## 3 Dynamic Heterogeneity Investigation into Debris Bed Safety Analysis
### Results and Discussion
#### 3.3.3 Cooling Characteristics Analysis
Moreover, the BC effect also causes a lower value of \(\left|\overset{\rightarrow}{V}_{f(p)}\right|_{Avg. }\) in the vertical direction in the Stratified model compared to the Mixed model (as shown in Table 9) due to the comparative lower position distribution of the heat-generating particles than in the Mixed model (as shown in Figure 14b) after particle redistribution. In the meantime, the BC effect on the \(\left|\overset{\rightarrow}{V}_{f(p)}\right|_{Avg. }\), along the vertical direction also contributed to the influence to weaken \(\text{Nu}_{p,Avg. }\), resulting in the value of \(\text{Nu}_{p,Avg. }\) in the Stratified model being lower than in the Mixed model, eventually (shown in Table 9). Regarding the particle temperature distribution in the Stratified model in Figure 16, it also displayed a similar trend with other models, in that the particle temperature is increased with suppressed inward flow velocity along the radial direction, and the particle temperature is decreased with the enhanced upward convective flow along the vertical direction. Finally, the \(T_{p,Max}\) of the Stratified model is also observed in the Stratified model, as shown in Figure 14b. Figure 16: Particle temperature distribution after stable cooling (at 100 s) (half region of the cylindrical calculation domain): **(a)** Homogeneous model, **(b)** Mixed model, and **(c)** Stratified model. Figure 15: The accumulated frequency of the heat-generating particle’s \(\text{Nu}_{p}\) after stable cooling (at 100 s), among three models. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Homogeneous Model** & **Mixed Model** & **Stratified Model** \\ \hline \(\left|\overset{\rightarrow}{V}_{f(p)}\right|_{Avg.}\) along \(R_{p}\) [m/s] * & 0.109 & 0.110 & 0.099 \\ \(\left|\overset{\rightarrow}{V}_{f(p)}\right|_{Avg.}\) along \(H_{p}\) [m/s] ** & 0.087 & 0.081 & 0.064 \\ \(\text{Nu}_{p,Avg.}\)[-] & 21.14 & 21.05 & 20.65 \\ \(T_{p,Max}\) [K] & 1118.88 & 1161.04 & 1170.37 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Data collected from the heat-generating particles after stable cooling (at 100 s) among three models. model (from the Fuel particle), located at the bottom central area of the debris bed, as well, was higher than in the Mixed model (shown in Table 9). This can reflect the total impact of the BC effect in the Stratified model on \(T_{p,Max}\), including the weakened \(\text{Nu}_{p,Avg. }\) of the debris bed and the deteriorated particle-particle heat conductive transfer for the Fuel particles due to the evident bed-centralized fissile material area on the bottom of the Stratified model without Structure particles inside. Following the same procedure in the criticality assessment, the PC and BC effects on the \(\text{Nu}_{p,Avg. }\) of the debris bed and the cooling safety margin for avoiding the particle re-melting accident (employing \(T_{p,melting}-T_{p,Max}\) as the criteria in this research, where \(T_{p,melting}\) is the MOX's melting point of 2800 K [44]) can be evaluated using Equations (31) and (32), and the results are listed in Table 10.  
To sum up, both PC and BC effects provided a dominant negative effect on the \(\text{Nu}_{p,Avg. }\) (in Table 10), mainly due to the relatively lower flow velocity around the heat-generating particles, relating to the lower located position after the particle redistribution. As for the cooling safety margin of \(T_{p,melting}-T_{p,Max}\), both PC and BC effects also exhibited total negative impacts (as shown in Table 10). Except for the effects from the suppressed \(\text{Nu}_{p,Avg.