## 3 Results
### Thermal Storage System
#### 3.2.1 Fundamental Contexts to Systemic Storage Densities  
For investigating of such a concept on its systemic storage densities, results depending on the heating wire assignment and the specific surface for an exemplary selected solution set with a void fraction of 42.5% are shown in Figure 5. Hereby the gravimetric systemic storage density (\(Q/m_{tot}\)) includes the mass of the honeycomb, the heating wire and the thermal insulation and the volumetric systemic storage density (\(Q/V_{tot}\)) includes the volume of the honeycomb and the thermal insulation.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \(\tau\) [min] & \(Q\) [kWh] & \(T_{W}\) [\({}^{\circ}\)C] & \(U\) [V] & \(I_{max}\) [A] \\ \hline
30 & 2.5 & 60 & 400 & 16 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Application-typical specifications as basis for storage system design investigations.  
The results show an increase in systemic storage densities up to a maximum value with increasing heating wire assignments at constant specific surfaces. This is due to the fact, that with this associated higher storage temperatures allow decreasing honeycomb masses or volumes, but increase simultaneously the heating wire and thermal insulation dimensions. Specifically, for efficient design solutions with high specific surfaces and hence the lowest honeycomb dimensions, this contrary effect leads to the observed maximum in gravimetric and the plateau in volumetric systemic storage density.  
The lower systemic storage densities with decreasing specific surfaces at constant heating wire assignments results from their corresponding smaller number of honeycomb channels. This leads-apart from increasing thermal conduction resistances-to shorter total heating wire lengths (\(L_{P}\)) and so to a moderate heating of the honeycomb structure and thus to higher storage masses.  
This context is illustrated in Figure 6 showing the systemic storage densities as a function of the resulting heating wire dimensions.  
The results show a direct correlation between the systemic storage densities and the heating wire dimensions. With increasing heating wire length, a maximum value in the systemic storage densities is reached limited by above-described contrary effect between honeycomb and heating wire or thermal insulation dimensions. Optimal solutions-here with heating wire length of about 30 m-can be directly derived from configurations with appropriate specific surfaces and heating wire assignments. Additionally, the results show correlating heating wire lengths to heating wire diameters (\(d_{P}\)) as illustrated in colored dots. This behavior is based on the specified electrical power supply in Table 4 forcing  
Figure 5: Gravimetric and volumetric systemic storage densities depending on heating wire assignment (\(x\)) and specific surface (\(a_{V}\)) at an exemplary void fraction (\(\epsilon\)) of 42.5%.  
Figure 6: Gravimetric, volumetric systemic storage densities and heating wire diameter (\(d_{P}\)) depending on heating wire lengths (\(L_{P}\)) at an exemplary void fraction (\(\epsilon\)) of 42.5%.  
a constant electrical resistance and thus increasing heating wire diameters with heating wire lengths.  
For the results presented here with an exemplary selected void fraction, maximum gravimetric and volumetric systemic storage densities of about 201 Wh/kg and 113 kWh/m3 are reached, whereby these are associated with design solutions for specific surfaces and heating wire assignments. In order to identify only such systems with maximum possible storage densities, iterative optimization simulation studies were performed. The corresponding results with this as well as the influence of void fraction are presented in the following.