Advances in radiation transport modeling using Lattice Boltzmann Methods

Abstract

This thesis extends the application of Lattice Boltzmann Methods (LBM) to radiation transport problems in thermal sciences and nuclear engineering. LBM is used to solve the linear Boltzmann transport equation through discretization into Lattice Boltzmann Equations (LBE). The application of weighted summations for the scattering integral as set forth by Bindra and Patil are used in this work. Simplicity and localized discretization are the main advantages of using LBM with fixed lattice configurations for radiation transport problems. Coupled solutions to radiation transport and material energy transport are obtained using a single framework LBM.

The resulting radiation field of a one dimensional participating and conducting media are in very good agreement with benchmark results using spherical harmonics, the P₁ method. Grid convergence studies were performed for this coupled conduction-radiation problem and results are found to be first-order accurate in space. In two dimensions, angular discretization for LBM is extended to higher resolution schemes such as D₂Q₈ and a generic formulation is adopted to derive the weights for Radiation Transport Equations (RTEs). Radiation transport in a two dimensional media is solved with LBM and the results are compared to those obtained from the commercial software COMSOL, which uses the Discrete Ordinates Method (DOM) with different angular resolution schemes. Results obtained from different lattice Boltzmann configurations such as D₂Q₄ and D₂Q₈ are compared with DOM and are found to be in good agreement. The verified LBM based radiation transport models are extended for their application into coupled multi-physics problems. A porous radiative burner is modeled as a homogeneous media with an analytical velocity field. Coupling is performed between the convection-diffusion energy transport equation with the analytical velocity field. Results show that radiative transport heats the participating media prior to its entering into the combustion chamber.

The limitations of homogeneous models led to the development of a fully coupled LBM multi-physics model for a heterogeneous porous media. This multi-physics code solves three physics: fluid flow, conduction-convection and radiation transport in a single framework.

The LBE models in one dimension are applied to solve one-group and two-group eigenvalue problems in bare and reflected slab geometries. The results are compared with existing criticality benchmark reports for different problems. It is found that results agree with benchmark reports for thick slabs (>4 mfp) but they tend to disagree when the critical slab dimensions are less than 3 mfp. The reason for this disagreement can be attributed to having only two angular directions in the one dimensional problems.