# Thermographic Stall Detection by Model-Inspired Evaluation of the Dynamic Temperature Behaviour
## 4 Results  
### Near Thermodynamic Steady State Condition  
In order to compare the different signal processing approaches for a measurement object in a near thermodynamic steady state, the location of the turbulent boundary separation for \(Re=2\cdot 10^{6}\) is identified at first. Surface pressure measurements on the suction side of the airfoil serve as a reference, and the dimensionless pressure coefficient \(c_{\rm p}\) is calculated by:  
\[c_{\rm p}=\frac{p-p_{\infty}}{0.5\rho_{\infty}U_{\infty}^{2}}, \tag{10}\]  
where \(p\) denotes the static pressure on the airfoil surface, \(p_{\infty}\) and \(U_{\infty}\) are the static pressure and the flow velocity of the undisturbed incoming flow, respectively, and \(\rho_{\infty}\) is the fluid density.  
Figure 6 shows the experimental values of the dimensionless pressure coefficient \(c_{\rm p}\), including the 99% confidence interval as error bars over the normalized chord position \(x/c\) for different angles of attack \(AoA\), where \(c\) is the chord length. In addition to the pressure distributions of the presented experiment with \(AoA=14^{\circ}\), the pressure distributions for experiments without flow separation, i.e., with lower angles of attack of \(2^{\circ}\), \(6^{\circ}\) and \(10^{\circ}\), are plotted for comparison. For the presented experiment, the turbulent boundary layer separation is detected at \(x/c=0.46\) due to the constant values of the dimensionless pressure coefficient induced by the constant static pressure in separated flow regions [2; 28]. For comparison, at lower angles of attack without flow separation, positive pressure gradients are visible in the region from \(x/c=0.46\) to \(x/c=1\).  
In order to estimate the position of the laminar-turbulent flow transition for the presented experiment with \(AoA=14^{\circ}\), the thermographic detectable movement of the transition position for the measurements with the angle of attack of \(2^{\circ}\), \(6^{\circ}\) and \(10^{\circ}\) is used as a reference. As shown in Figure 7, the transition position moves from \(x/c=0.55\) for \(AoA=2^{\circ}\) to \(x/c=0.15\) for \(AoA=10^{\circ}\). As a result, the position of the laminar-turbulent transition is expected to be near the leading edge for \(AoA=14^{\circ}\).  
The subsequent respective comparison of the thermographic flow visualization with the different signal processing concepts is performed on the basis of the evaluation criteria introduced in Section 2.3:  
* Identifiability of flow regions on the basis of characteristic flow-dependent features;
* Distinguishability between flow regions using the contrast-to-noise ratio.  
For this purpose, the image processing results of the mean temperature (classical approach) as well as the novel gradient-based and the around-an-operating-point signal processing approach are shown in Figure 8 for the flow condition \(Re=2\cdot 10^{6}\). Figure 8a-c show the output images in order to analyse the distinguishability between the different flow regions. The averaged profiles over the normalized chord position are shown in Figure 8d-f with the aim of identifying flow-dependent features.  
Figure 6: Distribution of experimental determined dimensionless pressure coefficients \(c_{\rm p}\) on the suction side of the airfoil of type DU96W180 for a Reynolds numbers of \(Re=2\cdot 10^{6}\).  
Figure 7: Comparison of the laminar-turbulent flow transition position (dashed lines) for variable angle of attack by means of the evaluation of thermographic image series with the harmonic signal processing approach. Experimental parameters: variable angle of attack, \(Re=2\cdot 10^{6}\).