## 4 Results
### DU96W180 Airfoil (Test Case 1)
#### 4.2.2 Flow Transition Localization  
Figure 9 shows the intensity profiles (blue) and respective intensity gradient profiles (orange) along the white dashed line depicted in the respective flow visualizations from Figure 8. The approximations of the intensity profiles and the gradient profiles are shown with a dashed line in the respective color. The results of each of the two flow transition localization methods are marked with a vertical dotted line. As mentioned before, the temporal standard deviation flow visualization offers no features that can distinguish flow regimes. This is confirmed by the intensity and the intensity gradient profiles shown in Figure 9, as no distinct plateaus or single gradient peaks exist, respectively. The flow transition localization therefore has a high systematic error. As expected by the low CNR between the flow regimes, no distinct plateaus with different intensities exist in the mean value. Consequently, the auto-positioning of the approximation fails, and the fitting curve does not center at the position of the flow transition. The intensity gradient profile has multiple peaks and no constant plateau around the flow transition, also resulting in a false positioning of the respective approximation. As a result, both methods have a high systematic error in the located position of the flow transition. Without a sharp temperature rise in the intensity profile and multiple peaks in the gradient profile, the random error is also expected to be high. In the PC 1 flow visualization, however, two distinct plateaus in the intensity profile exist, as expected by the high CNR. Therefore, the approximation successfully auto-positions at the position of the flow transition between these plateaus with a minimal systematic error. Additionally, the steep intensity step between the flow regimes, visible as a high distinct peak in the intensity gradient profile, minimizes the random error and allows for an approximation of the intensity gradient profile with minimal systematic and random error. A comparison of the two intensity profiles and the intensity gradient profiles of the mean value and the PC 1 highlights the advantage of the PCA method for creating flow  
Figure 9: The intensity profile (blue line), intensity gradient profile (orange line) along the white dotted line in the temporal mean value, temporal standard deviation and PC 1 flow visualization in Figure 8. The approximation of the intensity profile (blue dashed) and intensity gradient profile (orange dashed), respectively. The flow transition localization results of both methods are depicted with a vertical dotted line in the respective color. Different expressions of the intensity plateaus are visible in each profile with varying gradients between the plateaus. The most distinct expression of the two plateaus including a steep step between them exists in the PC 1.  
visualizations with two distinct intensity plateaus representing the two flow regimes and a steep step between them. Figure 10 compares the results of the two flow transition localization methods applied to all image rows of the temporal mean value, temporal standard deviation and PC 1 flow visualizations depicted in Figure 8. The flow transition line results located in the mean value image are plotted in red, the ones from the temporal standard deviation image in blue and from the PCA image in green. As a background image, one single thermographic raw image from the image series is used. A clear difference in the systematic and random localization errors between the PCA result and the two classical image processing methods is visible. Only the PCA result resembles the expected linear form of the flow transition line. The estimated systematic error \(\sigma_{\text{syst}}\) reads 0.34% and 0.30% the chord length \(c\) for the approximation method of the intensity and the intensity gradient profile, respectively.