Why will all air slow down by the same amount in an adverse pressure gradient?

Question

Boundary layer separation is caused by air slowing down to zero and reversing before reaching the end of the body. This is due to friction (viscous effects) + adverse pressure gradient.

The formation of an adverse pressure gradient can be explained by the geometry of the body. In the case of an airfoil, for example, the way I see this is that after air has been accelerated around the leading edge (strong curvature), it flows to the rear part of the airfoil (less curvature), and experiences a "collision" with the straighter surface. That collision causes a rise in pressure - an adverse pressure gradient.

Air inside and outside the boundary layer is slowed down by the same amount because of this pressure gradient. But I don't understand why. Air already slowed down by friction should "collide" less strongly with the surface, which implies a less intense adverse pressure gradient. Why will all air, regardless of some being decelerated by friction, experience an adverse pressure gradient of the same intensity?

There might be some misconceptions in my understanding, so I would appreciate any correction and assistance!

Answer 1

You write that air "experiences a collision" with the airfoil surface. That is a bit harsh - while air molecules collide among themselves all the time, few do it with the surface. The sum of those collisions can be interpreted as pressure: The more numerous and stronger the collisions between gas molecules are, the higher the pressure in the gas is.

High curvature produces suction in order to make the molecules change their flight path. Suction is the lack of pressure: While air further away from the suction area maintains the number and intensity of collisions, air close to the curved surface experiences fewer and less intense collisions. Consequently, fewer collisions happen with the surface. We measure lower pressure and the wing experiences lift.

Less curvature requires proportionally less suction until a straight contour will return pressure to its ambient value. A concave contour needs to increase pressure in order to push the flow along its path. In potential flow pressure is proportional to the curvature of a local streamline. Since curvature radii increase with more distance from the airfoil contour, pressure variations diminish equally. In other words: There is a (weak) pressure gradient along lines perpendicular to the airfoil contour.

So far, all this was true for inviscid flow. Viscous flow differs only in a small volume covering the surface and from a thickening of this volume with flow length, which in turn changes the streamlines around the airplane slightly. But the pressure effects are unaffected by this: What we measure as pressure are the collision components perpendicular to a surface. The change in flow speed from friction happens parallel to the surface. The slower flowing layer close to the surface still experiences the same collision intensity as the layers at a larger distance from the airplane surface. Therefore, pressure does not change in the boundary layer.

Answer 2

air ... experiences a "collision" with the straighter surface

Not if the airspeed is high enough. A "healthy" circulation has the airflow, trying, but not succeeding in flowing back to the wing surface. It continues downward aft of the rear trailing edge.

This, in simplest terms, is the "downwash" action of a given mass of air at a given velocity. The reaction is the lifting force of the wing.

When angle of attack reaches a critical stalling point, the adverse pressure (normal atmospheric) breaks down the low pressure bubble over the wing, resulting in turbulence and loss of lift.

air inside and outside the boundary layer is slowed down by the same amount by this pressure gradient

Right. What is observed is two effects reinforcing one another out. Looking at it from the "wind tunnel" point of view, the wing is stationary and the air moves. This is also true in flight from the wing frame of reference.

So, the wing friction will slow freestream air down and the adverse pressure will tend to reverse its direction under conditions of excessive AoA.

Air tends to flow from higher to lower pressure. With a lifting wing, the momentum of the airstream prevents the low pressure "lift bubble" from collapsing until critical angle of attack is exceeded.