Keywords: thermal radiation, participative gases, radiative transfer equation, discrete transfer ray method, statistical narrow band, machine learning, neural network.

This paper focuses on the modelling of the radiative transfer equation in a 2-D walled domain with participative gases. Aiming to reduce the computational cost of the physical resolution, a neural network-hybrid approach is introduced to model the radiative transfer equation. The solution of the radiative transfer equation is learned through two multi-layer perceptron networks whose inputs are the wall temperatures and the length and the temperature of the domain elements, and whose outputs are radiation intensities and transmissivities. To validate the approach, the results are compared with those of a proven in-house physical radiation solver in which the discrete transfer ray method is used to numerically solve radiative transfer equation with participative gases. To model the spectral behaviour of gases, the physical solver uses the spectral narrow band model with the Curtis-Godson modification. The dependency of the wall emissivity with the spectral wavelength was neglected. The approach was tested for a typical hydrocarbon combustion, at constant atmospheric pressure, with a range of wall and gas temperature between 300K to 3000K, for a fixed CO2 to H2O molar ratio. Comparison between the neural network hybrid approach and the physical solver are presented. For an academic use case discretized over 5 cells, precision of the hybrid approach shows a relative error under 3% with a speed-up factor around 10. First results are rather promising in terms of wall heat fluxes. The model could be extended by varying the gas composition and/or pressure.

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