1. Introdução à Camada Limite.
Aula Teórica 24
Introdução à Camada Limite.

2. Potential flow
No Friction; flow in front of the object is symmetric of the flow in the back and there is no pressure resistance, i.e. there is no drag.
If the flow did not follow the surface of the object, the velocity would not decrease and consequently the pressure could not increase.
This is what happens when BL separation occurs.

3. BL Separation

4. Boundary Layer Separation
The concavity of the velocity profile depends on the sign of the pressure gradient: is negative when the pressure decays and positive otherwise.

5. Favourable pressure gradient
There is no force that can invert the flow, i.e. there is no separation of the boundary layer.
Acceleration is the result of the pressure gradient and of the divergence od the diffusive flux (negative)

6. Null pressure gradient

7. Positive pressure gradient
Shear stress is maximum at the inflexion point, decreasing towards the wall. Faster fluid drags slower fluid.

8. Adverse pressure gradient
In case of the adverse pressure gradient pressure force decreases the velocity and can invert the sense of the flow.
For layers close to the wall the forward shear stress (above) is larger that the backward shear (below) and thus friction contribute to keep the forward movement, i.e. reduces the probability of flow separation.

9. Turbulent BL separate latter than laminar BL
BL separate latter in fusiform (aerodynamic) geometries.
Is this profile ok?

11. Cd for circular Cylinders

12. Shape and friction resitance

13. Flow around a cylinder for different values of Re

14. aerofoils

17. Sebenta de Mecânica dos Fluidos