## 3 Results  
### Validation and Independency Studies  
All independency studies and the validation were performed for the charging process. The influence of the mesh was studied by three times refining an initial mesh of 12,200 cells with a factor of 1.2 in both spatial directions and by three times coarsening with a factor of 1.5 in both spatial directions. The maximum difference in the global liquid fraction (at 2000, 4000, and 6000 s) between the 12,200 cells mesh to the next finer one was only 0.63%, but the simulation time increased by about 40 h. Therefore, for all other simulations, a mesh with 12,200 cells was taken. For solving the pressure-velocity coupling, the SIMPLE and the PISO scheme as well as a PISO scheme with extrapolation--here called PISO-extra--were investigated. No difference was found in the liquid fraction for the different schemes, but the PISO-extra scheme was the fastest one in terms of computational time and almost 46% faster than the slowest one (SIMPLE). All following simulations were performed with the PISO-extra scheme. The influence of the discretization of the convective fluxes within the momentum and energy equation was studied as well. Three methods were analyzed (in an ascending sequence according to their order): Power-Law, Second-Order-Upwind, and Quadratic Upstream Interpolation for Convective Kinematics (QUICK). The maximum difference in the global liquid fraction at 2000, 4000, and 6000 s was about 4.5% between the Power-Law and the Second-Order-Upwind scheme, and about 0.5% between the Second-Order-Upwind and the QUICK scheme. Accordingly, the QUICK scheme was used for all subsequent simulations. The time step was first calculated according to the ANSYS Fluent Guide [35] for natural convection to 0.0213 s. Subsequently, the time step was gradually increased and the results were compared. The simulation ran stable as long as a time step \(\leq\) 0.2 s was chosen and there were no visible differences in the results for all stable simulations. In addition, a reduction of the simulation time of about 85% occurred by increasing the time step from 0.0213 to 0.2 s. For this reason, a time step of 0.2 s is used for all further simulations. \begin{table}
\begin{tabular}{c c} \hline \hline
**Material Properties, Initial and Boundary Conditions** & **Variation** \\ \hline \(\rho\) & \(\pm 10\%\) \\ \(c_{s}\) & \(\pm 10\%\) \\ \(c_{l}\) & \(\pm 10\%\) \\ \(\lambda\) & \(\pm 10\%\) \\ \(L\) & \(\pm 10\%\) \\ \(\eta\) & \(\pm 10\%\) \\ \(\beta\) & \(\pm 10\%\) \\ C  
Finally \(C_{\rm I}\) was varied from \(10^{5}\) to \(10^{8}\). It was seen that the results are not significantly different for a \(C_{\rm I}\) of \(10^{7}\) and \(10^{8}\). Therefore, a value of \(10^{7}\) was chosen. To validate the model, numerical results were compared to melting experiments described in [PERSON] et al. [31]. As depicted in Figure 3, the height of the solid PCM in contact with the outer tube is in good agreement between experiment and simulation. Due to the opacity of the solid PCM, the shape of the melting front cannot be analyzed optically. A comparison of the temperature curves over time, though, shows some significant deviations. This is illustrated in Figure 4 for temperature curves from measuring points with an identical height, and in Figure 5 for temperature curves from measuring points with an identical radius. Besides, the absolute mean discharging power up to 7000 s is 10.6% higher in the simulation compared to the experiment and the charging power is 29.9% smaller in the simulation. In order to better assess the reason for these deviations, a sensitivity analysis is performed in the following chapter. Figure 4: Comparison between experiment (exp) and standard simulation (num) for temperature curves during charging of measurement points with an identical height. Figure 3: Comparison of the height of the solid PCM for the experimental [31] and numerical results during charging (blue indicates solid, red indicates liquid, and yellow as well as green indicate the mushy region).