Abstract
The pin-based pointwise energy slowing-down method (PSM), which is a resonance self-shielding method, has been refined to treat the nonuniformity of material compositions and temperature profile in the fuel pellet by calculating the exact collision probability in the radially subdivided fuel pellet under the isolated system. The PSM has generated the collision probability table before solving the pointwise energy slowing-down equation. It is not exact if the fuel pellet has nonuniform material compositions or temperature profile in all the subdivided regions. In the refined PSM-CPM, the pre-generated table is not required for directly calculating the collision probability in all the subdivided regions of the fuel pellet while solving the slowing-down equation. There are an advantage and a disadvantage to the method. The advantage is to exactly consider the nonuniformity of the material compositions and temperature profile in the fuel pellet. The disadvantage is the longer computing time than that of the PSM when the fuel pellet has more than five subdivided regions. However, in the practical use for UO2 pin-cells, it is still comparable for the computation time with the PSM and the conventional equivalence theory methods. In this article, using simple light water reactor 17 × 17 F A problems with a uniform material composition and temperature profile, it is demonstrated that PSMs (PSM and PSM-CPM) exhibit consistent accuracy in calculating the multiplication factor and the pin power distribution with no compromise in the computation time. More detailed accuracy assessments with various test cases, including problems representing the nonuniformity, are presented in the accompanying article.
Highlights
In reactor physics, all calculations are conducted with cross sections (XSs)
The pointwise energy slowing-down method (PSM) calculates the collision probability corresponding to the grid of the total XSs which is assumed to be constant in all the subdivided regions of the fuel pellet before solving the slowing-down equation
The PSM uses a pre-generated look-up table for the collision probability to reduce the calculation time, but it is only valid if the fuel pellet has a uniform material composition and temperature profile in the subdivided regions of the fuel pellet
Summary
All calculations are conducted with cross sections (XSs). The actual XSs for nuclides describe the very detailed energy resolution. Generating the collision probability during solving the slowing-down equation on the fly, a more rigorous method, PSM-CPM, has been developed to treat nonuniform material and temperature distributions in the fuel pellet. The achievements of the PSM are summarized as follows: RI or XS look-up tables are not required for resonance treatment; the distribution of the scattering sources in the fuel pellet is accurately modeled; and PSMs have a comparable computational cost with the equivalence theory. A proper correction is required to consider the shadowing effect from neighboring fuel rods and structural materials In this second step of the collision probability calculation, it is assumed that the shadowing effect is not significantly different for the individually subdivided regions of the fuel pellet. All the collision probabilities and escape probabilities, which are needed to solve the slowing-down equations in Eqs 4–6, are derived
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