External Turbulent Flows — Lesson 3

This lesson covers the derivation and simplification of Reynolds average Navier Stoke equations, focusing on the additional terms that appear due to velocity fluctuations. It delves into the concept of external flows, particularly flow over a flat plate, and how to model the unknowns in these equations. The lesson also explains the concept of two-dimensional steady state incompressible flow with constant properties. It further discusses the scale analysis and the process of dropping certain terms in the X momentum equations. The lesson concludes with the explanation of the closure problem of turbulence and the modeling of Reynolds stress.

Video Highlights

00:48 - Discussion on external flows and flow over a flat plate.
02:27 - Scale analysis to identify small terms.
08:27 - Discussion on the closure problem of turbulence.
13:03 - Discussion on the Bossinesque hypothesis for modeling Reynolds stress, Eddy viscosity and Prandtl's Mixing Length theory.
20:22 - Explanation of th universal velocity profile, y+ and viscous sublayer.
29:36 - Explanation of the fully turbulent layer and law of the wall.

Key Takeaways

- Reynolds average Navier Stoke equations have additional terms due to velocity fluctuations.
- The equations can be simplified by considering external flows and modeling the unknowns.
- Scale analysis helps in identifying which terms can be dropped from the equations.
- The closure problem of turbulence arises due to the lesser number of equations than unknowns.
- Reynolds stress can be modeled using the velocity gradient.