# Thermographic Stall Detection by Model-Inspired Evaluation of the Dynamic Temperature Behaviour
## 4 Results
### Near Thermodynamic Steady State Condition
#### 4.1.1 Identifiability  
Considering the evaluation criteria of the identifiability of flow regions on the basis of flow-dependent features, the mean temperature signal-processing approach as a classical concept is analysed at first. The mean temperature course over the normalized chord position in Figure 8d shows the estimated signal behaviour for the transition regions and enables distinguishing different flow regions. However, the temperature course within the single flow regions is mainly influenced by lateral heat conduction, see Section 2.1. In consequence, an unambiguous feature-based identification of flow regions is impossible. In particular, the identifiability of flow separation is reduced, as the temperature gradient along the chord position is similar in turbulent and separated flow regions.  
Since the measurement object is in a near thermodynamic steady state, the gradient-based evaluation in Figure 8e shows small absolute values of the temporal gradients. Within the laminar and the turbulent flow region, the convective heat input \(q_{\mathrm{c}}\) is higher than the heat emission by radiation \(q_{\mathrm{r}}\), which explains the positive gradient. For the normalized chord position (0.6-0.85) within the separated flow region, the surface of the measurement object is already approximately in a thermodynamic steady state. The increasing gradient and the local maximum at the normalized chord position (0.85-1) are explained by the increasing heat transfer coefficient, as well as a heat input by heat conduction from the pressure side of the airfoil. As a result, the different flow regions are only identifiable under a complex consideration of the cross-sensitivities.  
Figure 8: Comparison of the evaluation of thermographic image series by the mean temperature (**a,d**), gradient-based (**b,e**) and the harmonic signal processing approach (**c,f**) for a measuring object with near thermodynamic steady state behaviour. Left side (**a–c**): processed thermographic images, right side (**d–f**): averaged profiles over the chord position. Experimental parameters: \(Re=2\cdot 10^{6}\), \(AoA=14^{\circ}\).  
In contrast, the result of the harmonic signal processing approach around an operating point reflects the qualitative estimations of the heat transfer coefficient and enables the localisation of the flow regions, as follows:  
* Laminar boundary layer flow: \(0\leq\mathrm{x}/\mathrm{c}\leq 0.02\);
* Laminar-turbulent transition: \(0.02<\mathrm{x}/\mathrm{c}\leq 0.04\) (dashed lines);
* Turbulent-boundary layer flow: \(0.04<\mathrm{x}/\mathrm{c}\leq 0.46\);
* Turbulent separation point: about \(0.46\) (dashed lines);
* Turbulent separated boundary layer flow: \(0.46<\mathrm{x}/\mathrm{c}\leq 1\).  
The evaluation of the amplitude course in Figure 8f shows a continuously decreasing amplitude over the normalized chord position as a result of a decreasing wall shear stress within the attached flow regions. In contrast, the evaluated amplitude increases within the separated flow region due to the increasing heat transfer coefficient. Furthermore, sharp transitions are detectable as a result of the reduced influence of lateral heat conduction. In addition, the capability to detect surface modifications, which is a beneficial property of the harmonic signal processing approach around an operating point, is shown at the \(0.82\) normalized chord position with a clearly visible local amplitude maximum. Thus, the signal processing approach around an operating point provides a high degree of interpretability and enables an unambiguous feature-based identification of flow regions. In particular, the aim of an improved identifiability of flow separation is realised.