## 3 Dynamic Heterogeneity Investigation into Debris Bed Safety Analysis
### Results and Discussion
#### 3.3.3 Cooling Characteristics Analysis
By contrast, \(\left|\overset{\rightarrow}{V}_{f(p)}\right|\) presented the increased trend of the upward vertical flow velocity in both Mixed and Homogeneous models (as shown in Figure 14b), which reflected that \(\left|\overset{\rightarrow}{V}_{f(p)}\right|\) along the vertical direction was mainly affected by the dominant buoyance force relating to the heat-generating particles. Furthermore, compared with the Homogenous model, although the PC effect in the Mixed model caused the higher  
Figure 13: Historical data of the liquid sodium’s maximum temperature among three debris bed models. increased \(\left|\overset{\rightarrow}{V}_{f(p)}\right|\) gradient along the vertical direction (in Figure 14b) because of the higher value of the accumulated decay heat source along the vertical direction in the Mixed model, the \(\left|\overset{\rightarrow}{V}_{f(p)}\right|_{Avg. }\) on the vertical direction in the Mixed model was still lower than the Homogeneous model (listed in Table 9) since the heat-generating particles in the Mixed model were located at the relatively lower place of the debris bed after particle redistribution. Meanwhile, the average Nu\({}_{p}\) of the heat-generating particles in a debris bed (Nu\({}_{p,Avg. }\) [-]), which can represent the decay heat removal efficiency of the debris bed, also reflected the influence of the affected \(\left|\overset{\rightarrow}{V}_{f(p)}\right|\). Nu\({}_{p}\)'s accumulated frequency curve of Mixed/Homogeneous models and the corresponding Nu\({}_{p,Avg. }\) are presented in Figure 15 and Table 9, respectively. The lower Nu\({}_{p,Avg. }\) in the Mixed model compared to the Homogeneous model (as shown in Table 9) presented the PC effect, suppressing the \(\left|\overset{\rightarrow}{V}_{f(p)}\right|_{Avg. }\) along the vertical direction in the Mixed model, and playing the dominant factor in deteriorating the performance of the Mixed model's Nu\({}_{p,Avg.}\). Finally, the particle temperature distributions of Mixed and Homogeneous models after stable cooling are also exhibited in Figure 16. Although the relatively random distributions of the particle temperature existed in the Mixed model because of the uneven distribution of the heat-generating Fuel particles within the debris bed, both Mixed and Homogenous models still showed a similar trend in the spatial particle temperature distribution, which was related to the built flow pattern. Along the radial direction, the particle temperatures increased towards the center of the debris bed due to the declined inward flow velocity in both models. On the other hand, both models displayed the decreased gradient of the particle temperature along the upward vertical direction due to the enhanced convective flow velocity. Hence, for both models, the particle with maximum temperature after stable cooling was located at the bottom center area of the debris bed, and the values of the maximum particle temperature (\(T_{p,Max}\) [K]) for the corresponding models are listed in Table 9. The \(T_{p,Max}\) in the Mixed model (from the Fuel particle) was ultimately higher than in the Homogeneous model, which reflects the overall impact of the PC effect in the Mixed model, including the weakened Nu\({}_{p,Avg. }\) and the heightened heat source of each heat-generating particle due to the particle-centralized fissile material (Fuel particle) present in the Mixed model. Figure 14: The flow velocity distribution collected from where heat-generating particles are located after stable cooling (at 100 s) among three models: (**a**) along the radial direction (0.13 m \(\leq H_{p}\leq\) 0.26 m), and (**b**) along the vertical direction (0 m \(\leq R_{p}\leq\) 0.13 m). The BC effect in the Stratified model is subsequently discussed by comparing it with the Mixed model. As shown in the Mixed model, the Stratified model also exhibits a decreased trend of inward flow velocity along the radial direction of the debris bed (Figure 14a), and an increased trend of upward flow velocity along the vertical direction (Figure 14b).