## 3 Results
### Sensitivity Analysis
#### 3.2.3 Boundary and Initial Conditions  
Finally, the outcome of the variation of the initial and boundary conditions is presented and again an overview, including the sign of the resulting changes in the mean power is shown in the Appendix A in Table 12. When analyzing these results, one has to keep in mind that in general the  
Figure 10: Power over time curve for charging of the standard case and the case with an increased heat conductivity as well as the regarding relative deviation.  
Figure 9: Power over time curve for charging of the standard case and the case with an increased melting enthalpy as well as the regarding relative deviation.  
parameters are varied by \(\pm\)1 K and \(\pm\)10%, but the heat losses, the inlet temperature (constant value vs. curve) and the inlet velocity (constant vs. parabolic profile) are varied in an on/off manner. Therefore, the influence is in general in a plus and minus direction, and only in one direction for the parameters with on/off variations. Consequently, the later presented ranking is based on a comparison of a mean of the variation by +1 K and -1 K or +10% and -10% with a variation from off (e.g., constant value) to on (e.g., profile).  
Figure 11 shows the mean deviation of the charging and discharging powers. The highest absolute influence can be seen for the heat losses with 21.4% and 16.4% during charging and discharging, respectively. The initial temperature and the inlet temperature have an influence of 0.8% to 2.2% on the mean power when varied by \(\pm\)1 K. All other variations of the boundary conditions (inlet velocity, inlet temperature curve and inlet velocity profile) have almost no influence on the mean power.  
In Figure 12, the maximum deviations of the charging and discharging power are presented for the variations of the initial and boundary conditions. The highest influence can be seen for the heat loss with 43.3% and 56.3% followed by the inlet velocity profile with 43.7% and 53.4% and the inlet velocity with 33.8% to 42.2%. The variation of the remaining initial and boundary conditions has an influence of 9.3% to 18.0%. The power during the charging and the discharging is depicted in the Appendix A in Figures A3 and A4 respectively for the reference case and the one with heat losses. As a comparison, the charging process with an inlet velocity variation of +10% is also examined in the Appendix A in Figure A5. In general, for all initial and boundary condition variations--except for the heat losses--the largest deviations occur only for a very short time interval at the beginning of the charging and discharging process (see e.g., Figure A5). This is also the reason why they have only a rather small effect on the average performance.  
The maximal deviations of the global liquid fraction are shown in Figure 13 when varying the initial and boundary conditions. The heat loss has the greatest influence with 8.2% to 13.2%, followed by the inlet temperature with 2.4% to 2.8%. All other variations of the initial and boundary conditions have a minimal impact of 0.1% to 1.2% on the maximal deviation of the global liquid fraction.  
Figure 11: Absolute relative variation of the mean power for charging and discharging when varying the boundary and initial conditions.  
Lastly, a comparison between experimental and numerical results with and without heat losses is performed on the mean power during the charging and discharging process until 7000 s. For charging, the achieved absolute mean powers are 26.2 W, 18.3 W, and 20.7 W for the experiment, the simulation without heat losses, and the simulation with heat losses, respectively. In the same order, the absolute mean powers during discharging are 14.1 W, 15.6 W, and 14.5 W. This leads to an absolute relative deviation of the simulation with heat losses from the experiment of 20.8% and 2.5% for charging and discharging, respectively. This is a distinctive decrease compared to the numerical results without heat losses; here the absolute relative difference was 29.9% for charging and 10.6% for discharging.