Supersonic Flow Over Thin Aerofoil — Lesson 1

This lesson covers the study of steady and unsteady supersonic flow over a thin aerofoil. It explains the potential flow equation and how supersonic flow is the easiest to solve due to the restricted region of influence. The lesson further discusses the concept of a Mach cone and how disturbances in the flow travel at the speed of sound. It also explains how the speed of the body and the speed of sound influence the cone of influence. The lesson then delves into the mathematical equations and derivations related to the topic, including the steady 2D equation, the wave equation, and the boundary conditions. It also discusses the concept of radiation condition and how it affects the supersonic flow. The lesson concludes with the application of Laplace transform in solving the unsteady 2D supersonic flow equation.

Video Highlights

01:18 - Discussion on the influence of supersonic flow on the speed of sound.
12:46 - Explanation of the boundary conditions and pressure difference for supersonic flow.
39:46 - Introduction to unsteady 2D supersonic flow.
43:53 - Explanation of the Laplace transform method for solving unsteady supersonic flow.
52:21 - Explanation of the boundary conditions for unsteady supersonic flow.
70:49 - Explanation of the convolution integral in the Laplace transform.

Key Takeaways

- Supersonic flow is the easiest to solve in the potential flow equation due to the restricted region of influence.
- The speed of the body and the speed of sound play a crucial role in determining the cone of influence in supersonic flow.
- The steady 2D equation and the wave equation are fundamental in understanding the flow dynamics.
- The boundary conditions and the radiation condition are essential in solving the flow equations.
- The application of Laplace transform simplifies the process of solving the unsteady 2D supersonic flow equation.