## 5 Results
### Correlation of Aerodynamic Properties and Flow Characteristics  
The previous section examined airflow structure and behavior through flow visualizations. This section uses statistical correlation analysis to explore the quantitative relationships between key flow properties, consisting of temperature, air velocity, relative humidity, and TKE. Understanding how these variables are interrelated is essential for identifying the underlying patterns that govern indoor environmental conditions. By examining these correlations, we aimed to determine which parameters most strongly influenced others and how they collectively contributed to airflow behavior within the building. Reference classifications widely used in engineering and ventilation studies are provided in Table 4 to interpret the strength of the correlations [38]. This approach should support more informed decision-making for climate control and conservation planning in heritage buildings. Figure 19 presents the correlation coefficients for key airflow properties--air velocity, temperature, relative humidity (RH), and TKE--for five different wind directions (S, SSE, E, NE, and N). The main results from the numerical simulation were:  
* Velocity and Temperature: For all directions, there was a negative correlation between air velocity and temperature. The strongest negative correlation was for the northeast wind condition (NE = \(-\)0.55), indicating that higher air velocities were associated with lower temperatures. * Velocity and TKE: Correlation values between velocity and TKE were in the range \(-\)0.061 to 0.51. Depending on direction, this relationship was generally weak-to-moderate, with a strong positive response under north wind conditions (N = 0.51), indicating that a stronger airflow increased turbulence, especially from the north. * Velocity and Relative Humidity: There was a positive correlation between velocity and RH for all studied directions, ranging from 0.21 to 0.54. The strongest positive association was in the northeast wind direction (NE = 0.54), suggesting that a higher airflow can increased humidity mixing, potentially reducing localized moisture buildup. * Temperature and TKE: These correlations were generally weak and inconsistent, ranging from 0.002 to \(-\)0.64. The strongest inverse relationship was for north wind conditions (N = \(-\)0.64), suggesting that high turbulence may contribute to temperature reduction. * Temperature and RH: This relationship was strongly negative and remarkably consistent for all wind directions, with a value of \(-\)1.00 in each case. This suggested a perfectly inverse relationship--as the temperature increased, the relative humidity decreased--a well-established physical principle, confirming the reliability of the data. * TKE and RH: The relationship between TKE and RH was weak and varied with wind direction, ranging from \(-\)0.24 to 0.64. There was a moderate positive correlation for the north wind condition, indicating that increased turbulence may support hu \begin{table}
\begin{tabular}{c c} \hline \hline
**Correlation** & **Correlation Level** \\ \hline \(-\)1.00 to \(-\)0.70 & Strong negative \\ \(-\)0.70 to \(-\)0.40 & Moderate negative \\ \(-\)0.40 to \(-\)0.10 & Weak negative \\ \(-\)0.10 to 0.10 & No correlation \\ 0.10 to 0.40 & Weak positive \\ 0.40 to 0.70 & Moderate positive \\ 0.70 to 1.00 & Strong positive \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Classification of correlation strength based on correlation coefficient. midity distribution in some cases, though the relationship was inconsistent across all scenarios. These results revealed essential dependencies among the environmental variables under different wind conditions. The consistent inverse relationship between temperature and relative humidity is critical for managing internal moisture levels. At the same time, the moderate link between velocity and turbulence highlights the need to balance airflow strength to control both comfort and conservation risks.