טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentBavly Shir
SubjectApplying a Lattice Boltzmann Formulation in the Analysis of
Radiative Heat Transfer
DepartmentDepartment of Energy
Supervisor Professor Simon Brandon
Full Thesis textFull thesis text - English Version


Abstract

Thermal radiative heat transfer is important in high-temperature and/or low pressure applications such as solar technology, combustion chambers, nuclear reactors and space applications. The equation which lies at the heart of radiative heat transfer analysis, and describes the propagation of radiative intensity through space, is named the "Radiation Transfer Equation" (RTE). It is an integro-differential equation, which is sensitive to geometry. This typically leads to a level of complexity requiring almost all problems to be treated using numerical methods. Numerical solutions of realistic radiative heat transfer problems are often associated with a large computational expense.

            The Lattice Boltzmann Model (LBM) is used within the context of a relatively new numerical method, based in a sense on the concept of macroscopic dynamics being a result of the collective behavior of many virtual microscopic particles in the system. The LBM has been applied in the literature for the direct solution of the RTE based on the similarity between the RTE and the Boltzmann Transport Equation. Using this idea, intensities of radiation play the part of the particle distribution functions in LBM. A drawback of this technique involves the need for a large number of directions (a high level of angular discretization) especially for the case of optically thin media (small values of the extinction coefficient).

            Achieving increased discretization in the angular direction in the traditional way involves a loss of locality of calculation which is characterized by increased particle velocity values; this leads to a need for increased spatial discretization. In this thesis the aim is to improve on the traditional approach by first applying a modification, based on interpolation of intensities between nodes, in which high quality quadrature is used for the angular discretization; locality and the associated magnitude of particle velocities, are not significantly affected. An alternative non-trivial relaxation time based on an integrated RTE approach is also discussed; this relaxation time is more accurate and significantly improves the stability of the algorithm. In addition, in order to further increase accuracy, linear interpolation of the average ("equilibrium") intensity is also investigated. High accuracy results in a number of 1D and 2D test cases demonstrate the robustness, accuracy and stability of the approach proposed in this thesis. Finally, theoretical error analysis is applied and is shown to explain the behavior of the empirical error, as a function of discretization.