# Planck Mean Absorption Coefficients of H2O, CO2, CO and NO for radiation numerical modeling in combusting flows

### Abstract

TheWeighted-Sum-of-Gray-Gases Model (WSGGM), based on temperature dependent weighting factors, is an ecientmethod of determining the absorption coecients in numerical modeling of combusting flows. Weighting factors areobtained by polynomial fitting of experimental data for only two reagents (H2O and CO2) to the analytical equationfor emissivity. In this article the use of Planck Mean Absorption Coecients (PMAC) for H2O, CO2, CO and NOin combustion numerical modeling is proposed. The aim of the PMAC approach is to improve the initial solutionof temperature and species mass fraction profiles in numerical modeling of non-premixed methane combustion. Theproposed model is verified against the results of turbulent, non-premixed methane combustion experimental data. Theimplemented PMAC model represents the flue gas composition and temperature more accurately than the WSGGM.### References

[1] C. E. Baukal, Heat Transfer in Industrial Combustion. CRC Press, 2000.

[2] A.W. Lefebvre, Gas Turbine Combustion, Taylor & Francis, 1999.

[3] A. Schultz, Convective and radiative heat transfer in Combustors, Institute für Thermische Stromungsmachinen, Universitat Karlsruhe.

[4] S. Matarazzo, H. Laget, Modelling of the heat transfer in a gas turbine liner combustor, Chia Laguna, Italy, September 2011.

[5] V.S. Arpaci, R.J. Tabaczynski, Radiation-Affected Laminar Flame Propagation, Combustion and flame, 46, 1982, pp 315-322.

[6] H. Brocklehurst, J. Moss, C. Hurley, Scot and Radiation Modeling in Gas Turbine Combustion Chambers, Rolls-Royce plc, 1999.

[7] R.A. Cookson, An investigation of heat transfer from flames, Ph.D. thesis, University of Leeds, Leeds, U.K., 1960.

[8] R.S. Barlow, A.N. Karpetis, J. H. Frank, J.-Y. Chen, Scalar Profiles and NO Formation in Laminar Opposed-Flow Partially Premixed Methane/Air Flames, Combustion and Flame, vol. 127: 2102-2118, 2001.

[9] W.L. Grosshandler, RADCAL: A Narrow-Band Model for Radiation Calculations in a Combustion Environment, NIST technical note 1402, 1993.

[10] X. L. Zhu, J. P. Gore, A. N. Karpetis, R. S. Barlow, The Effects of Self-Absorption of Radiation on an Opposed Flow Partially Premixed Flame, Combustion and Flame 129:342-345, 2002.

[11] L.S. Rothman, I.E. Gordon, A. Barbe, D. ChrisBenner, P.F. Bernath, M. Birk, V. Boudon, L.R. Brown, A. Campargue, J.P. Champion, K. Chance, L.H. Coudert, V. Danaj, V.M. Devi, S. Fally, J.-M. Flaud, R.R. Gamache, A. Goldmanm, D. Jacquemart, I. Kleiner, N. Lacome, W.J. Lafferty, J.-Y. Mandin, S.T. Massie, S.N. Mikhailenko, C.E. Miller, N. Moazzen-Ahmadi, O.V. Naumenko, A.V. Nikitin, J. Orphal, V.I. Perevalov, A. Perrin, A. Predoi-Cross, C.P. Rinsland, M. Rotger, M. Šimečková, M.A.H. Smith, K. Sung, S.A. Tashkun, J. Tennyson, R.A. Toth, A.C. Vandaele, J. VanderAuwera, The HITRAN 2008 molecular spectroscopic database, Journal of Quantitative Spectroscopy & Radiative Transfer 110, 2009, pp 533–572.

[12] P.A.M. Kalt, Y.M. Al-Abdeli, A.R. Masri, R.S. Barlow, Swirling Turbulent Non-premixed Flames of Methane: Flowfield and Compositional Structure, Proc. Combust. Inst. 29:1913-1919, 2002.

[13] Y.M. Al-Abdeli, A.R. Masri, Recirculation and Flow Field Regimes of Unconfined Non-Reacting Swirling Flows, Experimental Thermal and Fluid Sciences, 27(5), 2003, pp 655-665.

[14] Y.M. Al-Abdeli, A.R. Masri, Stability Characteristics and Flow Fields of Turbulent Swirling Jet Flows, Combust. Theory and Modeling, 7, 2003, pp 731-766.

[15] A.R. Masri, P.A.M. Kalt, R.S. Barlow, The Compositional Structure of Swirl-Stabilised Turbulent Non-premixed Flames, Combust. Flame, 137, 2004, pp 1-37.

[16] Y.M. Al-Abdeli, A.R. Masri, Precession and Recirculation in Turbulent Swirling Isothermal Jets, Combust. Sci. Technol. 176, 2004, pp. 645-665.

[17] ANSYS, Inc., ANSYS FLUENT 14 Theory Guide, November 2011.

[18] T. F. Smith, Z. F. Shen, J. N. Friedman, Evaluation of Coefficients for the Weighted Sum of Gray Gases Model, J. Heat Transfer. 104, 1982. pp 602–608.

[19] A. Coppalle, P. Vervisch, The Total Emissivities of High-Temperature Flames, Combustion and Flame 49,1983, pp 101–108.

[20] C. L. Tien, W. H. Giedt, Experimental determination of infrared absorption of high-temperature gases in Advances in Thermophysical Properties at extreme Temperatures and Pressures, ASME, 1965, pp. 167-173.

[21] The MathWorks, Inc., MATLAB: Data Analysis, September 2013.

[22] ANSYS, Inc., ANSYS FLUENT 14: ANSYS Fluid Dynamics Verification Manual, August 2011.

[2] A.W. Lefebvre, Gas Turbine Combustion, Taylor & Francis, 1999.

[3] A. Schultz, Convective and radiative heat transfer in Combustors, Institute für Thermische Stromungsmachinen, Universitat Karlsruhe.

[4] S. Matarazzo, H. Laget, Modelling of the heat transfer in a gas turbine liner combustor, Chia Laguna, Italy, September 2011.

[5] V.S. Arpaci, R.J. Tabaczynski, Radiation-Affected Laminar Flame Propagation, Combustion and flame, 46, 1982, pp 315-322.

[6] H. Brocklehurst, J. Moss, C. Hurley, Scot and Radiation Modeling in Gas Turbine Combustion Chambers, Rolls-Royce plc, 1999.

[7] R.A. Cookson, An investigation of heat transfer from flames, Ph.D. thesis, University of Leeds, Leeds, U.K., 1960.

[8] R.S. Barlow, A.N. Karpetis, J. H. Frank, J.-Y. Chen, Scalar Profiles and NO Formation in Laminar Opposed-Flow Partially Premixed Methane/Air Flames, Combustion and Flame, vol. 127: 2102-2118, 2001.

[9] W.L. Grosshandler, RADCAL: A Narrow-Band Model for Radiation Calculations in a Combustion Environment, NIST technical note 1402, 1993.

[10] X. L. Zhu, J. P. Gore, A. N. Karpetis, R. S. Barlow, The Effects of Self-Absorption of Radiation on an Opposed Flow Partially Premixed Flame, Combustion and Flame 129:342-345, 2002.

[11] L.S. Rothman, I.E. Gordon, A. Barbe, D. ChrisBenner, P.F. Bernath, M. Birk, V. Boudon, L.R. Brown, A. Campargue, J.P. Champion, K. Chance, L.H. Coudert, V. Danaj, V.M. Devi, S. Fally, J.-M. Flaud, R.R. Gamache, A. Goldmanm, D. Jacquemart, I. Kleiner, N. Lacome, W.J. Lafferty, J.-Y. Mandin, S.T. Massie, S.N. Mikhailenko, C.E. Miller, N. Moazzen-Ahmadi, O.V. Naumenko, A.V. Nikitin, J. Orphal, V.I. Perevalov, A. Perrin, A. Predoi-Cross, C.P. Rinsland, M. Rotger, M. Šimečková, M.A.H. Smith, K. Sung, S.A. Tashkun, J. Tennyson, R.A. Toth, A.C. Vandaele, J. VanderAuwera, The HITRAN 2008 molecular spectroscopic database, Journal of Quantitative Spectroscopy & Radiative Transfer 110, 2009, pp 533–572.

[12] P.A.M. Kalt, Y.M. Al-Abdeli, A.R. Masri, R.S. Barlow, Swirling Turbulent Non-premixed Flames of Methane: Flowfield and Compositional Structure, Proc. Combust. Inst. 29:1913-1919, 2002.

[13] Y.M. Al-Abdeli, A.R. Masri, Recirculation and Flow Field Regimes of Unconfined Non-Reacting Swirling Flows, Experimental Thermal and Fluid Sciences, 27(5), 2003, pp 655-665.

[14] Y.M. Al-Abdeli, A.R. Masri, Stability Characteristics and Flow Fields of Turbulent Swirling Jet Flows, Combust. Theory and Modeling, 7, 2003, pp 731-766.

[15] A.R. Masri, P.A.M. Kalt, R.S. Barlow, The Compositional Structure of Swirl-Stabilised Turbulent Non-premixed Flames, Combust. Flame, 137, 2004, pp 1-37.

[16] Y.M. Al-Abdeli, A.R. Masri, Precession and Recirculation in Turbulent Swirling Isothermal Jets, Combust. Sci. Technol. 176, 2004, pp. 645-665.

[17] ANSYS, Inc., ANSYS FLUENT 14 Theory Guide, November 2011.

[18] T. F. Smith, Z. F. Shen, J. N. Friedman, Evaluation of Coefficients for the Weighted Sum of Gray Gases Model, J. Heat Transfer. 104, 1982. pp 602–608.

[19] A. Coppalle, P. Vervisch, The Total Emissivities of High-Temperature Flames, Combustion and Flame 49,1983, pp 101–108.

[20] C. L. Tien, W. H. Giedt, Experimental determination of infrared absorption of high-temperature gases in Advances in Thermophysical Properties at extreme Temperatures and Pressures, ASME, 1965, pp. 167-173.

[21] The MathWorks, Inc., MATLAB: Data Analysis, September 2013.

[22] ANSYS, Inc., ANSYS FLUENT 14: ANSYS Fluid Dynamics Verification Manual, August 2011.

Published

2015-07-04

How to Cite

CHMIELEWSKI, Maciej; GIERAS, Marian.
Planck Mean Absorption Coefficients of H2O, CO2, CO and NO for radiation numerical modeling in combusting flows.

**Journal of Power Technologies**, [S.l.], v. 95, n. 2, p. 97--104, july 2015. ISSN 2083-4195. Available at: <https://papers.itc.pw.edu.pl/index.php/JPT/article/view/611>. Date accessed: 14 july 2024.
Issue

Section

Combustion and Fuel Processing

### Keywords

radiation modeling; combustion; absorption coeficient; weighted sum of gray gases

Authors who publish with this journal agree to the following terms:

- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).