Why do wall-to-wall airfoils in wind tunnels produce no (or infinitesimal) downwash? There are several induced drag explanations out there saying that tip/wake vortices “come from” downwash and downwash “comes from” lift. I’m using quotes because the concept is that there are no cause and effect events but simultaneous events that occur in a flow.

Essentially, these explanations describe how the flow turns downwards immediately after leaving the trailing edge of a finite wing; examples in stackexchange can be found here and  here.

Apologies if I describe the above incorrectly, feel free to correct me.

What I want to ask is if someone can “adjust/adapt” these explanations to describe what happens on an airfoil placed wall-to-wall in a wind tunnel that has no (or extremely small) induced drag. I’m not talking about theoretical infinite wings and mathematical explanations, I’m looking for a physical description similar to the ones given above for finite wings.

The only difference between wind tunnels and free flight (in THIS case) is that in the wind tunnel the upper and lower surface flows can interact only at the TE while in free flight they can interact (touch, blend, etc.) at the TE and at the wing tip.

In this NASA page, it is said that “The wing tip vortices produce a downwash of air behind the wing which is very strong near the wing tips and decreases toward the wing root.” Although this is not technically correct (see wake vortex), the importance of exposing the wing tip to the flow seems to be underestimated in the explanations above so I’m looking for an explanation of the wall-to-wall airfoil behaviour through the above explanations.

About Peter Kampf’s reply:

Now I think we’re getting somewhere…

Wake vortex is certainly more important than tip vortices, this is why I used the word wake with tip when referring to vortices. Perhaps I wasn’t very consistent/clear with that (like the NASA page) so apologies for any confusion.  

You correctly say that the effect of the wake vortex is reduced by the tunnel walls and there are no tip vortices, which means induced drag is greatly reduced for a wall-to-wall airfoil (essentially a side effect taken care of by grating). If it was possible to add infinite size end plates with zero drag on real aircraft wings (acting as wind tunnel walls), the induced drag would be greatly reduced.

This is all I’ve been trying to say, that the only explanation for the induced drag increasing drastically when we move from a wall-to-wall model (2D) to a finite wing (3D), is that the wing tip is exposed to the flow.


Yes, a vortex sheet leaves the wing.
Yes, there's no spanwise spillage of lower flow towards the upper flow.
Yes, tip vortices do not create induced drag.


However, the free stream air “sliding” next to the wing tip (where the tunnel wall would be) definitely interacts (pushes, gets pushed, blends, etc.) with:


The upper and lower flows (vortices) as it travels the chord of the wing.
The “combined” upper/lower flow (vortex sheet) at/after the trailing edge.


so the more the wing tip is “walled”, the effects of this interaction get weaker and consequently the induced drag gets weaker....

The explanations correctly say that wingtip vortices do not create induced drag but, at least that’s how I understand it, neglect the importance of the physical exposure of the wing tips to the air flow that causes the “interaction” described above.

Thanks to everyone for bearing with me, I’ve never written about aerodynamics in a forum…
Who says that the flows only interact at the trailing edge?

The flow on each side of a wing creates (and is the creation of) a pressure field which influences what goes on on the opposite side in subsonic flow. Only in supersonic flow is that kind of interaction impossible because small pressure changes move only at the speed of sound.

First to the topic of flow turning. Half of that has already happened at the quarter point of the wing chord, so it is spread out over the whole wing. At the trailing edge the local flow direction is parallel to the trailing edge inclination if flow is not separated already. Past the trailing edge the flow readjusts to the downwash angle which is normally largest behind the center wing. In the case of an elliptic lift distribution, the downwash angle is constant over span, but it is almost never strongest near the wingtips. The experts at NASA certainly know that, too, but I wonder how often they are consulted by the marketing people who write those web pages.

Next to the tip vortex: It does not cause induced drag and is only a side effect of downwash. Please read this answer and try to follow all the links. There is not a single vortex but a vortex sheet leaving the wing, and to better understand what is happening it is best to forget all that.

Now to the conditions in a wind tunnel. The flow there is practically like one in ground effect, so no full downwash like in free flow is produced. In order to arrive at realistic results, wind tunnels use correction factors in order to make the results of their measurements close to those in free flow. If there is a gap between the trailing edge and the wind tunnel wall (and there certainly is), there is also some downwash, but less than in free flow. As explained in this answer, the part of the wake which flows down past the wing is smaller than the wingspan, so a crippled version of the wake behind a wing will also form in a wind tunnel, with air near the side walls moving up and air in the center moving down. Normally, this is all equalled out when the air flows through the next grating which is installed to remove turbulence or help the tunnel flow around the next corner.


  the explanations above describe downwash as the main (almost only) reason for induced drag and tip vortices as just a result of downwash.


Yes, tip vortices are indeed a result of downwash. You link already to two good explanations for that, so I need to go beyond those answers. The two vortex cores resulting from the rollup of the vortex sheet trailing behind the wing are not really the tip vortices you might see in humid air, like in the picture of an A340 below (picture source).



The condensation at the wingtip is from the high suction caused by flow locally negotiating the small radius of the winglet tip. This is the tip vortex. The much stronger vortex pair forming behind the wing is what the NASA page refers to, but that only happens when the air is already long past the wing. That is the wake vortex. In the cores of the wake vortex pair the pressure is lowest because the radius of the helical motion is smallest - vortex strength is the same for every point in a plane perpendicular to the direction of motion of the wing. Therefore, the NASA page is at least misleading, if not outright wrong.

In the wind tunnel the same happens (minus the tip vortex), but boxed in by the wind tunnel walls. They slow the wake vortex by wall friction and stop the wake from continuing downwards, just like the ground does in ground effect. But there is still a pair of vortices close to the bottom wind tunnel wall (or the top, if the wing section is mounted upside down).