Boundary Layer
BOUNDARY LAYER THEORY
INTRODUCTION
The concept of boundary layer was 1st introduced by L.Prandtl in 1904.
Figure 7-1. Viscous flow around airfoil
A structure having a shape that provides lift, propulsion, stability, or directional control in a flying object.
Boundary layer is formed whenever there is a relative motion between the boundary and the fluid.
Boundary layer thickness:
1. Standard thickness
- signified by ,” it is define as the distance from the boundary layer of solid body measured in y-direction to the point where the velocity of the fluid is approximately equal to 0.99 times the free stream (U) velocity of fluid”.
- Because the boundary layer thickness is defined in terms of the velocity distribution, it is sometimes called the velocity thickness or the velocity boundary layer thickness.
Figure 7-2 illustrates the boundary layer thickness.
Figure 7-2 Standard boundary layer(http://aerojockey.com/papers/bl/node2.html)
2. Displacement thickness: “it is the distance measured perpendicular to the boundary where the free/main stream is displaced on relation of formation of boundary layer”.
0
* 1
u
dy
U
It represents the amount of that the thickness of the body must be increased so that the invented uniform inviscid flow of the model has the same flow rate properties as the actual viscous flow.
Figure 7-3 Displacement thickness
3. Momentum thickness: “it is the distance measured perpendicular to the boundary of the solid body where the boundary should be displaced to compensate for reduction in momentum of the flowing fluid on relation of formation of boundary layer”.
u u
1 dy
U U
0
**See Munson,2010 textbook for Prandtl/Blasius Boundary layer solution**
Example 1:
The velocity distribution in the boundary layer at a plate is given by,
u 3 y y2
0.5 2
U 2
Calculate the ratio of displacement thickness to
INTRODUCTION
The concept of boundary layer was 1st introduced by L.Prandtl in 1904.
Figure 7-1. Viscous flow around airfoil
A structure having a shape that provides lift, propulsion, stability, or directional control in a flying object.
Boundary layer is formed whenever there is a relative motion between the boundary and the fluid.
Boundary layer thickness:
1. Standard thickness
- signified by ,” it is define as the distance from the boundary layer of solid body measured in y-direction to the point where the velocity of the fluid is approximately equal to 0.99 times the free stream (U) velocity of fluid”.
- Because the boundary layer thickness is defined in terms of the velocity distribution, it is sometimes called the velocity thickness or the velocity boundary layer thickness.
Figure 7-2 illustrates the boundary layer thickness.
Figure 7-2 Standard boundary layer(http://aerojockey.com/papers/bl/node2.html)
2. Displacement thickness: “it is the distance measured perpendicular to the boundary where the free/main stream is displaced on relation of formation of boundary layer”.
0
* 1
u
dy
U
It represents the amount of that the thickness of the body must be increased so that the invented uniform inviscid flow of the model has the same flow rate properties as the actual viscous flow.
Figure 7-3 Displacement thickness
3. Momentum thickness: “it is the distance measured perpendicular to the boundary of the solid body where the boundary should be displaced to compensate for reduction in momentum of the flowing fluid on relation of formation of boundary layer”.
u u
1 dy
U U
0
**See Munson,2010 textbook for Prandtl/Blasius Boundary layer solution**
Example 1:
The velocity distribution in the boundary layer at a plate is given by,
u 3 y y2
0.5 2
U 2
Calculate the ratio of displacement thickness to