## 5 Results
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Packing Factor [\%]** & **C1** & **C2** & **C3** \\ \hline
56.35 & 104.29 & \(8.03\times 10^{-10}\) & 0.206 \\
56.64 & 154.11 & \(10.4\times 10^{-10}\) & 0.238 \\
56.96 & 231.28 & \(5.68\times 10^{-10}\) & 0.307 \\
57.82 & 325.01 & \(5.66\times 10^{-10}\) & 0.373 \\
58.70 & 359.97 & \(5.27\times 10^{-10}\) & 0.371 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Reimann parameters fitted for the simulation data. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Bulk Density** & **Horizontal** & **Wall Friction** & **Height [m]** & **Diameter [m]** \\ \(\rho_{\text{b}}\)[kgm\({}^{-3}\)] & **Load Ratio [-]** & **Angle [\({}^{\circ}\)]** & **Angle [\({}^{\circ}\)]** & **Diameter [m]** \\ \hline
1440 & 0.4 & 48.7 & 40 & 10 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Material properties for the [PERSON] approach. Figure 5: Exerted pressure on the container wall. (**a**) “Cold” state of the packed bed; (**b**) thermally charged packed bed. For the cold packed bed, the results of the continuum model with packing factor 56.35% and 58.7% are in good agreement with the DEM data and [PERSON]'s approach. Near the bottom of the packed bed, there is a significant drop in pressure. The reasons for this are numerical inaccuracies due to the low number of elements and the chosen boundary conditions of the model. Furthermore, it can be observed that the two results for different packing factors deviate within up to 20% of each other. The more rigid packed bed with the higher packing factor exhibits slightly lower pressures. This result is unexpected at first, but can be explained by the limitations of the model: In the cold state of the packed bed, the occurring pressure is purely based on mechanical, gravity driven effects. Due to the higher effective Young's Modulus of the packed bed with the denser packing factor, the strain is lower, both vertically and horizontally. Thus, the exerted stresses on the container wall are lower for the less densely packed bed configuration. In comparison, the dependency of the packing factor on the results for the heated packed bed is more distinctive. In general, the results yield higher stresses for increasing packing factors. In the thermally charged state, the occurring stresses are primarily a result of thermal expansion. Due to the rigid walls of the model, the thermal expansion of the packed bed is converted directly into pressure on the wall. The pressures for a thermally charged packed bed simulated with the continuum model reach their peak values at around 15 m of bed height. The reason behind this is the applied thermal profile (see Figure 2), which has its highest temperature differences at that height. Compared to the DEM result of the thermally cycled packed bed, the continuum model tends to significantly overestimate the stresses of the packed bed for the upper half of the packed bed. In contrast, the stresses on the lower part of the packed bed fall of notably for the continuum model compared to the DEM results. Considering stochastical variance of the DEM results and the limitations of the continuum model due to simplifications, the agreement between those two approaches still is sufficient. In order to improve the accuracy of the continuum model, the changing condition of the packed bed, e.g., the densification and packing factor during thermal cycling, must be considered.