## 3 Dynamic Heterogeneity Investigation into Debris Bed Safety Analysis
### Simulation Settings
Figure 6: CFD mesh configurations in the mesh-independent examinations. In the MCN solver, the geometry setting of the calculating domain was the same as the one applied in the CFD-DEM solver, and the particle positions in the calculating domain were updated following the results calculated from the CFD-DEM solver. In addition, as well as the conception in the CFD-DEM solver, the Homogeneous particles, Fuel particles, and Structure particles were also discerned by assigning corresponding material compositions in the MCN solver, and the input parameters of the material compositions for different particles are summarized in Table 5. The material composition of the Structure particle was referred from the stainless steel [47]. In terms of the Fuel particle, the fresh MOX fuel composition, without accounting for the depletion process in SFRs, was utilized in this study for conservative concerns in the criticality safety assessment. Considering the transition stage from LWRs to SFRs, both types of reactors would be in service concurrently. This drives the possible scenario of supplying SFRs MOX fuel with transuranium (TRU) acquired from recycled LWR spent fuel [40]. Therefore, the fresh MOX fuel composition in this study was referred from the TRU composition of recycled spent fuel from Advanced LWR (ALWR) based on the scenario that the waiting time for decay heat cooling was 40 years from the state of an average discharge burnup of 60 GWd/t [40]. The contribution of the discharge boron materials from the backup CRGTs in prototype SFR is also considered in this research [2]. As the same approach was used to derive input parameters of physical properties for Homogeneous particles in the CFD-DEM solver, the composition materials of each Homogeneous particle in the MCN solver were generated using the volume-weighted average value of the total Fuel particles and Structures in either the Mixed model or the Stratified model. This study employed the continuous cross-section data library of JENDL-4.0 [48], setting the number of neutron histories and active batches as 10,000 and 220, respectively. In addition, the number of inactive batches excluded from statistical processing was set as 20. Based on these calculation conditions, the uncertainties of all the computed values of \(k_{eff}\) in this research were below 0.035%. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Number of CFD Meshes [-]** & \(T_{f,\,\text{Avg.}\,\,\text{[K]}}\) & **Relative Deviation of** \\  & & \(T_{f,\,\text{Avg.}\,\,\text{[\%]}}\) \\ \hline
34,516 & 960.34 & - \\
53,149 & 961.36 & 0.106 \\
88,088 & 961.83 & 0.049 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Results of mesh-independent examinations on the Homogeneous model. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Material** & **Fuel Particle *** & **Structure Particle *** & **Homogeneous Particle *** \\ \hline U235 & \(4.91\times 10^{-5}\) & - & \(3.11\times 10^{-5}\) \\ U238 & \(1.93\times 10^{-2}\) & - & \(1.23\times 10^{-2}\) \\ Pu238 & \(5.65\times 10^{-5}\) & - & \(3.58\times 10^{-5}\) \\ Pu239 & \(2.77\times 10^{-3}\) & - & \(1.76\times 10^{-3}\) \\ Pu240 & \(1.64\times 10^{-3}\) & - & \(1.04\times 10^{-3}\) \\ Pu241 & \(2.18\times 10^{-4}\) & - & \(1.38\times 10^{-4}\) \\ Pu242 & \(1.97\times 10^{-4}\) & - & \(1.25\times 10^{-4}\) \\ Np237 & \(2.74\times 10^{-5}\) & - & \(1.74\times 10^{-5}\) \\ Am241 & \(1.08\times 10^{-4}\) & - & \(6.83\times 10^{-5}\) \\ Am243 & \(5.34\times 10^{-5}\) & - & \(3.39\times 10^{-5}\) \\ Cm244 & \(5.32\times 10^{-5}\) & - & \(3.37\times 10^{-5}\) \\ O16 & \(4.89\times 10^{-2}\) & - & \(3.10\times 10^{-2}\) \\ B10 & \(6.28\times 10^{-4}\) & \(6.28\times 10^{-4}\) & \(6.28\times 10^{-4}\) \\ B11 & \(2.28\times 10^{-4}\) & \(2.28\times 10^{-4}\) & \(2.28\times 10^{-4}\) \\ Fe & - & \(7.01\times 10^{-2}\) & \(2.57\times 10^{-2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Input parameters of the material composition among different particles in the MCN solver.