## 2 Measurement Approach  
### Thermogram Characteristics and Measurands  
The measurement quantities from a thermogram of a rotor blade with a premature flow transition are the position \(x_{i}\) of the turbulence wedge and its size, consisting of the height \(h_{i}\) and the width \(w_{i}\), where \(i\) is the running index of the wedge number. In Figure 1 (left), a real thermogram is shown with the marked position and size of one turbulence wedge as an example. Note that the actual temperatures of the different flow regimes are irrelevant for the wedge detection algorithm, which is why all values in the thermograms are interpreted as intensities between 0 and 1 by normalizing with the maximum intensity \(I_{\text{max}}\). According to Figure 1, the thermogram shows the leading edge and the trailing edge of the rotor blade, as well as the natural transition line that indicates the position of the non-premature flow transition from laminar to turbulent. The region of interest for the detection of turbulence wedges lies between the leading edge and the natural transition line, i.e., their distance equals the maximal height \(h_{\text{max}}\) of a turbulence wedge. In general, \(N\in\mathbb{N}\) turbulence wedges are visible in one thermographic image. The height \(h_{i}\) of a turbulence wedge is defined as the orthogonal distance of the wedge's tip to the natural transition line, i.e., the wedge's base. The width \(w_{i}\) is defined as the width of the base. The position of the turbulence wedge is defined as \((x_{i},y_{i}),i\in\{1,\dots,N\}\), where \(x_{i}\) is the center of the wedge's base. The \(y\)-position of the wedge's base is set to \(y_{i}=y_{\text{NT}}(x_{i})\), where \(y_{\text{NT}}(x_{i})\) denotes the \(y\)-position of the natural transition line at \(x_{i}\). The position \(x_{i}\) together with the height \(h_{i}\) and the width \(w_{i}\) of each turbulence wedge are the measurement quantities returned by the wedge detection algorithm. Furthermore, the height and the width are used to calculate the area \(A_{i}\) of the turbulence wedge, with which the additional turbulent area due to premature transitions is quantified. One further characteristic feature of the turbulence wedge is its symmetry or the lateral tip position. The tips of turbulence wedges in real thermograms are often not centered below the middle of their base. An example is shown in Figure 1 (left), where the wedges are skewed to the right. The wedges can appear skewed due to the camera perspective or due to the rotational movement of the rotor blade, which implies crossflow. The tip's position can be described using the angle \(\alpha_{i}\) between the left edge of the turbulence wedge and the wedge's base. While the tip's position does not influence the size of the area of the turbulence wedge, it still needs to be taken into account for the detection of the turbulence wedge with the model-based algorithm. A detailed analysis of real thermograms revealed an intensity gradient in the region between the leading edge and natural transition line, which is characterized by decreasing pixel intensities towards the leading edge. Due to the curvature of the blade at the leading edge and the dependency of the emission on the observation direction [15], lower pixel  
Figure 1: A real thermogram of a rotor blade of a wind turbine in operation with two turbulence wedges (**left**) and a simulated thermogram with one turbulence wedge (**right**). In this case, the rotor blade is warmer than the surrounding fluid, which means that the rotor blade is cooled by the boundary layer flow. The cooler the temperature, the lower the pixel intensity. Important characteristics of the thermograms are indicated. intensities were captured in the thermogram at the leading edge. Furthermore, the heat transfer coefficient in the laminar flow regime was higher near the leading edge, where the laminar boundary layer was not yet fully developed, which also led to lower pixel intensities.