# Thermal and Acoustic Design of a Shelter for High-Voltage Electrical Equipment
## 4 Thermal Aspects
### Validation of the Model
#### 4.3.2 Comparison of the Experimental Results  
The thermal experiment performed on the downscaled model is based on a total of three measuring positions called \"Datalogger-Inside\", \"Datalogger-Aesthetic\" between the shelter and the aesthetic panel, and \"Ambient Thermometer\" measuring the outside temperature far from the downscaled model. The results of the comparison between measurements and simulations are given in Figure 8. The steady-state values obtained through the CFD simulation are represented as horizontal lines. The left of Figure 8 reports the values of the temperatures measured in the three selected positions in comparison with the average steady-state results of CFD simulations. To mitigate the impact of local temperature variations due to the stratification inside the volume, the temperature rise between the outside and the gap behind the aesthetic panel, and the temperature rise between the outside and the inside of the shelter over the same period are shown in the right of Figure 8.  
To provide a quantifiable assessment of the agreement of the simulated values to the measurement results, the root mean squared error, RMSE, mean bias error, MBE, and coefficient of variation of the root mean squared error, Cv(RMSE) were calculated as follows:  
\[RMSE=\sqrt{\frac{\Sigma_{i}^{N}\big{(}T_{CFD}-T_{expj}\big{)}^{2}}{N}} \tag{13}\]  
\[MBE=\frac{\sum_{i}^{N}\big{(}T_{CFD}-T_{expj}\big{)}}{\sum_{i}^{N}T_{expj}} \cdot 100 \tag{14}\]  
\[CV(RMSE)=\frac{RMSE}{\frac{1}{N}\cdot\sum_{i}^{N}T_{expj}}\cdot 100 \tag{15}\]  
Calculated values of the three indicators for the aesthetic panel gap temperature, the inside temperature and, for information, the outside temperatures, are given in Table 2.  
Figure 8: Time series of the temperatures recorded by the dataloggers. The verification upon the completion of a mesh convergence analysis is performed by verifying the equation of continuity through the inlets and outlet of the shelter [24]. With the air density being the same for practical purposes, as the range of temperature variations is small enough, only the volume flow rates are compared. It was found that the volume flow rate through the inlets is 8726.7 cm\({}^{3}\)/s, whereas that through the outlet is 8221.9 cm\({}^{3}\)/s, with a 5.78% difference. The agreement shown in Figure 8 is acceptable. The outside temperature was not constant, due to various factors such as the variation of temperature, wind, and occasional cloud cover. This has led to a long duration of the experiment before a steady state could be established. Although it is subjective, it can be said that the steady state was fairly established between 16:00 and 16:30. In Figure 9, the agreement of the temperature differences between the experiment and the simulation is illustrated. The left of Figure 9 shows that the temperature difference between the air inside the volume and the air in the gap predicted by CFD is about 7.22 \({}^{\circ}\)C, which is roughly what the experiment also suggests in the final part of the acquisition. There is some discrepancy between the experiment and its corresponding CFD simulation. There can be many factors contributing to this discrepancy. One major factor is the variation of ambient temperature throughout the experiment. In the simulation, such a difference is neglected, and the outdoor temperature is considered constant and set to be equal to 29.5 \({}^{\circ}\)C. Moreover, in the simulation, the initial air speed was neglected, implying that there was no wind. This condition was not respected during the experiment, with the wind being weak but varying. Another major factor is solar irradiation. In the simulations, a constant solar heat flux of 813 \(\mathrm{W/m^{2}}\) from a direction corresponding to the sun position at 4 p.m. was entered.