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Comparison of different WSGG correlations in the computation of thermal radiation in a 2D axisymmetric turbulent non-premixed methane–air flame

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Abstract

This study makes an analysis of the radiation heat transfer in a turbulent non-premixed methane–air cylindrical combustion chamber. The highly complex dependence of the radiative properties with the wavenumber spectrum is modeled with the weighted-sum-of-gray-gas (WSGG), making use of the classical correlations of Smith et al. (J Heat Transfer 104:602–608, 1982) and of the more recently in obtained correlations of Dorigon et al. (IJHMT 64:863–873, 2013), based on HITEMP2010. The reaction rates were considered as the minimum values between the Arrhenius and Eddy Break-Up rates. A two-step global reaction mechanism was used, and turbulence modeling was considered via standard k–ε model. The source terms of the energy equation consisted of the energy involved in the reaction rates and radiation exchanges. The discrete ordinates method (DOM) was employed to solve the radiative transfer equation (RTE). The results show that the temperature, the radiative heat source, and the wall heat flux can be importantly affected by the WSGG correlations, while their influence on the species concentrations tends to be negligible. Numerical results considering the WSGG model with the new correlations were closer to experimental data presented in the literature.

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Abbreviations

a j (T) :

Emission weighted factor (WSGG), dimensionless

b j :

Polynomial coefficients of the WSGG model, units can vary

c :

Each reaction on mechanism, dimensionless

c p,α :

Specific heat, J/(kg K)

C 1,ε , C 2,ε :

Constants of the turbulence model, dimensionless

C μ :

Constant of the turbulence model, dimensionless

CH4 :

Methane

CO:

Carbon monoxide

CO2 :

Carbon dioxide

f rad :

Radiant fraction, dimensionless

h :

Specific enthalpy, J/kg

\( h_{\alpha }^{0} \) :

Formation enthalpy of species α, J/kg

H2O:

Water vapor

I :

Total radiative intensity, W/m²

I η :

Spectral radiative intensity, W/(m² m−1)

K :

Turbulent kinetic energy, m²/s²

k j :

Absorption coefficient for the j-th gray gas for WSGG model, m−1

k p,j :

Pressure absorption coefficient for the j-th gray gas for WSGG model, m−1 atm−1

\( \bar{M}\bar{M}_{\alpha } \) :

Molar mass, kg/kmol

n :

Vector normal to the surface element, dimensionless

N G :

Number of gray gases (WSGG), dimensionless

N2 :

Nitrogen

O2 :

Oxygen

p :

Pressure, Pa

\( p_{{{\text{H}}_{ 2} {\text{o}}}} /p_{{{\text{CO}}_{ 2} }} \) :

Ratio of H2O and CO2 partial pressures, dimensionless

p* :

Modified pressure, Pa

Pr t , Sc t :

Turbulent Prandtl and Schmidt numbers, dimensionless

\( {\mathbf{q}}_{r} \) :

Radiative heat flux, W/m²

r :

Radial coordinate, m

\( \bar{R} \) :

Universal gas constant, J/(kmol K)

R α :

Volumetric rate of formation or destruction of α, kg/(m³ s)

s :

Distance traveled by the radiation intensity, m

s :

Vector in the direction of the radiation intensity, dimensionless

S rad :

Radiative heat source, W/m³

S ϕ :

Source term for ϕ, W/m³

T :

Temperature, K

u :

Axial velocity, m/s

v :

Radial velocity, m/s

w :

Angular velocity, m/s

y α :

Mass fraction, kgα/kgmix

z :

Axial coordinate, m

ε :

Dissipation rate of k, m²/s³

ε w :

Wall emissivity, dimensionless

ϕ :

Generic variable, units can vary

φ :

Angular coordinate, rad

Γ ϕ :

Diffusive coefficient for ϕ, N s/m²

κ η :

Spectral absorption coefficient, m−1

μ :

Viscosity, N s/m²

μ t :

Turbulent viscosity, N s/m²

μ, ς, ξ :

Discrete ordinates method directions

ρ :

Density, kg/m³

σ k , σ ε :

Prandtl numbers for k and ε, dimensionless

Ω :

Solid angle, sr

b :

Blackbody

Dorigon:

WSGG model coefficients from Dorigon et al. [6]

j :

Each gray gas of the WSGG model

rad:

Radiation

ref:

Reference

Smith:

WSGG model coefficients from Smith et al. [25]

w :

Wall

α :

Each chemical species

η :

Wavenumber, m−1

References

  1. Bidi M, Hosseini R, Nobari MRH (2008) Numerical analysis of methane–air combustion considering radiation effect. Energy Convers Manage 49:3634–3647

    Article  Google Scholar 

  2. Coelho PJ (2007) Numerical simulation of the interaction between turbulence and radiation in reactive flows. Prog Energy Combust Sci 33:311–383

    Article  Google Scholar 

  3. Coelho PJ, Teerling OJ, Roekaerts D (2003) Spectral radiative effects and turbulence/radiation interaction in a non-luminous turbulent jet diffusion flame. Combust Flame 133:75–91

    Article  Google Scholar 

  4. Crnomarkovic N, Sijercic M, Belosevic S, Tucakovic D, Zivanovic T (2013) Numerical investigation of processes in the lignite-fired furnace when simple gray gas and weighted sum of gray gases models are used. IJHMT 56:197–205

    Article  Google Scholar 

  5. Demarco R, Consalvi JL, Fuentes A, Melis S (2011) Assessment of radiative property models in non-gray sooting media. Int J Therm Sci 50:1672–1684

    Article  Google Scholar 

  6. Dorigon LJ, Duciak G, Brittes R, Cassol F, Galarça M, França FHR (2013) WSGG correlations based on HITEMP 2010 for computation of thermal radiation in non-isothermal, non-homogeneous H2O/CO2 mixtures. IJHMT 64:863–873

    Google Scholar 

  7. Eaton AM, Smoot LD, Hill SC, Eatough CN (1999) Components, formulations, solutions, evaluations and applications of comprehensive combustion models. Prog Energy Combust Sci 25:387–436

    Article  Google Scholar 

  8. (2009) In: Fluent (ed) Fluent Theory Guide. Fluent Incorporated, New Hampshire

  9. Garréton D, Simonin O (1994) “Final results”, Proceedings of the First Workshop of Aerodynamics of Steady State Combustion Chambers and Furnaces, EDF–ERCOFTAC, vol 25, pp 29–35

  10. Guedri K, Borjini MN, Jeguirim M, Brilhac J, Saïd R (2011) Numerical study of radiative heat transfer effects on a complex configuration of rack storage fire. Energy 36:2984–2996

    Article  Google Scholar 

  11. Hottel HC, Sarofim AF (1967) Radiative Transfer. McGraw-Hill Book Company, New York

  12. Johansson R, Leckner B, Andersson K, Johnsson F (2011) Account for variations in the H2O to CO2 molar ratio when modeling gaseous radiative heat transfer with the weighted-sum-of-grey-gases model. Combust Flame 158:893–901

    Article  Google Scholar 

  13. Kangwanpongpan T, França FHR, 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. IJHMT 55:7419–7433

    Article  Google Scholar 

  14. Krishnamoorthy G (2010) A new weighted-sum-of-gray-gases model for CO2–H2O gas mixtures. Int Comm Heat Mass Transf 37:1182–1186

    Article  Google Scholar 

  15. Li G, Modest MF (2002) Importance of turbulence–radiation interactions in turbulent reacting flows, Proceedings of the 2002 ASME International Mechanical Engineering Congress and Exhibition, New Orleans, Louisiana, USA

  16. Magel HC, Schnell U, Hein KRG (1996) Modeling of hydrocarbon and nitrogen chemistry in turbulent combustor flows using detailed reaction mechanisms, Proceedings of the 3rd Workshop on Modeling of Chemical Reaction Systems, Heidelberg

  17. Magnussen BF, Hjertager BH (1977) On mathematical models of turbulent combustion with special emphasis on soot formation and combustion, Proceedings of the 16th Symposium (International) on Combustion, The Combustion Institute. Cambridge, MA, USA, pp 719–729

  18. Modest MF (1991) The weighted-sum-of-gray-gases model for arbitrary solution methods in radiative transfer. ASME J Heat Transf 113:650–656

    Article  Google Scholar 

  19. Nieckele AO, Naccache MF, Gomes MSP, Carneiro JE, Serfaty R (2001) Models evaluations of combustion process in a cylindrical furnace, Proceedings of 2001 ASME International Mechanical Engineering Congress and Exposition, New York, NY, USA

  20. Patankar SV (1980) Numerical heat transfer and fluid flow. Hemisphere, Washington, DC

    MATH  Google Scholar 

  21. 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. JQS & RT 111:2130–2150

    Google Scholar 

  22. Silva CV, França FHR, Vielmo HA (2007) Analysis of the turbulent, non-premixed combustion of natural gas in a cylindrical chamber with and without thermal radiation. Combust Sci Tech 179:1605–1630

    Article  Google Scholar 

  23. Silva CV, Indrusiak MLS, Beskow AB (2010) CFD analysis of the pulverized coal combustion processes in a 160 MWe tangentially-fired-boiler of a thermal power plant. JBSMSE 32:427–436

    Google Scholar 

  24. Smith TF, Al-Turki AM, Byun KH, Kim TK (1987) Radiative and conductive transfer for a gas/soot mixture between diffuse parallel plates. J Thermophys Heat Transf 1:50–55

    Article  Google Scholar 

  25. Smith TF, Shen ZF, Friedman JN (1982) Evaluation of coefficients for the weighted sum of gray gases model. J Heat Transf 104:602–608

    Article  Google Scholar 

  26. Spalding DB (1979) Combustion and mass transfer. Pergamon Press, Inc., New York

    Google Scholar 

  27. Turns SR (2000) An introduction to combustion: concepts and applications, McGraw-Hill, New York

  28. Yadav R, Kushari A, Eswaran V, Verma AK (2013) A numerical investigation of the Eulerian PDF transport approach for modeling of turbulent non-premixed pilot stabilized flames. Combust Flame 160:618–634

    Article  Google Scholar 

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Acknowledgments

Authors FHRF and HAV thank CNPq (Brazil) for research Grants 304728/2010-1, 473899/2011-6 and 470325/2011-9, 303823/2012-7, respectively.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Federal University of Rio Grande do Sul, UFRGS, Sarmento Leite Street, no. 425, Porto Alegre, RS, 90050-170, Brazil

    Felipe Roman Centeno, Fabiano Cassol, Horácio A. Vielmo & Francis Henrique Ramos França

  2. Universidade Regional Integrada do Alto Uruguai e das Missões, URI, Sete de Setembro Avenue, no. 1621, Erechim, RS, 99700-000, Brazil

    Cristiano Vitorino da Silva

Authors
  1. Felipe Roman Centeno
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  2. Fabiano Cassol
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  3. Horácio A. Vielmo
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  4. Francis Henrique Ramos França
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  5. Cristiano Vitorino da Silva
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Correspondence to Francis Henrique Ramos França.

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Technical Editor: Luis Fernando Figueira da Silva.

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Centeno, F.R., Cassol, F., Vielmo, H.A. et al. Comparison of different WSGG correlations in the computation of thermal radiation in a 2D axisymmetric turbulent non-premixed methane–air flame. J Braz. Soc. Mech. Sci. Eng. 35, 419–430 (2013). https://doi.org/10.1007/s40430-013-0040-z

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