# A Critical Review of Supersonic Flow Control for High-Speed Applications
## 2 High-Speed Flow Development in Nozzle  
For supersonic flow development and investigations, a CD nozzle is utilized in most studies. A nozzle with no expanding part cannot produce supersonic air [3]; the flow is sonic at the throat; therefore, an asterisk denotes conditions at a sonic level. At the throat, the Mach number \(=1\), (V = a) and the throat area (a). Figure 2 illustrates a basic CD nozzle model [4] and the parameters with an asterisk are defined as critical values. If a high-pressure tank is connected to a pipe, then the velocity at the pipe exit changes depending on the backpressure. At any other region of the nozzle, the Mach number velocity and the local area can be derived by the continuity equation [5; 6; 7]. Even though it is possible to study one-dimensional flow behavior directly, it is only a particular case of  
Figure 1: Sudden expansion flow field. Reprinted with permission from ref. [2]. Copyright 2021 Springer. two-dimensional flow. One of the known one-dimensional flow phenomena is the normal shock and formation of oblique shock waves. The occurrence of oblique shock waves in different flow fields occurs, such as flight at high Mach numbers, aircraft design, diffusers, and supersonic nozzles. In previous studies, a particular flow rate was solved and analyzed mathematically to solve the energy equations, using a two-dimensional model of a nozzle. The measured iteration method improved the static tension, temperature, and velocity flows. The nozzle is produced and meshed with an automated technique and the sizing of the meshing processes and various values. The CD nozzle with sudden expansion was used to investigate the effect of expansion ratio for creeping expansion flows of fluid in the study of [8; 9; 10; 11]. The CD nozzle was used to generate a supersonic flow and was simulated, using the ANSYS fluent software. The generic formula for the nozzle was determined manually, and the results were compared [3; 12; 13; 14]. Nevertheless, the greatest difficulty in the CD nozzle outflow is in the subsonic and supersonic flow regimes. An abrupt expansion of the problem has various applications in the industry. In jet and rocket engine test cells, we observed that the system is used to simulate high-altitude conditions; the discharging of the jet results in inadequate discharge pressure, which is sub-atmospheric. [PERSON] et al. [15] controlled the base pressure with the active control method, using microjets. In the active control method, the microjets were placed in the base region of the sudden expansion duct, and these microjets were directly connected to the settling chamber with the air directly passing to the duct. The inlet flow of the microjets reduced the recirculation zone, which resulted in decreasing the drag formation. A detailed study on these active flow control can be seen in Section 4. Usually, the fluid flows are three-dimensional; the terms one, two, or three refer to the amount of coordinated space required to demonstrate the flow. The physical motion usually tends to be three-dimensional. At the same time, these are hard to evaluate and call for the most significant possible simplification. This is done by ignoring the flow variation in any direction, thus simplifying the problem. A three-dimensional problem can be reduced to a two-dimensional one and, subsequently, can be further simplified to one-dimensional one. The continuity equation, Bernoulli's equation, and momentum equation are used to study the one-dimensional flow case as methods of solution [5; 16; 17; 18; 19]. General classification and examples of flow fields can be seen in Refs. [20; 21] which provided the information of 3D flows and sediment transport models for open channel flows [20]. [PERSON] et al. [21] classified the 3D flow, considering the first-order coupled linear differential equation, using three matrix variations for both compressible and incompressible flows.