Chanel: Science of Fluids,    / scienceoffluids  
Playlist: Fluids made easy: 06 Fundamentals of potential flow theory
   • Playlist  

You may have noticed that in most textbooks, only 3D potential flows would be dealt with the Green's theorem, while there is no such method introduced for 2D potential flows. In fact, this is a rare situation for fluid dynamics: to obtain the boundary integral equation for 2D flows is much more complicated than for 3D flows. More specifically, we can not obtain the boundary integral equation in a similar manner as in 3D flows, where in 3D flows, the beautiful mathematical derivations would lead to the boundary integral equations, while in 2D flows, the boundary integral equation is more built on the physical understandings of the problem, and the mathematical derivations is not so strict as that in 3D flows. This is why no books talking about the mathematical derivations in 2D flow.
In this talk, a comparison would be made for such boundary integral equations for 3D and 2D flows, and we have shown why we can not use such mathematical derivation to obtain the boundary integral equation for 2D flows. and following the famous test book, Anderson's 'Fundamentals of Aerodynamics', the 2D panel method for potential flows can be established, and a simple example of a uniform flow past a cylinder shows the 2D panel method could predict the pressure coefficient correctly, even using merely 8 panels for the cylinder.
In this talk, following contents are included:
1) A brief introduction of 3D boundary integral equation
2) Differences of the boundary integral equations for 2D and 3D flows
3) 2D potential flows: a direct panel method
4) 2D panel method: boundary integral equation
5) 2D panel method: an example uniform flow past a circle