Applied Physics B

, Volume 119, Issue 4, pp 577–606 | Cite as

Modeling laser-induced incandescence of soot: a new approach based on the use of inverse techniques

  • Romain Lemaire
  • Mohammed Mobtil


Two LII models derived from the literature have been tested to simulate signals provided in a recently published extensive set of experimental data collected in a non-smoking laminar diffusion flame of ethylene. The first model classically accounts for particle heating by absorption and cooling by radiation, sublimation and conduction. The second one also integrates an alternative absorption term that accounts for saturation of the linear, single-photon and multi-photon absorption leading to C2-photodesorption at high fluence, a heating flux attributable to oxidation and a cooling process based on thermionic emission. Obtained results illustrate that both models fail to reproduce the LII signals experimentally monitored on a wide range of fluences (up to ~1 J cm−2) regardless of the value implemented for the main parameters involved in the energy- and mass-balance equations. We therefore originally proposed a new modeling approach based on the use of inverse techniques to gain information about the specific terms that should be integrated into the calculation. The inverse procedure allows inferring the temporal evolution of the soot diameter as well as the temporal and fluence dependence of additional energy rates that have to be considered to fulfill the particle energy and mass balances while providing a complete fit with experimental data. Conclusions issued from the present work indicate that modeling soot LII using only absorption, radiation, conduction and sublimation rates (as these fluxes are generally expressed and computed in the literature) is inadequate to correctly simulate the soot heating and cooling mechanisms over a wide range of fluences. The inverse modeling procedure also gave insights concerning the relevance of integrating photolytic mechanisms such as multi-photon absorption and carbon cluster photodesorption as previously proposed by Michelsen. Additional calculations performed using a new model formulation integrating such processes finally led to predictions merging on a single curve with experimental data. Additional works should be undertaken, however, to complete this first-approach analysis especially to address the large uncertainties existing in the input parameters and equations accounting for photolytic processes that are likely to significantly impact soot LII.


Carbon Cluster Soot Volume Fraction Sublimation Rate Soot Temperature Thermal Accommodation Coefficient 
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.



This study was supported by ARMINES, the French ANR (Agence Nationale pour la Recherche) and the Carnot M.I.N.E.S. Institute.


  1. 1.
    C.A. Pope III, R.T. Burnett, G.D. Thurston, M.J. Thun, E.E. Calle, D. Krewski, J.J. Godleski, Circulation 109, 71 (2004)CrossRefGoogle Scholar
  2. 2.
    M.Z. Jacobson, Nature 409, 695 (2001)CrossRefADSGoogle Scholar
  3. 3.
    R.F. Service, Science 319, 1745 (2008)CrossRefGoogle Scholar
  4. 4.
    H. Richter, J.B. Howard, Prog. Eng. Combust. Sci. 26, 565 (2000)CrossRefGoogle Scholar
  5. 5.
    C.S. McEnally, L.D. Pfefferle, B. Atakan, K. Kohse-Höinghaus, Proc. Eng. Combust. Sci. 32, 247 (2006)CrossRefGoogle Scholar
  6. 6.
    H. Wang, Proc. Combust. Inst. 33, 41 (2011)CrossRefGoogle Scholar
  7. 7.
    P. Desgroux, X. Mercier, K.A. Thomson, Proc. Combust. Inst. 34, 1713 (2013)CrossRefGoogle Scholar
  8. 8.
    C. Schulz, B.F. Kock, M. Hofmann, H. Michelsen, S. Will, B. Bougie, R. Suntz, G. Smallwood, Appl. Phys. B 83, 333 (2006)CrossRefADSGoogle Scholar
  9. 9.
    L.A. Melton, Appl. Opt. 23, 2201 (1984)CrossRefADSGoogle Scholar
  10. 10.
    N.P. Tait, D.A. Greenhalgh, Berichte der Bunsengesellschaft fuer Physikalische Chemie 97, 1619 (1993)CrossRefGoogle Scholar
  11. 11.
    R.L. Vander Wal, K.J. Weiland, Appl. Phys. B 59, 445 (1994)CrossRefADSGoogle Scholar
  12. 12.
    T. Ni, J.A. Pinson, S. Gupta, R.J. Santoro, Appl. Opt. 34, 7083 (1995)CrossRefADSGoogle Scholar
  13. 13.
    C.R. Shaddix, K.C. Smyth, Combust. Flame 107, 418 (1996)CrossRefGoogle Scholar
  14. 14.
    R.L. Vander, Wal. Proc. Combust. Inst. 27, 59 (1998)CrossRefGoogle Scholar
  15. 15.
    C. Schoemaecker Moreau, E. Therssen, X. Mercier, J.F. Pauwels, P. Desgroux, Appl. Phys. B 78, 485 (2004)CrossRefADSGoogle Scholar
  16. 16.
    P. Desgroux, X. Mercier, B. Lefort, R. Lemaire, E. Therssen, J.F. Pauwels, Combust. Flame 155, 289 (2008)CrossRefGoogle Scholar
  17. 17.
    R.L. Vander Wal, T.M. Ticich, A.B. Stephens, Combust. Flame 116, 291 (1999)CrossRefGoogle Scholar
  18. 18.
    H. Bladh, J. Johnsson, P.-E. Bengtsson, Appl. Phys. B 96, 645 (2009)CrossRefADSGoogle Scholar
  19. 19.
    H. Bladh, J. Johnsson, N.-E. Olofsson, A. Bohlin, P.-E. Bengtsson, Proc. Combust. Inst. 33, 641 (2011)CrossRefGoogle Scholar
  20. 20.
    S. Will, S. Schraml, A. Leipertz, Opt. Lett. 20, 2342 (1995)CrossRefADSGoogle Scholar
  21. 21.
    S. Will, S. Schraml, K. Bader, A. Leipertz, Appl. Opt. 37, 5647 (1998)CrossRefADSGoogle Scholar
  22. 22.
    H.A. Michelsen, P.O. Witze, D. Kayes, S. Hochgreb, Appl. Opt. 42, 5577 (2003)CrossRefADSGoogle Scholar
  23. 23.
    R. Hadef, K.P. Geigle, W. Meier, M. Aigner, Int. J. Thermal Sci. 49, 1457 (2010)CrossRefGoogle Scholar
  24. 24.
    J. Reimann, S.A. Kuhlmann, S. Will, Appl. Phys. B 96, 583 (2009)CrossRefADSGoogle Scholar
  25. 25.
    E. Therssen, Y. Bouvier, C. Schoemaecker Moreau, X. Mercier, P. Desgroux, M. Ziskind, C. Focsa, Appl. Phys. B 89, 417 (2007)CrossRefADSGoogle Scholar
  26. 26.
    H.A. Michelsen, P.E. Schrader, F. Goulay, Carbon 48, 2175 (2010)CrossRefGoogle Scholar
  27. 27.
    H.A. Michelsen, P.E. Schrader, F. Goulay, Carbon 50, 740 (2012)CrossRefGoogle Scholar
  28. 28.
    J. Yon, R. Lemaire, E. Therssen, P. Desgroux, A. Coppalle, K.F. Ren, Appl. Phys. B 104, 253 (2011)CrossRefADSGoogle Scholar
  29. 29.
    S. Bejaoui, R. Lemaire, E. Therssen, P. Desgroux, Appl. Phys. B 116, 313 (2014)CrossRefADSGoogle Scholar
  30. 30.
    D.R. Snelling, F. Liu, G.J. Smallwood, Ö.L. Gülder, Combust. Flame 136, 180 (2004)CrossRefGoogle Scholar
  31. 31.
    X. Lopez-Yglesias, P.E. Schrader, H.A. Michelsen, J. Aerosol Sci. 75, 43 (2014)CrossRefGoogle Scholar
  32. 32.
    H.A. Michelsen, F. Liu, B.F. Kock, H. Bladh, A. Boiarciuc, M. Charwath, T. Dreier, R. Hadef, M. Hofmann, J. Reimann, S. Will, P.-E. Bengtsson, H. Bockhorn, F. Foucher, K.-P. Geigle, C. Mounaïm-Rousselle, C. Schulz, R. Stirn, B. Tribalet, R. Suntz, Appl. Phys. B 87, 503 (2007)CrossRefADSGoogle Scholar
  33. 33.
    H.A. Michelsen, J. Chem. Phys. 118, 7012 (2003)CrossRefADSGoogle Scholar
  34. 34.
    G.J. Smallwood, D.R. Snelling, F. Liu, Ö.L. Gülder, J. Heat Transfer 123, 814 (2001)CrossRefGoogle Scholar
  35. 35.
    F. Liu, K.J. Daun, D.R. Snelling, G.J. Smallwood, Appl. Phys. B 83, 355 (2006)CrossRefADSGoogle Scholar
  36. 36.
    H. Bladh, J. Johnsson, P.-E. Bengtsson, Appl. Phys. B 90, 109 (2008)CrossRefADSGoogle Scholar
  37. 37.
    H. Bladh, P.-E. Bengtsson, Appl. Phys. B 78, 241 (2004)CrossRefADSGoogle Scholar
  38. 38.
    D.R. Snelling, F. Liu, G.J. Smallwood, Ö.L. Gülder, Proceeding of NHTC 2000, 34th Natural Heat Transfer Conference, Pittsburgh, PA, 20–22 August 2000Google Scholar
  39. 39.
    H. Bladh, P.-E. Bengtsson, J. Delhay, Y. Bouvier, E. Therssen, P. Desgroux, Appl. Phys. B 83, 423 (2006)CrossRefADSGoogle Scholar
  40. 40.
    D.J. Krajnovich, J. Chem. Phys. 102, 726 (1995)CrossRefADSGoogle Scholar
  41. 41.
    C.B. Stipe, J.H. Choi, D. Lucas, C.P. Koshland, R.F. Sawyer, J. Nanopart. Res. 6, 467 (2004)CrossRefGoogle Scholar
  42. 42.
    H.A. Michelsen, M.A. Linne, B.F. Kock, M. Hofmann, B. Tribalet, C. Schulz, Appl. Phys. B 93, 645 (2008)CrossRefADSGoogle Scholar
  43. 43.
    H.A. Michelsen, Appl. Phys. B 94, 103 (2009)CrossRefADSGoogle Scholar
  44. 44.
    F. Goulay, P.E. Schrader, X. López-Yglesias, H.A. Michelsen, Appl. Phys. B 112, 287 (2013)CrossRefADSGoogle Scholar
  45. 45.
    D.L. Hofeldt, SAE Technical Paper 930079 (1993). doi: 10.4271/930079
  46. 46.
    F. Liu, D.R. Snelling, Appl. Phys. B 89, 115 (2007)CrossRefADSGoogle Scholar
  47. 47.
    L.E. Fried, W.M. Howard, Phys. Rev. B 61, 8734 (2000)CrossRefADSGoogle Scholar
  48. 48.
    T.L. Farias, Ü.Ö. Köylü, M.G. Carvalho, Appl. Opt. 35, 6560 (1996)CrossRefADSGoogle Scholar
  49. 49.
    C.F. Bohren, D.R. Huffman, Absorption and scattering of light by small particles, ISBN 978-0-471-29340-8, Wiley-VCH (2004)Google Scholar
  50. 50.
    D.R. Snelling, K.A. Thomson, G.J. Smallwood, Ö.L. Gülder, E.J. Weckman, R.A. Fraser, AIAA J. 40, 1789 (2002)CrossRefADSGoogle Scholar
  51. 51.
    W.H. Dalzell, A.F. Sarofim, J. Heat Transfer 91, 100 (1969)CrossRefGoogle Scholar
  52. 52.
    S.C. Lee, C.L. Tien, Proc. Combust. Inst. 18, 1159 (1981)CrossRefGoogle Scholar
  53. 53.
    Z.G. Habib, P. Vervisch, Combust. Sci. Technol. 59, 261 (1988)CrossRefGoogle Scholar
  54. 54.
    H. Chang, T.T. Charalampopoulos, Proc. R. Soc. Lond. A: Mathematical Phys. Sci. 430, 577 (1990)CrossRefGoogle Scholar
  55. 55.
    Ü.Ö. Köylü, G.M. Faeth, J. Heat Transfer 118, 415 (1996)CrossRefGoogle Scholar
  56. 56.
    Ü.Ö. Köylü, Combust. Flame 109, 488 (1996)CrossRefGoogle Scholar
  57. 57.
    A.C. Eckbreth, J. Appl. Phys. 48, 4473 (1977)CrossRefADSGoogle Scholar
  58. 58.
    E. Vietzke, A. Refke, V. Philipps, M. Hennes, J. Nucl. Mater. 241–243, 810 (1997)CrossRefGoogle Scholar
  59. 59.
    V.I. Bukatyi, E.P. Zhdanov, A.M. Shaiduk, Combust. Explo. Shock. 18, 309 (1982)CrossRefGoogle Scholar
  60. 60.
    V.I. Bukatyi, I.A. Sutorikhin, A.M. Shaiduk, Combust. Explo. Shock. 19, 69 (1983)CrossRefGoogle Scholar
  61. 61.
    V.I. Bukatyi, V.N. Krasnopevtsev, A.M. Shaiduk, Explo. Shock. 24, 37 (1988)CrossRefGoogle Scholar
  62. 62.
    B.J. McCoy, C.Y. Cha, Chem. Eng. Sci. 29, 381 (1974)CrossRefGoogle Scholar
  63. 63.
    M.W. Chase Jr, C.A. Davies, J.R. Downey Jr, D.J. Frurip, R.A. McDonald, A.N. Syverud, J. Phys. Chem. Ref. Data 14, 1 (1985)CrossRefGoogle Scholar
  64. 64.
    K.J. Daun, Int. J. Heat Mass Transfer 52, 5081 (2009)CrossRefzbMATHGoogle Scholar
  65. 65.
    J. Nagle, R.F. Strickland-constable, Proceeding in Fifth Conference Carbon, 154 (1962)Google Scholar
  66. 66.
    J.R. Walls, R.F. Strickland-Constable, Carbon 1, 333 (1964)CrossRefGoogle Scholar
  67. 67.
    R. Hiers, J. thermophysics Heat Transfer 11, 232 (1997)CrossRefGoogle Scholar
  68. 68.
    K.R. McManus, J.H. Frank, M.G. Allen, W.T. Rawlins, Proc. AIAA 36, 98 (1998)Google Scholar
  69. 69.
    E. Hairer, G. Wanner, Solving ordinary differential equations II: stiff and differential-algebraic problems, Springer Series in Computational Mathematics, 144, Springer, Berlin Heidelberg, ISBN: 978-642-05220-0 (1996)Google Scholar
  70. 70.
    H. Bladh, On the use of laser-induced incandescence for soot diagnostics, PhD Thesis, Lund University, Lund Reports on Combustion Physics, LRCP 119, Lund, Sweden, ISBN 978-91-628-7142-0 (2007)Google Scholar
  71. 71.
    L.O. Jay, SIAM J. Numer. Anal. 38, 1369 (2000)CrossRefzbMATHMathSciNetGoogle Scholar
  72. 72.
    M. Mobtil, R. Lemaire, Fifth International Workshop on Laser-induced Incandescence, Vol. 865, paper no. 16, Ed. CEUR Workshop Proceedings, ISSN: 1613-0073 (2012)Google Scholar
  73. 73.
    M. Mobtil, R. Lemaire, 34th International symposium on combustion (Warsaw University of Technology, Warsaw, 2012)Google Scholar
  74. 74.
    R. Lemaire, M. Mobtil, Rec. Prog. Gen. Proc., 104, Ed. SFGP, Paris, France, ISBN: 978-910239-78-7 (2013)Google Scholar
  75. 75.
    A. Kirsch, An introduction to the mathematical theory of inverse problems, Applied Mathematical Sciences, 120, Springer-Verlag, New York, ISBN 978-1-4419-8473-9 (2011)Google Scholar
  76. 76.
    J.V. Beck, B. Blackwell, C.R. St. Clair: inverse heat conduction: Ill posed problems, Wiley, New York, ISBN 978-0-471-08319-1 (1985)Google Scholar
  77. 77.
    O.M. Alifanov, Inverse heat transfer problems, international series in heat and mass transfer, Springer, Berlin Heidelberg, ISBN: 978-3-642-76438-7 (1994)Google Scholar
  78. 78.
    C.T. Kelley, Iterative methods for optimization, Frontiers in Applied Mathematics, 18, Society for Industrial and Applied Mathematics, ISBN: 978-0-898714-33-3 (1999)Google Scholar
  79. 79.
    M.N. Özisik, H.R.B. Orlande, Inverse heat transfer, fundamentals and applications, Taylor & Francis, New York, ISBN 1-56032-838-X (2000)Google Scholar
  80. 80.
    S.S. Rao, Engineering optimization, theory and practice, 4th edition, Wiley, Hoboken, ISBN 978-0-470-18352-6 (2009)Google Scholar
  81. 81.
    W.C. Davidon, SIAM J. Optim. 1, 1 (1991)CrossRefzbMATHMathSciNetGoogle Scholar
  82. 82.
    L. Lukšan, E. Spedicato, J. Comput. Appl. Math. 124, 61 (2000)CrossRefADSzbMATHMathSciNetGoogle Scholar
  83. 83.
    F. Kowsary, A. Behbahaninia, A. Pourshaghaghy, Int. Commun. Heat Mass Transfer 33, 800 (2006)CrossRefGoogle Scholar
  84. 84.
    Z.Z. Zhang, D.H. Cao, J.P. Zeng, Appl. Math. Lett. 17, 437 (2004)CrossRefMathSciNetGoogle Scholar
  85. 85.
    C.M. Murea, Comput. Math Appl. 49, 171 (2005)CrossRefzbMATHMathSciNetGoogle Scholar
  86. 86.
    C.R. Vogel, Computational methods for inverse problems, frontiers in applied mathematics, society for industrial and applied mathematics, ISBN: 978-0-89871-550-7 (2002)Google Scholar
  87. 87.
    A.G. Ramm, Inverse problems, mathematical and analytical techniques with applications to engineering, Springer, New York, ISBN: 978-0321070746 (2005)Google Scholar
  88. 88.
    H.A. Michelsen, A.V. Tivanski, M.K. Gilles, L.H. Van Poppel, M.A. Dansson, P.R. Buseck, Appl. Opt. 46, 959 (2007)CrossRefADSGoogle Scholar
  89. 89.
    F. Gouley, P.E. Schrader, L. Nemes, M.A. Dansson, H.A. Michelsen, Proc. Comb. Inst. 32, 963 (2009)CrossRefGoogle Scholar
  90. 90.
    J. Yon, F. Liu, A. Bescond, C. Caumont-Prim, C. Rozé, F.X. Ouf, A. Coppalle, J. Quant. Spectrosc. Radiat. Transf. 133, 374 (2014)CrossRefADSGoogle Scholar
  91. 91.
    R.P. Bambha, M.A. Dansson, P.E. Schrader, H.A. Michelsen, Appl. Phys. B 112, 343 (2013)CrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Département Energétique IndustrielleEcole des Mines de DouaiDouai CedexFrance

Personalised recommendations