## 4 Exploring the TES Performances Improvement by a Numerical Parametric Study
### Temperature and Flow Rate Sensitivity Analysis  
Two monitoring parameters have been explored over a larger range than the one allowed by the experimental campaign: the inlet storage temperature and the HTF mass flow rate.  
The influence of the inlet temperature on the charging time, the total energy stored and the storage efficiency is depicted in Figure 9. The responsiveness decreased and the amount of energy stored increased with the inlet temperature: \(\tau_{95\%}\) dropped from 7.7 h to 4.9 h and the energy stored rose from 3.5 kWh to 4.6 kWh with a respective temperature increase from 60 to 80 \({}^{\circ}\)C. However, the influence of the inlet temperature is less important after a certain temperature for these two parameters. The storage efficiency proportionally decreased when the inlet temperature increased, as the tank insulation was not modified, inducing higher thermal losses. Besides hits, the aging study revealed that the PCM thermo-physical properties could be damaged above 75 \({}^{\circ}\)C: given the decreasing gains in time and energy and the degradation risks, the most suitable inlet temperature has been defined as 70 \({}^{\circ}\)C.  
The influence of the mass flow rate \(\dot{m}\) is shown in Figure 10.  
The charging and discharging times were similarly reduced by convective heat transfer intensification due to the flow rate's increase, with a stabilization above 0.05 kg/s. The discharge performances should also be assessed via an estimation of the valuable energy, i.e., the thermal energy available at a minimum temperature threshold. Under real operating conditions, the downstream process drives this threshold. For this parametric study, it was arbitrary set around 10 \({}^{\circ}\)C below the PCM melting temperature, at 45 \({}^{\circ}\)C. It appears that the valuable energy decreased when the flow rate increased: the convective heat transfer enhancement may be driven to a higher power but cool down faster the heat storage materials, inducing a higher proportion of thermal energy discharge at lower temperatures. The proportion of available valuable energy should be optimized by a mass flow rate adaptation during the discharge to fit with the heat demand. To pursue the  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Charge**} & \multicolumn{3}{c}{**Discharge**} \\ \cline{2-7}  & \(E_{stored}\) & \(E_{losses}\) & **Provided** & \(E_{discharged}\) & \(E_{losses}\) & **Recovered** \\ \hline Model & 4.1 kWh & 2.1 kWh & 6.2 kWh & 4.5 kWh & 1.2 kWh & 3.3 kWh \\ Experiment & 3.9 kWh & 2.5 kWh & 6.4 kWh & 4.1 kWh & 1.2 kWh & 2.9 kWh \\ Deviation & 5.1\% & 16\% & 3.1\% & 9.8\% & - & 13.8\% \\ \hline \hline \end{tabular}
\end{table}
Table 6: Energy balance—model and experiment comparison. Case study: 2 \({}^{\circ}\)C/h, charge 43.0–69.9 \({}^{\circ}\)C at 180 L/h and discharge 62.1–40.8 \({}^{\circ}\)C at 194 L/h.  
Figure 8: Discharge mode from 62.1 to 40.8 \({}^{\circ}\)C at 2 \({}^{\circ}\)C/h and 194 L/h.  
parametric study, the reference was set to a constant value of 0.05 kg/s (180 L/h), which is a compromise between the charge/discharge time and the valuable energy.