## 3 Dynamic Heterogeneity Investigation into Debris Bed Safety Analysis
### Simulation Settings
Finally, the geometry size of the assigned conical space can be determined by the total volume of the MOX fuel and stainless steel in the debris bed, the average porosity of the debris bed, and the initial slope angle. The total volume of the MOX fuel and the stainless steel can be estimated by their densities (11,000 kg/m\({}^{3}\) for MOX fuel [26], 7850 kg/m\({}^{3}\) for stainless steel [42]) with their mass discussed above. An average porosity value of 0.59 is assumed here, referred from the FARO/THERMOS experimental results of spatial porosity distribution via injecting molten UO\({}_{2}\) into the liquid sodium [20]. To the best of our knowledge, there are currently no data available on the slope angle needed to cause particle avalanching in the debris bed of the prototype SFR. Instead, research for Light Water Reactor (LWR) has shown that the slope angle to induce particle avalanching for the debris bed has a lower boundary of 22\({}^{\circ}\)[22; 27; 28], and an initial slope angle of 30\({}^{\circ}\) was selected in this study. Therefore, the height (2.485 m) and the bottom radius (1.434 m) of the assigned conical space could be evaluated and utilized to set the initial bed configurations for this research. Except for the initial geometry parameters, the input parameters for discerning different materials between particles (e.g., Fuel particles made of MOX fuel; Structure particles made of stainless steel) in the calculation are also necessary information for creating the different initial heterogeneous configurations of the debris bed models, as shown in Figure 4. The input parameters of the physical properties of Fuel and Structure particles in the DEM solver are summarized in Table 3. The Young's modulus and Poisson's ratio, relating to the particle-particle momentum exchange due to collision, are referenced to the physical properties of MOX fuel [43] and stainless steel [42], respectively. The parameters of either static friction coefficient or rolling resistance coefficient (also relating to the particle-particle collision calculation) are settled as the same number between Fuel and Structure particles based on the same surface roughness assumption between particles (discussed in Section 3.1), and the values are the default numbers provided in STAR-CCM+. As for the heat capacity and thermal conductivity relating to the particle-particle energy exchange, the settled parameters in the Fuel particle and the Structure particle are also referred from the material properties of the MOX fuel [44] and stainless steel [42]. The decay heat generation rate settled for the Fuel particle in this research was referred from the hypothetical scenario of ULOF in an SFR, which implemented a fuel assembly with an inner duct structure (Fuel Assembly with Inner Duct Structure: FAIDUS). The previous studies suggest that the time from the start of core melting to the onset of FCI is about a few minutes, after which the debris bed is estimated to be piled up on the debris catcher of the lower plenum in around one minute, considering the debris falling rate [1; 45]. Therefore, the decay heat generation rate of the debris bed in such a short time can be considered equivalent to the decay heat soon after the normal reactor shutdown (6-7% of operating power) [46]. Based on conservative concern, the total decay heat generation rate of the debris bed in this research was estimated according to the assumption of one third of the total core molten fuel of the prototype SFR, maintaining at 7% of one third of its thermal operating power [40]. The value of the heat