Assessment of a transient homogeneous reactor through in situ adaptive tabulation

  • Americo Cunha JrEmail author
  • Luís Fernando Figueira da Silva
Technical Paper


The development of computational models for the numerical simulation of chemically reacting flows operating in the turbulent regime requires the solution of partial differential equations that represent the balance of mass, linear momentum, chemical species, and energy. The chemical reactions of the model may involve detailed reaction mechanisms for the description of the physicochemical phenomena. One of the biggest challenges is the stiffness of the numerical simulation of these models and the nonlinear nature of species rate of reaction. This work presents a study of in situ adaptive tabulation (ISAT) technique, focusing on the accuracy, efficiency, and memory usage in the simulation of homogeneous stirred reactor models using simple and complex reaction mechanisms. The combustion of carbon monoxide with oxygen and methane with air mixtures are considered, using detailed reaction mechanisms with 4 and 53 species, 3 and 325 reactions, respectively. The results of these simulations indicate that the developed implementation of ISAT technique has a absolute global error smaller than 1 %. Moreover, ISAT technique provides gains, in terms of computational time, of up to 80 % when compared with the direct integration of the full chemical kinetics. However, in terms of memory usage the present implementation of ISAT technique is found to be excessively demanding.


Thermochemistry reduction In situ adaptive tabulation Stirred reactor simulation Detailed reaction mechanism 



The authors acknowledge the support awarded to this research from CNPq, FAPERJ, ANP and Brazilian Combustion Network. The authors are indebted to Professor Guenther Carlos Krieger Filho from Universidade de São Paulo (USP), for providing the code that served as example to the code developed in this work, and for his hospitality during the authors' visit to USP. This work was performed while the second author was on leave from Institut Pprime, CNRS, France.


  1. 1.
    Andrade FO (2009) Contribuition to the large eddy simulation of a turbulent premixed flame stabilized in a high speed flow. D.Sc. Thesis, Pontifícia Universidade Católica do Rio de Janeiro (in Portuguese)Google Scholar
  2. 2.
    Andrade FO, Figueira da Silva LF, Mura A (2011) Large eddy simulation of turbulent premixed combustion at moderate Damköhler numbers stabilized in a high-speed flow. Combust Sci Technol 183:645–664. doi: 10.1080/00102202.2010.536600 CrossRefGoogle Scholar
  3. 3.
    Chen JY, Chang WC, Koszykowski M (1995) Numerical simulation and scaling of NO X emissions from turbulent hydrogen jet flames with various amounts of helium dilution. Combust Sci Technol 110–111(1):505–529. doi: 10.1080/00102209508951938 CrossRefGoogle Scholar
  4. 4.
    Correa SM (1993) Turbulence-chemistry interactions in the intermediate regime of premixed combustion. Combust Flame 93(1–2):41–60. doi: 10.1016/0010-2180(93)90083-F CrossRefGoogle Scholar
  5. 5.
    Cunha Jr A (2010) Reduction of complexity in combustion thermochemistry. M.Sc. Dissertation, Pontifícia Universidade Católica do Rio de JaneiroGoogle Scholar
  6. 6.
    Figueira da Silva LF, Deshaies B (2000) Stabilization of an oblique detonation wave by a wedge: a parametric numerical study. Combust Flame 121:152–166. doi: 10.1016/S0010-2180(99)00141-8 CrossRefGoogle Scholar
  7. 7.
    Fox RO (2003) Computational models for turbulent reacting flows. Cambridge University Press, CambridgeGoogle Scholar
  8. 8.
    Frank-Kamenetskii DA (1940) Conditions for the applicability of the Bodenstein method in chemical kinetics. Zhurnal Fizicheskoy Himii 14:695–700 (in Russian)Google Scholar
  9. 9.
    Gardiner W (2000) Gas Phase Combustion Chemistry, Springer, New YorkGoogle Scholar
  10. 10.
    Golub GH, Van Loan CF (1996) Matrix computations. 3rd edn. John Hopkins University Press, BaltimoreGoogle Scholar
  11. 11.
    Holmes P, Lumley JL, Berkooz G (1998) Turbulence, coherent structures, dynamical systems and symmetry. Cambridge University Press, CambridgeGoogle Scholar
  12. 12.
    Ihme M, Schmitt C, Pitsch H (2009) Optimal artificial neural networks and tabulation methods for chemistry representation in LES of a bluff-body swirl-stabilized flame. Proc Combust Inst 32(1):1527–1535. doi: 10.1016/j.proci.2008.06.100
  13. 13.
    Keck J (1990) Rate-controlled constrained-equilibrium theory of chemical reactions in complex systems. Progress Energy Combust Sci 16(2):125–154. doi: 10.1016/0360-1285(90)90046-6 CrossRefMathSciNetGoogle Scholar
  14. 14.
    Knuth DE (1998) The art of computer programming. Sorting and searching, vol 3, 2nd edn. Addison-Wesley Professional, BostonGoogle Scholar
  15. 15.
    Lam SH, Goussis DA (1994) The CSP method for simplifying kinetics. Int J Chem Kinetics 26(4):461–486. doi: 10.1002/kin.550260408 CrossRefGoogle Scholar
  16. 16.
    Law CK (2006) Combustion physics. Cambridge University Press, New YorkGoogle Scholar
  17. 17.
    Liu BJD, Pope SB (2005) The performance of in situ adaptive tabulation in computations of turbulent flames. Combust Theory Model 9(4):549–568. doi: 10.1080/13647830500307436 CrossRefzbMATHGoogle Scholar
  18. 18.
    Lu L, Pope SB (2009) An improved algorithm for in situ adaptive tabulation. J Comput Phys 228(2):361–386. doi: 10.1016/ CrossRefzbMATHMathSciNetGoogle Scholar
  19. 19.
    Maas U, Pope SB (1992) Simplifying chemical kinetics: intrinsic low-dimensional manifolds in composition space. Combust Flame 88(3–4):239–264. doi: 10.1016/0010-2180(92)90034-M CrossRefGoogle Scholar
  20. 20.
    Orbegoso EM, Romeiro C, Ferreira S, Figueira da Silva LF (2011 a) Emissions and thermodynamic performance simulation of an industrial gas turbine. J Propuls Power 27:78–93. doi: 10.2514/1.47656 CrossRefGoogle Scholar
  21. 21.
    Orbegoso EMM, Figueira da Silva LF, Novgorodcev Jr AR (2011 b) On the predictability of chemical kinetics for the description of the combustion of simple fuels. J Brazilian Soc Mech Sci Eng 33:492–505. doi: 10.1590/S1678-58782011000400013 Google Scholar
  22. 22.
    Pimentel CAR, Azevedo JLF, Figueira da Silva LF, Deshaies B (2002) Numerical study of wedge supported oblique shock wave-oblique detonation wave transitions. J Brazilian Soc Mech Sci Eng 24:149–157. doi: 10.1590/S0100-73862002000300002 Google Scholar
  23. 23.
    Pope SB (1985) PDF methods for turbulent reactive flows. Progress Energy Combust Sci 11(2):119–192. doi: 10.1016/0360-1285(85)90002-4 CrossRefGoogle Scholar
  24. 24.
    Pope SB (1997) Computationally efficient implementation of combustion chemistry using in situ adaptive tabulation. Combust Theory Model 1(1):41–63. doi: 10.1080/713665229 CrossRefzbMATHMathSciNetGoogle Scholar
  25. 25.
    Pope SB (2008) Algorithms for Ellipsoids. Tech. Rep. FDA-08-01, Cornell University, IthacaGoogle Scholar
  26. 26.
    Ren Z, Pope SB, Vladimirsky A, Guckenheimer JM (2006) The invariant constrained equilibrium edge preimage curve method for the dimension reduction of chemical kinetics. J Chem Phys 124(11):114,111. doi: 10.1063/1.2177243
  27. 27.
    Sabel’nikov V, Figueira da Silva LF (2002) Partially stirred reactor: study of the sensitivity of the Monte-Carlo simulation to the number of stochastic particles with the use of a semi-analytic, steady-state, solution to the PDF equation. Combust Flame 129:164–178. doi: 10.1016/S0010-2180(02)00336-X
  28. 28.
    Sabel’nikov V, Deshaies B, Figueira da Silva LF (1998) Revisited flamelet model for nonpremixed combustion in supersonic turbulent flows. Combust Flame 114:577–584. doi: 10.1016/S0010-2180(97)00296-4 Google Scholar
  29. 29.
    Singer MA, Pope SB (2004) Exploiting ISAT to solve the reaction-diffusion equation. Combust Theory Model 8(2):361–383. doi: 10.1088/1364-7830/8/2/009 CrossRefzbMATHMathSciNetGoogle Scholar
  30. 30.
    Smith GP, Golden DM, Frenklach M, Moriarty NW, Eiteneer B, Goldenberg M, Bowman CT, Hanson RK, Song S, Gardiner WC, Lissianski VV, Qin Z GRI mechanism.
  31. 31.
    Tonse SR, Moriarty NW, Brown NJ, Frenklach M (1999) PRISM: piece-wise reusable implementation of solution mapping. an economical strategy for chemical kinetics. Israel J Chem 39(1):97–106CrossRefGoogle Scholar
  32. 32.
    Turányi T (1994) Application of repro-modeling for the reduction of combustion mechanisms. Symp Combust 25(1):949–955. doi: 10.1016/S0082-0784(06)80731-9 CrossRefGoogle Scholar
  33. 33.
    Vedovoto JM (2011) Mathematical and numerical modeling of turbulent reactive flows using a hybrid LES/PDF methodology. D.Sc. Thesis, Universidade Federal de UberlândiaGoogle Scholar
  34. 34.
    Vedovoto JM, Silveira Neto A, Mura A, Figueira da Silva LF (2011) Application of the method of manufactured solutions to the verification of a pressure-based finite-volume numerical scheme. Comput Fluids 51:85–99. doi: 10.1016/j.compfluid.2011.07.014 Google Scholar
  35. 35.
    Walter MAT, Figueira da Silva LF (2006) Numerical study of oblique detonation wave stabilization by finite length wedges. AIAA J 44:353–361. doi: 10.2514/1.12417 Google Scholar
  36. 36.
    Williams FA (1985) Combustion theory, 2nd edn. Wesley, CambridgeGoogle Scholar
  37. 37.
    Yang B, Pope SB (1998) An investigation of the accuracy of manifold methods and splitting schemes in the computational implementation of combustion chemistry. Combust Flame 112(1–2):16–32. doi: 10.1016/S0010-2180(97)81754-3 CrossRefGoogle Scholar

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2013

Authors and Affiliations

  • Americo Cunha Jr
    • 1
    Email author
  • Luís Fernando Figueira da Silva
    • 1
  1. 1.Department of Mechanical EngineeringPontifícia Universidade Católica do Rio de JaneiroRio de JaneiroBrasil

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