## 3 Research Methods
### Experimental Facility  
The JF-14 shock tunnel--which is based on the backward-running detonation driving technique--structure and wave diagram is shown in Figure 3. It consists of a driving tube of 15 m in length, a driven tube of 11 m in length with an attached axisymmetric Laval nozzle, a vacuum tank, and a 3-m long damping section. The inner diameter of the driving and driven tubes reaches 224 mm. A premixed hydrogen-oxygen-nitrogen explosive gas is filled into the evacuated driving tube and ignited with a 520-V electric spark close to a 1-mm thick steel main diaphragm, which separates the driving and driven tubes. Then, after the test gas is filled into the evacuated driven tube and the pressure of the gas in the driving tube jumps across the detonation wave and causes a fast rupture of the main diaphragm, the high-pressure gas enters the driven tube and forms an incident shock wave. When the incident shock wave ruptures the second diaphragm, separating the driven section and nozzle, the shock wave is simultaneously reflected, which further compresses and stagnates the gas in the driven tube, thereby forming the high-temperature and high-pressure gas in the nozzle inlet. As the diaphragm ruptures, a quasi-steady nozzle flow is established after the start transient [39]. Figure 2: Grid diagram (**a**) and enlarged grid diagram near the wall (**b**). In order to study the impacts of the starting waves on the test data, and to verify the accuracy of the program, the experiment uses the half-sphere with a radius of 20 mm to measure the heat flux at the stagnation point and nearby, and uses the pitot rod to measure the pressure at the stagnation point. The hemispheres, shown in Figure 4 (left), are made of stainless steel. Five E-type coaxial thermocouple heat flux sensors are mounted on the surface of the sphere, with an interval of 15\({}^{\circ}\). The three hemispheres are installed side by side on the horizontal direction of the pitot narrow, with a center distance of 100 mm and the leading edge of the spheres flush with the nozzle outlet, as shown in Figure 4 (right). The Pitot rod has a front radius of 8 mm and is equipped with a piezoresistive sensor. The thermocouples are homemade type-E coaxial thermocouple heat flux sensors, as shown in Figure 5 (left). This has the advantages of strong erosion resistance, high-temperature resistance, and quick response. The measurement error is less than 8% after many experiments. More details are available in the literature [40; 41; 42; 43; 44; 45; 46]. The pressure gauges are NS-3 pressure sensors from the Shanghai Tianmu company, as shown in Figure 5 (right). The grade of accuracy is 0.2%, and the working temperature is \(-\)30 \({}^{\circ}\)C\(\rightarrow\)480 \({}^{\circ}\)C. The characteristics are high measurement accuracy and reliability. Figure 4: Sphere model (**left**) and installation diagram (**right**). Figure 3: Schematic diagram of the high-enthalpy shock tunnel facility. During the experiment, the driving section is filled with a 2:1:2 hydrogen, oxygen and nitrogen mixture at a pressure of 0.33 MPa. The air pressure in the driven section is 2600 Pa, and the measured pressure of the reservoir region is 1.333 MPa. From the incident shock wave velocity and the initial components of the driven section, the temperature of the reservoir region is calculated to be 4120 K by assuming the region is in chemical equilibrium. The numerical results and experimental data are shown in Figure 6a--heat flux; Figure 6b--pitot tube pressure. These results reveal that the heat flux has two obvious peaks corresponding to the starting shock wave and the second shock wave. The comparison between the numerical the experimental results reveals that there is a difference in the wave height, but the take-off time and the stable heat flux value are basically the same. For the stagnation point pressure, the calculation results show the same wave characteristics as those of the heat flux results, and there are also two peaks, but they fail to appear in the experimental results.