## 4 Results
### Verification
#### 4.1.2 Contrast of Turbulence Wedge  
The analysis of the image noise in real measurements as reference yields a standard deviation for the laminar flow regime of \(\sigma_{\mathrm{lam}}=2.0\) and the turbulent flow regime of \(\sigma_{\mathrm{turb}}=1.4\). With the mean intensity \(\overline{I}_{\mathrm{lam}}=250\) and \(\overline{I}_{\mathrm{turb}}=204\), the contrast to noise ratio (CNR) between the flow regimes, calculated by  
\[\mathrm{CNR}_{a-b}=\frac{(\overline{I}_{a}-\overline{I}_{b})^{2}}{\sigma_{a}^ {2}+\sigma_{b}^{2}} \tag{5}\]  
is \(\mathrm{CNR}_{\mathrm{lam-turb}}=348\). In order to evaluate the robustness of the introduced image processing methods for localizing premature flow transitions with respect to the magnitude of the local gradient maxima, the simulated image from Figure 7a is reconstructed with varying contrast between the turbulence wedge and the surrounding laminar flow regime. By keeping the magnitude of the image noise equal to the level measured in real measurements, this results in a reduction of the CNR between the respective surface areas. To enable a more intuitive understanding, the turbulence wedge contrast \(c_{\mathrm{wed}}\) is defined relative to the contrast between the laminar and turbulent flow regime on rotor segments without premature flow transitions (\(c_{\mathrm{wed}}=100\%\)). Turbulence wedges with a low intensity, see case C in Section 1.2, have a \(c_{\mathrm{wed}}<100\%\); a contrast of \(c_{\mathrm{wed}}=0\%\) represents a turbulence wedge indistinguishable from the surrounding laminar flow regime. Typically occurring values for \(c_{\mathrm{wed}}\) in real measurement images are between 30% and 80%. Figure 8a-c shows the same simulated flow visualization as in Figure 7 with three different relative contrast values \(c_{\mathrm{wed}}\) of the turbulent wedges of 75%, 50%, and 25%, respectively. The final computed flow transition line of the evaluation method A (blue) and B (green) as well as the state-of-the-art method are shown for each image. The CNR value of the three images is 163, 73, and 18, respectively. For the high contrast, see Figure 8a, methods A and B of the introduced image processing are able to locate the flow transition line with much lower uncertainties compared to the state-of-the-art method that is only able to locate individual premature flow transitions. For a contrast of \(c_{\mathrm{wed}}=50\%\), the introduced methods prove to be able to detect the turbulence wedge which remains undetected by the  
Figure 7: Simulated thermographic flow visualization image with premature flow transitions along the flanks of a turbulence wedge. (**a**) Rotor blade surface section with a laminar (brighter) and turbulent (darker) flow regime. The rectangle marks the selected area shown in panels (**b–d**). (**b,c**) Evaluation of local gradient maxima for both introduced image processing methods A (blue) and B (green) and the state-of-the-art method (red). (**d**) True flow transition line in black as a reference as well as all image processing resultsstate-of-the-art method. For the low contrast of 25%, the premature flow transitions remain undetected for all evaluation methods. Figure 9 shows the mean euclidean distance between the true transition line and the evaluation results for 10 calculations between 100% (fully turbulent) and 0% (fully laminar) relative contrast \(c_{\text{wed}}\) between the turbulence wedge and the surrounding laminar flow regime in a simulated image similar to Figure 8. The sharp increase of the mean euclidean distance at \(c_{\text{wed}}=40\%\) for method A (blue) and B (green) can be explained by the use of a natural flow transition threshold. A low relative contrast \(c_{\text{wed}}\) of the turbulence wedge increases the local gradients at the position of the natural flow transition, see case C in Section 1.2. If these gradients are above a certain threshold, all local gradient maxima stream upwards that might represent premature flow transitions are discarded. As a consequence, the turbulence wedge is not detected.