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

## Abstract

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.

## Keywords

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

## .

*a*_{λ}Local absorption coefficient

*A*_{i}Elemental area

*i**D*Grid size of discretization

*e*_{λb}Planck function

*f*_{v}Soot volume fraction

*F*_{ij}View factor between

*A*_{i}and*A*_{j}*F*_{ss,xx}Generic exchange factor (xx = pd, pp)

*L*_{ij,xx}Center-to-center distance between

*A*_{i}and*A*_{j}(xx = pd, pp)*L*_{pd, x}Mean beam length between two perpendicular elemental areas (

*x*= soot, gas)*L*_{pp}Mean beam length between two parallel elemental areas

*n*_{x},*n*_{y},*n*_{z}Dimensionless distances for

*A*_{j}relative to*A*_{i}- \(P_{{{\text{CO}}_{2} }}\)
Partial pressure of CO

_{2}- \(P_{{{\text{H}}_{2}{\text{O}} }}\)
Partial pressure of H

_{2}O*P*_{g}Total pressure of an N

_{2}/H_{2}O/CO_{2}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

- ss
Surface–surface exchange factor

- SS
Total surface–surface exchange factor

*T*_{g}Gas temperature

*T*_{w}Wall temperature

- \(X_{{{\text{CO}}_{2} }}\)
Mole fraction of CO

_{2}*X*,*Y*,*Z*Dimensions of an enclosure

## Greek Symbols

*α*Total absorptivity (sum of soot and gas absorptivity)

*α*_{s}Soot absorptivity

- Δ
*α* Gas absorptivity

*β*_{xx}Normalized mean beam length (xx = pd, pp)

*λ*Wavelength

*ε*Emissivity of gas mixture

*σ*Stefan–Boltzmann constant

## Subscripts

- pd
Perpendicular

- pp
Parallel

## Notes

### Acknowledgements

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

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