Shock-Boundary Layer Interaction in Converging-Diverging Nozzles

Introduction
In the design of converging-diverging nozzles, it is important to consider the phenomenon of shock-boundary layer interaction. This interaction occurs when a supersonic flow encounters a boundary layer, which is a thin layer of air or gas that develops near a solid surface due to viscosity.

Explanation
The shock-boundary layer interaction takes place in the diverging portion of a converging-diverging nozzle. Let's understand why this is the case.

Converging Portion
In the converging portion of the nozzle, the flow is subsonic and the boundary layer is relatively thick. The flow accelerates as it moves through the converging section, but it remains subsonic. In this region, the boundary layer stays attached to the surface of the nozzle without any significant interaction with the shock wave.

Throat
The throat of the nozzle is the point of maximum constriction, where the flow reaches its sonic condition. At this location, the flow velocity is equal to the local speed of sound. The boundary layer is still relatively thick, but the flow is supersonic downstream of the throat.

Inlet
The inlet of the nozzle is where the flow enters the nozzle. In this region, the flow is usually subsonic, and the boundary layer is thick. The flow gradually accelerates as it moves through the converging section, but there is no shock wave present to interact with the boundary layer.

Diverging Portion
In the diverging portion of the nozzle, the flow expands and accelerates further. As the flow accelerates, it reaches a critical point where it becomes supersonic. At this point, a shock wave is formed. The shock wave is a sudden change in flow properties, such as pressure and velocity, and it is accompanied by a significant increase in temperature.

The shock wave interacts with the boundary layer in the diverging portion of the nozzle. This interaction can have several effects, including increased drag, flow separation, and loss of thrust. The shock wave can cause the boundary layer to thicken and separate from the surface of the nozzle, leading to a decrease in performance.

Conclusion
In a converging-diverging nozzle, the shock-boundary layer interaction takes place in the diverging portion of the nozzle. This is where the flow becomes supersonic and a shock wave is formed. Understanding and managing this interaction is crucial for optimizing the performance of converging-diverging nozzles in various applications, such as rocket engines and supersonic aircraft.