## 3 Results
### Sensitivity Analysis
#### 3.2.2 Material Properties  
The outcome of the variation of the material properties is presented hereafter and an overview of the results including the sign of the resulting changes in the mean power can be found in the Appendix A in Table 16. Figure 6 shows the absolute relative variation of the mean power for charging and discharging with varied material properties. The variation of the density has the highest influence within the material properties of about 7.1% to 9.2%, followed by the melting enthalpy with 5.2% to 6.4%. The influence of the melting temperature, heat capacities and heat conductivity is always below 2.0%, but still noticeable. The influence is higher during charging compared to discharging for density, melting enthalpy as well as heat capacities and lower for heat conductivity and melting temperature. A variation of \(\eta\), \(\beta\), the Darcy constant \(C_{\rm I}\) and the mushy zone width \(T_{1}-T_{\rm s}\) by \(\pm\)10% and \(\pm\)1 K, respectively, has almost no influence on the mean power for the chosen conditions. In general, the impact is somewhat higher when lowering the parameter than when increasing it. Figure 5: Comparison between experiment and standard simulation for temperature curves during charging of measurement points with an identical radius. The maximal absolute relative influence of a variation in material properties on the charging and discharging power over time is depicted in Figure 7. The highest influencing parameter is density with 13.3% to 18.4%, followed by melting enthalpy with 10.8% to 13.6%, heat conductivity with 7.9% to 9.8% and melting temperature with 5.5% to 7.8%. All other material properties have always an influence of less than 6.0% and \(C_{\text{I}}\) has almost no impact. For \(\rho\), \(\lambda\), \(L\), \(c_{\text{s}}\) and especially \(c_{\text{I}}\) the influence is higher during discharging than during charging and for \(T_{m}\) it is vice versa. Again, the impact is, in general, somewhat higher when lowering the parameters than when increasing them. Figure 6: Absolute relative variation of the mean power for charging and discharging when varying the material properties by \(\pm\)10% or \(\pm\)1 K.  
Figure 7: Absolute maxima of the relative variation of the power for charging and discharging when varying the material properties by \(\pm\)10% or \(\pm\)1 K.  
The maximal absolute relative influence on the global liquid fraction is presented in Figure 8 as a function of the variation in material properties. The highest influencing parameter is density with a variation of 4.3% to 4.8%, followed by melting enthalpy with 3.3% to 4.2%, melting temperature with 2.5% to 3.7%, and thermal conductivity with 2.6% to 3.6%. For the other parameters, the influence is always below 2.0% and \(C_{1}\), \(\eta\) and \(\beta\) as well as \(c_{l}\) during charging and \(c_{s}\) during discharging have almost no impact. By analyzing the results as a whole, the material properties can be divided into three groups:  
* Material properties that have no, or only little effect, if they are varied like indicated here: only \(C_{1}\) has an influence that is always below 1% (maximum of 0.12%). Here, one has to keep in mind that \(C_{1}\) is varied by several orders of magnitude in literature, and not only by \(\pm\)10%. * Material properties that have an influence on the power and the global liquid fraction, but none on the mean power (i.e., the total heat transferred): the material properties \(\eta\), \(\beta\), \(\lambda\) and \(T_{1}-T_{s}\) mainly influence the maximum deviations and not the mean power. The reason why \(\lambda\) also has a slight influence on the average output is that the storage system can still absorb or release a certain amount of sensible heat at the end of charging and discharging.