## 5 Discussion of Future Prospects
Preliminarily, considering the gas-injection cases, the modeling frameworks can be developed as follows: \[I=K_{\text{GI}}\left[K_{\text{MS}}K_{\text{NS}}K_{\text{B}}\times\frac{\left( \frac{v_{\text{PF}}}{v_{\text{C}}}\right)^{a}\left(\frac{H_{\text{B}}^{2}}{DW }\right)^{b}}{\left(\frac{\rho_{\text{P}}-\rho_{1}}{\rho_{1}}\right)^{c}\left( \frac{h_{\text{V}}T_{\text{G}}}{\rho_{1}}\right)^{d}}\right]\] (20) where \(K_{\text{GI}}\) is a new extension scheme. Theoretically, \(K_{\text{GI}}\) is required to ensure two points: (1) \(K_{\text{GI}}\) should monotonously increase as \(Q_{\text{g}}\) becomes larger to represent the effects of the gas flow rate on promoting pool convection and diminishing particle inertial impact; and (2) \(K_{\text{GI}}\) should become 1.0 if no gas is injected (i.e., \(Q_{\text{g}}=0\) L/min) to guarantee the applicability of the base model for non-bubbling cases. Here, it is also noted that the gas flow rate considered in our previous investigations may not cover the possible range of vapor flow rates from the drastic boiling induced by the accumulated debris beds in an actual CDA of an SFR [59, 83]. Therefore, further experiments with wider ranges of gas flow rates may also be necessary to ensure the predictability of the extended model under accidental conditions. 5. Further investigations under large-scale 3D conditions. Although essentially consistent parametric effects on characteristics of DBF were confirmed in both 2D flow regime and 3D accumulated-bed experiments, it should be highlighted again that an insufficiently large range of parameters for the 3D accumulated-bed experiments in the comparison to that of actual accident conditions may cause the loss of valuable evidence (such as additional variation in particle bed shape). Through elaborately performing the large-scale 3D experiments, insights obtained from 2D flow-regimeexperiments are expectable to be further verified under the large-scale 3D conditions. It can be expected that a more applicable and dependable empirical model associating the flow regime and accumulated-bed characteristics can be developed for application in reactor safety assessments. In fact, referring to the previous modeling studies on debris bed self-leveling behavior [14,84], it can be expected that the flow regime boundary lines (or empirical constants) determined for the predictive model under 2D conditions can possibly vary to some degree for large-scale 3D predictions. Such a predictive model is supposed to be useful in the improved designs of in-vessel core catchers along with the developments and validations of SFR safety analysis codes. Formal analysis, R.X. ; Investigation, R.X. ; Data Curation, R.X. and S.C.; Writing--Original Draft Preparation, R.X. ; Writing--Review and Editing, S.C. and R.X. ; Supervision, S.C.; Project Administration, S.C.; Funding Acquisition, S.C. All authors have read and agreed to the published version of the manuscript. The current work is financially supported by Guangdong Basic and the Applied Basic Research Foundation, grant number 2022A1515011582, and the Science and Technology Program of Guangdong Province, grant number 2021A0505030026, in China. Not applicable. Data Availability Statement: Data is contained within the article. The authors