 2003.
  • W.P. Jones and B.E. Launder, The prediction of laminarization with a two-equation model of turbulence, Int. J. Heat Mass Transf. 15 (1972), pp. 301–314. doi: 10.1016/0017-9310(72)90076-2
  • B.E. Launder and B.I. Sharma, Application of the energy-dissipation model of turbulence to the calculation of flow near a spinning disk, Lett. Heat Mass Trans. 1 (1974), pp. 131–137. doi: 10.1016/0094-4548(74)90150-7
  • H.K. Versteeg and W. Malalasekera, An Introduction to Computational Fluid Dynamics: The Finite Volume Method, Pearson Prentice Hall, Harlow, 1995.
  • G.P. Smith, D.M. Golden, M. Frenklach, N.W. Moriarty, B. Eiteneer, M. Goldenberg, C.T. Bowman, R.K. Hanson, S. Song, W.C. Gardiner Jr, V.V. Lissianski, and Z. Qin, Gri 3.0 Mechanism. Online; accessed September 20th, 2008. Available at http://www.me.berkeley.edu/gri_mech/, 1999.
  • E.L. Petersen, M.H. Joel, D.S. Schuyler, J. de Vries, A.R. Amadio, and M.W. Crofton, Ignition of lean methane-based fuel blends at gas-turbine pressures, J. Eng. Gas Turbine. Power 129 (2007), pp. 937–944. doi: 10.1115/1.2720543
  • D.G. Goodwin “An open-source, extensible software suite for CVD process simulation”, Proceedings-electrochemical society PV 1 (2003), pp. 155–162.
  • B. Talbot, N. Mazellier, B. Renou, L. Danaila, and M.A. Boukhalfa, Time-resolved velocity and concentration measurements in variable-viscosity turbulent jet flow, Exp. Fluids 47 (2009), pp. 769–787. doi: 10.1007/s00348-009-0729-z
  • W. Kollman and J. Janicka, The probability density function of a passive scalar in turbulent shear flows, Phys. Fluids 25 (1982), p. 1755. doi: 10.1063/1.863653
  • S.B. Pope, A Monte Carlo method for the PDF equations of turbulent reactive flow, Combust. Sci. Technol. 25 (1981), pp. 159–174. doi: 10.1080/00102208108547500
  • R.G. Batt, Turbulent mixing of passive and chemical reacting species in a low-speed shear layer. J. Fluid Mech. 82 (1977), pp. 53–95. doi: 10.1017/S0022112077000536
  • M.G. Mungal and P.E. Dimotakis, Mixing and combustion with low heat release in a turbulent shear layer, J. Fluid Mech. 148 (1984), pp. 349–382. doi: 10.1017/S002211208400238X
  • K.S. Venkataramani, N.K. Tutu, and R. Chevray, Probability distributions in a round heated jet, Phys. Fluids 18 (1975), pp. 1413–1420. doi: 10.1063/1.861038
  • S. Subramaniam and S.B. Pope, A mixing model for turbulent flows based on euclidian minimum spanning trees, Combust. Flame 115 (1998), pp. 487–514. doi: 10.1016/S0010-2180(98)00023-6
  • J. Janicka, W. Kolbe, and W. Kollman, Closure of the transport equation for the probability density function of turbulent scalar fields, J. Non-Equilib. Thermodyn. 4 (1979), pp. 47–66. doi: 10.1515/jnet.1979.4.1.47
  • C. Dopazo and E.E. O'Brien, An approach to the autoignition of a turbulent mixture, Acta. Astronaut. 1 (1974), pp. 1239–1266. doi: 10.1016/0094-5765(74)90050-2
  • C. Dopazo and E.E. O'Brien, Statistical treatment of non-isothermal chemical reactions in turbulence, Combust. Sci. Technol. 13 (1976), pp. 99–122. doi: 10.1080/00102207608946731
  • S.B. Pope, Turbulent Flows, Cambridge University Press, Cambridge, 2009.
  • J. Warnatz, U. Maas, and R.W. Dibble, Combustion: Physical and Chemical Fundamentals, Modeling and Simulation, Experiments, Pollutant Formation, Springer, Berlin, 1996.
  • R. Courant and D. Hilbert, Methods of Mathematical Physics, Vol. 2, Interscience Publishers, a division of John Wiley & Sons, New York, 1962.
  • R.W. MacCormack, The effect of viscosity in hypervelocity impact cratering, Number AIAA 69-354, 1969.
  • B. van Leer, Towards the ultimate conservative difference scheme, V: A second-order sequel to Godunov's method, J. Comput. Phys. 32 (1979), pp. 101–136. doi: 10.1016/0021-9991(79)90145-1
  • C.K. Westbrook and F.L. Dryer, Simplified reaction mechanisms for the oxidation of hydrocarbon fuels in flames, Combust. Sci. Technol. 27 (1981), pp. 31–43. doi: 10.1080/00102208108946970
  • B.J. Isaac, A. Parente, C. Galletti, J.N. Thornock, P.J. Smith, and L. Tognotti, A novel methodology for chemical time scale evaluation with detailed chemical reaction kinetics, Energy Fuels 27 (2013), pp. 2255–2265. doi: 10.1021/ef301961x

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