Expert: Paul Soderman - 9/27/2011

Question
Sir,

When separation occurs under an adverse pressure gradient on an airfoil, eddies are formed and the streamline flow "lifts off" from the surface. What is the physics behind loss of lift due to formation of such eddies? Wouldn't a eddied flow cause loss of pressure on the top surface of the airfoil and therefore support a larger net lift force upwards?

Answer
Sangeeth
Pressures in a separated flow region can be strong, but they are unsteady, cause drag to increase and are detrimental to the average lift. Consider the flow around a cylinder.  At very low speeds a fluid element arriving at the stagnation point will be carried by the pressure distribution along the surface all the way around to the opposite side - no flow separation occurs.  As Reynolds number increases, the same element finds that it cannot overcome the pressures on the downwind side and will separate from the surface.  When that occurs, reverse flow creates vortices that shed from the cylinder in a street - that is in a pattern of shed vorticity that alternates from the upper and lower surfaces.  When a vortex is shed from the upper surface it will induce a strong velocity locally on the downwind side of the cylinder.  From Bernoulli's law we know that a strong pressure will result.  That pressure will induce a strong force primarily in the drag direction but also in the lift direction.  But a moment later a lower surface vortex will shed and do the same thing.  Thus a fluctuating drag will be created along with a fluctuating lift force (upward and downward).  The time averaged drag will be increased.

A similar effect will occur on an airfoil during flow separation, though usually not so dramatically. The flow in the separation region will be partly vortical and partly turbulent in nature.  The resulting unsteady forces are hard to predict accurately, but from experimental studies we know that flow separation causes the average lift to decrease and the average drag to increase compared to an airfoil with less flow separation. The biggest effect on lift will occur at large angles of attack because stall will be induced early and the maximum lift will decrease compared to an airfoil with less separation. The mechanisms are similar to those of a cylinder as discussed above and illustrated by Schlichting (Boundary Layer Theory).  He also shows a flow separation flow field behind an airfoil.

Sorry, I should have said that a vortex shed from a cylinder upper surface will induce a low pressure on the cylinder.  It is strong in the sense of the absolute value relative to ambient pressure.  In any case, the induced force is in the drag and lift direction as described above.
Paul