## 4 Results
### DUB6W180 Airfoil (Test Case 2)
#### 4.3.2 Flow Transition Localization  
Figure 12 shows the intensity profile, intensity gradient profile, the approximations for locating the flow transition as well as the resulting flow transition positions equivalent to the last section, see Section 4.2. All intensity profiles have a high gradient at \(x\approx 148\,\mathrm{px}\) that enables a flow transition localization with minimal random error with either localization method. However, the systematic gradients within the laminar flow regimes in both the mean value and the temporal standard deviation have the effect that no distinct intensity \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{\(x_{\text{tr}}\)/\(c\) in \%} & \multicolumn{3}{c}{\(\sigma_{\text{rand}}\)/\(c\) in \%} & \multicolumn{3}{c}{\(\sigma_{\text{syst}}\)/\(c\) in \%} \\ \cline{2-10}  & **Mean** & **std** & **PCA** & **Mean** & **std** & **PCA** & **Mean** & **std** & **PCA** \\ \hline Intensity approximation & 53.1 & 40.9 & 46.1 & 17.62 & 22.07 & 0.25 & 6.96 & 7.08 & 0.34 \\ Intensity gradient approximation & 50.7 & 41.0 & 46.1 & 5.50 & 23.00 & **0.24** & 4.28 & 5.51 & **0.30** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Located flow transition position \(x_{\text{tr}}\) and corresponding random and systematic error \(\sigma_{\text{rand}}\) and \(\sigma_{\text{syst}}\) by means of both localizations methods for each image processing methods’ resulting flow visualization in the DU96W180 test case 1 at a \(\text{Re}=2\times 10^{6}\). Temporal mean value (mean), temporal standard deviation (std) and PCA. All values are normalized to the chord length \(c\). Figure 11: Thermographic flow visualization of the DU96W180 airfoil in cross-flow with a Reynolds number of \(3\times 10^{6}\). Temporal mean value and temporal standard deviation as well as principal components (PC) no. 1–3 from the PCA of the image series. Systematic inhomogeneities in the flow regimes are reduced in the PC, while a contrast between the laminar and turbulent flow regime is maximized in the mean value with \(\text{CNR}=1.79\). plateaus representing the two flow regimes exist. As a consequence, the approximation of the intensity does not auto-center at the position of flow transition, resulting in a systematic error of the localization. In the PC flow visualization, however, the reduction in the systematic gradients lead to the existence of two clearly distinct intensity plateaus between which the intensity approximation successfully centers. Figure 13 shows the result of the entire flow transition line localization over all image rows based on the temporal mean value (red), the temporal standard deviation (blue) and the PCA (green) result. Due to the high gradient at the position of the flow transition, the localization by means of the intensity gradient approximation has minimal random and systematic error in each flow visualization. The spatial temperature gradient in the laminar flow regime due to the changing heat flux and thermal reflection in the mean value and the temporal standard deviation results in a higher systematic error compared to the PCA result if the flow transition is located by means of the intensity profile approximation. Nonetheless, the minimal random error \(\sigma_{\text{rand}}\) and systematic error \(\sigma_{\text{syst}}\) amount to 0.13% \(c\) and 0.52% \(c\) for the approximation of the intensity gradient profile in the mean value. All errors are listed in Table 3.  
Figure 12: 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 11. 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 gradient amplitudes between the plateaus.