## 2 Theoretical Analysis of Low Re Flow with Chemical Reaction
### Composition and Working Principle of Diffuser  
As illustrated in Figure 2, a supersonic diffuser based on active gas pressurization is composed of an isolated section, a nozzle, a uniform cross section, a mixing chamber, a flat section, and an expansion section. By arranging nozzles in a traditional supersonic diffuser structure, high-pressure active gas is sprayed. The high-pressure active gas and exhaust gas from the upstream flow enter the mixing chamber after initial mixing in the uniform cross section. The mixing chamber is a cross-sectional contraction. It is assumed that the two kinds of airflows are fully mixed and interact with each other in the mixing chamber, and a uniform airflow is finally formed. On the other hand, the velocity of the supersonic flow is gradually slowed due to the cross-sectional area's contraction of the mixing chamber. Following its traversal through a series of oblique shock waves in a flat section, the mixed flow finally changes into a subsonic flow. The subsonic flow was further decelerated and pressurized in the expansion section. The prediction and control of the flow process of the sprayed active gas and exhaust gas from the upstream flow in a mixing chamber are some of the most important problems in the study of supersonic diffusers. It was assumed in this study that the sprayed active gas and exhaust gas from the upstream flow formed a uniformly mixed airflow in the mixing chamber, and the change law of the main flow parameters of the airflow in the mixing chamber can be described by the momentum equation as follows:  
\[\dot{m}_{3}V_{3}-(\dot{m}_{1}V_{1}+\dot{m}_{2}V_{2})=(p_{1}A_{1}+p_{2}A_{2})-p_ {3}A_{3}+\int_{wall}p(l)dl \tag{1}\]  
where subscripts 1 and 2 represent the parameters of the active and exhaust gases, respectively, and subscript 3 represents the parameters of the gas after uniform mixing. In addition, \(\dot{m}\), \(V\), and \(p\) are the mass flow rate, velocity, and pressure of the airflow, respectively; \(A\) is the area of the airflow channel; and \(p(l)\) is the distribution law of the airflow pressure in the mixing chamber, which reflects the interaction and mixing process of the active and exhaust gases in the mixing chamber and is also closely related to the geometric shape of the mixing chamber. The key to solving the momentum equation of the mixing chamber is to determine the wall pressure distribution law of the mixing chamber. If the wall pressure distribution law used differs significantly from the actual distribution, the design result will not meet the requirements. Because the shape of the flow channel is generally rectangular with a large aspect ratio, the shock string structure in a flow channel with this cross-sectional shape is relatively long for supersonic flow, which is unfavorable for engineering applications of supersonic diffusers. Therefore, several active gas nozzles can be arranged in the gas flow channel by forming an ejection support plate to ensure that the airflow channel can be divided into several channels with smaller equivalent sizes. This reduces the length of the shock string structure and supersonic diffusion section. Compressed cold air can be used as a high-pressure active gas. The use of cold air can eliminate the exothermic effect of the exhaust gas flow. At the exit of the active gas nozzle, the difference between the static pressure of the active gas and exhaust gas should not be excessively large; otherwise, a pneumatic throat effect will occur, resulting in airflow congestion. If the static pressure of the exhaust gas is significantly higher than that of the active gas, the active gas will be strongly compressed, which may lead to failure of  
Figure 2: Diagram of supersonic diffuser. the establishment of the active gas flow field. If the static pressure of the active gas is significantly higher than that of the exhaust gas, it may cause the exhaust gas flow to choke, the expected flow field cannot be established, and the upstream components cannot function properly.