Understanding Subsonic and Supersonic Flow Conversion

The question asks about the type of duct used to convert a subsonic flow to supersonic flow. This involves understanding how the shape of a duct affects the speed of a fluid (like air) flowing through it, particularly at different flow regimes (subsonic and supersonic).

Flow through Ducts: Convergent vs. Divergent

The behavior of fluid flow in a duct depends on whether the flow is subsonic (slower than the speed of sound) or supersonic (faster than the speed of sound). Key duct shapes are convergent (area decreases in the direction of flow) and divergent (area increases in the direction of flow).

• Convergent Duct:
  • For subsonic flow, a decrease in area leads to an increase in velocity.
  • For supersonic flow, a decrease in area leads to a decrease in velocity.
• Divergent Duct:
  • For subsonic flow, an increase in area leads to a decrease in velocity.
  • For supersonic flow, an increase in area leads to an increase in velocity.

Converting Subsonic to Supersonic Flow

To convert a subsonic flow to a supersonic flow, we need to accelerate the flow past the speed of sound. As discussed above, a convergent duct accelerates subsonic flow. However, once the flow reaches sonic speed (Mach 1), a convergent duct can no longer accelerate it further. To accelerate the flow from sonic speed to supersonic speed, a divergent duct is needed.

Therefore, to accelerate a flow from subsonic all the way to supersonic, the duct must first be convergent to accelerate the flow to sonic speed, and then divergent to accelerate the flow from sonic speed to supersonic speed. This type of duct is called a Convergent-Divergent (C-D) duct.

Nozzles vs. Diffusers

C-D ducts are used for two main purposes:

• C-D Nozzle: Used to accelerate a flow. It takes subsonic flow, accelerates it through the convergent section to sonic speed at the throat (the narrowest point), and then accelerates it further to supersonic speed in the divergent section. This converts internal energy into kinetic energy.
• C-D Diffuser: Used to decelerate a flow. It takes supersonic flow, decelerates it through the divergent section to sonic speed at the throat, and then decelerates it further to subsonic speed in the convergent section. This converts kinetic energy back into pressure/internal energy.

Conclusion

Since the goal is to convert a subsonic flow to a supersonic flow, we need a device that accelerates the flow. This is the function of a nozzle. Specifically, to accelerate flow from subsonic to supersonic, a Convergent-Divergent nozzle is required.

Let's evaluate the options:

• Divergent: Accelerates supersonic flow, decelerates subsonic flow. Not suitable for converting subsonic to supersonic.
• Convergent: Accelerates subsonic flow up to sonic speed, but decelerates supersonic flow. Cannot achieve supersonic flow from subsonic alone.
• C-D diffuser: Decelerates supersonic flow to subsonic flow. The opposite of what is needed.
• C-D nozzle: Accelerates subsonic flow through the convergent section to sonic speed and then further accelerates it through the divergent section to supersonic speed. This matches the requirement.

Thus, a C-D nozzle is the type of duct used to convert a subsonic flow to supersonic flow.