## 3 Results  
### Pressure Drop in the TES Systems  
The different TES systems studied were first characterized in terms of the pressure drop required to circulate the HTF through the system at room temperature. For its operation as a fluidized and as a confined bed, the average pressure drop in the TES system based on granular material was determined as the mean value of the pressure drop measured with an acquisition frequency of 100 Hz for 2 min. Measurements of the pressure drop in the TES system based on granular material were conducted with a variable rate of volumetric air flow measured at ambient temperature, ranging from 0 to 1300 lpm in intervals of 100 lpm, corresponding to a range of superficial air velocities, defined as the ratio of the volumetric flow rate to the bed cross-section, from 0 to 0.65 m/s. The experimental measurements of the average pressure drop in the granular material TES system operated as a confined bed followed a quadratic trend with the superficial gas velocity, as predicted by the Ergun correlation [30], via Equation (7), for a fluid percolating through a bed of static small particles. In fact, the experimental measurements for the pressure drop in the confined-bed system were in good agreement with the estimation of the Ergun correlation for porosity of the confined bed \(\varepsilon\) of 0.36, as shown previously [28]. \[\Delta p=\frac{150\mu H}{d_{s}^{2}}\frac{\left(1-\varepsilon\right)^{2}}{e^{3 }}u+\frac{1.75\rho H}{d_{s}}\frac{\left(1-\varepsilon\right)}{\varepsilon^{2} }u^{2}, \tag{7}\]  
The pressure drop of the granular material TES system operated as a fluidized bed increased quadratically with the superficial air velocity for values below the minimum fluidization velocity of the solids when the system was operated in a fixed-bed regime, in agreement with the correlation proposed by the Ergun correlation in Equation (7). However, for air velocities higher than the minimum fluidization velocity when the bed was fluidized, the pressure drop was uniform with the gas velocity and equal to the hydrostatic pressure of the bed. The minimum fluidization velocity of the granular material was measured to be 0.27 m/s, corresponding to an volumetric air flow rate of 539.5 lpm measured at ambient temperature [28]. Therefore, the discharge tests carried out on the granular material TES system performed at a volumetric air flow rate of 700 lpm at room temperature were performed for a superficial gas velocity greater than the minimum fluidization velocity of the silica sand, specifically 0.35 m/s, corresponding to a bubbling fluidized-bed regime when the system was operated with no confinement and a packed or fixed bed when a gas distributor was installed to mechanically confine the material. It should be noted that the air velocity in the bed was even higher during the discharge process due to the acceleration of the air caused by the high temperature of the granular material TES system [31]. In the case of the alumina block TES system, the average pressure drop was determined as the mean value of the pressure drop measured with an acquisition frequency of 50 Hz for 1 min. The measurements were performed for varying rates of volumetric air flow measured at room temperature between 0 and 1200 lpm in intervals of 100 lpm, corresponding to superficial air velocities, defined as the ratio of the volumetric flow rate to the bed cross-section, from 0 to 3.1 m/s. The value of the pressure drop in the alumina block TES system was two orders of magnitude lower than that of the granular material TES system. Figure 2 represents the pressure drop in the alumina block system as a function of the superficial gas velocity. As shown in Figure 2, the pressure drop of the alumina block TES system varied quadratically with the superficial gas velocity. The experimental measurements of this pressure drop were fitted to a quadratic expression with the superficial gas velocity, given by Equation (8), obtaining a determination coefficient of the fitting R\({}^{2}\) of 0.998.