Search

The discrete ordinates method (also called the SN method) has been widely used in radiation transport calculations. However, the ray effect and complicated geometry modeling are major shortcomings of the SN calculation compared to the Monte Carlo method. AETIUS is an in-house 3D neutron/photon transport code. It uses the first collision source method on a point or volume source and an unstructured tetrahedral mesh to overcome the two shortcomings mentioned above. A three-dimensional un-collided flux and first collision source code, FNSUNCL3, was previously developed for TORT in three-dimensional X-Y-Z geometry and its benchmark results on Kobayashi problems showed good agreement with the reference. We adapted the methodology used in FNSUNCL3 by modifying the volume source to several pseudo-point sources and summing the contributions from all pseudo-point sources. However, the AETIUS code uses unstructured tetrahedral mesh such that we can apply the first collision source method to any shape of volume sources. The AETIUS results for the original Kobayashi Benchmark Problems and for the Modified Kobayashi Benchmark Problem 2, are shown here to demonstrate the efficacy of using unstructured tetrahedral mesh. These new results show good agreement with reference results.

In a pebble-bed type very high temperature gas-cooled reactor (VHTGR), a typical fuel pebble consists of over ten thousand five-layer TRISO particles in a graphite-matrix. The high heterogeneity in composition leads to difficulty in explicit thermal calculation of pebble fuels. Thus, a homogenization model becomes essential. Currently, a simple volumetric-average thermal conductivity approach is used. However, this approach is non-conservative and underestimates the fuel temperature. In this paper, we describe a homogenization model that is not only easy to implement but also gives a more realistic temperature distribution in a fuel pebble, providing the fuel-kernel and graphite-matrix temperatures separately. Steady-state and transient thermal analyses are performed using the homogenization model, and the point kinetics model is then coupled with the homogenization model to incorporate fuel-kernel temperature feedback.

In the conventional discrete ordinates approach, the scattering source is approximated as a truncated Legendre series. In case of highly anisotropic scattering problems (e.g., incident beam problems), the truncated Legendre scattering cross-sections give unphysical negative cross-sections in some values of μ (cosine of scattering angle). These unphysical artifacts cause negative scattering sources and negative angular fluxes. In addition to that, negative angular fluxes may cause wrong scalar flux as well. A new method to generate non-negative scattering cross-sections, which is very efficient and deterministic, is proposed in this paper. The main idea of this method is to make non-negative scattering cross-sections that produce equivalent scattering sources. This method does not have a practical limitation to generate non-negative scattering cross-sections because the calculations of the scattering sources are performed with the conventional truncated cross-section data provided from the standard processing codes. In the both neutron and the photon/electron coupled cases, an inadequate truncated Legendre order causes problems, e.g., inaccurate angular distribution of scattering for low order, oscillations of differential scattering cross-sections where cross-sections are small for high order expansions, and negative differential scattering cross-sections in some values of μ . In the neutron case, if the anisotropy is very high compared to the truncated Legendre order, inaccurate angular distributions of scattering occur especially in within-group scattering. Even if the truncated Legendre order is quite high to represent angular distribution of scattering in the photon/electron coupled case, it still causes oscillations where the cross-sections are small. The method in this paper achieves both an accurate angular distribution of scattering and non-negative scattering cross-sections for neutron and photon/electron coupled cases. The generated non-negative scattering cross-sections with the new method are compared to the conventional scattering cross-sections and tested in the transport calculations. The numerical results tested in the transport calculation give accurate results without unphysical negative angular fluxes.