Nuclear Methods For Solving Radiation Transport Problems

Radiation heat transport problems in high-temperature thermal systems have received considerable attention in recent years. Many thermal engineering applications, require better understanding of radiation heat transport to improve the processes or designs. Therefore, transport theory has become a very important subject in physics and engineering applications. Generally, the exact treatment of radiation transport equation in participating media is very difficult for actual problems. The radiation transport problems are solved to obtain the radiation intensity of the radiation transport equation or radiation energy and radiation heat flux of radiation integral transport equation. Many numerical methods have been developed to solve these two kinds of equations. However, each method has advantage and disadvantage.The Synthetic Kernel (SK_N) method deals with the integral equation and involves an exponential approximation to the transfer kernel. Then, the integral equation is reducible to a set of coupled second order differential equations for which proper boundary conditions can be derived. The method was first proposed for solving integral neutron transport equation, and it was later successfully developed and applied to homogeneous, inhomogeneous, one- and multi-group constant source as well as eigenvalue problems in one- and two-dimensional optically thin systems. Up to now, The Synthetic Kernel method has been successfully used to solve radiation transport problems in rectangular, parallel-plane, spherical, and cylindrical geometries. However, There are many problems existed in the Synthetic Kernel method, such as, in the slab geometry, when the parallel-plane is very thin and scattering coefficient is very large, the error of the Synthetic Kernel method is larger. And the convergence of the Synthetic Kernel method is slower.Based on the investigation of the literature, some formulas are derived, some isotropic and linearly anisotropic scattering codes of the Synthetic Kernel method and the discrete ordinates method in slab and cylindrical geometries are compiled. Radiation transport models in slab and cylindrical geometries are computed, and compared with the results in the literature, therefore, these codes are correct. Then, for one-dimensional parallel-plane, computational error and convergence of the Synthetic Kernel method are analyzed by using numerical method. The new quadrature sets-Set-E1, Set-E2, Set-E3 and error amendment method are proposed to improve the accuracy of the Synthetic Kernel method. For isotropic part of the radiation energy, Set-El is used, anisotropic Set-E2, and for isotropic part of the radiation heat flux, Set-E2 is used, anisotropic Set-E3. For isotropic scattering parallel-plane medium, error amendment method is used. Radiation transport benchmark problems in the homogenous and inhomogenous parallel-plane medium are computed, and compared with the exact solutions. The Synthetic kernel approximation yields more accurate results even for low orders by using new quadrature sets and amending error.This paper has five chapters. After simply introduced the background and research object, we give the radiation transport equation in general form and derive the radiation integral transport equation. In third chapter, we derive the synthetic kernel equation, and analyze the error and convergence of the Synthetic Kernel method. Additionally, the new quadrature sets are proposed. In fourth chapters, we give the improvement method of the Synthetic Kernel method, and give the results of some benchmark problems. Finally, we give the conclusion and the next step's work.