Thermodynamically Consistent Modelling of Gas Turbine Combustion Sprays

  • A. SadikiEmail author
  • M. Chrigui
  • A. Dreizler
Part of the Fluid Mechanics and Its Applications book series (FMIA, volume 1581)


In order to support the design procedure and increase the reliability and safety of combustion engines fired with liquid fuel at a reasonable cost, numerical prediction tools well validated by comprehensive experimental data are needed. As there is today enough evidence that Large Eddy Simulation (LES) is able to well capture intrinsically time and space dependent phenomena, LES will be employed. However, in most LES based spray modules for predicting spray combustion the interactions between both phases and between evaporating droplets and combustion are either not adequately considered or not incorporated at all. The objective of this work is to develop and validate a thermodynamically consistent spray module for Large Eddy Simulation that allows describing accurately the essential processes featuring spray combustion in gas turbine combustion chambers. These include besides the injection of liquid fuel, the turbulent droplet dispersion, the vaporization of the droplets and mixture formation and the subsequent spray combustion. In particular, (1) a physically consistent SGS-model describing the influence of droplet diameter and interface transport on the gas phase turbulence as well as the effect of the droplet evaporation on the mass and scalar transport processes (turbulence modulation) has been adapted for LES into an Eulerian–Lagrangian framework. (2) Apart from classical evaporation models valid in atmospheric conditions, an advanced evaporation model, the so called non-equilibrium model, appropriate for gas turbine conditions have been integrated and validated. (3) The chemistry-turbulence interaction under droplet evaporating conditions has been considered according to a presumed (filtered) probability density function while the combustion process itself is described following a tabulated detailed chemistry based on FGM (Flamelet Generated Manifold). (4) All the developed sub-models along with the complete model have been implemented in the working package FASTEST/LAG3D and validated in non-reacting and reacting configurations with available experimental data. Comparisons include exhaust gas temperature, droplet velocities and corresponding fluctuations, droplet mean diameters and spray volume flux at different distances from the exit planes. An overall good agreement with experimental data has been achieved. Parts of this contribution has been already reported as mentioned throughout the paper.


Thermodynamically consistent modelling Acetone spray Evaporation Partially premixed combustion Eulerian–Lagrangian method LES 



The authors are grateful to the financial support by the German Research Council (DFG) through the SFB568.


  1. 1.
    Sadiki, A., Goryntsev, D., Wegner, B., Janicka, J.: Design of technical combustion systems using LES: state of the art and perspectives. In: 7th International ERCOFTAC Symposium on Engineering Turbulence Modelling and Measurements, (ETMM7), Limassol, Cyprus, 4–6 June 2008Google Scholar
  2. 2.
    Olbricht, C., Hahn, F., Sadiki, A., Janicka, J.: Analysis of subgrid scale mixing using a hybrid LES-Monte-Carlo PDF method. Int. J. Heat Fluid Flow 28(6), 1215–1226 (2007)CrossRefGoogle Scholar
  3. 3.
    Chrigui, M., Sadiki, A., Janicka, J., Zgahl, A.: Study of n-heptane spray evaporation and dispersion within premixed combustion in complex geometry configuration. In: Accepted to the 32th International Symposium on Combustion, McGill University, Montreal, Canada (2008)Google Scholar
  4. 4.
    Chrigui, M., Sadiki, A., Janicka, J.: Numerical analysis of spray dispersion, evaporation and combustion in a single gas turbine combustor. In: ASME TURBO-EXPO, GT2008-51253, Berlin, Germany (2008)Google Scholar
  5. 5.
    Chrigui, M., Batarseh, F.Z., Sadiki, A., Roisman, I., Tropea, C.: Numerical and experimental study of spray produced by an airbalst atomizer under elevated pressure conditions. In: ASME TURBO-EXPO, GT2008-51305, Berlin, Germany (2008)Google Scholar
  6. 6.
    Ahmad, W., Chrigui, M., Sadiki, A., Ngoma, G.D.: Effect of evaporation on the combustion behaviour of kerosene spray flame. In: ASME Turbo Expo 2010 (GT2010-22641), Glasgow, Scotland, UK, 14–18 June 2010Google Scholar
  7. 7.
    Chrigui, M., Sadiki, M., Ngoma, G.D.: Unsteady, turbulent, two‐phase flow using an Euler/Lagrange approach devoted to two-way coupling conditions. In: International Conference on Multiphase Flow 2010 (ICMF-2010), Florida, USA, 30 May–4 June 2010Google Scholar
  8. 8.
    Chrigui, M., Hage, M., Sadiki, A., Janicka, J., Dreizler, A.: Experimental and numerical analysis of spray dispersion and evaporation in a combustion chamber. At. Spray 19, 929–955 (2009)CrossRefGoogle Scholar
  9. 9.
    Chrigui, M., Roisman, I., Batarseh, F., Sadiki, A., Tropea, C.: Spray generated by an airblast atomizer under elevated ambient pressures. J. Propuls. Power AIAA 26(6), 1170–1183 (2010)CrossRefGoogle Scholar
  10. 10.
    Chrigui, M.: N-Hpetane spray evaporation and dispersion in turbulent flow within a complex geometry configuration. J. Comput. Therm. Sci. 2(1), 55–78 (2010)CrossRefGoogle Scholar
  11. 11.
    Chrigui, M., Sadiki, A., Janicka, J.: Evaporation and dispersion of N heptane droplets within premixed flame. J. Heat Mass Trans. 46(8–9), 869–880 (2010)Google Scholar
  12. 12.
    Chrigui, M., Schneider, L., Zghal, A., Sadiki, A., Janicka, J.: Droplet behavior within a LPP ambiance. J. Fluid Dyn. Mater. Process. 6(4), 399–408 (2010)Google Scholar
  13. 13.
    Pantangi, P., Sadiki, A., Janicka, J., Hage, M., Dreizler, A., van Oijen, J.A., Hassa, C., Heinze, J., Meier, U.: LES of pre-vaporized kerosene combustion at high pressures in a single sector combustor taking advantage of the flamelet generated manifolds method. In: Proceedings of ASME Turbo Expo 2011 (GT2011-45819), Vancouver, Canada, 6–10 June 2011Google Scholar
  14. 14.
    Chrigui, M., Moesl, M.K., Ahmadi, W., Sadiki, A., Janicka, J.: Partially premixed prevaporized kerozene spray combustion in turbulent flow. Exp. Therm. Fluid Sci. 34(1), 308–315 (2010)CrossRefGoogle Scholar
  15. 15.
    Hahn, F., Sadiki, A., Janicka, J.: Large eddy simulation of a particle laden swirling flow based on an Euler-Lagragian approach. In: 6th International Conference on Multiphase Flow (ICMF2007), Leipzig, Germany (2007)Google Scholar
  16. 16.
    Chrigui, M., Zghal, A., Sadiki, A., Janicka, J.: Spray evaporation and dispersion of n-heptane droplets within premixed flame. Heat Mass Trans. 46, 869–880 (2010)CrossRefGoogle Scholar
  17. 17.
    Sadiki, A., Ahmadi, W., Chrigui, M., Janicka, J.: Towards the impact of fuel evaporation-combustion interaction on spray combustion in gas turbine combustion chambers. Part I: effect of partial fuel vaporization on spray combustion. In: Merci, B., Roeckaerts, D., Sadiki, A. (eds.) Experiments and Numerical Simulations of Diluted Spray Turbulent Combustion, Proceedings of the 1st International Workshop on Turbulent Spray Combustion, Chap. 3, pp. 69–110. Springer, Dordrecht/Heidelberg/London/New York (2011)Google Scholar
  18. 18.
    Sadiki, A., Ahmadi, W., Chrigui, M., Janicka, J.: Towards the impact of fuel evaporation-combustion interaction on spray combustion in gas turbine combustion chambers. Part II: influence of high combustion temperature on spray droplet evaporation. In: Merci, B., Roeckaerts, D., Sadiki, A. (eds.) Proceedings of the 1st International Workshop on Turbulent Spray Combustion, Chap. 3, pp. 111–132. Springer, Dordrecht/Heidelberg/London/New York (2011)Google Scholar
  19. 19.
    Chrigui, M., Gounder, J., Sadiki, A., Masri, A.R., Janicka, J.: Partially premixed reacting acetone spray using LES and FGM tabulated chemistry combustion and flame 10.1016/j.combustflame.2012.03.009 (2012)
  20. 20.
    Chrigui, M.: N-Heptane spray evaporation and dispersion in turbulent flow within a complex geometry configuration. J. Comput. Therm. Sci. 2(1), 55–78 (2010)CrossRefGoogle Scholar
  21. 21.
    Oefelein, J.C.: Large eddy simulation of turbulent combustion processes in propulsion and power systems. Prog. Aerosp. Sci. 42, 2–37 (2006)CrossRefGoogle Scholar
  22. 22.
    Bellan, J., Selle, L.C.: Large eddy simulation composition equations for single-phase and two-phase fully multicomponent flows. Proc. Combust. Inst. 32(2), 2239–2246 (2009)CrossRefGoogle Scholar
  23. 23.
    Senoner, J.M., Sanjosé, M., Lederlin, T., Jaegle, F., García, M., Riber, E., Cuenot, B., Gicquel, L., Pitsch, H., Poinsot, T.: Eulerian and Lagrangian large-eddy simulations of an evaporating two-phase flow. Comptes Rendus Mécanique 337(6–7), 458–468 (2009)zbMATHCrossRefGoogle Scholar
  24. 24.
    Apte, S.V., Mahesh, K., Moin, P.: Large-eddy simulation of evaporating spray in a coaxial combustor. Proc. Combust. Inst. 32(2), 2247–2256 (2009)CrossRefGoogle Scholar
  25. 25.
    Pitsch, H., Desjardins, O., Balarac, G., Ihme, M.: Large-eddy simulation of turbulent reacting flows. Prog. Aerosp. Sci. 44(6), 466–478 (2008)CrossRefGoogle Scholar
  26. 26.
    Lederlin, T., Pitsch, H.: Large-eddy simulation of an evaporating and reacting spray. In Center for Turbulence Research, Annual Research Briefs, pp. 479–490. Stanford University (2008)Google Scholar
  27. 27.
    Sanjosé, M., Lederlin, T., Gicquel, L., Cuenot, B., Pitsch, H., García-Rosa, N., Lecourt, R., Poinsot, T.: LES of two-phase reacting flows. In: Center for Turbulence Research Proceedings of the Summer Program, pp. 251–263. Stanford University (2008)Google Scholar
  28. 28.
    Bini, M., Jones, W.P.: Large eddy simulation of an evaporating acetone spray. Int. J. Heat Fluid Flow 30(3), 471–480 (2009)CrossRefGoogle Scholar
  29. 29.
    Pera, C., Réveillon, J., Vervisch, L., Domingo, P.: Modeling subgrid scale mixture fraction variance in LES of evaporating spray. Combust. Flame 146(4), 635–648 (2006)CrossRefGoogle Scholar
  30. 30.
    Patel, N., Menon, S.: Simulation of spray–turbulence–flame interactions in a lean direct injection combustor. Combust. Flame 153(1–2), 228–257 (2008)CrossRefGoogle Scholar
  31. 31.
    Bray, K.N.C., Peters, N.: Laminar flamelets in turbulent reacting flows. In: Libby, P.A., Williams, F.A. (eds.) Turbulent Reacting Flows, pp. 63–113. Academic, London (1994)Google Scholar
  32. 32.
    Hanjalic, K.: Will RANS survive LES: a view of perspectives. ASME J. Fluids Eng. 127, 831–839 (2005)CrossRefGoogle Scholar
  33. 33.
    Carbonell, D., Perez-Segarra, C.D., Coelho, P.J., Oliva, A.: Flamelet mathematical models for non-premixed laminar combustion. Combust. Flame 156(2), 334–347 (2009)CrossRefGoogle Scholar
  34. 34.
    Mortensen, M., Bilger, R.W.: Derivation of the conditional moment closure equations for spray combustion. Combust. Flame 156(1), 62–72 (2009)CrossRefGoogle Scholar
  35. 35.
    Dianat, M., Yang, Z., McGuirk, J.J.: Large-Eddy Simulation of a Two-Phase Plane Mixing-Layer. Advances in Turbulence XII, Springer Proceedings in Physics, Part 11, vol. 132, pp. 775–778. (2009)Google Scholar
  36. 36.
    Yuichi, I., Nobuyukiles, T.: LES of spray combustion flows. J. Jpn. Sci. Technol. (J-EAST) 7, 27–28 (2005)Google Scholar
  37. 37.
    Abramzon, B., Sirignano, W.A.: Droplet vaporization model for spray combustion calculations. Int. J. Heat Mass Trans. 32, 1605–1618 (1989)CrossRefGoogle Scholar
  38. 38.
    Apte, S.V., Gorokhovski, M., Moin, P.: LES of atomizing spray with stochastic modelling of secondary breakup. Int. J. Multiphase Flow 29, 1503–1522 (2003)zbMATHCrossRefGoogle Scholar
  39. 39.
    Riber, E., Moureau, V., García, M., Poinsot, T., Simonin, O.: Evaluation of numerical strategies for large eddy simulation of particulate two-phase recirculating flows. J. Comput. Phys. 228(2), 539–564 (2008)CrossRefGoogle Scholar
  40. 40.
    Pitsch, H.: Large-eddy simulation of turbulent combustion. Annu. Rev. Fluid Mech. 38, 453–482 (2006)MathSciNetCrossRefGoogle Scholar
  41. 41.
    Shotorban, B., Zhang, K.K.Q., Mashayek, F.: Improvement of particle concentration prediction in large-eddy simulation by defiltering. Int. J. Heat Mass Trans. 50(19–20), 3728–3739 (2007)zbMATHCrossRefGoogle Scholar
  42. 42.
    Fede, P., Simonin, O.: Numerical study of the subgrid fluid turbulence effects on the statistics of heavy colliding particles. Phys. Fluids 18, 045103 (2006)CrossRefGoogle Scholar
  43. 43.
    Miller, R.S., Harstad, K., Bellan, J.: Evaluation of equilibrium and non-equilibrium evaporation models for many gas–liquid flow simulations. Int. J. Multiphase Flow 24, 1026–1055 (1998)CrossRefGoogle Scholar
  44. 44.
    Garcia, M., Sommerer, Y., Schönfeld, T., Poisot, T.: Assessment of Euler-Euler and Euler-Lagrange strategies for reactive large-eddy simulation. In: CERFACS, IMFT – Toulouse, France, pp. 1–10 (2004)Google Scholar
  45. 45.
    Harstad, K., Bellan, J.: Modeling evaporation of Jet A, JP-7, and RP-1 drops at 1 to 15 bars. Combust. Flame 137, 163–177 (2004)CrossRefGoogle Scholar
  46. 46.
    Bekdemir, C., Somers, L.M.T., de Goey, L.P.H.: First application of the flamelet generated manifold (FGM) approach to the simulation of an igniting diesel spray. In: 19th International Multidimensional Engine Modeling User’s Group Meeting at the SAE Congress, Detroit, Michigan, April 2009Google Scholar
  47. 47.
    Peters, N.: Fifteen lectures on laminar and turbulent combustion, ERCOFTAC Summer School, p. 174 (1992)Google Scholar
  48. 48.
    Ge, H.-W., Gutheil, E.: Simulation of a turbulent spray flame using coupled PDF gas phase and spray flamelet modeling. Combust. Flame 153, 173–185 (2008)CrossRefGoogle Scholar
  49. 49.
    Bastiaans, R.J.M., van Oijen, J.A., de Goey, L.P.H.: Application of flamelet generated manifolds and flamelet analysis of turbulent combustion. Int. J. Multiscale Comput. Eng. 4(3), 307–317 (2006)CrossRefGoogle Scholar
  50. 50.
    Baurle, R.A., Girimaji, S.S.: Assumed PDF turbulence-chemistry closure with temperature-composition correlations. Combust. Flame 134, 131–148 (2003)CrossRefGoogle Scholar
  51. 51.
    Patel, N., Kırtaş, M., Sankaran, V., Menon, S.: Simulation of spray combustion in a lean-direct injection combustor. Proc. Combust. Inst. 31(2), 2327–2334 (2007)CrossRefGoogle Scholar
  52. 52.
    Workshop on Quality Assessment of Unsteady Methods for Turbulent Combustion Predictions and Validation, Seeheim-Jugenheim, Germany, 16.–17.06.2005, see (2005)
  53. 53.
    Merci, B., Rockaerst, D., Sadiki, A. (eds.): Experiments and Numerical Simulations of Diluted Spray Turbulent Combustion, Proceedings of the 1st International Workshop on Turbulent Spray Combustion. Springer, Dordrecht (2011)Google Scholar
  54. 54.
    Meftah, H., Reveillon, J., Mir, A., Demoulin, F.X.: SGS analysis of the evolution equations of the mixture fraction and the progress variable variances in the presence of spray combustion. Int. J. Spray Combust. Dyn. 2(1), 21–48 (2010)CrossRefGoogle Scholar
  55. 55.
    Chiguier, N.: Group combustion and laser diagnostic methods in sprays: a review. Combust. Flame 51, 127–139 (1983)CrossRefGoogle Scholar
  56. 56.
    Luo, K., Pitsch, H., Pai, M.G.: DNS of three-dimensional swirling n-heptane spray flames, In Center for Turbulence Research, Annual Research Briefs, pp. 171–183. Stanford University (2009)Google Scholar
  57. 57.
    Reveillon, J., Vervisch, L.: Analysis of weakly turbulent diluted-spray flames and spray combustion regimes. J. Fluid Mech. 537, 317–347 (2005)zbMATHCrossRefGoogle Scholar
  58. 58.
    Domingo, P., Vervisch, L., Reveillon, J.: DNS analysis of partially premixed combustion in spray and gaseous turbulent flame-bases stabilized in hot air. Combust. Flame 140, 172–195 (2005)CrossRefGoogle Scholar
  59. 59.
    Gutheil, E.: Modeling and Simulation of Droplet and Spray Combustion, Handbook of Combustion. Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim (2010)Google Scholar
  60. 60.
    Sazhin, S.S.: Advanced models for fuel droplet heating and evaporation. Prog. Energy Combust. Sci. 32, 162–214 (2006)CrossRefGoogle Scholar
  61. 61.
    Masri, A.R., Gounder, J.D.: Turbulent spray flames of acetone and ethanol approaching extinction. Combust. Sci. Technol. 182(4–6), 702–715 (2010)CrossRefGoogle Scholar
  62. 62.
    Chiu, H.H., Kim, H.Y., Croke, E.J.: Internal group combustion of liquid droplets. In: The Combustion Institute (ed.) Proceedings of 19th Symposium on Combustion, Pittsburgh, Pennsylvania (1982)Google Scholar
  63. 63.
    Pozorski, J., Apte, S.A.: Filtered particle tracking in isotropic turbulence and stochastic modeling of subgrid-scale dispersion. Int. J. Multiphase Flow 35(2), 118–128 (2009)CrossRefGoogle Scholar
  64. 64.
    Apte, S.V., Mahesh, K., Lundgren, T.: Accounting for finite-size effects in disperse particle-laden flows. Int. J. Multiphase Flow 34, 260–271 (2008)CrossRefGoogle Scholar
  65. 65.
    Pozorski, J., Luniewski, M.: Analysis of SGS effects on dispersed particles in LES of heated channel flows. In Quality and Reliability of LES II, ERCOFTAC Series, pp. 171–180. Springer, ISBN 978-1-4020-8577-2, e-ISBN: 978-1-4020-8578-9 (2010)Google Scholar
  66. 66.
    Fiorina, B., Gicquel, O., Vervisch, L., Carpentier, S., Darabiha, N.: Premixed turbulent combustion modeling using tabulated detailed chemistry and PDF. Proc. Combust. Inst. 30, 867–874 (2005)CrossRefGoogle Scholar
  67. 67.
    Weber, J., Peters, N.: Calibration of spray model constants for CFD-simulations of DI diesel engines using the representative interactive flamelet (RIF) model. Int. J. Veh. Des. 41(1–4), 143–164 (2006)CrossRefGoogle Scholar
  68. 68.
    Groh, B.: Grobstruktursimulation turbulenter Mehrphasenströmungen mit und ohne Phasenübergang. In: Dissertation, Fortschritt-Berichte VDI, Reihe 7 Strömungstechnik, Nr. 467, pp. 112–119. VDI Verlag GmbH, Düsseldorf (2005)Google Scholar
  69. 69.
    Landenfeld, T., Sadiki, A., Janicka, J.: A turbulence-chemistry interaction model based on a multivariate presumed Beta-PDF method for turbulent flames. Flow Turbul. Combust. 68, 111–135 (2002)zbMATHCrossRefGoogle Scholar
  70. 70.
    Lehnhäuser, T., Schäfer, M.: Improved linear interpolation practice for finitevolume schemes on complex grids. Int. J. Numer. Meth. Fluids 38(7), 625–645 (2002)zbMATHCrossRefGoogle Scholar
  71. 71.
    Sagaut, P.: Large Eddy Simulation for Incompressible Flows. Springer, Berlin (2001)zbMATHCrossRefGoogle Scholar
  72. 72.
    Wegner, B., Maltsev, A., Schneider, C., Sadiki, A., Dreizler, A., Janicka, J.: Assessment of unsteady RANS in predicting swirl flow instability based on LES and experiments. Int. J. Heat Fluid Flow 25, 528–536 (2004)CrossRefGoogle Scholar
  73. 73.
    Pierce, C.D., Moin, P.: Large eddy simulation of a confined coaxial jet with swirl and heat release, AIAA paper 98–2892 (1998)Google Scholar
  74. 74.
    Vreman, A.W., Albrecht, B.A., van Oijen, J.A., de Goey, L.P.H., Bastiaans, R.J.M.: Premixed and non-premixed generated manifolds in large-eddy simulation of Sandia flame D and F. Combust. Flame 153, 394–416 (2008)CrossRefGoogle Scholar
  75. 75.
    Poinsot, T., Veynante, D.: Theoretical and Numerical Combustion, 3rd edn. CNRS, Toulouse (2011)Google Scholar
  76. 76.
    Janicka, J., Sadiki, A.: Large eddy simulation of turbulent combustion systems. Proc. Combust. Inst. 30, 537–547 (2005)CrossRefGoogle Scholar
  77. 77.
    Balachandar, S., Eaton, J.K.: Turbulent dispersed multiphase flow. Annu. Rev. Fluid Mech. 42, 111–133 (2010)CrossRefGoogle Scholar
  78. 78.
    Sadiki, A., Chrigui, M., Janicka, J., Maneshkarimi, M.R.: Modeling and simulation of effects of turbulence on vaporization, mixing and combustion of liquid fuel sprays. Flow Turbul. Combust. 75, 105–130 (2005)zbMATHCrossRefGoogle Scholar
  79. 79.
    De, S., Lakshmisha, K.N., Bilger, R.W.: Modeling of nonreacting and reacting turbulent spray jets using a fully stochastic separated flow approach. Combust. Flame 158(10), 1992–2008 (2011)CrossRefGoogle Scholar
  80. 80.
    Sadiki, A.: Extended thermodynamics as modeling tool of turbulence in fluid flows. In: Trends in Applications of Mathematics to Mechanics, pp. 451–462. Shaker Verlag, Aachen (2005)Google Scholar
  81. 81.
    Geiss, S., Dreizler, A., Stojanovic, Z., Chrigui, M., Sadiki, A., Janicka, J.: Investigation of turbulence modification in a non-reactive two-phase flow. Exp. Fluids 36, 344–354 (2004)CrossRefGoogle Scholar
  82. 82.
    Chrigui, M., Ahmadi, G., Sadiki, A.: Study on interaction in spray between evaporating droplets and turbulence using second-order turbulence RANS models and a Lagrangian approach. Prog. Comput. Fluid Dyn. 4(3–5), 162–174 (2004)CrossRefGoogle Scholar
  83. 83.
    Garcia, M.: Développement et validation du formalisme Euler-Lagrange dans un solveur parallèle et non-structuré pour la simulation aux grandes INP Toulouse, France Thèse (2009)Google Scholar
  84. 84.
    Lee, J., Choi, H., Park, N.: Dynamic global model for large eddy simulation of transient flow. Phys. Fluids 22(7). 10.1063/1.3459156 (2010)
  85. 85.
    Löffler, M., Pfadler, S., Beyrau, F., Leipertz, A., Dinkelacker, F., Huai, Y., Sadiki, A.: Experimental determination of the sub-grid scale scalar flux in a non-reacting jet flow. Flow Turbul. Combust. 1386–6184, 1573–1987 (Online) (2007)Google Scholar
  86. 86.
    Yoshizawa, A., Horiuti, K.: A statistically-derived subgrid-scale kinetic energy model for large eddy simulation of turbulent flow. J. Phys. Soc. Jpn. 54(8), 2834–2839 (1985)CrossRefGoogle Scholar
  87. 87.
    Eguz, U., Somers, L.M.T., de Goey, L.P.H.: Modeling of PCCI combustion with the FGM approach. In: 13th International Conference on Numerical Combustion, Corfu, Greece, 27–29 April 2011Google Scholar
  88. 88.
    Hu, Z., Cracknel, R., Somers, L.M.T.: Computational study of fuel effects in premixed charge compression ignition (PCCI) engine combustion. In: 8th International Symposium Towards Clean Diesel Engines TCDE 2011, Chester, U.K., 8–9 June 2011Google Scholar
  89. 89.
    Marinov, N.M.: A detailed chemical kinetic model for high temperature ethanol oxidation. Int. J. Chem. Kinet. 31, 183–220 (1999)CrossRefGoogle Scholar
  90. 90.
    Mashayek, F., Taulbee, D.B., Givi, P.: Modeling and simulation of two phase turbulent flow. In: Roy, D.G. (ed.) Propulsion Combustions: Fuels to Emissions, Kapitel 8, pp. 241–280. Taylor & Francis, Washington, D.C. (1998)Google Scholar
  91. 91.
    Yeh, F., Lei, U.: On the motion of small particles in a homogeneous turbulent shear flow. Phys. Fluids 3(11), 2758–2776 (1999)Google Scholar
  92. 92.
    Lei, K., Taniguchi, N., Kobayashi, T.: A new dynamic SGS-Model for large eddy simulation of particle-laden flows. In: Third AFOSR International Conference on DNS/LES (TAICDL) (2001)Google Scholar
  93. 93.
    Crowe, C.T.: A review of carrier-phase turbulence in dispersed flows. In: Proceedings of the 4th International Conference on Multiphase Flow, Paper-No. 604 (2001)Google Scholar
  94. 94.
    Tsuji, Y.: Activities in discrete particle simulation in Japan. Powder Technol. 113, 278–286 (2000)CrossRefGoogle Scholar
  95. 95.
    Lain, S., Sommerfeld, M.: Turbulence modulation in dispersed two-phase flow laden with solids from a Lagrangian perspective. Int. J. Heat Fluid Flow 24, 616–625 (2003)CrossRefGoogle Scholar
  96. 96.
    Sommerfeld, M., Qui, H.H.: Detailed measurements in a swirling particulate two-phase flow by a phase-Doppler-anemometer. Int. J. Heat Fluid Flow 12, 20–28 (1991)CrossRefGoogle Scholar
  97. 97.
    Sommerfeld, M., Qui, H.H.: Experimental studies of spray evaporation in turbulent flow. Int. J. Heat Fluid Flow 19, 10–22 (1998)CrossRefGoogle Scholar
  98. 98.
    Klein, M., Sadiki, A., Janicka, J.: A digital filter based generation of inflow data for spatially developing direct numerical or large eddy simulation. J. Comput. Phys. 186, 652–665 (2003)zbMATHCrossRefGoogle Scholar
  99. 99.
    Elghobashi, S., Truesdell, G.C.: On the two-way interaction between homogenous turbulence and dispersed solid particles I: turbulence modification. Phys. Fluids A 5, 1790–1796 (1993)zbMATHCrossRefGoogle Scholar
  100. 100.
    Faeth, G.M.: Mixing, transport and combustion in sprays. Prog. Energy Combust. Sci. 13, 293–345 (1987)CrossRefGoogle Scholar
  101. 101.
    Ahmadi, G., Cao, J., Schneider, L., Sadiki, A.: A thermodynamically formulation for chemically active multiphase turbulent flows. Int. J. Eng. Sci. 44, 699–720 (2006)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Institute for Energy and Powerplant Technology, Mechanical EngineeringTechnische Universität DarmstadtDarmstadtGermany
  2. 2.Institute of Reactive Flow and Diagnostics, Mechanical EngineeringTechnische Universität DarmstadtDarmstadtGermany
  3. 3.Center of Smart Interface, Mechanical EngineeringTechnische Universität DarmstadtDarmstadtGermany

Personalised recommendations