Consider an airfoil (a wing) in an airflow. When angle of attack increases, at some point the flow start to separate from trailing edge. By increasing the angle of attack more, this separation area increase toward the leading edge up to stall condition which must be avoided. We know that it will cause to reduce the lift and increase the drag suddenly.

But i don't remember what was the exact reason behind this. Whats the magnitude of pressure inside separated regions of flow (wakes)? is it higher or lower than normal flow patterns before separation occur?

I read (for example here) that separation increase 'Pressure Drag' as the pressure inside wakes are lower(?) and we get a more net back force comparing front side and back side of the airfoil:

In aerodynamics, flow separation can often result in increased drag, particularly pressure drag which is caused by the pressure differential between the front and rear surfaces of the object as it travels through the fluid

But if this is true, then how could we say that this lower pressure in upside of the airfoil decrease the Lift? as the lift is produced from pressure difference of top and bottom of the airfoil.

Note: i can explain the reason using newton third law and change in flow directions. but not sure about exact pressure profiles.

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You need to distinguish between boundary layer flow and outer flow.

Separation means that a parcel of low energy air moves with the wing (here the pressure is about -0.2, expressed as a pressure coefficient). For the outer flow, the contour of the airfoil changes to one of the original airfoil plus the parcel of separated flow. Since this is on the rear upper side of the airfoil, the airfoil "looks" thicker and longer, effectively presenting to the outer flow a body of less camber and angle of attack.

This in turn will reduce the suction in the region of attached flow right past the nose, where normally a high suction peak produces both lift and nose thrust. With a reduced suction peak, the airfoil produces more drag and less lift.

Viscous and inviscid pressure distribution at 12° AoA

Viscous and inviscid pressure distribution at 12° AoA, calculated with XFOIL 5.4. The dashed lines show the inviscid pressure distribution where flow separation does not happen, while the solid lines show the viscous pressure distribution with separated flow over the last 20% of the upper side. The lines around the airfoil contour show the boundary between the boundary layer and the outer flow. Separation thickens the boundary layer, substantially altering the shape around which the outer flow streams.

The altered airfoil shape causes a reduction in the effective angle of attack, so both the suction on top and the pressure on the bottom are lower. This means that separation causes lift loss; once separation starts, the lift curve slope becomes flatter and can reverse (which indicates a full stall).

In the sample shown above, only on the last 12% of the upper side would separation cause pressure to be lower than in the inviscid case. Note that pressure on the bottom is also lower, so the difference between both (which causes lift) is quite unchanged by separation. Without separation, viscous and inviscid pressure distribution are quite similar, therefore the inviscid distribution is a valid first-order approximation of the viscous pressure distribution without separation.

The reduced suction peak at the nose and the higher suction on those last 12% is what causes more pressure drag. Note that the area around the suction peak points forward and that near the trailing edge points a little backward (especially at high angle of attack). This means that less of the nose thrust pulls the airfoil forward and also there is less pushing from the pressure near the trailing edge.

To estimate the drag increase due to separation of the full airplane configuration, assume a drag increase as if the lift would increase linearly, without separation taking place, including induced drag. Combine this drag with the "real" lift, including losses due to separation, and you will arrive at a surprisingly realistic lift-to-drag ratio of the aircraft between separation onset and stall.

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  • $\begingroup$ thanks for your explanations. but this is not what i asked exactly. this does not answer the paradox of: reducing pressure above the wing produce more pressure drag because of left/right pressure difference, but how could it reduce the lift (we expect less pressure on upper surface produce more lift) $\endgroup$ – S.Serpooshan Aug 27 '17 at 7:38
  • $\begingroup$ @S.Serp: I guess I need to add pictures. What do you mean by left/right pressure? $\endgroup$ – Peter Kämpf Aug 27 '17 at 9:10
  • $\begingroup$ i mean the front and rear surfaces of the airfoil as it travels through the fluid (as usually flow considered in horizontal direction, it become left and right sides) $\endgroup$ – S.Serpooshan Aug 27 '17 at 9:36
  • $\begingroup$ can you also take a look at my answer and improve your answer or provide your comments? i appreciate your effort and knowledge as i see many technical questions are answered by you in this site! +1 for your third paragraph as it make sense to me now, specially the suction peak and nose thrust phrases (better if add some pics as you said). but the last paragraph is not so clear. $\endgroup$ – S.Serpooshan Aug 27 '17 at 9:55
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    $\begingroup$ @Daniel: As far as I know, yes. The speed of the reverse flow is slow, so there isn't much change in pressure possible. $\endgroup$ – Peter Kämpf May 9 at 1:07

Based on my understandings, the tip is about this fact that most of the lift is produced by initial sections of leading edge (eg. the first 20% of the chord) as shown in this figure.

Now compare the green(before separation) and pink (after separation) plots in the following figure.

Before separation, the pressure near leading edge (first 20% of chord) is very lower than ambient pressure (eg. -5 to -2), but after it the pressure vary linearly toward the ambient pressure such that at the trailing edge it is about 0.

After separation, the pressure all over the wakes change toward a (constant) value which is a little lower than the ambient pressure (e.g. -1 as shown for pink plot) as the wakes are some circular flow independent of main stream which pass above them.

This means an higher pressure in the first 20-30% of the chord, but lower pressure on the remaining 70-80% of the chord (when compare green with pink lines).

So, the suction of the wing at its leading edge region (20-30% c) reduces which means less lift (as the most portion of lift is produced by this section).

But the remaining 70-80% of the chord will have lower pressure which increase the net pressure differential between the front and rear surfaces of the airfoil and so increase the pressure drag.

Note also that this 70-80% of chord is placed at a high angle (angle of attack) and so has a great effect when we compute its horizontal component (drag). In the other side, that first section of airfoil leading edge is approximately an horizontal surface so the pressure vector is most normal to airflow and has more effect on lift when we compute its vertical component.

pressure coefficient before and after separation

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From "Fundamentals of Aerodynamics" by J.D.Anderson Jr (Fifth edition, page 384, 385). I just copy and paste in the case you don't have the book: enter image description here

Here the airfoil at a large angle of attack (thus with flow separation) is shown with the real surface pressure distribution symbolized by the solid arrows. Pressure always acts normal to the surface. Hence the arrows are all locally perpendicular to the surface. The length of the arrows is representative of the magnitude of the pressure. A solid curve is drawn through the base of the arrows to form an “envelope” to make the pressure distribution easier to visualize. However,if the flow were not separated, that is, if the flow were attached, then the pressure distribution would be that shown by the dashed arrows (and the dashed envelope).

The solid and dashed arrows in Figure 4.47 should be compared carefully. They explain the two major consequences of separated flow over the airfoil. The first consequence is a loss of lift. The aerodynamic lift (the vertical force shown in Figure 4.47) is derived from the net component of the pressure distribution in the vertical direction in Figure 4.47 (assuming that the free stream relative wind is horizontal in this figure). High lift is obtained when the pressure on the bottom surface is large and the pressure on the top surface is small. Separation does not affect the bottom surface pressure distribution. However, comparing the solid and dashed arrows on the top surfacejust downstream of the leading edge,we find the solid arrows indicating a higher pressure when the flow is separated. This higher pressure is pushing down, hence reducing the lift. This reduction in lift is also compounded by the geometric effect that the position of the top surface of the airfoil near the leading edge is approximately horizontal in Figure 4.47. When the flow is separated, causing a higher pressure on this part of the airfoil surface, the direction in which the pressure is acting is closely aligned to the vertical, and hence, almost the full effect of the increased pressure is felt by the lift. The combined effect of the increased pressure on the top surface near the leading edge, and the fact that this portion of the surface is approximately horizontal, leads to the rather dramatic loss of lift when the flow separates. Note in Figure 4.47 that the lift for separated flow (the solid vertical vector) is smaller than the lift that would exist if the flow were attached (the dashed vertical vector).

Now let us concentrate on that portion of the top surfacenear the trailing edge. On this portion of the airfoil surface, the pressure for the separated flow is now smaller than the pressure that would exist if the flow were attached. Moreover, the top surface near the trailing edge geometrically is inclined more to the horizontal, and, in fact, somewhat faces in the horizontal direction. Recall that the drag is in the horizontal direction in Figure 4.47. Because of the inclination of the top surface near the trailing edge, the pressure exerted on this portion of the surface has a strong component in the horizontal direction. This component acts towards the left, tending to counter the horizontal component of force due to the high pressure acting on the nose of the airfoil pushing toward the right. The net pressure drag on the airfoil is the difference between the force exerted on the front pushing toward the right and the force exerted on the back pushing toward the left. When the flow is separated, the pressure on the back is lower than it would be if the flow were attached. Hence, for the separated flow, there isless force on the back pushing toward the left, and thenetdrag acting toward the right is therefore increased. Note in Figure 4.47 that the drag for separated flow (the solid horizontal vector) is larger than the drag that would exist if the flow were attached (the dashed horizontal vector). Therefore, two major consequences of the flow separating over an airfoil are:

  1. A drastic loss of lift (stalling).

  2. A major increase in drag, caused by pressure drag due to flow separation.

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  • $\begingroup$ thanks for your answer. but from the pressure profile of your figure its not obvious why drag increases. based on your figure, it seems that the pressure increase in most portion of airfoil which will reduce the drag. based on drawn geometry, we can't say easily only last portion of trailing edge is affecting drag, the curvature slope is almost the same for most part of airfoil after its initial portion $\endgroup$ – S.Serpooshan Oct 2 '17 at 7:41
  • $\begingroup$ You are right, I have read this part of the book but still not fully understood the author's idea, it's kind of vague. Need a better answer... $\endgroup$ – Dat Oct 2 '17 at 10:46

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