Boundary-layer Thickness - Displacement Thickness

The displacement thickness, δ* or δ1 is the distance by which a surface would have to be moved in the direction perpendicular to its normal vector away from the reference plane in an inviscid fluid stream of velocity to give the same flow rate as occurs between the surface and the reference plane in a real fluid.

In practical aerodynamics, the displacement thickness essentially modifies the shape of a body immersed in a fluid to allow an inviscid solution. It is commonly used in aerodynamics to overcome the difficulty inherent in the fact that the fluid velocity in the boundary layer approaches asymptotically to the free stream value as distance from the wall increases at any given location.

The definition of the displacement thickness for compressible flow is based on mass flow rate:

The definition for incompressible flow can be based on volumetric flow rate, as the density is constant:

Where and are the density and velocity in the 'free stream' outside the boundary layer, and is the coordinate normal to the wall.

For boundary layer calculations, the density and velocity at the edge of the boundary layer must be used, as there is no free stream. In the equations above, and are therefore replaced with and .

The displacement thickness is used to calculate the boundary layer's shape factor.

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