Evaluation of the discretization in the spectral resolution for the solution of the line-by-line method in problems with participating gases

  • Aline ZiemniczakEmail author
  • Felipe Ramos Coelho
  • Fernando Marcelo Pereira
  • Paulo Roberto Pagot
  • Francis Henrique Ramos França
Technical Paper


Despite the complexity to solve problems involving radiation heat transfer in participating media, especially due to the strong spectral dependence of the absorption coefficient, thermal radiation cannot be neglected in several applications, such as in combustion processes. This study proposes modeling of the spectral absorption coefficient by means of line-by-line integration method (LBL), which can take into account in full detail the complex spectral dependence of the absorption coefficient. The HITEMP 2010 database is used to generate the absorption cross-sections. An evaluation as to the spectral resolution for the LBL integration is performed; the results show that, even for a considerably low spectral refinement, the LBL can still provide accurate results. The lower spectral resolutions are obtained through a methodology to reduce the LBL spectral discretization based on a reference spectrum, which contributes significantly to the satisfactory accuracy reported in this study. The analysis is applied to a set of one-dimensional, non-isothermal medium slabs. In this way, the LBL integration gains space to solve more complex engineering problems with viable computational time and may even be a viable alternative to the use of simpler spectral models such as SLW, WSGG, among others.


Thermal radiation Participating gas model HITEMP LBL integration Spectral resolution 



  1. 1.
    Rothman LS, Gordon IE, Babikov Y, Barde A, Chris Benner D, Bernath PF, Birk M, Bizzocchi L, Boudon V, Brown LR, Campargue A, Chance K, Cohen EA, Coudert LH, Devi VM, Drouin BJ, Fayt A, Flaud J-M, Gamache RR, Harrison JJ, Hartmann J-M, Hill C, Hodges JT, Jacquemart D, Jolly A, Lamouroux J, Le Roy RJ, Li G, Long DA, Lyulin OM, Mackie CJ, Massie ST, Mikhailenko S, Müller HSP, Naumenko OV, Nikitin AV, Orphal J, Perevalov V, Perrin A, Polovtseva ER, Richard C, Smith MAH, Starikova E, Sung K, Tashkun S, Tennyson J, Toon GC, Tyuterev VLG, Wagner G (2013) The HITRAN 2012 molecular spectroscopic database. J Quant Spectrosc Radiat Transf 130:4–50CrossRefGoogle Scholar
  2. 2.
    Rothman LS, Gordon IE, Barber RJ, Dothe H, Gamache RR, Goldman A, Perevalov VI, Tashkun SA, Tennyson J (2010) HITEMP, the high-temperature molecular spectroscopic database. J Quant Spectrosc Radiat Transf 111:2139–2150CrossRefGoogle Scholar
  3. 3.
    Chu H, Liu F, Zhou H (2011) Calculations of gas thermal radiation transfer in one-dimensional planar enclosure using LBL and SNB models. Int J Heat Mass Transf 54:4736–4745CrossRefGoogle Scholar
  4. 4.
    Rivière P, Soufiani A (2012) Updated band model parameters for H2O, CO2, CH4 and CO radiation at high temperature. Int J Heat Mass Transf 55(13–14):3349–3358CrossRefGoogle Scholar
  5. 5.
    Pearson JT, Webb BW, Solovjova VP, Ma J (2013) Updated correlation of the absorption line blackbody distribution function for H2O based on the HITEMP2010 database. J Quant Spectrosc Radiat Transf 128:10–17CrossRefGoogle Scholar
  6. 6.
    Pearson JT, Webb BW, Solovjova VP, Ma J (2014) Efficient representation of the absorption line blackbody distribution function for H2O, CO2, and CO at variable temperature, mole fraction, and total pressure. J Quant Spectrosc Radiat Transf 138:82–96CrossRefGoogle Scholar
  7. 7.
    Pearson JT, Webb BW, Solovjova VP, Ma J (2014) Effect of total pressure on the absorption line blackbody distribution function and radiative transfer in H2O, CO2, and CO. J Quant Spectrosc Radiat Transf 143:100–110CrossRefGoogle Scholar
  8. 8.
    Liu F, Chu H, Zhou H, Smallwood GJ (2013) Evaluation of the absorption line blackbody distribution function of CO2 and H2O using the proper orthogonal decomposition and hyperbolic. J Quant Spectrosc Radiat Transf 128:27–33CrossRefGoogle Scholar
  9. 9.
    Modest MF, Zhang H (2002) The full-spectrum correlated-k distribution for thermal radiation from molecular gas-particulates mixtures. J Heat Transf 124:30–38CrossRefGoogle Scholar
  10. 10.
    Modest MF, Singh V (2005) Engineering correlations for full spectrum k-distribution of H2O from HITEMP spectroscopic databank. J Quant Spectrosc Radiat Transf 93:263–271CrossRefGoogle Scholar
  11. 11.
    Cai J, Modest MF (2014) Improved full-spectrum k-distribution implementation for inhomogeneous media using a narrow-band database. J Quant Spectrosc Radiat Transf 141:65–72CrossRefGoogle Scholar
  12. 12.
    Kangwanpongpan T, França FHR, da Silva RC, Schneider PS, Krautz HJ (2012) New correlations for the weighted-sum-of-gray-gases model in oxy-fuel conditions based on HITEMP 2010 database. Int J Heat Mass Transf 55:7419–7433CrossRefGoogle Scholar
  13. 13.
    Dorigon LJ, Duciak G, Brittes R, Cassol F, Galarça M, França FHR (2013) WSGG Correlations based on HITEMP2010 for computation of termal radiation in non-isotheral, non-homogeneous H2O/CO2 mixtures. Int J Heat Mass Transf 64:863–873CrossRefGoogle Scholar
  14. 14.
    Cassol F, Brittes R, França FHR, Ezekoye OO (2014) Application of the weighted-sum-of-gray-gases model for media composed of arbitrary concentrations of H2O, CO2 and soot. Int J Heat Mass Transf 79:796–806CrossRefGoogle Scholar
  15. 15.
    Bordbar MH, Wecel G, Hyppänen T (2014) A line by line based weighted sum of gray gases model for inhomogeneous CO2–H2O mixture in oxy-fired combustion. Combust Flame 161:2435CrossRefGoogle Scholar
  16. 16.
    Guo J, Li X, Huang X, Liu Z, Zheng C (2015) A full spectrumk-distribution based weighted-sum-of-gray-gases model for oxy-fuel combustion. Int J Heat Mass Transf 90:218–226CrossRefGoogle Scholar
  17. 17.
    Brittes R, Centeno FR, Ziemniczak A, França FHR (2017) WSGG model correlations to compute non-gray radiation from carbon monoxide in combustion applications. J Heat Transfer 139:863–873CrossRefGoogle Scholar
  18. 18.
    Centeno FR, Brittes R, Rodrigues LGP, Coelho FC, França FHR (2018) Evaluation of the WSGG model against line-by-line calculation of thermal radiation in a non-gray sooting medium representing an axisymmetric laminar jet flame. Int J Heat Mass Transf 124:475–483CrossRefGoogle Scholar
  19. 19.
    Modest MF (2013) Radiative heat transfer, 3rd edn. Academic Press, New YorkGoogle Scholar
  20. 20.
    Chu H, Consalvi JL, Gu M, Liu F (2017) Calculations of radiative heat transfer in an axisymmetric jet diffusion flame at elevated pressures using different gas radiation models. J Quant Spectrosc Radiat Transf 197:12–25CrossRefGoogle Scholar
  21. 21.
    Chu H, Gu M, Consalvi J, Liu F, Zhou H (2016) Effects of total pressure on non-grey gas radiation transfer in oxy-fuel combustion using the LBL, SNB, SNBCK, WSGG, and FSCK methods. J Quant Spectrosc Radiat Transf 172:24–35CrossRefGoogle Scholar
  22. 22.
    Chu H, Ren F, Feng Y, Gu M, Zheng S (2017) A comprehensive evaluation of the non gray gas thermal radiation using the line-by-line model in one- and two-dimensional enclosures. Appl Therm Eng 124:362–370CrossRefGoogle Scholar
  23. 23.
    Siegel R, Howell J (2002) Thermal Radiation Heat transfer, 4th edn. Taylor and Francis, New YorkGoogle Scholar

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringFederal University of Rio Grande do SulPorto AlegreBrazil
  2. 2.CENPES/PDEP/TPP – PETROBRASPetróleo Brasileiro S. A.Rio de JaneiroBrazil

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