## 4 Experiments Results and Discussion
### Results and Discussion  
#### 4.3.1 Results of the Detonation Shock Tunnel Test  
In the detonation shock tunnel, a mixture of 2H\({}_{2}\) + O\({}_{2}\) + 2N\({}_{2}\) was used as the initial driver gas, and air was used as the initial test gas in the driven section. The initial pressure values were 0.27 MPa and 3800 Pa, respectively. The test parameters are listed in Table 2; the total pressure was 1.22 MPa, and the temperature was 3570 K. The reservoir pressure was measured using pressure transducers mounted at the end of the shock tube. The other reservoir parameters were computed using the measured shock tube filling pressure, shock speed, and nozzle reservoir pressure. The stagnation pressure history is shown in Figure 13. The plateau pressure is maintained for about 14 ms. Based on the reservoir conditions, the free-stream was subsequently determined by numerically rebuilding the nozzle flow [37]. Figure 14 shows the temperature curve obtained from the NTC-10 in flat plate 1 and the corresponding calculated heat flux curve. As shown in Figure 14b, the variation of the heat flux over time reflects the stages of flow field starting and stability processes. The heat flux is relatively stable during the effective test time, and the steady flow duration lasts about 14 ms. Since the free-stream flow parameters are known (Table 2), the surface heat flux of the flat plate can be obtained theoretically. The reference enthalpy method [38] is used to calculate the theoretical heat flux:  
\[q_{w}=0.332\rho_{e}u_{e}\mathrm{Pr}^{-2/3}\mathrm{Re}_{x}^{-0.5}\sqrt{\frac{ \rho^{*}\mu^{*}}{\rho_{e}\mu_{e}}}(h_{aw}-h_{w}) \tag{15}\]  
where \(\rho^{*}\), \(\mu^{*}\) are the gas parameters corresponding to the reference temperature; \(h_{aw}\) is the adiabatic wall enthalpy, namely the recovery enthalpy; \(h_{w}\) is the wall enthalpy; \(\rho_{e}\), \(\mu_{e}\) are the incoming flow parameters from the outer edge of the boundary layer, i.e., the gas parameters after the oblique shock wave for the wedge model. The repeatability of the experiments and the measurements was investigated. Figure 15 shows the obtained heat flux histories of C01 (NTC-10) for three measurements for the same nominal test conditions. The value between 15 ms and 25 ms in Figure 15 is used as the experimental heat flux. The relative standard deviation of the heat flux in the three tests is about 1.7%. The average heat flux amounts to 0.192 MW/m\({}^{2}\). Table 3 summarizes the results of heat flux values obtained from the three NTC-10 sensors and the theoretical value. The experimental value is slightly lower than the theoretical value, which is due to the heat flux loss from the CVD diamond. The measurement deviations between the experimental and theoretical values are within 6%, and the relative standard deviations of all sensors are within 2%. Thus, the results show that the NTC sensor with air as a backing material provides acceptable results even without corrections, and the results correspond to the simulated results, as shown in Figure 6.  
Figure 14: Temperature and heat flux curves of three NTC-10 sensors in run 3. (**a**) Temperature curves; (**b**) Heat flux curves. Figure 16 shows the comparison of the three heat flux measurement results of the sensor C05 (NTC-2.5) in plate 2, and the sensor C02 (NTC-10) at the same position in plate 1. The results of the NTC-2.5 sensor are about 30% lower than the theoretical value. This result is expected, since the epoxy in the NTC-2.5 absorbs a considerable amount of energy from the CVD diamond, resulting in deviations, as calculated in Section 2.2. However, the repeatability of the NTC-2.5 sensor is also very good. The corrections of the results of the NTC-2.5 in Figure 16 are performed using Equation (14). However, the \(\rho ck\) value of the epoxy needs to be obtained.