## 4 Results and Discussion
### Sizing Thermal Storage Tank  
The proposed energy storage tank design was based on a piping system coupled to the tank to carry out the energy charge process from the source and the discharge process to heat exchangers connected to the power block (PB). Due to the high energy density of the PCM material, it was proposed to connect the storage tank to a power block made up of 3 Stirling engines, with a capacity to dispatch 9 [kWe] jointly. It was achieved by making  
Figure 8: Diagram of flow components in the TES, similar to that proposed by [52].  
Figure 7: Time-dependent thermal power balance.  
parallel connections, that is, by subdividing the mass flow into three parts, which returns the total to the tank after delivering the required energy to the heat exchangers.  
The charging process begins with an increase in the temperature of the HTF in a central receiver located at the top of a solar concentration tower. Once the HTF reaches 600 \({}^{\circ}\)C, it is sent to the tank through the distributors at the thermocline. Next, the charged HTF transfers its heat to the PCM AlSi12 material inside the tank but outside the tubes. The PCM can store energy through the heat for 13 h. As for the lower temperature, HTF moved to the bottom of the tank is maintained at a minimum of 290 \({}^{\circ}\)C. Finally, as a side note, the inner steel tunnels undergo a surface heat treatment to protect against corrosion by the PCM.  
In the discharge process, cold HTF that was used by the heat exchangers in the power block is pumped to the bottom of the tank. It displaces the hot HTF from the upper part and moves it towards the respective exchangers to provide thermal energy to the engines. Additionally, the motors individually generate waste heat varying between 45 \({}^{\circ}\)C and 55 \({}^{\circ}\)C that can be used for other applications.  
The thermal storage tank and power block components are housed in a commercial container, so the global system acquires modularity. Furthermore, it allows the storage capacity to be varied according to the application requirements. In this case, 43 pipes with a nominal diameter of 2 \(\frac{1}{2}^{\prime\prime}\) SCH 80 (0.0635 [m]) and a height equal to the thermocline were selected and distributed, as specified in Figure 9. Each pipe is assigned a surrounding material of 90 [mm] diameter. From this relationship, the geometric parameters of the tank can be determined. Finally, Table 3 shows the main dimensions of the proposed storage tank. AlSi12 was selected due to its advantageous properties for thermal energy storage applications. Specifically, its high thermal conductivity and latent heat capacity make it efficient for energy storage and retrieval. Additionally, its compatibility with the operational temperature range of the system and its ability to undergo phase changes without significant volume expansion contribute to the system's overall efficiency and durability. This choice emphasizes the material's suitability for achieving high energy storage density and effective heat transfer in the thermocline tank configuration.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value** & **Unit** \\ \hline Capacity & 384.8 & [kWh] \\ Working fluid & Cerrolow 117 & - \\ PCM material & AlSi12 & - \\ Thermal Conductivity & 121 & [W/mK] \\ Melting Point (average) & 578 & [\({}^{\circ}\)C] \\ Specific Heat Capacity & 963 & [J/kg K] \\ Density & 2.66 & [g/cm\({}^{5}\)] \\ Latent Heat of Fusion & 389 & [J/g] \\ Download time & 13 & [h] \\ Loading time & 13 & [h] \\ Tank height & 1.8 & [m] \\ Tank diameter & 0.85 & [m] \\ Volume & 0.81 & [m\({}^{3}\)] \\ Porosity & 0.21 & - \\ Mass flow & 0.49 & [kg/s] \\ \(T_{H}\) & 600 & [\({}^{\circ}\)C] \\ \(T_{C}\) & 290 & [\({}^{\circ}\)C] \\ Configuration & Block with multiple tunnels & - \\ \hline \hline \end{tabular}
\end{table}
Table 3: Main parameters of the proposed design for the TES.