Flow separation

The flow reversal is primarily caused by adverse pressure gradient imposed on the boundary layer by the outer potential flow. The streamwise momentum equation inside the boundary layer is approximately stated as

${\displaystyle u{\partial u \over \partial s}=-{1 \over \rho }{dp \over ds}+{\nu }{\partial ^{2}u \over \partial y^{2}}}$

where ${\displaystyle s,y}$ are streamwise and normal coordinates. An adverse pressure gradient is when ${\displaystyle dp/ds>0}$, which then can be seen to cause the velocity ${\displaystyle u}$ to decrease along ${\displaystyle s}$ and possibly go to zero if the adverse pressure gradient is strong enough.^[5]

The tendency of a boundary layer to separate primarily depends on the distribution of the adverse or negative edge velocity gradient ${\displaystyle du_{o}/ds(s)<0}$ along the surface, which in turn is directly related to the pressure and its gradient by the differential form of the Bernoulli relation, which is the same as the momentum equation for the outer inviscid flow.

${\displaystyle \rho u_{o}{du_{o} \over ds}=-{dp \over ds}}$

But the general magnitudes of ${\displaystyle du_{o}/ds}$ required for separation are much greater for turbulent than for laminar flow, the former being able to tolerate nearly an order of magnitude stronger flow deceleration. A secondary influence is the Reynolds number. For a given adverse ${\displaystyle du_{o}/ds}$ distribution, the separation resistance of a turbulent boundary layer increases slightly with increasing Reynolds number. In contrast, the separation resistance of a laminar boundary layer is independent of Reynolds number — a somewhat counterintuitive fact.

Boundary layer separation can occur for internal flows. It can result from such causes such as a rapidly expanding duct of pipe. Separation occurs due to an adverse pressure gradient encountered as the flow expands, causing an extended region of separated flow. The part of the flow that separates the recirculating flow and the flow through the central region of the duct is called the dividing streamline.^[6] The point where the dividing streamline attaches to the wall again is called the reattachment point. As the flow goes farther downstream it eventually achieves an equilibrium state and has no reverse flow.

When the boundary layer separates, its remnants form a shear layer^[7] and the presence of a separated flow region between the shear layer and surface modifies the outside potential flow and pressure field. In the case of airfoils, the pressure field modification results in an increase in pressure drag, and if severe enough will also result in stall and loss of lift, all of which are undesirable. For internal flows, flow separation produces an increase in the flow losses, and stall-type phenomena such as compressor surge, both undesirable phenomena.^[8]

Another effect of boundary layer separation is regular shedding vortices, known as a Kármán vortex street. Vortices shed from the bluff downstream surface of a structure at a frequency depending on the speed of the flow. Vortex shedding produces an alternating force which can lead to vibrations in the structure. If the shedding frequency coincides with a resonance frequency of the structure, it can cause structural failure. These vibrations could be established and reflected at different frequencies based on their origin in adjacent solid or fluid bodies and could either damp or amplify the resonance.

• Triple-deck theory
• Aerodynamics
• D'Alembert's paradox
• Magnus effect