## 2 Theoretical Analysis of Low Re Flow with Chemical Reaction
### Low Re Flow with Chemical Reaction  
The working medium of the SCRP is a supersonic flow containing a chemical reaction, and the reaction flow typically has a low Re number and supersonic flow containing a chemical reaction. When the SCRP operates normally, the gain medium in the optical cavity is a supersonic gas operating under negative pressure. When operating normally, the pressure in the optical cavity must be maintained within 1000 Pa, and the exhaust gas must be discharged quickly. High pressure in the optical cavity or poor flow field structure in the optical cavity adversely affects the performance of the SCRP. Owing to the low airflow pressure, the Re number of the flow is lower than that of conventional supersonic flows. The supersonic diffuser of the SCRP is generally arranged between the laser optical cavity and the exhaust system, and its main functions include the following: (1) reducing the incoming flow speed, increasing the static pressure of the airflow, and reducing the burden of the downstream exhaust system; and (2) isolating the downstream disturbance of the airflow upstream and maintaining the smooth state of the flow field of the optical cavity.  
A supersonic flow with a low Re number and a chemical reaction has the following characteristics:  
1. Unlike general diffusers, the entrance of an SCRP diffuser is rectangular and has a large aspect ratio. The airflow in this channel significantly differs from that in a circular tube. The airflow in the corner of the channel is subject to a strong three-dimensional effect and may produce separation.
2. A chemical reaction occurs in the supersonic airflow in the optical cavity, generating excess amounts of energy. If the pressure of the optical cavity is excessively high or the flow field structure in the optical cavity is poor, the energy generated cannot be extracted into the laser energy normally. Instead, it is converted into the internal energy of the air stream to ensure that the temperature of the air stream rises. In severe cases, the gas stream becomes \"hot-blocked\", preventing the laser from working normally.
3. The characteristic Re number of the flow in an optical cavity is generally at least one order of magnitude lower than that of conventional supersonic flows (such as a flow in a supersonic wind tunnel). Consequently, the boundary layer in the channel is thicker, the growth rate is faster, and the viscous effect is more evident.  
Therefore, it is necessary to control the boundary layer in the channel. The advantages of using suction for boundary layer control include effectively preventing the shock wave-boundary layer interaction, making the downstream boundary layer thinner, and reducing flow distortion; however, part of the mass flow is lost. The flow in the optical cavity of the SCRP is a supersonic flow with a low Re number and chemical reaction. This unique flow state stands apart from that in supersonic wind tunnels and inlets in two distinct aspects: first, the boundary layer develops more rapidly owing to the lower Re number; second, an exothermic chemical reaction is conducted in the optical cavity, which increases the static pressure of the airflow and decreases the Mach number. These two factors affect each other, such that the flow in the optical cavity is easily choked. Therefore, controlling the development of the boundary layer within the optical cavity is an effective strategy for enhancing SCRP performance.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value** & **Unit** \\ \hline Ma & 2.0 & \\ T\({}_{0}\) & 500 & K \\ \(\gamma\) & 1.586 & \\ R & 708 & J/(kg\(\cdot\)K) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters of the exhaust gas.