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Issues in Computational Studies of Turbulent Spray Combustion

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Experiments and Numerical Simulations of Diluted Spray Turbulent Combustion

Part of the book series: ERCOFTAC Series ((ERCO,volume 17))

Abstract

Turbulent spray combustion occurs in many technical applications such as internal engine combustion, gas turbine combustion, liquid-fueled rockets, and industrial burners. Major challenges are the modeling of detailed processes including the atomization process, the turbulent flow field, particle motion and interaction, chemical reactions as well as the strong coupling between these processes. The method of choice to achieve an integral model for the modeling and simulation of turbulent spray combustion is the detailed modeling of fundamental processes and simplification of these models before they enter a more complex tool. Thus, it is guaranteed that models are based on physical grounds and the degree of detailedness is sufficient to capture the essential features of the underlying process. The final tool then is based on physical grounds and it is not burdened with details not contributing to the main features of the flame structure.

The present work aims to present an overview on the state of the art with respect to underlying physical models and challenges that need to be addressed in the near future. They include the modeling and simulation of turbulence, turbulent mixing as well as the interaction of evaporation with the turbulent flow field and the chemical reactions. Principal approaches to modeling sprays in a turbulent flow field such as RANS (Reynolds averaged Navier-Stokes equations), DNS (direct numerical simulation) and LES (large eddy simulation) are addressed. Moreover, Reynolds stress models (RSM), PDF (probability density function), and CMC (conditional moment closure) models will be presented and discussed. These approaches can act both as general spray models and as subgrid models for LES.

In order to address environmental concerns, detailed chemical kinetics need to be considered to account for the prediction of pollutant emission and its reduction. Appropriate methods such as direct closure methods and (spray) flamelet models for turbulent spray flames are addressed. Also, reduced chemical mechanisms are discussed.

It is shown that most often gas flame models are not appropriate for spray flame modeling because of the high impact that both spray dynamics and evaporation have on spray combustion.

Moreover, numerical results using different models and experimental data mainly of research burners are discussed. The scope is the evaluation of present models, and future research areas of interest are identified.

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References

  1. Faeth, G.M.: Current status of droplet and liquid combustion. Prog. Energy Combust. Sci. 3, 191–224 (1977)

    Article  Google Scholar 

  2. Reitz, R.D.: Modeling atomization processes in high-pressure vaporizing sprays. Atomisation Spray Technol. 3, 309 (1987)

    Google Scholar 

  3. Su, T.F., Patterson, M.A., Reitz, R.D., Farrell, P.V.: Experimental and numerical studies of high-pressure multiple injection sprays. SAE Technical Paper Series, Paper 960861, Society of Automotive Engineers, Inc., Warrendale, PA (1996)

    Google Scholar 

  4. Chryssakis, C., Assanis, D.N.: A unified fuel spray breakup model for internal combustion engine applications. Atomiz. Sprays 18, 1–52 (2008)

    Article  Google Scholar 

  5. Ko, G.H., Ryou, H.S.: Droplet collision processes in an inter-spray impingement system. Aerosol Sci. 36, 1300–1321 (2005)

    Article  Google Scholar 

  6. O’Rourke, P.J.: Convective droplet effects on vaporizing liquid sprays. Ph.D. thesis, Mechanical and Aerospace Engineering, Princeton University (1981)

    Google Scholar 

  7. Chigier, N.A., Mullinger, P.J.: The design and performance of internal mixing multijet twin fluid atomizers. J. Inst. Fuel 47, 251–262 (1974)

    Google Scholar 

  8. Faeth, G.M., Hsiang, l.-P., Wu, P.-K.: Structure and breakup properties of sprays. Int. J. Multiphase Flow 21(Suppl.) 99–127 (1995)

    Google Scholar 

  9. Schlottke, J., Weigand, B.: Direct numerical simulation of evaporating droplets. J. Comp. Phys. 227, 5215–5237 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  10. Spalding, D.B.: The combustion of liquid fuels. Proc. Combust. Inst. 4, 847–864 (1953)

    Google Scholar 

  11. Godsave, G.A.E.: Studies of the combustion of drops in a fuel spray – the burning of single drops of fuel. Proc. Combust. Inst. 4, 818–830 (1953)

    Google Scholar 

  12. Amsden, A.A.: KIVA-3V: A block-structured KIVA program for engines with vertical or canted valves, LA-13313-MS, UC-1412, Los Alamos National Laboratory, Los Alamos, NM (1977)

    Google Scholar 

  13. Williams, F.A.: Combustion Theory, 2nd edn. Benjamin/Cummings, Menlo Park (1985)

    Google Scholar 

  14. Sirignano, W.A.: Fluid Dynamics and Transport of Droplets and Sprays. Cambridge University Press, Cambridge (1999)

    Book  Google Scholar 

  15. Williams, A.: Combustion of droplets of liquid fuels: a review. Combust. Flame 21, 1–31 (1973)

    Article  Google Scholar 

  16. Hubbard, G.L., Denny, V.E., Mills, A.F.: Droplet evaporation: effects of transient and variable properties. Int. J. Heat Mass Tran. 18(9), 1003–1008 (1975)

    Article  Google Scholar 

  17. Marchese, A.J., Dryer, F.L.: Effect of liquid mass transport on the combustion and extinction of bi component liquid droplets of methanol and water. Combust. Flame 105, 104–122 (1996)

    Article  Google Scholar 

  18. Aouina, Y., Gutheil, E., Maas, U., Riedel, U., Warnatz, J.: Mathematical modeling of droplet heating, vaporization, and ignition including detailed chemistry. Combust. Sci. Tech. 173, 1–29 (2001)

    Article  Google Scholar 

  19. Strauch, R., Lipp, S., Maas, U.: Detailed numerical simulations of the autoignition of single n-heptane droplets in air. Combust. Flame 145(3), 533–542 (2006)

    Article  Google Scholar 

  20. Stauch, R., Maas, U.: The ignition of methanol droplets in a laminar convective environment. Combust. Flame 153(1–2), 45–57 (2008)

    Article  Google Scholar 

  21. Düwel, I., Schorr, J., Wolfrum, J., Schulz, C.: Laser-induced fluorescence of tracers dissolved in evaporating droplets. Appl. Phys. B 78, 127–131 (2004)

    Article  Google Scholar 

  22. Ge, H.W., Urzica, D., Vogelgesang, M., Gutheil, E.: Modeling and simulation of turbulent non-reacting and reacting spray flows. In: Jäger, W., Rannacher, R., Warnatz, J. (eds.) Reactive Flows, Diffusion and Transport. Springer, Berlin (2006)

    Google Scholar 

  23. Urzica, D., Düwel, I., Schulz, C., Gutheil, E.: Laser-induced evaporation of a single droplet – An experimental and computational investigation. In: Proceedings of the 20th Annual Conference of ILASS, Europe, pp. 241–246 (2005)

    Google Scholar 

  24. Aulisa, E., Manservisi, S., Scardovelli, R., Zaleski, S.: A geometrical area-preserving volume-of-fluid method. J. Comput. Phys. 192, 355–364 (2003)

    Article  MATH  Google Scholar 

  25. Fu, W.B., Hou, L.Y., Wang, L., Ma, F.H.: A unified model for the micro-explosion of emulsified droplets of oil and water. Fuel Process. Technol. 79(2), 107–119 (2002)

    Article  Google Scholar 

  26. Shabde, V.S., Emets, S.V., Mann, U., Hoo, K.A., Carlson, N.N., Gladysz, G.M.: Modeling a hollow micro-particle production process. Comput. Chem. Eng. 29, 2420–2428 (2005)

    Article  Google Scholar 

  27. Kim, I., Elghobashi, S.E., Sirignano, W.A.: Three-dimensional flow over two spheres placed side-by-side. J. Fluid Mech. 246, 465–468 (1993)

    Article  MATH  Google Scholar 

  28. Srinivas, Y., Gutheil, E.: Modelling of droplet interaction in convective gas flows. Prog. Computat. Fluid Dyn. 4(3–5), 250–256 (2004)

    Article  Google Scholar 

  29. Kaltz, T.L., Long, L.N., Micc, M.M., Little, J.K.: Supercritical vaporization of liquid oxygen droplets using molecular dynamics. Combust. Sci. Tech. 136, 279–301 (1998)

    Article  Google Scholar 

  30. Malevanets, A., Kapral, R.: Mesoscopic, multi-particle collision model for fluid flow and molecular dynamics. Lecture Notes in Physics, vol. 640, pp. 116–149 (2004)

    Google Scholar 

  31. Tseng, L.-K., Ruff, G.A., Faeth, G.M.: Effects of gas density on the structure of liquid jets in still gases. AIAA J. 30(6), 1537–1544 (1992)

    Article  Google Scholar 

  32. Faeth, G.M.: Spray combustion phenomena. Proc. Combust. Inst. 26, 1593–1612 (1996)

    Google Scholar 

  33. Vujanović, M., Edelbauer, W., von Berg, E., Tatschl, R., Duić, N.: Enhancement and validation of an Eulerian-Eulerian approach for diesel sprays. In: Proceedings of the ILASS Europe Conference, Paper 2–4, Como (2008)

    Google Scholar 

  34. Bayoro, F., Habachi, C., Daniel, E.: Numerical and physical basis of an Eulerian multi-phase flow model for the simulation of the liquid injection in internal combustion engines. In: Proceedings of the ILASS Europe Conference, Paper 2–5, Como (2008)

    Google Scholar 

  35. Drew, D.A., Passman, L.A.: Theory of Multicomponent Fluids. Springer, Berlin (1999)

    Google Scholar 

  36. Herrmann, M.: A Eulerian level set/vortex sheet method for two-phase interface dynamics. J. Comput. Phys. 203, 539–571 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  37. Sussman, M., Fatemi, E.: An efficient, interface-preserving level set redistancing algorithm and its application to interfacial incompressible fluid flow. SIAM J. Sci. Comput. 20(4), 1165–1191 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  38. Enright, D., Fedkiw, R., Ferziger, J., Michell, I.: A hybrid particle level set method for improved interface capturing. J. Comput. Phys. 148, 2–22 (2002)

    Google Scholar 

  39. Stiesch, G.: Modeling Engine Spray and Combustion Processes (Heat and Mass Transfer). Springer, Berlin (2003)

    Google Scholar 

  40. Hollmann, C., Gutheil, E.: Modeling of turbulent spray diffusion flames including detailed chemistry. Proc. Combust. Inst. 26(1), 1731–1738 (1996)

    Google Scholar 

  41. McDonell, V.G., Samuelsen, G.S.: An experimental data base for the computational fluid dynamics of reacting and nonreacting methanol sprays. J. Fluids Eng. 117, 145–153 (1995)

    Article  Google Scholar 

  42. Ge, H.-W., Düwel, I., Kronemayer, H., Dibble, R.W., Gutheil, E., Schulz, C., Wolfrum, J.: Laser based experimental and Monte Carlo PDF numerical investigation of an ethanol/air spray flame. Combust. Sci. Technol. 180, 1529–1547 (2008)

    Article  Google Scholar 

  43. Laurent, F., Massot, M.: Multi-fluid modelling of laminar polydisperse spray flames: origin, assumptions and comparison of sectional and sampling methods. Combust. Theory Modell. 5, 537–572 (2001)

    Article  MATH  Google Scholar 

  44. Laurent, F., Massot, M., Villedieu, P.: Eulerian multi-fluid modeling for the numerical simulation of coalescence in polydisperse dense liquid sprays. J. Comput. Phys. 194, 505–543 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  45. Williams, F.A.: Spray combustion and atomization. Phys. Fluids. 1, 541–545 (1958)

    MATH  Google Scholar 

  46. Marchisio, D.L., Fox, R.O.: Solution of population balance equations using the direct quadrature method of moments. Aerosol Sci. 36, 43–73 (2005)

    Article  Google Scholar 

  47. Vikas, V., Wang, Z.J., Fox, R.O., Passalacqua, A.: A fully coupled fluid-particle flow solver using a quadrature-based moment method with high-order realizable schemes on unstructured grids. In: Proceedings of the International Conference on Multiphase Flow, Florida (2010).

    Google Scholar 

  48. Fox, R.O., Laurent, F., Massot, M.: Numerical simulation of spray coalescence in an Eulerian framework: direct quadrature method of moments and multi-fluid method. J. Comput. Phys. 227(6), 3058–3088 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  49. Rigopoulos, S.: Population balance modelling of polydispersed particles in reactive flows. Prog. Energy Combust. Sci. 36, 412–443 (2010)

    Article  Google Scholar 

  50. Réveillon, J.: Direct numerical simulation of sprays: turbulent dispersion, evaporation and combustion. In: Marchisio, D.L., Fox, R.O. (eds.) Multiphase Reacting Flows: Modelling and Simulation. Springer, New York (2007)

    Google Scholar 

  51. Wang, Y., Rutland, C.J.: Direct numerical simulation of ignition in turbulent n-heptane liquid-fuel spray jets. Combust. Flame 149(4), 353–365 (2007)

    Article  Google Scholar 

  52. Xia, J., Luo, K.H.: Direct numerical simulation of diluted combustion by evaporating droplets. Proc. Comb. Inst. 32, 2267–2274 (2009)

    Article  Google Scholar 

  53. Apte, S.V., Mahesh, K., Moin, P.: Large-eddy simulation of evaporating spray in a coaxial combustor. Proc. Comb. Inst. 32, 2247 (2009)

    Article  Google Scholar 

  54. Derksen, J.J.: Lattice-Boltzmann method for multiphase fluid flow simulations and Euler-Lagrange Large-Eddy simulations. In: Marchisio, D.L., Fox, R.O. (eds.) Multiphase Reacting Flows: Modelling and Simulation. Springer, New York (2007)

    Google Scholar 

  55. Boileau, M., Pascaud, S., Riber, E., Cuenot, B., Gicquel, L.Y.M., Poinsot, T.J., Cazalens, M.: Investigation of two-fluid methods for large eddy simulation of spray combustion in gas turbines. Flow Turbul. Combust. 80(3), 291–321 (2008)

    Article  Google Scholar 

  56. Subramanian, G., Colin, O., Pires da Cruz, A., Vervisch, L., Bruneaux, G.: Modeling turbulent mixing of an evaporating spray. In: Proceedings of the ICDERS, Montréal (2005)

    Google Scholar 

  57. Demoulin, F.X., Borghi, R.: Modeling of turbulent spray combustion with application to diesel like experiment. Combust. Flame 129, 281–293 (2002)

    Article  Google Scholar 

  58. Réveillon, J., Vervisch, L.: Spray vaporization in nonpremixed turbulent combustion modeling: a single droplet model. Combust. Flame 121, 75–90 (2000)

    Article  Google Scholar 

  59. Launder, B.E.: On the effects of a gravitational field on the turbulent transport of heat and momentum. J. Fluid Mech. 67(3), 569 (1975)

    Article  Google Scholar 

  60. Landenfeld, L., Kremer, A., Hassel, E., Janicka, J.: Comparison of Reynolds stress closures for strongly swirling combusting jets. In: 11th Symposium on Turbulent Shear Flows, Grenoble (1997)

    Google Scholar 

  61. Beishuizen, N.: PDF modeling and particle-turbulence interaction of turbulent spray flames. Ph.D. thesis, TU Delft, The Netherlands (2007)

    Google Scholar 

  62. Libby, P.A., Williams, F.A.: Turbulent Reactive Flows. Academic, London (1994)

    Google Scholar 

  63. Vogelgesang, M.: Reynolds stress modeling for turbulent spray flames. Ph.D. thesis (in German), Heidelberg University (2005)

    Google Scholar 

  64. Daly, H.J., Harlow, H.: Transport equations in turbulence. Phys. Fluids 13, 2634–2649 (1970)

    Google Scholar 

  65. Gibson, M.M., Younis, B.A.: Calculation of swirling jets with a Reynolds stress closure. Phys. Fluids 29(1), 38 (1986)

    Article  Google Scholar 

  66. Launder, B.E., Reece, G.J., Rodi, W.: Progress in the development of a Reynolds-stress turbulent closure. J Fluid Mech. 68(3), 537–566 (1975)

    Article  MATH  Google Scholar 

  67. Hollmann, C., Gutheil, E.: Flamelet-modeling of turbulent spray diffusion flames based on a laminar spray flame library. Combust. Sci. Technol. 135(1–6), 175 (1998)

    Article  Google Scholar 

  68. Pope, S.N.B.: PDF methods for turbulent reactive flows. Prog. Energy Combust. Sci. 11, 119–192 (1985)

    Article  MathSciNet  Google Scholar 

  69. Ge, H.-W., Gutheil, E.: PDF simulation of turbulent spray flows. Atomiz. Sprays 16(5), 531–542 (2006)

    Article  Google Scholar 

  70. Masri, A.R., Pope, S.N.B.: PDF calculations of piloted turbulent nonpremixed flames of methane. Combust. Flame 81, 13–29 (1990)

    Article  Google Scholar 

  71. Curl, R.L.: Dispersed phase mixing: I theory and effects in single reactors. AIChE J. 9, 175–181 (1963)

    Article  Google Scholar 

  72. Janicka, J., Kolbe, W., Kollmann, W.: Closure of the transport equation for the probability density function of turbulent scalar fields. J. Non-Equilib. Thermodyn. 4, 47–66 (1979)

    Article  MATH  Google Scholar 

  73. Masri, A.R., Subramaniam, S., Pope, S.N.B.: A mixing model to improve the PDF simulation of turbulent diffusion flames. Proc. Combust. Inst. 26, 49–57 (1996)

    Google Scholar 

  74. Miller, R.S., Bellan, J.: On the validity of the assumed probability density function method for modeling binary mixing/reaction of evaporated vapor in gas-liquid turbulent shear flow. Proc. Combust. Inst. 27, 1065–1072 (1998)

    Google Scholar 

  75. Ge, H.-W., Gutheil, E.: Simulation of a turbulent spray flame using coupled PDF gas phase and spray flamelet modeling. Combust. Flame 153(1–2), 173–185 (2008)

    Article  Google Scholar 

  76. Kee, R.J., Miller, J.A., Jefferson, T.H.: CHEMKIN: A general-purpose, problem-independent, transportable, Fortran chemical kinetics code package, Sandia Report SAN 80-8003, Sandia National Laboratories, Livermore, CA (1989)

    Google Scholar 

  77. Li, S.C.: Spray stagnation flames. Prog. Energy Combust. Sci. 23(4), 303–347 (1997)

    Article  Google Scholar 

  78. Continillo, G., Sirignano, W.A.: Counterflow spray combustion modelling. Combust. Flame 81(3–4), 325–340 (1990)

    Article  Google Scholar 

  79. Amantini, G., Frank, J.H., Smooke, M.D., Gomez, A.: Computational and experimental study of steady axisymmetric non-premixed methane counterflow flames. Combust. Theory Modell. 11(1), 47–72 (2007)

    Article  MATH  Google Scholar 

  80. Dakhlia, R.B., Giovangigli, V., Rosner, D.E.: Soret effects in laminar counterflow spray diffusion flames. Combust. Theory Modell. 6(1), 1–7 (2002)

    Article  MATH  Google Scholar 

  81. Gutheil, E., Sirignano, W.A.: Counterflow spray combustion modeling including detailed transport and detailed chemistry. Combust. Flame 113(2), 92–105 (1998)

    Article  Google Scholar 

  82. Schlotz, D., Gutheil, E.: Modeling of laminar mono- and bidisperse liquid oxygen/hydrogen spray flames in the counterflow configuration. Combust. Sci. Tech. 158, 195–210 (2000)

    Article  Google Scholar 

  83. Gutheil, E.: Structure and extinction of laminar ethanol/air spray flames. Combust. Theory Modell. 5, 1–15 (2001)

    Article  Google Scholar 

  84. Gutheil, E.: Multiple solutions for structures of laminar counterflow spray flames. Prog. Comput. Fluid Dyn. 5(7), 414–419 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  85. http://www.me.berkeley.edu/gri-mech/

  86. Warnatz, J., Maas, U., Dibble, R.W.: Combustion. Springer, Berlin (1999)

    MATH  Google Scholar 

  87. Schlichting, H., Gertsen, K.: Boundary Layer Theory, 8th Revised and Enlarged Edition. Springer, Berlin Heidelberg New York (2000)

    Google Scholar 

  88. Peters, N.: Numerical and asymptotic analysis of systematically reduced reaction schemes for hydrocarbon flames. In: Glowinski, R., Larrouturou, B., Temam, R. (eds.) Numerical Simulation in Combustion Phenomena. Lecture Notes in Physics, vol. 241, pp. 90–109 (1985)

    Google Scholar 

  89. Peters, N., Rogg, B.: Reduced Kinetic Mechanisms for Applications in Combustion Systems. Springer, Berlin (1993)

    Book  Google Scholar 

  90. Maas, U., Pope, S.B.: Simplifying chemical kinetics: intrinsic low-dimensional manifolds in composition space. Combust. Flame 88, 239–264 (1992)

    Article  Google Scholar 

  91. Peters, N.: Turbulent Combustion. Cambridge University Press, Cambridge (2000)

    Book  MATH  Google Scholar 

  92. Bastiaans, R.J.M., Martin, S.M., Pitsch, H., van Oijen, J.A., de Goey, L.P.H.: Flamelet analysis of turbulent combustion. Lecture Notes in Computer Science, vol. 3516, pp. 64–71 (2005)

    Article  Google Scholar 

  93. Peters, N.: Laminar flamelet concepts in turbulent combustion. Proc. Combust. Inst. 21, 1231–1250 (1986)

    Google Scholar 

  94. 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)

    Article  Google Scholar 

  95. Bongers, H., van Oijen, J.A., Somers, L.M., de Goey, L.P.H.: The flamelet generated manifold method applied to steady planar partially premixed counterflow flames. Combust. Sci. Tech. 177(12), 2373–2393 (2005)

    Article  Google Scholar 

  96. Selle, L.C., Bellan, J.: Evaluation of assumed PDF methods in two-phase flows using direct numerical simulation. Proc. Comb. Inst. 31, 2273–2281 (2007)

    Article  Google Scholar 

  97. Klimenko, A.Y., Bilger, R.W.: Conditional moment closure for turbulent combustion. Prog. Energy Comb. Sci. 25, 595–687 (1999)

    Article  Google Scholar 

  98. Mortensen, M., Bilger, R.W.: Derivation of the conditional moment closure equations for spray combustion. Combust. Flame 156, 62–72 (2009)

    Article  Google Scholar 

  99. Merci, B., Mastorakos, E., Mura, A.: Modeling of turbulent combustion. In: Lackner, M., Winter, F., Agarwal, A.K. (eds.) Handbook of Combustion. Wiley-VCH, Weinheim (2010)

    Google Scholar 

  100. Wright, Y.M., de Paola, G., Boulouchos, K., Mastorakos, E.: Simulations of spray autoignition and flame establishment with two-dimensional CMC. Combust. Flame 143, 402–419 (2005)

    Article  Google Scholar 

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Gutheil, E. (2011). Issues in Computational Studies of Turbulent Spray Combustion. In: Merci, B., Roekaerts, D., Sadiki, A. (eds) Experiments and Numerical Simulations of Diluted Spray Turbulent Combustion. ERCOFTAC Series, vol 17. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1409-0_1

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