Question

Necessary and sufficient condition for flow separation

Answer 1

Answer:

for boundary-layer, adverse pressure gradient (dp/dx>0) is a necessary condition for flow separation. Also, when the wall-friction becomes zero ( τw=µ ∂u/ ∂y=0) , the flow separates, and turbulence happens.

Explanation:

Whenever there is relative movement between a fluid and a solid surface, whether externally round a body, or internally in an enclosed passage, a boundary layer exists with viscous forces present in the layer of fluid close to the surface. Boundary layers can be either laminar or turbulent. A reasonable assessment of whether the boundary layer will be laminar or turbulent can be made by calculating the Reynolds number of the local flow conditions.

Flow separation or boundary layer separation is the detachment of a boundary layer from a surface into a wake.[1] Separation occurs in flow that is slowing down, with pressure increasing, after passing the thickest part of a streamline body or passing through a widening passage, for example. Flowing against an increasing pressure is known as flowing in an adverse pressure gradient. The boundary layer separates when it has travelled far enough in an adverse pressure gradient that the speed of the boundary layer relative to the surface has stopped and reversed direction.[2][3] The flow becomes detached from the surface, and instead takes the forms of eddies and vortices. The fluid exerts a constant pressure on the surface once it has separated instead of a continually increasing pressure if still attached.[4] In aerodynamics, flow separation results in reduced lift and increased pressure drag, caused by the pressure differential between the front and rear surfaces of the object. It causes buffeting of aircraft structures and control surfaces. In internal passages separation causes stalling and vibrations in machinery blading and increased losses(lower efficiency) in inlets and compressors. Much effort and research has gone into the design of aerodynamic and hydrodynamic surface contours and added features which delay flow separation and keep the flow attached for as long as possible. Examples include the fur on a tennis ball, dimples on a golf ball, turbulators on a glider, which induce an early transition to turbulent flow; vortex generators on aircraft; and leading edge extensions for high angles of attack on the wings of aircraft such as the F/A-18 Hornet.

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