Numerical modeling of radiation heat transfer in absorbing, emitting and scattering media
Godoy, William Fredie
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The objective of this dissertation is the development of numerical models for simulation of radiative heat transfer for a general 3D Cartesian, non-homogeneous, emitting, absorbing, scattering and non-gray media. The overall problem is divided in three parts consisting of: (i) the acceleration in the calculation of the non-gray radiative properties of the gas and droplets, (ii) the solution of the radiative transfer equation (RTE) and (iii) the coupling of radiation effects with the gas phase and particles for time integration solution. For the first part of the study, Mie theory and the HITEMP database are used to construct the exact radiative properties of the particle-gas media on a line by line basis. A correlated-k method is devised to represent the gas ( H 2 O and CO 2 ) absorption coefficients in terms of frequency distribution for later coupling with the scattering from the particles (water droplets) on a narrow band basis. A scaling procedure using the Sauter mean diameter is developed in order to accelerate the calculation of the radiative properties of the particle distribution resulting in significant computational savings with little loss of accuracy. Next, a classical Discrete Ordinates Method (DOM-SN) with flux limiters or total variation diminishing (TVD) schemes for the angular and spatial discretization is formulated for the solution of the RTE in a 3D absorbing, emitting and scattering enclosure, being the final system of equations solved using a Newton-Krylov method. Inclusion of TVD schemes shows that convergence, accuracy and stability in the RTE solution are superior to classical step (upwind) or diamond (central) schemes. A first solution for the interaction of the radiative field with the participating media composed of a two-phase particle-gas mixture is shown for the evaporation of water sprays due to the absorption of radiative energy. The study shows that the evolution of the diameter size distribution due to radiation effects can be modeled through its first two moments and the introduction of a non-symmetric density function. Overall, results suggest that the proposed numerical approaches for each aspect of the complicated radiative transfer problem may lead to a potential practical solution in real situations. Through these methods, radiation calculations are made feasible since accuracy is balanced with the required computational times. The latter encourages the inclusion of radiation effects on practical engineering applications such as, fluid mechanics, combustion processes, 3D atmospheres, among others. This inclusion may improve the understanding of the physics behind these applications, including radiation effects, allowing for further development of high fidelity modeling approaches.