Abstract
The pin-based pointwise energy slowing-down method (PSM) has been refined through eliminating the approximation for using the pre-tabulated collision probability during the slowing-down calculation. A collision probability table is generated by assuming that material composition and temperature are constant in the fuel pellet using the collision probability method (CPM). Refined PSM (PSM-CPM), which calculates the collision probability in the isolated fuel pellet during the slowing-down calculation using CPM, can consider nonuniform material and temperature distribution. For the methods, the extensive comparative analysis is performed with problems representing various possible conditions in a light water reactor (LWR) design. Conditions are categorized with the geometry, material distribution, temperature profile in the fuel pellet, and burnup. With test problems, PSMs (PSM and PSM-CPM) have been compared with conventional methods based on the equivalence theory. With overall calculation results, PSMs show the accuracy in the eigenvalue with differences in the order of 100 pcm compared to the reference results. There was no noticeable difference in the multigroup cross sections, reaction rates, and pin power distributions. However, PSM-CPM maintains the accuracy in the calculation of the fuel temperature coefficient under the condition with 200% power and nonuniform temperature distribution in the fuel pellet. PSM shows the difference in the eigenvalue in the order of 2,000 pcm for the fictitious pin-cell problem with highly steep temperature profiles and material compositions, but PSM-CPM shows the difference in the eigenvalue within 100 pcm.
Highlights
The resonance treatment is an essential and challenging process to solve the multigroup neutron transport equation that requires the effective multigroup cross sections (XSs)
The methods used in the comparisons are as follows: 1) EQ: the conventional equivalence theory 2) Distributed Resonance Integral (DRI): the distributed resonance integral method used in CASMO-5 (Xu et al, 2009) 3) SDDM: the spatially dependent Dancoff method used in PARAGON (Matsumoto et al, 2005) 4) MCXS: simulation with tallied multigroup XSs using the
pointwise energy slowing-down method (PSM) has been briefly reviewed, and a PSM-collision probability method (CPM) that is refined with respect to the way to calculate the collision probability in the isolated fuel pellet is introduced
Summary
The resonance treatment (or resonance self-shielding calculation) is an essential and challenging process to solve the multigroup neutron transport equation that requires the effective multigroup cross sections (XSs). SDGM and SDSS use the Stoke–Weiss method to compute the fuel escape probability for subdivided regions in the isolated fuel, and both methods consider gray resonance with optimum rational approximation (Rhodes et al, 2006b; Choi et al, 2015). Another error source of the equivalence-based methods is the approximation of the scattering source with narrow or intermediate resonance approximation. Because PSMCPM calculates the collision probability in the isolated fuel pellet solving the pointwise slowing-down equation, different total XSs in each subdivided region with the nonuniform material compositions or temperature profiles are explicitly considered. The detailed XS and reaction rate comparison is presented to show the accuracy of PSMs, in which it is compared with the results of the conventional equivalence theory methods
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