# Thermographic Stall Detection by Model-Inspired Evaluation of the Dynamic Temperature Behaviour
## 2 Principle of Measurement
### Criteria for Flow Region Identification and Distinguishability  
Independent of the signal processing approach, the flow regions can only be identified by comparing the processed thermographic images with the flow-dependant heat transfer coefficient \(\alpha\). Therefore, the first criteria for the evaluation of the proposed signal-processing approaches is the unambiguous _identification_ of flow regions by means of flow-dependent heat transfer features on the processed thermographic images. As a result, an estimation of the local heat transfer coefficient is needed.  
In order to estimate the qualitative behaviour of the local heat transfer coefficient, the well-known heat transfer behaviour on a smooth circular cylinder with supercritical cross-flow is used as a reference. The following features of the heat transfer coefficient are available to realize an identification of different flow regions [23; 26]:  
* Laminar flow region: \(\alpha\) decreases as a result of the decreasing wall shear stress.
* Laminar-turbulent flow transition: \(\alpha\) increases sharply as a result of the increased turbulent mixing in the turbulent flow region.
* Turbulent flow region: \(\alpha\) decreases as a result of the decreasing wall shear stress.
* Separated flow region: \(\alpha\) increases, due to the increased transverse exchange of fluid in the turbulent separated flow region induced by grown vortices. In contrast to attached flow regions, large-scale vortices are the dominant mechanism for convective heat transfer in separated flow regions.  
The result of the harmonic signal processing approach around an operating point corresponds directly to the presented features of the heat transfer coefficient and enables a subsequent identification of flow regions. In contrast, the gradient-based evaluation for transient input signals requires a consideration of the initial surface temperature \(T_{0}\) in order to be able to detect flow-dependent features and identify the different flow regions. Note that the mentioned qualitative local heat transfer features are approximately expected for the flow velocities and rotor blade profiles at wind turbines, due to the underlying boundary layer mechanisms. However, a precise estimation of the local heat transfer behaviour requires a more detailed consideration of the geometry and surface properties of the measurement object as well as the incoming flow conditions.  
As second evaluation criteria, the contrast-to-noise ratio (CNR) is calculated, which is a common approach in order to quantify the _distinguishability_ between a pair of flow regions. The CNR between the flow regions \(a,b\) is calculated by  
\[\text{CNR}=\frac{\left|\overline{C}_{a}-\overline{C}_{b}\right|}{\sqrt{( \frac{1}{N_{a}}\sum_{i=1}^{N_{a}}\text{ s}_{a,i})^{2}+(\frac{1}{N_{b}}\sum_{j=1}^{N _{b}}\text{ s}_{b,j})^{2}}}. \tag{5}\]  
The spatial image dimension is \(M\) x \(N\) pixel, where \(M\) represents the model span and \(N\) the chord length. \(\overline{C}_{a}\), \(\overline{C}_{b}\) are the spatial mean of the pixels within a flow region. While \(s_{a,i}\), \(s_{b,j}\) describes the corresponding standard deviation transverse to the flow direction. The standard deviation is calculated transverse to the flow direction in order to reduce the influence of gradients on the processed images along the flow direction.