Where Does the Normal Shock Occur in a Supersonic CD-Nozzle?

[santasanjai]

Homework Statement

Hi everybody! I have a question about this type of flow. I have a Convergent divergent passage, with supersonic flow upstream and downstream, the flow iside of it is unknowm. The question is that , knowing that one normal shock occurs within the canal, either in the convergent or the divergent part, which one is the right answer? I know it happens in the convergent part but why? I know that decelerating the supersonic flow entering the convergent part would cause a rise in pressure, density and temperature, but I´m not able to motivate more than that. Anybody can help me? The convergent part is between 1 and 2, the divergent between 2 and 3.

 

[anathema]

Hello! Thank you for your question. First of all, it is important to understand the basics of supersonic flow and the role of shocks in it. In supersonic flow, the Mach number (ratio of flow velocity to the speed of sound) is greater than 1. This means that the flow is moving faster than the speed of sound and therefore, the flow field is characterized by high velocities and high temperatures.

In a Convergent-Divergent (CD) passage, the flow is initially supersonic at the inlet (point 1) and then it passes through a converging section (between 1 and 2) which further accelerates the flow, leading to an even higher Mach number. The flow then enters a diverging section (between 2 and 3) where it decelerates and the Mach number decreases. The flow then exits the passage at point 3.

Now, coming to your question about the occurrence of a normal shock in the CD passage. A normal shock is a type of shock wave that occurs when a supersonic flow is decelerated to a subsonic flow. In the CD passage, the flow decelerates in the diverging section (between 2 and 3) and this is where the normal shock will occur. This is because the flow is moving from a wider to a narrower section, which causes a decrease in flow velocity. This decrease in velocity leads to an increase in pressure, density and temperature, as you correctly mentioned.

In summary, the normal shock occurs in the diverging section of the CD passage because the flow is decelerated from supersonic to subsonic speeds. I hope this helps to clarify your question. If you have any further doubts, please let me know.