A "new" theory of lift ?

[rb1957]

i'd like some more informed aerodynamists' opinion on Mr (Dr?) Johnson's opinion that lift is not caused by circulation. From

http://knol.google.com/k/the-spell-of-kutta-zhukovsky-s-circulation-theory#

...

"it is shown that the lift you experience when you fly, comes without circulation, as displayed in the following figure showing the lift and circulation of a Naca0012 wing as function of the angle of attack, computed by solving the Navier-Stokes equations for the flow around the wing:

pic doesn't show, sigh

We see that the lift increases linearly with the angle of attack up to 16 degrees, while the circulation stays
basically zero up to 10 degrees: Lift and circulation are not equivalent as in Kutta-Zhukovsky's formula"

there is an impressive looking pic showing lift increasing with AoA, as expected, but "circulation" remaining constant, and close to zero. this sort of breaks the linkage between circulation and lift, but i'm smart enough not to take things I can't derive myself at face value.

As far as I've read Johnson doesn't propose a consistent new theory, but tries to explain lift and drag at near separation AoA.

opinions ?

 

[KENAT]

Vortexman, I meant to imply that bound vortex & circulation were the same thing (or at least closely related). I have no confusion about my understanding of it.

As to 1/4 chord, I think that was rb1957 mixing things up, I was just saying that I'm fairly confident it's correct and not just an arbitrary convention.

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[IRstuff]

This article, a bit dated, would suggest otherwise.

TTFN

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[KENAT]

Which article?

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[IRstuff]

oops, sorry, someone interrupted me;

http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19930091215_1993091215.pdf

TTFN

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[KENAT]

Was that article posted in response to the 1/4 chord question? If so where in it am I meant to look, as I had trouble finding it?

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[IRstuff]

Yes, there are some graphs in the latter part of the book that appear to show the CoP wandering across the chord.

TTFN

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[aeroafrix2]

Just curious, has any one observed this circulation phenomenon in a closed lop wind tunnel either using "white smoke" or "white bubbles" instead of air? And for those that have, how far the chord length does the circulation go? Does the circulation go around the wing and if this is the case how does this circulation differ in the case of "slat" and "flaps" in a full wing assembly -- (sorry its doing my head in ;D)

Granted this theory is not new. However, most Aerodynamic lectures hardly dwell on it rather they go straight into the Momentum theory of Lift.

 

[IRstuff]

I think that one needs to separate the the fact that the velocities are different on the top and bottom, resulting in a nonzero line integral of velocity around the wing, from an actual air flow going around the wing.

TTFN

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[rb1957]

IR ... i don't know how you can separate the velocities near the upper and lower surfaces of the wing from circulation around the wing ??

aero ... "how far the chord length does the circulation go?" ... certainly it is 100% of the chord, and i think 100% of the span, with varying strength ... i think strongest at the tip.

 

[aeroafrix2]

@IR, vortexman & rb1957, how does this 100% chordwise circulation playout during take off and/or landing of an aircraft when the slats and flaps are fully deployed. Take for example during take off the flap is fully extended, and there would be a certain 'gap' between the leading edge of the the flap and the trailing edge of the wing. Now how does this 100% chordwise circulation around the flap and the wing playout at the leading edge of the flap and at the trailing of the wing?

See the attached sketch (excuse my freehand drawing in word) if that would help explain what I mean.

 

[IRstuff]

Circulation, mathematically, is a line integral of the velocity around the wing, so a non-zero result means that the velocities between the top and bottom are different, as discussed. HOW that arises is the question. The obvious explanation, is that there is a "circulation" of air around the wing satifies the mathematical model. But, my argument is that there is no physical basis for claiming that there is an actual circular flow around the wing, moving in counterflow on the bottom side of the wing.

Both the "new" theory and the momentum theory basically throws away actual air "circulation" and replaces it with other physical phenomenon.

TTFN

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[vortexman]

IRstuff,

Start by considering all the different shaped bodies that could be placed in a uniform flow. Would you expect all of them to result in a flow field with zero circulation? If so, why? This is just as valid as to ask for the physical mechanism that results in non-zero circulation. It would also be just as valid to ask why some shapes deflect the air downward, which would be, in effect, questioning the so-called momentum theory. So why would one seek the mechanism behind "circulation theory" and not seek the mechanism behind "momentum theory"? Are you comfortable that you could explain the mechanism that results in downward deflection of the air? If so, you will have identified the mechanism responsible for non-zero circulation, because the same mechanism causes both. If you're OK with 'momentum theory' but not with 'circulation theory', you could respond now with your explanation before you read any further.

The short, shallow and unsatisfying answer is that some shapes will exert a combination of normal and shear stresses on the fluid that will cause non-zero circulation. One could say the same about 'deflection'.

More to your point, the mechanism that causes the circulation is the fact that non-zero viscosity prevents attached flow from going around the sharp corner of the trailing edge. This is, in essence, the Kutta Condition. This fact is what resolves D'Alembert's Paradox (check Wiki), and makes it possible for any body to generate lift, and circulation. Of course, this works for bodies that don't have sharp trailing edges as well, because non-zero viscosity inhibits the fluid from going around less-than-sharp trailing edges.

Picture a symmetric airfoil at zero angle of attack. The air hits it and leaves it at the leading and trailing edges, so the flow is symmetric, and results in zero lift and zero circulation (and zero 'deflection'). If you start to bend the trailing edge down, the viscosity will force the flow to continue to depart the airfoil at the sharp trailing edge. Intuitively, you can see how this causes the flow to be downstream over a larger and larger portion of the upper surface, and a lower and lower portion of the lower surface, essentially because the upper surface is being stretched, and the lower surface is being squished. If you were to draw a closed curve fairly close to the wing surface, you can see how the line integral of velocity would become nonzero, and larger, as the trailing edge is bent down more and more (in other words, the wing is given camber), because the portions of the line integral from the upper and lower surface regions no longer cancel out. The same effect would be observed if you simply give the symmetric wing a positive angle of attack. To get a visual on that, you need to picture what happens to the leading stagnation point as the angle of attack is made positive. Many pictures of this are to be found via Google.

vortexman

 

[IRstuff]

I have never said that there isn't an imbalance of velocities. What you're describing is the physical basis for momentum theory, not circulation of air around the ENTIRE wing, only around the trailing edge. That's the only distinction I've made or intended to make.

TTFN

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[rb1957]

aeroafix, to me 100% chord means the airflow is circulating around the airfoil. if it is a multi-element airfoil, then it'd be circulating around each one and/or around the envelop ... there'd be stronger circulation around the element causing the most lift/with the highest Cl ... ther'd be flow thru the slot (between the elements) in one direction only.

do you have an alternate idea about circulation around <100% chord ??

 

[gerritgroot]

@vortexman:

"Euler flow solutions (inviscid but not irrotational), interestingly, have not typically required the imposition of the Kutta condition, although, since the solutions are inviscid, one might have expected that the lift could not be determined by such methods. It seems that the numerical errors in Euler simulations have an effect similar to physical viscosity."

Your assumption is right. Euler CFD gives the right lift, only because of the discretisation itself. It's the hidden numerical velocity that makes the flow leave at the trailing edge. If an analytical solution of the Euler equations would exist, you'd need a Kutta condition again to get it working.

 

[vortexman]

IRstuff,

I'm kind of running out of ways to explain it. As I said before, the physical basis of one 'theory' is also the physical basis of the other 'theory'. You don't get to pick which phenomenon you think is really happening; they both are. There is downward deflection of the airflow, and there is also circulation. They are just different manifestations of the same phenomenon, and neither of them happens just at the trailing edge.

In particular, circulation must be evaluated around the entire wing section, and the curve on which you evaluate the line integral can't go through the wing. There is a 'velocity mismatch', as you call it, and it isn't limited to the trailing edge. Recall that we could invoke yet another 'theory', the Bernoulli Equation, which reminds us that the velocity on the upper surface of a lifting wing is higher than that on the bottom surface. It all fits together, and if it didn't, something would be very wrong.

vortexman

 

[aeroafrix2]

@rb1957.Sorry I asked that question 'cos I remember doing some wing tunnel experiment some yars ago using 3D wing and one of the things we were hoping to observe was this 100% chord wise circulation and we also wanted to know how far off the "circulation flow field" was from the chord line of the wing and unfortunately it wasnt so easy to observe in the closed loop recirculation wind tunnel we were using.I am not completely convinced of this "circulation theory" even though mathematically it seems to add up, in reality it raises more questions than answers.

@vortexman
"....There is downward deflection of the airflow, and there is also circulation. They are just different manifestations of the same phenomenon, and neither of them happens just at the trailing edge..."

care to explain further how these two phenomenon then combine to produce Lift? bearing in mind that the bottom line of either theory is thier attempt to justifiy (or explain)pressure differential between the top and bottom of the airfoil which in return results in lift. Also, I disagree that all the theories all fits together in an attempt to explain how lift in generated on airfoil and Bernoulli theory can be faulted 'cos it realies so much on the "continuity equation" i.e. in a nutshell can be explained as smaller area, higher pressure and bigger area lower pressure which may not be completely true in the case of flow over a body surface.

 

[vortexman]

aeroafrix2,

I don't think I can explain these things to your satisfaction, especially in this limited forum. I can only recommend reading some standard Aerodynamics texts. All this stuff is there, and is standard theory that is widely understood and commonly used in practice. To say "I am not convinced of this 'circulation theory'", and "Bernoulli theory can be faulted" based on your evidently uniformed intuition is a little bit silly. What about that ridiculous "Force equals mass times acceleration" theory; do you have some problems with that too?

If you want understand this stuff, you'll probably have to do it the way Aerodynamics undergraduates have been doing it for decades.

vortexman

 

[rb1957]

maybe i'm being a bit slow this morning ... earlier in this discussion i thought it was (often) said that circulation was a mathematical artifice as opposed to a physical phenomenon ? this looks to be the crux of discussion.

it would appear that Johnson's paper (incorrectly) uses spanwise circulation ... yes?

one thread i pick up is is circulation caused by lift or lift caused by circulation ??

 

[vortexman]

rb1957,

Circulation is a real physical phenomenon. The only context in which you could view it as a "mathematical artifice" is the use of the potential flow approximation to predict real flows. In this situation, one is required to specify the circulation, because the potential equations have an infinite number of solutions for a given body and far-field flow conditions. The trick to choosing which of these solutions corresponds to physical reality is to select the "right" value of the circulation. This isn't really a mathematical artifice, it's the use of empirical knowledge to choose the physically meaningful solution. We know, by experimentation, that the flow departs a wing at the sharp trailing edge (for the meaningful range of angles of attack). We also know that this phenomenon is due to the fact that the air has non-zero viscosity. So, specifying the departure point of the flow (imposing the Kutta condition) has the effect of choosing the value of circulation that corresponds to viscous flow. I would call this an empirical adjustment, not a mathematical artifice. The bottom line is that if you were to experimentally measure the circulation around a lifting wing, it would be very close to the "theoretical" value. It's a real physical phemonenon that comes along with lift. It isn't very easy to measure, so no one does. No one measures momentum either. Engineers directly measure the lift, and visualize the flow to learn more about the details, when necessary.

No, this was made clear in at least one previous post. Johnson made reference to streamwise vorticity, which is NOT the same thing as circulation. It's in the wrong dimension, and it's not a line integral. This is why his "thory" is nonsense.

We humans like the idea of causation, but the question doesn't make sense. There is no such thing as causation between lift and circulation. If you move a wing-shaped body through the air, the resulting flow field will exhibit lift, and circulation, and deflection of the air, and a bunch of other characteristics. It would be completely arbitrary to say that some of these are causing the others. The assignment of causation to assist our intuition really is an artifice.

vortexman