Performance of the Various $Sn$ Approximations of DOM in a 3D Combustion Chamber

We have carried out a three-dimensional numerical study to investigate the radiative heat transfer in a model gas turbine combustor. The combustion chamber is a representative of the Rolls-Royce Tay engine combustor. The discrete ordinate method $(Sn)$ in general body-fitted coordinate system is developed and then applied to solve the filtered radiative transfer equation for the radiation modeling, and this has been combined with a large eddy simulation of the flow, temperature, and composition fields within the combustion chamber. Various approximations of $Sn$ have been considered and their performances in the investigation of the radiative heat transfer are presented in the paper. The radiation considered in this work is due only to the hot combustion gases, notably carbon dioxide $(CO2)$ and water vapor $(H2O)$ also known as nonluminous radiation. The instantaneous results of the radiation properties such as the incident radiation and the radiative energy source or sink as the divergence of the radiative heat fluxes are computed inside the combustion chamber and presented graphically. Effects of the wall emissivity on the incident radiation inside the combustion chamber have been examined, and it has been found that the radiative energy is enhanced with the increment of the wall emissivity.