Boundary layer

Said fluid-dynamic boundary layer, often referred to simply as a " boundary layer " is the area of a flowing fluid on a wall, in which the friction has an influence on the velocity profile normal to the wall.

The knowledge of the behavior of the fluid-dynamic boundary layers on to or over streamed bodies is very important especially for the construction of the aircraft ( wing ), wind power plant, turbine ( turbine blades ) and shipbuilding ( flow around the hull, the rudder and the propeller blades ).

Boundary layer theory

The boundary layer theory is a field of fluid mechanics that deals with fluid motion with very little friction.

Ludwig Prandtl introduced the boundary layer theory in 1904, one at a lecture at the Heidelberg Congress of Mathematicians.

He divided the flow around a body in two areas on:

For sufficiently small Reynolds number (Re ) is the fluid-dynamic boundary layer is laminar, i.e., all parts of the boundary layer of a parallel flow of the main flow is the same direction. On the wall the fluid is brought to a standstill by friction ( no slip condition ). The further a fluid particle is removed from the wall, the higher its speed. Since the rate theoretically never can reach the surroundings of the flow rate, the end of the boundary layer is usually defined as the attainment of 99% of the ambient speed. From the wall up to the limit of the boundary layer, the velocity profile can be approximated as a quadratic function.

In the flow direction, the thickness of the fluid dynamic boundary layer increases in channels or pipes, the boundary layers on both sides can fro grow together, so that the laminar flow is fully developed and the velocity is a parabolic function to the distance to the wall.

At high Reynolds numbers, the flow is turbulent, ie within the boundary layer, the parts of the flow down to the molecular level take any direction, its thickness remains very limited. In the main flow, the velocity remains constant spread ( " plug flow "). The value of the Reynolds number for transition to turbulence depends on the considered geometry and other factors. When the flow provided through a pipe wall roughness technically conventional, the value is approximately 2300.

The boundary layer theory led to significant simplifications in the Navier -Stokes equations. The computational effort of a body in flow (eg, an airplane, a car or ship) is considerably reduced, and can be solved analytically so. The simplified due to the boundary layer assumptions Navier -Stokes equations are also called boundary-layer equations.