## 3 Dynamic Heterogeneity Investigation into Debris Bed Safety Analysis
### Simulation Settings  
This section discusses the input parameters of three debris bed models (Homogeneous, Mixed, and Stratified models) used in the bed safety assessment via the CFD-DEM-MCN solver in this research. These models rely on the assumptions discussed in the previous section and the current understanding of stochastically occurring processes during severe accidents. Following the explanation in Section 3.1, the calculating domain in the CFD-DEM solver was set as a simplified three-dimensional cylindrical container referring to the prototype SFR's lower plenum [38]. The calculating domain contains the working fluid of the liquid sodium (continuous liquid phase in the CFD solver) for removing the decay heat generated from the particulate debris bed (discrete solid phase in DEM solver). The input parameters used to describe the liquid sodium's physical properties in the CFD solver are summarized in Table 1, and the polynomial function of the temperature is applied to the equation of the state in liquid sodium [39]. The geometry parameters are presented in Figure 5, and the origin of the coordinates was set at the bottom center of the calculating domain. On the top surface of the domain, four cold legs and an outlet were pertained. The inlet flowrates of these cold legs were settled to zero in the CFD solver; therefore, the mechanism of decay heat removal from the debris bed to the outlet (set as a constant pressure boundary of 1 atm) was mainly based on the natural circulation. In addition, the adiabatic condition was also assigned to the other surfaces of the calculating domain. As for the preparation of the debris bed's initial configurations among the three models, the particle injector in the DEM solver (provided by STAR-CCM+) was utilized to fill discrete solid particles in an assigned three-dimensional conical space within the calculating domain; thus, the parameters of the debris bed, such as the total mass of the debris bed, discrete particles' shapes and size, and the geometry size of the assigned conical space, were the required information, and are summarized in Table 2. Firstly, under the postulated severe accident in the prototype SFR, the total mass of the debris bed in this research was estimated based on the discharged molten core materials composed of the binary mixture materials of MOX fuel (as the molten fuel) and stainless steel (to simulate the molten structure). From the previous numerical analysis of the hypothetical severe accident (Unprotected Loss Of Flow, ULOF) in SFR, the results show that around 15% of the total molten core material will be discharged to the lower plenum [3], and one third of the total molten core material leaked to the lower plenum in the prototype SFR is assumed here based on the conservative concern. Based on this conservative assumption, considering the referred parameters of the total MOX fuel inventory [40] and the volume ratio of fuel-to-structure (0.64: 0.36 [41]) in the prototype SFR, the MOX fuel and stainless steel mass of the debris bed in this research were estimated as 27,045.45 kg and 10,856.60 kg, and the total mass of the debris bed could also be derived from the summation of the previous two values. Subsequently, the total materials of the debris bed were discrete because of the simplified spherical particles used to fill in the assigned conical space in the calculating domain, with a postulated radius of 0.065 m referred from the DEFOR-A experiments [17], which consider the potential phenomenon of agglomeration during the fragmentation of \begin{table}
\begin{tabular}{c c} \hline \hline
**Physical Properties** & **Value** \\ \hline Dynamic viscosity [kg/m-s] & 2.01 \(\times\) 10\({}^{-4}\) \\ Heat capacity [J/kg-K] & 1252 \\ Thermal conductivity [W/m-K] & 58.34 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Input parameters of the liquid sodium’s physical properties in the CFD solver. Figure 5: Schematics and geometry parameters of the calculating domain in the CFD–DEM–MCN coupled solver. the molten core materials.