Simulation of Turbulent Combustion in Porous Materials with One- and Two-Energy Equation Models

  • Marcelo J. S. de LemosEmail author
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 2)


The objective of this chapter is to present one- and two-dimensional numerical simulations of combustion of an air/methane mixture in porous materials using a mathematical model that explicitly considers the intra-pore levels of turbulent kinetic energy. Transport equations are written in their time-and-volume-averaged form and a volume-based statistical turbulence model is applied to simulate turbulence generation due to the porous matrix. Four different thermo-mechanical models are compared, namely Laminar, Laminar with Radiation Transport, Turbulent, Turbulent with Radiation Transport. Combustion is modeled via a unique simple closure. Preliminary testing results indicate that a substantially different temperature distribution is obtained depending on the model used. In addition, for high excess air peak gas temperature are reduced and the flame front moves towards the exit of the burner. Also, increasing the inlet flow rate for stoichiometric mixture pushes the flame out of the porous material.


Flame Front Radiation Transport Local Thermal Equilibrium Solid Temperature Porous Burner 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The author is indebted to CNPq, CAPES and FAPESP, Brazil, for their invaluable continuous support during the course of his research work at ITA, Brazil.


  1. 1.
    Howell, J.R., Hall, M.J., Ellzey, J.L.: Combustion of hydrocarbon fuels within porous inert media. Progress in Energy and Combustion Sciences 22(2), 121–145 (1996)CrossRefGoogle Scholar
  2. 2.
    Oliveira, A.A.M., Kaviany, M.: Non equilibrium in the transport of heat and reactants in combustion in porous media. Progress in Energy and Combustion Sciences 27(5), 523–545 (2001)CrossRefGoogle Scholar
  3. 3.
    Henneke, M.R., Ellzey, J.L.: Modeling of filtration combustion in a packed bed. Combust. Flame 117(4), 832–840 (1999)CrossRefGoogle Scholar
  4. 4.
    Bouma, P.H., De Goey, L.P.H.: Premixed combustion on ceramic foam burners. Combust. Flame 119(1–2), 133–143 (1999)CrossRefGoogle Scholar
  5. 5.
    Babkin, V.S.: Filtration combustion of gases – present state of affairs and prospects. Pure Appl. Chem. 65(2), 335–344 (1993)CrossRefGoogle Scholar
  6. 6.
    Leonardi, S.A., Viskanta, R., Gore, J.P.: Analytical and experimental study of combustion and heat transfer in submerged flame metal fiber burners/heaters. J. Heat Transf. 125(1), 118–125 (2003)CrossRefGoogle Scholar
  7. 7.
    Lammers, F.A., De Goey, L.P.H.: A numerical study of flash back of laminar premixed flames in ceramic-foam surface burners. Combust. Flame 133(1–2), 47–61 (2003)CrossRefGoogle Scholar
  8. 8.
    Mohamad, A.A., Ramadhyani, S., Viskanta, R.: Modeling of combustion and heat-transfer in a packed-bed with embedded coolant tubes. Int. J. Heat Mass Transf. 37(8), 1181–1191 (1994)CrossRefGoogle Scholar
  9. 9.
    Wood, S., Harries, A.T.: Porous burners for lean-burn applications. Progress in Energy and Combustion Sciences 34, 667–684 (2008)CrossRefGoogle Scholar
  10. 10.
    Abdul, M.M., Abdullah, M.Z., Abu Bakar, M.Z., Mohamad, A.A., Abdullaha, M.K.: A review of investigations on liquid fuel combustion in porous inert media. Progress in Energy and Combustion Sciences 35, 216–230 (2009)CrossRefGoogle Scholar
  11. 11.
    Hsu, P.-F., Howell, J.R., Matthews, R.D.: A numerical investigation of premixed combustion within porous inert media. J. Heat Transf. 115, 744–750 (1993)CrossRefGoogle Scholar
  12. 12.
    Peard, T.E., Peters, J.E., Brewster, B., Buckius, R.O.: Radiative heat transfer augmentation in gas-fired radiant tube burner by porous inserts: effect on insert geometry. Exp. Heat Transf. 6, 273–286 (1993)CrossRefGoogle Scholar
  13. 13.
    Lim, I.G., Matthews, R.D.: Development of a model for turbulent combustion within porous inert media. Transp. Phenom. Therm. Eng., Begell House Inc. Publ., pp. 631–636 (1993)Google Scholar
  14. 14.
    Jones, W.P., Launder, B.E.: The prediction of laminarization with two-equation model of turbulence. Int. J. Heat Mass Transf. 15, 301–314 (1972)CrossRefGoogle Scholar
  15. 15.
    Sahraoui, M., Kaviany, M.: Direct simulation vs time-averaged treatment of adiabatic. Premixed flame in a porous medium. Int. J. Heat Mass Transf. 18, 2817–2834 (1995)Google Scholar
  16. 16.
    Pedras, M.H.J., de Lemos, M.J.S.: Computation of turbulent flow in porous media using a low- Reynolds k-epsilon model and an infinite array of transversally displaced elliptic rods. Numer. Heat Transf. A Appl. 43(6), 585–602 (2003)CrossRefGoogle Scholar
  17. 17.
    de Lemos, M.J.S.: Turbulent kinetic energy distribution across the interface between a porous medium and a clear region. Int. Commun. Heat Mass Transf. 32(1–2), 107–115 (2005)Google Scholar
  18. 18.
    de Lemos, M.J.S.: Turbulence in Porous Media: Modeling and Applications. Elsevier, Amsterdam (2006). 384 pgs. ISBN 0-08-044491-1Google Scholar
  19. 19.
    Santos, N.B., de Lemos, M.J.S.: Flow and heat transfer in a parallel-plate channel with porous and solid baffles. Numer. Heat Transf. A Appl. 49(5), 471–494 (2006)CrossRefGoogle Scholar
  20. 20.
    Assato, M., Pedras, M.H.J., de Lemos, M.J.S.: Numerical solution of turbulent channel flow past a backward-facing step with a porous insert using linear and nonlinear k-epsilon models. J. Porous Mater. 8(1), 13–29 (2005)CrossRefGoogle Scholar
  21. 21.
    Braga, E.J., de Lemos, M.J.S.: Turbulent natural convection in a porous square cavity computed with a macroscopic kappa-epsilon model. Int. J. Heat Mass Transf. 47(26), 5639–5650 (2004)CrossRefGoogle Scholar
  22. 22.
    Slattery, J.C.: Flow of viscoelastic fluids through porous media. AIChE J. 13, 1066–1071 (1967)CrossRefGoogle Scholar
  23. 23.
    Whitaker, S.: Advances in theory of fluid motion in porous media. Ind. Eng. Chem. 61, 14–28 (1969)CrossRefGoogle Scholar
  24. 24.
    Gray, W.G., Lee, P.C.Y.: On the theorems for local volume averaging of multiphase system. Int. J. Multiphas. Flow 3, 333–340 (1977)CrossRefGoogle Scholar
  25. 25.
    de Neef, M., Knabner, P., Summ, G.: Numerical bifurcation analysis of premixed combustion in porous inert media. Unpublished (1999).
  26. 26.
    Saito, M.B., de Lemos, M.J.S.: A correlation for interfacial heat transfer coefficient for turbulent flow over an array of square rods. J. Heat Transf. 128, 444–452 (2006)CrossRefGoogle Scholar
  27. 27.
    Kuwahara, F., Shirota, M., Nakayama, A.: A numerical study of interfacial convective heat transfer coefficient in two-energy equation model for convection in porous media. Int. J. Heat Mass Transf. 44, 1153–1159 (2001)CrossRefGoogle Scholar
  28. 28.
    Mohamad, A.A., Viskanta, R., Ramadhyani, S.: Numerical prediction of combustion and heat transfer in a packed bed with embedded coolant tubes. Combust. Sci. Technol. 96, 387–407 (1994)CrossRefGoogle Scholar
  29. 29.
    Kwo, K.K.: Principles of Combustion. Wiley, New York (1986)Google Scholar
  30. 30.
    Trimis, D., Durst, F.: Combustion in a porous medium – advances and applications. Combust. Sci. Technol. 121, 153–168 (1996)CrossRefGoogle Scholar
  31. 31.
    Zhou, X.Y., Pereira, J.C.F.: Comparison of four combustion models for simulating the premixed combustion in inert porous media. Fire Mater. 22, 187–197 (1998)CrossRefGoogle Scholar
  32. 32.
    Mohamad, A.A.: Axial and radial porous burners. In: Ingham, D.B., Mamut, E., Bejan, A., Pop, I. (eds) Chap 24 in Emerging Technologies and Techniques in Porous Media. Springer, Berlin (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Instituto Tecnológico de Aeronáutica - ITASão PauloBrazil

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