Analysis of an Earthquake-Initiated-Transient in a PBR Page: 3 of 13
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A. M. Ougouag, J. Ortensi, H. Hiruta
compacted models. In addition, two earthquake durations are used in the analysis, 5 and 15
seconds, respectively, with a nominal global packing fraction of 0.61. Their corresponding
compacted models have used the predicted pebble bed packing fractions of 0.62 and 0.64, where
the latter can be recognized as the commonly reached limit packing level from shaking until a
maximally random jammed packed state arises [4]. In these simulations, the core height
decreases by 17.7 cm and 51.6 cm and the densification-induced reactivity insertions for the two
earthquake events are 60 cents and 180 cents, respectively.
2. PEBBLE BED REACTOR EARTHQUAKE ANALYSIS METHOD
During the starting of operations of a PBR reactor with a recirculation scheme, the core
experiences two physically distinct time dependent phenomena. The first is the approach to an
asymptotically packed core, which is determined by the geometric compaction of the pebbles as
they are re-circulated. The approach to an asymptotic bumup distribution in the core is the
second phenomenon, which occurs at a later time and is a consequence of the recirculation of
pebbles in the presence of a neutron flux. During an earthquake, the reactor core evolves toward
denser packing levels as the shaking rearranges the pebbles, thus departing from the asymptotic
packing. In models, this compaction can be directly translated into a shifting of the calculation
mesh that captures the average behavior of the pebbles and their corresponding physical effects.
Since it is expected that the neutronic phenomena, including temperature feedback, dominate the
transient behavior, the new method is primarily concerned with modeling neutronic parameters.
The foundation of the method relies on the assumption that local, relative small, changes in
packing fractions do not significantly affect, or change, the neutron spectrum in the calculation
cell. This assumption allows the modification of the diffusion parameters with a simple cell
volume weighting scheme within the neutron dynamics code without recourse to running a
spectrum code.
2.1. Volume Weighting Method for Diffusion Parameters
The homogeneous macroscopic cross-section for a given interaction in a calculation cell k is
described by Eq. 1. In the model of an earthquake event, the pebble bed reactor (PBR) fuel
cannot be considered static, because the effective fuel densification normally affects both of the
parameters in this equation. Therefore, the diffusion parameters (macroscopic cross sections and
diffusion coefficients) from any library that describes the asymptotically packed core would be
invalidated and would require modification or re-calculation.
M
k" = Npi (1)
where,
N = Number density of the it isotope
6 = microscopic cross-section of the ith isotope
The rigorous approach would be to re-compute the number densities, microscopic cross sections,
and the diffusion parameters during the transient, but these are very computationally intensive
tasks. However, an approximate method is possible if the compaction of the pebble bed is
2009 International Conference on Mathematics, Computational 2/12
Methods & Reactor Physics (M&C 2009), Saratoga Springs, NY, 2009
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Ougouag, A. M.; Ortensi, J. & Hiruta, H. Analysis of an Earthquake-Initiated-Transient in a PBR, article, May 1, 2009; [Idaho Falls, Idaho]. (https://digital.library.unt.edu/ark:/67531/metadc896667/m1/3/: accessed April 18, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.