## 3 Dynamic Heterogeneity Investigation into Debris Bed Safety Analysis  
### Explanation of the Investigated Debris Bed Models  
Because the primary purpose of this research is to examine the capability of the CFD-DEM-MCN coupled solver among different heterogeneous bed configuration's transformation processes during particle redistribution, the hypothetically intermediate states of the bed formation in prototype SFRs were prepared as the initial conditions of the investigated bed models for conducting bed safety assessments. The concept of the model settings is explained in this section. Firstly, all the initial states of the investigated debris bed models in this research are located at the center of the in-vessel debris catcher in SFR's lower plenum, assuming that all the model geometries are the typical conical shape [24,25] with the same initial bed size and slope angle. This research was not concerned with the simulating process of FCI and the falling of the fragmented particles; therefore, in order to initialize the transformation process of the heterogeneous bed configuration, the initial slope angle in this study was placed higher than the reposed angle to induce particle redistribution (based on the gravity-driven particle avalanching). Subsequently, the sources used to provide different heterogeneous bed configuration transformations among the investigated debris bed models were from (1) the non-uniformity of the debris particles and (2) the initial distribution of these non-uniform particles. As in the primitive examination of this coupled solver on the bed safety assessment, the particle size, shape, and surface roughness were kept the same, and only the non-uniformity factor of the material between particles was selected in this research, realized by introducing binary mixture particles, including the Fuel particle (composed of MOX fuel) and the Structure particle (composed of stainless steel) shown in Figure 4. Because the composite materials differ between Fuel and Structure particles, other accompanying non-uniformity factors, such as decay heat generating rate, particle density, and other relative physical properties, were also considered in this bed safety assessment. This research's first investigated heterogeneous model was prepared by randomly positioning Fuel particles and Structure particles within the debris bed as the initial heterogeneous configuration, named the \"Mixed model\". On the other hand, considering the potential scenario in which the molten fuel, when not accompanying the molten structure, creates different discharge orders from the core area to the lower plenum [2], the other  
Figure 4: Schematics of the three debris bed models’ initial configurations in the CFD–DEM–MCN coupled solver (vertical cross-section of the debris bed). investigated heterogeneous debris bed model, named the \"Stratified model\", was also prepared in this research by settling Fuel particles on the bottom layer of the debris bed to create an initial stratified configuration, as shown in Figure 4. In addition to the reference material used to compare the heterogeneous models, the \"Homogeneous model\", composed of homogeneous particles, was also prepared in this study. It should be noted that all the investigated debris bed models in this research were assumed from the same discharged molten core materials with the same volume; hence, the homogeneous particles' material composition and other related physical properties were derived from the volume-weighted average values of the total Fuel particles and Structure particles in either the Mixed or Stratified models. For example, the particle density of the Homogeneous particle (\(\rho_{i,H}\)) can be derived as below:  
\[\rho_{i,H}=\frac{\rho_{i,F}V_{T,F}}{V_{T,F}+V_{T,S}}+\frac{\rho_{i,S}V_{T,S}}{ V_{T,F}+V_{T,S}}, \tag{28}\]  
where \(\rho_{i,F}\) and \(\rho_{i,S}\) are the particle density of the Fuel particle and the Structure particle.