## 2 Investigations Focusing on Overall Accumulated-Bed Characteristics
### Investigations with Single-Sized and Single-Signed Solid Particles  
#### 2.1.1 Experimental Materials and Methods  
Aimed at phenomenologically understanding the fundamental characteristics of DBF behavior, some pioneering simulated experiments by using water and single-sized and single-shaped solid particles to simulate sodium coolant and debris were conducted by [PERSON] et al. [23; 29; 62; 63] and [PERSON] et al. [65], concentrating on the overall accumulated-bed characteristics. Table 1 shows the comparison of material proprieties. Figure 3a shows the experimental system used by [PERSON] et al. [65], where a water tank measuring \(27\times 36\times 38\) cm and different release pipes were employed to obtain particle-releasing rates of 50-350 g/s. Nine experiments were performed by releasing a 1.7 kg single-sized spherical lead particle with a diameter of 1.8 mm into the water, transitioning from room temperature to 343K. Figure 3b displays the experimental apparatus, including a cylindrical container (375 mm inner diameter (\(D_{\text{in}}\)), 1020 mm height) and an upper particle injection device followed by a cylindrical releasing nozzle. In total, 119 sets of experiments, including 43 sets using non-spherical particles, were conducted. To investigate the characteristics of accumulated particle beds, six key initial parameters, including particle density (\(\rho_{\text{p}}\)), particle diameter (\(d_{\text{p}}\)), particle shape (spherical or non-spherical), particle volume (\(V_{\text{p}}\), 3-10 L), nozzle diameter (\(d_{\text{n}}\), 20-40 mm), and nozzle height (\(H_{\text{n}}\), 0.47-0.72 m), were considered. As shown in Figure 4, five important quantities related to bed characteristics, including the final bed height (\(H_{\text{b}}\)), final mound height (\(H_{\text{m}}\)), final mound dimple area (\(A_{\rm dim}\)), final dimple volume (\(V_{\rm dim}\)), and final repose angle (\(\theta_{\rm r}\)) of the bed mound, were noted.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{2}{c}{**Physical Quantities**} & \multicolumn{3}{c}{**Condition**} \\ \cline{2-4}  & \multicolumn{1}{c}{**Reactor Accident**} & \multicolumn{1}{c}{**Experiments Focusing on Overall Accumulated-Bed Characteristics**} & \multicolumn{1}{c}{**Experiments Focusing on Flow-Regime Characteristics**} \\ \hline Material of debris & Mixture of MOX fuel and SS & Al\({}_{2}\)O\({}_{3}\), ZrO\({}_{2}\), and SS & Glass, Al\({}_{2}\)O\({}_{3}\), ZrO\({}_{2}\), SS, Cu, and Pb \\ \hline Density of debris (kg/m\({}^{3}\)) & 7620 (SS)\(\sim\)10,800 (MOX fuel) & 3600 (Al\({}_{2}\)O\({}_{3}\)), 6000 (ZrO\({}_{2}\)), 7800 (SS) at 298 K & 2600 (Glass), 3600 (Al\({}_{2}\)O\({}_{3}\)), 6000 (ZrO\({}_{2}\)), 7900 (SS), 8900 (Cu), and 11,340 (Pb) at 298 K \\ \hline Diameter of debris & 0.1 mm to several millimeters & 1.1–6.0 mm & 0.125–8.0 mm \\ \hline Liquid coolant & Sodium & Water & Water \\ \hline Coolant density (kg/m\({}^{3}\)) & 830 & 997 & 997 \\ \hline Viscosity (Pa.s) & \(2.40\times 10^{-4}\) & 8.91 \(\times\) 10\({}^{-4}\) & 8.91 \(\times\) 10\({}^{-4}\) \\ \hline \end{tabular}
\end{table}
Table 1: Comparison of material proprieties in experiments and reactor accidents (CDAs of SFRs) [24, 29, 68, 74].  
Figure 3: Experimental system for the investigations focusing on overall accumulated-bed characteristics: (**a**) used by [PERSON] et al. [65], and (**b**) used by [PERSON] et al. [29].