# The Experiments and Stability Analysis of Hypersonic Boundary Layer Transition on a Flat Plate
###### Abstract  
Experimental and linear stability theory (LST) investigation of boundary layer transition on a flat plate was conducted with a flow of Mach number 5. The temperature distributions and second-mode disturbances on the flat plate surface at different unit Reynolds number (\(Re_{\text{unit}}\)) values were captured by infrared thermography and PCB technology, respectively, which revealed the transition location of the flat-plate boundary layer. The PCB sensors successfully captured the second-mode disturbances within the boundary layer initially at a frequency of about 100 kHz, with a gradually expanding frequency range as the distance travelled downstream increased. The evolution characteristics of the second-mode instabilities were also investigated by LST and obtained for the second mode, ranging from 100 to 250 kHz. The amplitude amplification factor (\(N\)-factor) of the second-mode instabilities was calculated by the \(e^{N}\) method. The \(N\)-factor of the transition location in the wind tunnel experiment predicted by LST is about 0.98 and 1.25 for \(Re_{\text{unit}}\) = 6.38 \(\times\) 10\({}^{6}\) and 8.20 \(\times\) 10\({}^{6}\), respectively. hypersonic boundary layer; transition; LST; \(e^{N}\) method; infrared thermography +
Footnote †: journal: Applied sciences  
number freestream conditions and pointed out the significance of ensuring consistent total temperature of the inflow in wind tunnel experiments. With the advancement of measurement technology, some instantaneous measurement methods that have high spatial and temporal resolution, such as PCB [10; 11] and ALTP [12], are used for identifying the disturbance modal in the boundary layer. Infrared thermography appears to be a potential tool for investigating boundary layer transitions. [PERSON] et al. [13] employed IR technology to study the boundary layer transition of HIFiRE-5b at a freestream Mach number 6. The findings suggest that IR can clearly depict high- and low-temperature streaks in the streamwise direction on the model surface and capture the transition process. In addition to surface disturbance measurements, some flow visualization techniques are used to capture the process of boundary layer transition, too. [PERSON] et al. [14] used infrared thermography and wall pressure tests to obtain the turning position and the development and interaction law of unstable modes of a flat delta wing in a hypersonic wind tunnel. [PERSON] et al. [15] successfully captured the process of the second-mode wave growth and breaking into turbulence in the boundary layer of a conical surface using NPLS technology and found that a single forward-facing step (FFS) could suppress the second-mode wave and delay the cone's hypersonic boundary layer transition at AOA 0. [PERSON] et al. [16] used the Rayleigh scattering technique to successfully capture second modes of rope waves in the boundary layer of a flared cone and found that the amplitude of the second mode decays before transition to turbulence. [PERSON] et al. [17] used infrared thermography to study the effect of different roughness elements on the transition of a flat plate at Mach number 6, with a special study of the roughness element wake vortex structure. In addition to wind tunnel experiments, due to the development of computer computing power, many researchers have begun to use direct numerical simulation (DNS) to study the sensitivity of the hypersonic boundary layer of the flat plate and the propagation of disturbance [18; 19]. Various theoretical analysis techniques, including linear stability theory (LST) and parabolized stability equations (PSE), have been employed for the investigation and prediction of hypersonic boundary layer transition. [PERSON] [20] conducted a comprehensive examination of hypersonic boundary layer transition prediction, emphasizing the potential applicability of the \(e^{N}\) method for predicting two-dimensional hypersonic transition locations in his work [21]. Additionally, [PERSON] et al.