## 4 Conclusions  
The discharge of TES systems based on granular material operated as fluidized or confined beds and a TES system based on alumina blocks were analyzed and compared. The temperature in the fluidized-bed TES system was homogeneous, whereas thermal segregation was present in the confined-bed TES system, with a thin thermocline separating the hot zone at the top of the bed and the cold zone at the bottom. In the case of the alumina block TES system, thermal segregation was also observed, although the temperature variation zone was much more diffuse compared with the confined-bed system.  
The HTF outlet temperature of the fluidized-bed system decreased following an inverse exponential trend with time during the discharge process, since the granular material cooled down with no temperature gradient in the solids due to their small particle size. The temperature reduction was roughly linear for the alumina block TES system, in which the wall of the alumina blocks was cooled down by the HTF while the center of the alumina walls remained hot. In contrast, the confined-bed TES system provided a uniform high outlet temperature for the HTF during the discharge of the system, because of the stationary character of the solids imposed by the mechanical confinement, which led to a progressive cooling of the confined bed in the direction of motion of the HTF, i.e., from bottom to top. Thus, the confined-bed TES system is preferred for applications in which a uniform temperature of the HTF is desired. The pressure drop of the fluidized bed was steady during the discharge, oscillating around 0.2 bar, while the confinement of the bed induced a higher pressure drop that decreased from 0.65 to 0.3 bar during the discharge process. Compared with the granular material TES system, the alumina block TES system was characterized by a much lower pressure drop, only varying between 7 and 5 Pa during the discharge. The exergy efficiency of each TES system throughout the discharge process was calculated, obtaining an inverse exponential and parabolic decrease for the fluidized bed and the alumina blocks, respectively, while the exergy efficiency of the confined bed was roughly uniform during the discharge, in line with the evolution of the outlet temperature of the HTF. Therefore, the granular material TES system operating as a confined bed was found to be optimal for the discharge of the system, considering its  
Figure 6: Evolution of the exergy efficiency of each TES system during the discharge process: (**a**) assigning the HTF pressure drop to the TES system, (**b**) considering the HTF pressure drop of the TES system as a parasitic consumption, i.e., with \(\Delta p=0\).  
energy efficiency and its capability to supply HTF at a high and uniform temperature to the power block of the plant.  
Conceptualization, A.S.-V., G.C. and A.S.-G.; methodology, A.S.-V., A.S.-G. and N.G.-H.; software, A.S.-V. and N.G.-H.; validation, A.S.-V., G.C., A.S.-G. and N.G.-H.; formal analysis, A.S.-V. and A.S.-G.; investigation, A.S.-V., G.C., A.S.-G. and N.G.-H.; resources, A.S.-V. and N.G.-H.; data curation, A.S.-V. and A.S.-G.; writing--original draft preparation, A.S.-V. and G.C.; writing--review and editing, A.S.-V., G.C., A.S.-G. and N.G.-H.; visualization, A.S.-V., G.C., A.S.-G. and N.G.-H.; supervision, A.S.-V. and N.G.-H.; project administration, A.S.-V. and N.G.-H.; funding acquisition, A.S.-V. and N.G.-H. All authors have read and agreed to the published version of the manuscript.  
This research was funded by Spanish Government, grant number PID2019-109224 RA-100. The research was also supported by a USA-Spain Fulbright grant under the Florida Polytechnic University program.  
Not applicable.  
The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.  
The authors declare no conflicts of interest.