Shock Expansion Theory; Flow Through Converging Diverging Nozzle — Lesson 6

This lesson covers the in-depth understanding of the shock expansion theory and the flow through a converging-diverging nozzle. It discusses the flow structures, shocks, expansion fans, and pressure distribution in the context of a flat plate at an angle of attack to a supersonic free stream. The lesson also explains the concept of quasi one-dimensional flow through a converging-diverging nozzle and the conditions under which such flows occur. It further elaborates on the conservation equations and the area-velocity relation in the context of supersonic flow applications. For instance, it explains how a subsonic flow can be accelerated to a supersonic condition using a converging-diverging nozzle.

Video Highlights

02:50 - Explanation of the flow structure and forces generated in a diamond wedge airfoil.
09:40 - Explanation of the area-velocity relation for quasi one-dimensional flow.
13:40 - Discussion on the variation of Mach number in a converging-diverging nozzle under different conditions.
23:16 - Discussion on the implications of the area-velocity relation for subsonic and supersonic flows.
32:15 - Discussion on the variation of Mach number and mass flow rate with change in exit pressure in a converging diverging nozzle.

Key Takeaways

- The shock expansion theory is applicable for simple geometries like a flat plate at an angle of attack to a supersonic free stream.
- The flow structures, shocks, expansion fans, and pressure distribution are uniform on the upper and lower surfaces of the flat plate.
- Quasi one-dimensional flow occurs when the stream tube area varies gradually along the flow direction.
- The area-velocity relation is a crucial concept in supersonic flow applications, explaining how the velocity changes as the area of the stream tube changes.
- A converging-diverging nozzle can be used to accelerate a subsonic flow to a supersonic condition and vice versa.