Boundary Layer Separation

•    Effect of pressure gradient on boundary layer surface:

Consider steady flow and apply boundary condition at the solid boundary where  y = 0, u = 0

[ ∂²y / ∂x² ] _{y = 0}  = 1 dp / μ dx

Depending upon the curvature the boundary, there are three possible cases,

(i)    There is gradual increase in velocity and drop in pressure as the flow passes from 1 to 2 i.e. pressure drop in the direction of flow, dp / dx < 0. The entire boundary layer moves forward, till the pressure gradient less than zero. This condition is called as favorable pressure gradient.

(ii)    The flow retards and pressure increases as flow passes down stream from section 2. This condition is called as adverse pressure gradient. Both pressure and shear force produced continuous retardation in the flow momentum and a stage comes when the momentum of the fluid is unable to overcome the surface resistance. It is develop near the curved surface where velocity gradient du / dy = 0 i.e. at section 3. This point at which the boundary layer is on the verge of separation form the surface is called as point of separation.

(iii)    The fluid separated from the surface due to continuous retardation of flow. It has tendency to flow in a direction opposite to the main flow. It occurs beyond the point 3.Where dp / dx > 0

• Location of separation point:

For the given velocity profile, there are three conditions for location of separating point:

(1)    If (du / dy) _{y = 0} is positive, the flow wil remain attached with the surface.
(2)    If (du / dy)_{y= 0} is zero, the flow is on the verge of separation.
(3)    If (du / dy)_{y = 0} is negative, the flow is separated.

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