## 4 Modelling & Simulation Results
### Control and Shutdown System Interaction  
The basic approach for this study will be taken by initiating the shutdown from the critical state of the three cases with varying reflector thicknesses at the appropriate reflector position. The configuration of the critical state core with a 30 cm-thick reflector, with the reflector positioned at \(-29\) cm from the original position, leads to a \(\mathrm{k_{eff}}\) of 1.0003, and different openings of the shutdown system are presented in Figure 13. From the stepwise figures, it is clear that the combination of the control and the shutdown system always tends to lead to a configuration such as that found in cases 1 and 3 in Figure 5, with the streaming path for the neutrons to the side mostly or completely blocked by the side reflector. Figure 12: 2D study of the differences in the neutron spectrum caused by the control system for the 35% enriched reflected (lower core part) and unreflected (upper core part) core configuration using the heavy metal-rich salt system. The efficiency of the shutdown system will be evaluated regarding the different openings of the shutdown system as well as regarding the influence of the thickness of the side reflector on the shutdown reactivity. The shutdown reactivity for the three different openings combined with the critical side reflector position is presented in Figure 14. On first glance, the reactivity change follows the expected pattern with an increasing negative reactivity effect when the width of the opening is increased. The other effect, the increase in the negative reactivity caused by the increase in the core slice split off from the core from a 10 cm-thick slice to a 30 cm-thick slice, coincides with the results presented in Figure 7. A better evaluation of the absolute values for the 30 cm opening for cases 1 and 2 of Figure 7 is shown on the left axis. These markers indicate that the combined shutdown and control case can be seen as a type of intermediate solution between the two cases, with the 30 cm-thick core layer split tending to be closer to case 2. In general, the influence of the radial reflector positions does not seem to have a very strong influence on the efficiency of the shutdown system. This finding will be very helpful for the future core design, but to deliver convincing results to the regulator, a study of a wider variety of combinations between the shutdown and the control system position will be required to demonstrate the efficiency of the shutdown system under all possible operational circumstances. Figure 13: Shutdown system opening steps with increasing opening of the gap in the core from top left to bottom right (top left 5 cm, top right 10 cm, bottom left 20 cm, and bottom right 30 cm) analyzing the critical system (30 cm case with 140 cm diameter and 140 height, reflector position \(-\)29 cm). It is essential to understand the interaction of the control system and the shutdown system for any consideration of the safety of a zero-power reactor. However, for reactor design, it is also important to understand, in addition, the effect of the thickness of the reflector on the efficiency of the shutdown system, as shown in Figure 15. From this figure, it is clear that the reflector thickness does not have a major influence on the shutdown reactivity; thus, there seems to be only a weak interdependence, which is important to know to guide future investigations and to create freedom for the design of a future zero-power reactor core. The most important information is that there is almost no influence of the small openings on the reactivity change. Thus, the shutdown system characteristics shortly after initiation of the shutdown are not affected by the reflector thickness, and even at the very large opening, the effect of the reflector thickness on the shutdown margin is very limited. Figure 14: Shutdown reactivity from critical system dependent on the opening width of the shutdown system based on the 30 cm case with 140 cm diameter and 140 cm height.