# 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.

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:

1. The upper and lower flows (vortices) as it travels the chord of the wing.

2. 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…

• "the flow turns downwards immediately after leaving the trailing edge" -- That is not true, although the same mistake is made in the question in your first link. Also, what makes you think downwash can occur only in the presence of wingtip vortices? Mar 10 '18 at 17:47
• I'm not saying I agree with the explanations; I'm just trying to find out how, and if, they explain what's happening to a wall-to-wall model. Mar 10 '18 at 18:39

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).

• My reply/comments are too long for a comment, how else can I write them? Sorry new to the forum... Mar 10 '18 at 20:37
• @user9251544: Add them to your question. After all, it seems my answer is incomplete. Mar 10 '18 at 20:44
• "Please read this answer and try to follow all the links" I ended up with 30 opened panels and stuck in infinite recursion as one of them led back here :D Dec 29 '18 at 11:39
• @PeterKämpf, "Yes, tip vortices are indeed a result of downwash." Isnt tip vortices "result" of pressure differential between upper and lower surface at tip ?And two wake vortices are "result" of downwash far behind the wing?
– user50657
Aug 18 '20 at 20:52
• @NoahPrandtl Tip vortices are indeed the result of the pressure differential at the tip, but in that case I used a citation from the question in which the word "tip vortex" was used instead of the more correct "wake vortex". When you read on you will notice that I gently correct the terminology. Aug 18 '20 at 23:03

An airfoil in a wind tunnel cannot cause a net downward movement of the air, because of the bottom wall of the wind tunnel. If the airfoil stretches only part way across the tunnel, there can be a downwash behind the airfoil, balanced by an upwash outside its tips, so that the overall mass continues "straight" along the tunnel, with a swirl in it. But, if the airfoil stretches all the way across, this cannot happen. Instead what happens is that the air pressure below the airfoil becomes higher than the air pressure above it. The higher air pressure below, and lower air pressure above, offset the airfoil's "attempts" to generate downwash. There is no downwash, but there IS a pressure differential (assuming a lifting airfoil) and a lift force on the airfoil.

Because there is no downwash, induced drag is very low. People tend to think about induced drag as having something to do with the tip vortices, but there's a more useful way to think about it. When air flows past a wing under normal conditions, it is deflected downward at some angle $a$. The downward deflection gives the air a vertical velocity component equal to $v \cdot sin(a)$, and the reaction to that change in momentum creates lift. But, the deflection also means the air's horizontal velocity component is reduced a bit, from $v$ to $v \cdot cos(a)$. That slight reduction in horizontal momentum creates induced drag - drag induced by creating lift.

In the case of the fully-spanned wind tunnel (or, to a large extent, ground effect), the top and bottom walls prevent downwash, by forcing a pressure differential that stops it. With no change in the direction of the flow, there is no loss of horizontal momentum in the air flow, and thus very little induced drag. There is still some, due to the work done on the air by compressing it under the wing and expanding it above the wing, but with an adiabatic assumption (close to true) the effect is very small.

• Thank you so much, i was desperately reading article after article about this and still did not understand. This reply finaly rescued me from the curse. Dec 29 '18 at 12:04
• @finbarsheehy,"In the case of the fully-spanned wind tunnel (or, to a large extent, ground effect), the top and bottom walls prevent downwash, by forcing a pressure differential that stops it. With no change in the direction of the flow, there is no loss of horizontal momentum in the air flow, and thus very little induced drag. There is still some, due to the work done on the air by compressing it under the wing and expanding it above the wing, but with an adiabatic assumption (close to true) the effect is very small.."..I agree with you
– user50657
Aug 17 '20 at 7:15

Any lift producing object always produces downwash. To achieve lift an object basically directs the airflow downwards. So there cannot be lift without downwash. Tip vortices might also be directed downwards and have downwash in a sense. That does however not mean that there couldn't be downwash without wingtip vortices.

• You're saying what the others say but you're not answering the question. How can a wall-to-wall model in a wind tunnel have lift but no, or infinitesimal, downwash? Mar 10 '18 at 19:47
• @user9251544 You keep missing the point: it can’t, and it doesn’t. Any idea you had about “infinitesimal” downwash in the wall-to-wall case is simply mistaken. Mar 10 '18 at 20:05
• David K The explanations above suggest that induced drag is caused almost exclusively by downwash so I'm trying to understand what they're saying because OF COURSE downwash for a wall-to-wall airfoil is zero.... sorry for the confusion! Mar 10 '18 at 20:40
• It is not zero. That is the whole point. Mar 11 '18 at 6:45
• Thanks Vladimir, pls see my revised reply to Peter Kampf for clarifications Mar 11 '18 at 10:03

The NASA page about wing tip vortices does not try to explain the "wall-to-wall" model; they have many other pages that do that. (The model on those other pages is usually said to be an "infinite wingspan" model, but the effect is the same: there's no way to get from the bottom of the wing to the top by going around the wingtip.)

I think of wingtip vortices as an additional effect that occurs when you take away the wall (or when you reduce the wingspan from infinite to finite). The wording of the page might let you think this effect is the only thing that people ever mean when they say "downwash." But people also use the term downwash to describe a much-larger-than-infinitesimal effect that occurs in the infinite-wingspan model. For example, see the figures in this answer, or the chapter cited in that answer, which says:

Near the wing the bound circulation due to lift leads to an up-wash ahead of the wing and downwash behind the wing similar to the flow produced by a two-dimensional lifting wing of infinite span.

The downwash associated with the wingtip vortices is mentioned as an additional component of the motion of the air near the wing (including air in front of the wing as well as behind it), distinct from the downwash mentioned in the quoted passage above.

To the extent that the NASA page could allow you to have ideas about the word "downwash" that contradict the way the term is used elsewhere, then yes, I suppose the page is wrong. I think this NASA page, which as far as I can tell is describing circulation patterns and vortices according to the infinite-wingspan model, makes a mistake by linking the word "downwash" (used in that context) to the page about wingtip vortices. It seems to me that would tend to give the false impression that the deflection of flow is caused only by the wingtip vortices.

• Thanks David but I’m not saying that wing tip vortices create induced drag, pls see my revised answer to Peter Kampf Mar 11 '18 at 10:02

One of the first things discovered about vortices, even before induced drag was understood, was that a vortex cannot end in a fluid (e.g. a wingtip), but it can end at a solid surface (e.g. the bottom of a coffee cup you're stirring). In a wind tunnel the bound vortex along the airfoil, which is part and parcel of the lift, simply ends at the wind tunnel walls. Because the bound vortex ends at the wind tunnel walls, there are no trailing vortices. And because there are no trailing vortices, there is no downwash.