## 2 Materials and Methods
### Experimental Systems
#### 2.2.1 Experimental Setup of the TES System Based on Granular Material  
The TES system based on granular material was cylindrical in shape, with an inner diameter of 20.5 cm. At the bottom of the vessel, a perforated plate with a mesh aperture of 100 \(\upmu\)m was used as a gas distributor to uniformly distribute the flow of air, used as HTF, in the cross-section of the system and to prevent the granular material from falling into the plenum chamber. A mass of 55 kg of regular silica sand with an average particle size of 600 \(\upmu\)m was used as granular storage material in the cylindrical TES system, corresponding to a fixed bed height of 1 m. The walls of the cylindrical vessel were surrounded by 4 electric heaters with an individual power of 1.5 kW to heat up the complete TES system to the desired initial temperature. The lateral wall of the system was isolated with a mineral wool shell of 5 cm thickness to minimize heat loss to the ambient air.  
The granular material TES system was capable of operation as a fluidized bed for air velocities above the minimum fluidization velocity of the silica sand that was employed, which was measured to be 0.27 m/s, corresponding to a volumetric flow rate of 539.5 lpm at room temperature [28]. For operation of the granular material TES system in the bubbling fluidized bed regime, a 2 m extension of the vessel was installed at the top of the system to prevent the particles ejected by the bubbles in the fluidized bed from escaping the TES system. The TES system based on granular material was also operated as a confined bed by removing the extension of the vessel and including perforated plate gas distribution at the top, similar to that used at the bottom of the system, to mechanically confine the bed of silica sand from the top. The pressure exerted by this gas distributor on the bed of granular material prevented the fluidization of the solids even at high air velocities by restricting the motion of the silica sand particles, which remained static in the confined bed. Thus, the operation regime of the confined bed was similar to that of a fixed or packed bed, even for air velocities higher than the minimum fluidization velocity of the granular material [25].  
Regardless of the regime of operation, the measuring system of the granular material TES system consisted of 19 type K thermocouples located at the axis of the cylindrical vessel and uniformly distributed along the 1 m height of the TES system, separated 5 cm apart. The pressure drop of the TES system based on granular material was measured by a differential pressure sensor OMEGA PMX309-007 GI (Norwalk, CT, USA) with a range from 0 to 7 bar and an accuracy of 0.25% of the full scale. The air flow rate was controlled by a pressure regulator and measured by an air flow meter SMC PF2A703H (Noblesville, IN, USA), with a range from 150 to 3000 lpm. The wall temperature of each of the electric heaters surrounding the TES system was regulated by independent proportional integral derivative (PID) temperature controllers. All the signals measured were monitored and registered by a Labview(r) interface, including a compact DAQ chassis cDAQ 9178 (Austin,  
Figure 1: Schematic of the experimental systems.  
TX, USA), a NI-9214 module to collect all the temperature measurements, and an NI-9203 module for the pressure drop measurements.