# The Experiments and Stability Analysis of Hypersonic Boundary Layer Transition on a Flat Plate
## 3 Experimental Results and Stability Analyses  
### IR Results  
Figure 5 shows the surface temperature distribution of a flat plate under different unit Reynolds numbers. At a lower Reynolds number (Figure 5a), the temperature at the leading edge of the flat plate is the highest and gradually decreases downstream. With the increase in Reynolds number (Figure 5b,c), the plate surface shows a different temperature distribution, and there is an obvious temperature difference along the flow direction. It can be seen from the IR image that the transition region presents an irregular \"wavy shape\". [PERSON] et al. [32] also found this \"wavy\" transition non-uniformity in the study of the boundary layer transition of the flat plate and concluded that it may be caused by the natural incoming flow and the disturbance non-uniformity of the forefront of the flat plate.  
Figure 4: Comparation of mean flow variables at x = 0.1 m.  
The mean Stanton number distributions calculated from IR images are shown in Figure 6. The black and red dashed lines represent the Stanton numbers for the flat-plate boundary layer in all laminar and turbulent states, respectively. The curve of discrete points in the Figure 6 shows the distribution of mean Stanton numbers along the x-direction calculated from the wind tunnel experiments, where the surface of a flat plate develops from laminar flow through turning to turbulence. In the transition region, the Stanton number increases rapidly and reaches the value for turbulent flow. In the case of a lower unit Reynolds number (Figure 6a), limited by the length of the plate, the IR images only capture the beginning of the BL transition. With the increase in the unit Reynolds number, the transition position moves upstream, whereas the transition Reynolds number increases, and the complete laminar transition to turbulent processes can be observed. As a comparison, the results of full laminar flow and full turbulence are also given as a reference. The calculation results of infrared thermal imaging are in good agreement with the calculation results in the laminar flow area, and the change of the flow direction Stanton number is within the range of laminar flow and turbulence.  
Figure 7 represents the transition Reynolds number distribution at different spanwise positions under different unit Reynolds numbers. Moreover, the transition Reynolds number calculated by the compressibility-modified transition model \(\gamma\)-Re\(\mathbf{\mathrm{t}}\)([PERSON] et al., 2016) (shown as CC in the Figure 7) is given. It can be found that for the lower unit Reynolds number (Figure 7a), the transition Reynolds number is also relatively small; with the increase in the unit Reynolds number of the freestream, the transition Reynolds number increases accordingly. In addition, it also shows that the spanwise distribution of transition position on the surface of the flat plate is uneven, and the spanwise distribution of transition Reynolds number increases with the increase in the unit Reynolds number, similarly as in Figure 5. In this paper, the unit Reynolds number has a great influence on the transition Reynolds number, whereas some wind tunnel experiments show the opposite results. A more in-depth investigation is warranted to explore the impact of unit Reynolds number on the transition Reynolds number.  
Figure 6: Mean Stanton number distribution of plate flow direction under different unit Reynolds numbers: (**a**) \(R_{\text{unit}}=2.56\times 10^{6}\); (**b**) \(R_{\text{unit}}=6.38\times 10^{6}\); (**c**) \(R_{\text{unit}}=8.20\times 10^{6}\).