## 1 Introduction  
With an increase in the flight Mach number of an aircraft, the temperature of the gas near the stagnation point rises sharply. When flying at an altitude of 30 km at Mach number 10, the stagnation point temperature of the gas is about 4500 K. However, when the flight Mach number is increased to 20, the total temperature of the gas is as high as 10,000 K [1]. Vibrational excitation, dissociation, ionization and other phenomena are more intense in high-temperature air, making the air a complex medium for constant thermochemical reactions [2], which complicates the phenomenon of high-enthalpy flow. Due to the strong nonlinearity and complexity of the high-enthalpy flow, theoretical research is extremely difficult. The numerical calculation greatly simplifies the flow process, and the accuracy of the results needs to be experimentally verified, which makes the experimental study an indispensable means to study the high-enthalpy flow. The experimental study of this problem depends on flight tests and shock tunnel tests. A flight test reproduces the real flight environment and is the most accurate. However, due to its high cost, it is often used to verify the aircraft model after confirmation. Previous hypersonic flight experiments were conducted in shock tunnels. A high-enthalpy shock tunnel is a type of pulse tunnel that produces high-enthalpy flow by compressed air with strong shock waves [3, 4]. It is widely used in hypersonic fields, such as Earth reentry, planet entry, hypersonic aircraft, scramjet, etc. However, due to the excessive power of high-enthalpy shock tunnels [5], it is very difficult to develop continuously-running shock tunnels. At the same time, the effective test duration is far less than the theoretical value due to the interaction of tunnel waves, viscous boundary layer interference [6,7], diaphragm rupture, the nozzle starting process, and other factors [8,9]. Furthermore, with the increase of the total enthalpy of the gas, the test duration decreases further [10]. For example, the T4 high-enthalpy shock tunnel at the University of Queensland has a length of 26 m and an inner diameter of 229 mm [11]. When the total enthalpy of the test gas is 7.6 MJ/kg, there is 1 ms for conducting the test. However, when the total enthalpy exceeds 15 MJ/kg, the effective test duration is shortened to 0.5 ms [12, 13, 14, 15]. It also takes some time to start up the model, which will further shorten the efficient test time [16,17]. The T5 high-enthalpy shock tunnel at GALCIT (Graduate Astronautics Laboratory, California Institute of Technology, Pasadena, CA, USA) [18] extended the duration by enlarging the equipment, but the effective test duration is still only 1 ms when it is running in high-enthalpy conditions (the total enthalpy is greater than 20 MJ/kg) [19,20]. Other well-known shock tunnels in the world, such as the HEG (High Enthalpy shock tunnel Gottingen) in Germany and HIEST (High-Enthalpy Shock Tunnel) in Japan, when operating under high-enthalpy conditions, the effective test duration is also around 1 ms [21, 22, 23, 24]. There are various factors that restrict the effective test duration of a high-enthalpy shock tunnel, one of which is the nozzle starting process. Nozzle starting refers to the process by which the test gas enters the nozzle to form a steady flow field at the nozzle outlet. Under the influence of the starting wave [25], the flow field in the starting process is unstable and the experimental data fluctuates greatly. In addition, since there is no obvious interface between the nozzle starting process flow field and the steady flow field, this part of the data is connected with effective data, and although they are close in some cases, they cannot reflect the real situation and therefore, must be accurately eliminated. In past years, the starting process of a supersonic nozzle driven by a shock tunnel has been investigated experimentally and numerically by many researchers.