Oblique Shock; Prandtl Meyer Expansion — Lesson 5

This lesson covers the concepts of oblique shock waves and Prandtl-Meyer expansion fans in fluid dynamics. It delves into the properties of oblique shock waves, including the normal and tangential components of velocity, the deflection of flow, and the wave angle. The lesson also explains the conservation equations applied to a control volume and the conditions for a shock to occur. It further discusses the Prandtl-Meyer expansion fan, where the flow properties change due to the expansion of the flow. The lesson concludes with the application of these concepts in calculating supersonic flow past a flat plate using the shock expansion theory. For instance, if a flat plate is immersed in a supersonic free stream, the pressure distribution on the upper and lower surfaces of the plate results in a resultant force, which can be resolved into lift and drag forces.

Video Highlights

01:13 - Discussion on the deflection of the flow by an angle theta and the wave angle beta.
04:59 - Explanation of the normal shock tables and how they can be used for calculations.
10:00 - Discussion on the theta beta m relation and how it can be used to determine the wave angle and deflection angle.
19:39 - Introduction to prandtl mirror expansion and how it affects the flow properties.
23:37 - Explanation of the prandtl mirror function and how it can be used to calculate flow properties.
27:39 - Discussion on the application of oblique shocks and expansion in supersonic flow fields.
30:36 - Explanation of the shock expansion theory and how it can be used to calculate the forces acting on a lifting surface in a supersonic flow field.

Key Takeaways

- Oblique shock waves involve normal and tangential components of velocity, deflection of flow, and wave angle.
- Conservation equations applied to a control volume can help determine the conditions for a shock to occur.
- Prandtl-Meyer expansion fans occur when the flow properties change due to the expansion of the flow.
- The shock expansion theory can be used to calculate supersonic flow past a flat plate.
- The pressure distribution on the upper and lower surfaces of a flat plate immersed in a supersonic free stream results in a resultant force, which can be resolved into lift and drag forces.