# Mean Reattachment Length of Roof Separation Bubbles Using Proper Orthogonal Decomposition
## 3 Methodology  
### Data Collection for Roof Pressure on Low-Rise Building  
Wind-induced roof pressure data for this study were sourced from turbulent boundary layer simulations conducted in a wind tunnel at MS Engineering Corp. in Haman-gun, South Korea. The wind tunnel has external dimensions of 6.4 m (W) \(\times\) 4.9 m (H) \(\times\) 34.0 m (L), and the size of the test section is 3.0 m (W) \(\times\) 2.0 m (H) \(\times\) 15.0 m (L), as shown in Figure 3. It can generate wind speeds exceeding 15 m/s, with a turbulence homogeneity of \(\pm\) 0.8% at 10 m/s.  
In this study, hot-wire anemometry was utilized to measure wind velocity and turbulent intensity (\(I_{u}\)) profiles, while an electronically scanned pressure measurement system (Scanivalve MPS4264 miniature pressure scanner) was used to measure the roof pressure. The MPS4264 offers accuracy within \(\pm\) 0.2% for \(\pm\) 4 inches of water (in H\({}_{2}\)O) of the full scale.  
Prior to the experiments, the hot-wire anemometer was calibrated using a series of known airspeeds in a controlled environment. This calibration involved correlating the anemometer's readings with the known airspeeds to establish a reliable relationship between the electrical signal and the wind velocity. The pressure measurement system was calibrated by applying a known standard pressure, adjusting its settings for alignment, and confirming the accuracy across its entire operating range.  
The experimental setup is depicted in Figure 4. In this study, the building model was a rectangular prism, measuring 800 mm in width, 800 mm in length, and 400 mm in height with a geometry length scale of 1:40. Within the wind tunnel, this model produced a blockage ratio of 5.3%.  
The experiment primarily focused on assessing the impact of turbulence changes on the reattachment lines that bound roof separation bubbles. Rather than simulating the boundary layer for a specific wind exposure category, the experiment emphasized variations in turbulence intensity (\(I_{u}\)) at the roof height of 400 mm, with wind velocities scaled down to 1:4.  
Figure 5 shows the wind velocity and turbulence intensity (\(I_{u}\)) profiles for two turbulent flow conditions: intermediate and low turbulence. For the intermediate turbulence condition, the boundary layer was defined by a power law index of 0.20. At the roof height, the wind velocity and turbulence intensity (\(I_{u}\)) were approximately 6.8 m/s and 12.7%, respectively. On the other hand, under the low turbulence condition, the boundary layer had a power law index of 0.16, and at the roof height, the wind velocity and turbulence intensity (\(I_{u}\)) were approximately 8.0 m/s and 0.6%, respectively.  
Figure 3: Configuration of the wind tunnel.  
To examine the influence of wind direction on the mean reattachment length (\(X_{r}\)) of roof separation bubbles, wind pressures on the model's roof were measured under intermediate turbulence intensity (\(I_{u}=12.7\%\)) for two wind angles (\(\alpha\)) of \(0^{\circ}\) and \(5^{\circ}\), as shown in Figure 6. Additionally, to assess the effect of different turbulence intensities on the mean reattachment length (\(X_{r}\)), wind pressures were measured under low turbulence intensity (\(I_{u}=0.6\%\)) with a wind angle (\(\alpha\)) of \(0^{\circ}\).  
The roof pressure was measured at 486 taps using the MPS4264, with a sampling rate of 350 Hz. Each pressure record consisted of 16,384 data points per channel, ensuring the stationarity of signals.  
Figure 4: Low-rise building model and location of pressure taps on roof: (a) low-rise building model, (b) location of the pressure taps on the roof (unit: mm).  
Figure 5: Mean wind speed and turbulence intensity (\(I_{u}\)) profiles: (a) mean wind speed (m/s); (b) turbulence intensity (\(I_{u}\)) (%).