Assessment of Radiation Solvers for Fire Simulation Models Using RADNNET-ZM

  • Wai Cheong TamEmail author
  • Walter W. Yuen
Conference paper


The paper presents a neural-network-based zonal method (RADNNET-ZM) for the analysis of radiative heat transfer in an arbitrary Cartesian enclosure with an isothermal, homogeneous, non-gray medium. The model accounts for the non-gray effect of absorbing species in a combustion environment and the geometric effect of any three-dimensional enclosures. The model is verified against benchmark solutions. Maximum local error is observed to be less than 4%. Prediction accuracy of an existing zonal radiation solver is assessed. Results demonstrate that RADNNET-ZM can provide a substantial improvement to zone fire simulation models for the prediction of radiative heat transfer without a significant increase in computation cost.


Neural network Zonal method Non-gray Multi-dimensional Fire simulation model 




Local absorption coefficient


Elemental area i


Grid size of discretization


Planck function


Soot volume fraction


View factor between Ai and Aj


Generic exchange factor (xx = pd, pp)


Center-to-center distance between Ai and Aj (xx = pd, pp)

Lpd, x

Mean beam length between two perpendicular elemental areas (x = soot, gas)


Mean beam length between two parallel elemental areas

nx, ny, nz

Dimensionless distances for Aj relative to Ai

\(P_{{{\text{CO}}_{2} }}\)

Partial pressure of CO2

\(P_{{{\text{H}}_{2}{\text{O}} }}\)

Partial pressure of H2O


Total pressure of an N2/H2O/CO2 mixture

\(\dot{q}_{\text{g}}^{\prime \prime }\)

Incident heat flux due to emission of mixture medium

\(\dot{q}_{\text{w}}^{\prime \prime }\)

Incident heat flux due to emission of wall


Surface–surface exchange factor


Total surface–surface exchange factor


Gas temperature


Wall temperature

\(X_{{{\text{CO}}_{2} }}\)

Mole fraction of CO2

X, Y, Z

Dimensions of an enclosure

Greek Symbols


Total absorptivity (sum of soot and gas absorptivity)


Soot absorptivity


Gas absorptivity


Normalized mean beam length (xx = pd, pp)




Emissivity of gas mixture


Stefan–Boltzmann constant








The authors would like to thank Kevin B. McGrattan for his constructive comments and valuable suggestions to this manuscript.


  1. 1.
    Hottel, H. C., & Sarofim, A. F. (1967). Radiative transfer. McGraw-Hill.Google Scholar
  2. 2.
    Fiveland, W. A. (1987). Discrete ordinate methods for radiative heat transfer in isotropically and anisotropically scattering media. Journal of Heat Transfer, 109(3), 809–812.CrossRefGoogle Scholar
  3. 3.
    Carvalho, M., Farias, T., & Fontes, P. (1991). Predicting radiative heat transfer in absorbing, emitting, and scattering media using the discrete transfer method. Fundamentals of radiation heat transfer, 160(1), 17–26.Google Scholar
  4. 4.
    Grosshandler, W. L. (1993). RADCAL: A narrow-band model for radiation calculations in a combustion environment. Gaithersburg, MD: National Institute of Standards and Technology.Google Scholar
  5. 5.
    Mazumder, S., & Modest, M. F. (2002). Application of the full spectrum correlated-k distribution approach to modeling non-gray radiation in combustion gases. Combustion and Flame, 129(4), 416–438.CrossRefGoogle Scholar
  6. 6.
    Cumber, P. S., Fairweather, M., & Ledin, H. S. (1998). Application of wide band radiation models to non-homogeneous combustion systems. International Journal of Heat and Mass Transfer, 41(11), 1573–1584.CrossRefGoogle Scholar
  7. 7.
    Choi, C. E., & Baek, S. W. (1996). Numerical analysis of a spray combustion with nongray radiation using weighted sum of gray gases model. Combustion Science and Technology, 115(4–6), 297–315.CrossRefGoogle Scholar
  8. 8.
    Yuen, W. W., Tam, W. C., & Chow, W. K. (2014). Assessment of radiative heat transfer characteristics of a combustion mixture in a three-dimensional enclosure using RAD-NETT (with application to a fire resistance test furnace). International Journal of Heat and Mass Transfer, 68, 383–390.CrossRefGoogle Scholar
  9. 9.
    Yuen, W. W. (2009). RAD-NNET, a neural network based correlation developed for a realistic simulation of the non-gray radiative heat transfer effect in three-dimensional gas-particle mixtures. International Journal of Heat and Mass Transfer, 52(13), 3159–3168.CrossRefGoogle Scholar
  10. 10.
    Tam, W. C. (2013). Analysis of heat transfer in a building structure accounting for the realistic effect of thermal radiation heat transfer (Ph.D. thesis). The Hong Kong Polytechnic University, Hong Kong, China.Google Scholar
  11. 11.
    Peacock, R. D., McGrattan, K. B., Forney, G. P., & Reneke, P. A. (2015). CFAST—Consolidated fire and smoke transport (version 7). Volume 1: Technical reference guide. Technical Note, NIST, Gaithersburg, Maryland, 1, pp. 69–71.Google Scholar
  12. 12.
    McGrattan, K., Hostikka, S., McDermott, R., Floyd, J., Weinschenk, C., & Overholt, K. (2013). Fire dynamics simulator technical reference guide volume 1: mathematical model. NIST Special Publication, 1018(1), 175.Google Scholar
  13. 13.
    Fluent, A. N. S. Y. S. (2011). Ansys fluent theory guide. ANSYS Inc., USA, 15317, pp. 724–746.Google Scholar
  14. 14.
    Yuen, W. W., & Takara, E. E. (1997). The zonal method: A practical solution method for radiative transfer in nonisothermal inhomogeneous media. Annual Review of Heat Transfer 8(8).Google Scholar
  15. 15.
    Yuen, W. W., & Tam, W. C. (In preparation). RADNNET-ZM—The generalized zonal method for radiative transfer in multi-dimensional non-gray media.Google Scholar
  16. 16.
    Liu, F. (1999). Numerical solutions of three-dimensional non-gray gas radiative transfer using the statistical narrow-band model. Journal of Heat Transfer, 121(1), 200–203.CrossRefGoogle Scholar
  17. 17.
    Coelho, P. J. (2002). Numerical simulation of radiative heat transfer from non-gray gases in three-dimensional enclosures. Journal of Quantitative Spectroscopy and Radiative Transfer, 74(3), 307–328.CrossRefGoogle Scholar
  18. 18.
    Yuen, W. W. (2014). Development of the concept of mean temperatures in the analysis of radiative heat transfer in an inhomogeneous non-isothermal non-gray medium. International Journal of Heat and Mass Transfer, 68, 259–268.CrossRefGoogle Scholar

Copyright information

© This is a U.S. government work and not under copyright protection in the U.S.; foreign copyright protection may apply 2020

Authors and Affiliations

  1. 1.Fire Research DivisionNational Institute of Standards and TechnologyGaithersburgUSA
  2. 2.Department of Mechanical EngineeringUniversity of California at Santa BarbaraSanta BarbaraUSA

Personalised recommendations