In the year 1904, Ludwig Prandtl the German scientist was first to introduce the concept of boundary layer. The viscous flows can be analyzed by dividing the flow into two regions; one close to the solid boundaries and the other covers the rest of the flow as suggested by Prandtl. The regions close to the solid boundary is boundary layer, in which the effects of viscosity are encountered by the flow. In the regions outside the boundary layer, the effect of viscosity is negligible and the fluid is considered as inviscid. Therefore, the boundary layer is a buffer region between the wall and the inviscid free-stream. With this approach, it can be allowed the complete solution of viscous fluid flows that would have been impossible with the Navier-Stokes approach.
A thin layer of fluid flowing is in contact with a surface such as internal surface of pipe, and external surface of a flat plate is known as Boundary layer. Shearing forces are induced by the fluid in the boundary layer. When fluid is in contact with the surface, velocity ranges from maximum to zero across the boundary layer. At the starting point of surface, flow is laminar as it grows it becomes turbulent in the trailing or downstream portion. Figure 1 depicts the boundary layer transition from L.E to T.E.
Figure 1 Representation of boundary layer on a flat plate
At leading edge of the flat plate, laminar boundary layer is initiated for a short distance and continues to downstream. The transition occurs over a region, after certain length in the downstream and then flow becomes fully turbulent boundary layers. The transition is generally encounter at a distance where the Reynolds number is about 500,000 for typical calculations. Let us consider air at standard conditions, transition velocity of 30m/s, then the transition is expected to occur at a distance of about 250mm.
Boundary layer thickness (δ): The fluid should attain the zero velocity at the wall, as the no-slip conditions need to be satisfied at the solid surface. The viscosity effects likely to reduce and the fluid within this layer will try to approach the free stream velocity above the wall. Therefore, velocity gradient develops within the fluid layers inside the small regions near to solid surface.
The distance from the surface to a point, where the velocity reaches 99 % of the free stream velocity is known as boundary layer thickness. Figure 2 shows the velocity profiles of boundary layer.
Figure 2 (a) Boundary layer thickness; (b) Free Stream flow; (c) Concepts of displacement thickness
Displacement thickness (δ*): The distance that a streamline just outside of the boundary layer is deflected away from the wall due to the effect of the boundary layer is known as displacement thickness. Figure 3 shows the displacement thickness of boundary layer.
Displacement thickness is expressed as follows,
Figure 3 (a) Displacement thickness of boundary layer; (b) Displacement thickness of laminar flat plate; (c) Displacement thickness of actual wall approximation
Momentum thickness (θ): The loss of momentum flux per unit width divided by ρU2 due to pressure of the growing boundary layer is known as momentum thickness.
Momentum thickness is expressed as follows,
Boundary Layer with Pressure Gradient:
Generally, an example for external flow is flow over an airplane wing. The front portion of the wing body is subjected to a favourable pressure gradient of boundary layer, whereas rear portion is subjected to adverse pressure gradient of boundary layer as shown in the Figure 4.
Figure 4 Boundary Layer along a Airfoil body
The boundary layer tends to separate from the walls, if the adverse pressure gradient is high. The boundary layer remains attached over the complete lower surface of the airfoil, but it separates someplace near the rear potion of the upper surface. Separation bubble is the closed streamline, which indicates the region of recirculating flow. This leads to reverse flow near the wall, that terminating the parabolic nature of the flow field and resulting into boundary layer equations inapplicable. Example of boundary layers separation is shown in the Figure 5.
Figure 5 Example of boundary layer separation (a) Airplane wing at moderate angle of attack; (b) AIrplane wing at a high angle of attack; (c) a wide-angle diffuser