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 ?

 

[vortexman]

Professor Johnson's 'theory' is unmitigated nonsense. There is nothing new there, and you might as well spend your time explaining to someone that evolution doesn't violate the second law of thermodynamics. Circulation is a physical reality, in the sense that a wing generation non-zero lift will indeed have non-zero circulation around it, and the two quantities will generally exhibit the relationship predicted by 'circulation theory'.

In numerical solutions that assume potential (inviscid, irrotational) flow, it is indeed necessary to indirectly specify the circulation to get the 'right' value of lift. This is done by imposing the 'Kutta condition', which specifies that the flow departs at the trailing edge, and how it does so. This is not really a mathematical artifice. In reality, it is a way to impose the effects of viscosity on a non-viscous solution. It works because the main effect of viscosity on an 'almost inviscid' flow, which is what the flow around an unstalled wing is, is to force the flow to depart at leading edge, rather than upstream of it. Although this is expressed mathematically, it is an empirically determined way to make the potential flow equations solvable, and to make the solution physically meaningful, in the sense of predicting lift.

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.

Navier Stokes simulations, of course, have no need for the Kutta condition. A 'good' Navier Stokes solution will predict lift, and also will predict a circulation close to the 'idealized' circulation associated with that value of lift.

vortexman

 

[btrueblood]

"I think the modern CFD programs can now run the full-blown Navier-Stokes equations."

Yes, but. Simulations of the full N-S equations, including length scales (grid size) small enough to capture turbulent motion have been run for very simple flow conditions (flat plates) up to Reynold's numbers of a few thousand or so. Doing so requires many hours (weeks) of running on massively parallel supercomputers, just to conclude that the laminar flow boundary layer models (aka Von Karman equations) and the DNS simulations show very good agreement (surprise, they both agree with wind tunnel data too!). Past that, and for typical airfoils at typical Reynolds numbers (10^5 and up), a turbulence model is typically run (k-e models or similar) to model small scale motions. Good agreement can be found using these codes for certain conditions (quasi-2d airfoil flows are one), while for more complex 3d geometry, they can leave a lot to be desired. Panel codes, essentially inviscid flow approximations that include circulation are still used for airfoil design.

 

[rb1957]

thx for your contribution vortexman, you appear to know way more about CFD than i do (not difficult). it was interesting to read that CFD applies KZ (at least, in a way).

two observations ...
care to comment on Johnson's plots of circulation vs lift ? as i remember it, he plots that circulation is constant but lift is increasing (and if lift depends on circulation, it should be increasing, no?).

care to comment on his CFD plots, particularly if his CFD code embeds KZ.

based on the last two posts, it seems circulation is alive and well and living inside CFD codes. then it is more than just another thing i learned at school, but an active working theory.

 

[KENAT]

It concerns me that we're talking about CFD as it' there are only one or two approaches to it.

There are many, many algorithms and formulas that people have tried to use for various applications. My entire final year aero course was essentially a list of all the the different approaches my prof knew about and the math behind them.

I lost track of all the ones that were highly dependent on inputs & boundary conditions etc. to give a remotely meaning full answer.

I'm sure things have developed a long way from there, but I'll be honest, to this day I have trouble relying too much on CFD that hasn't been validated by wind tunnel or other testing.

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[btrueblood]

"to this day I have trouble relying too much on CFD that hasn't been validated by wind tunnel or other testing."

Spot on.

 

[vortexman]

Hi rb1957,

I haven't read all of his text word for word, but I did look at the color plots of velocity, pressure, and streamwise vorticity, and read the paragraph immediately after. I think this partially explains Professor Johnson's confusion. There are three components of vorticity, just as there are three components of velocity. Circulation, which is the line integral of velocity around a closed curve that encircles the wing, would be affected by the spanwise component of vorticity, not the streamwise component. The streamwise vorticity is irrelevant, and this would seem to be the source of his disconnect from reality. Those plots demonstrate nothing about his novel theory of lift.

The curves below showing drag, lift, and 'circulation' as a function of angle of attack are unlabeled, and thus hard to interpret, but I suspect that he has chosen to refer to streamwise vorticity and circulation interchangably, which is incorrect. I can't say it emphatically enough: nothing this guys is saying is correct. If he understood aerodynamics at the undergrad level, he wouldn't be making this mistake.

The only way that "KZ is built into" CFD methods is the application of the Kutta condition in potential flow CFD codes, as far as I know. This is an expediency required to get approximations to a "slightly viscous" flow with a fundamentally invisicid, irrotational computational method. No assumptions about "circulation theory" are built into other CFD methods, because they're not needed.

Kenat,

No argument about that, there are many different approaches to CFD. All of them are dependent on 'inputs and boundary conditions' to give valid results. Moreover, virtually all of them have limitations that must be accounted for by the user in order to produce useful results. Having said that, wind tunnel results aren't a sure-fire thing either. My favorite saying on that topic: "The only guy who believes CFD results is the guy who ran them, and the only guy who doesn't believe wind tunnel results is the guy who measured them". It's really hard to get good wind tunnel results. Just like CFD, it takes a good understanding, and there are limitations.

CFD is now used fairly routinely for some problems without experimental verification, particularly early in the design process. This requires a good understanding of what the CFD codes can and can't do, which has been acquired through long experience.

vortexman

 

[KENAT]

Thanks vortexman, I figured things had probably improved a little, and you make a valid point that wind tunnel tests have their own issues.

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[aeroafrix2]

Vortexman,
while I appreciate your comments on Johnson's theory, in section of your comment below on the effect of the spanwise component of vorticity on circulation;

"... Circulation, which is the line integral of velocity around a closed curve that encircles the wing, would be affected by the spanwise component of vorticity, not the streamwise component. The streamwise vorticity is irrelevant, and this would seem to be the source of his disconnect from reality. Those plots demonstrate nothing about his novel theory of lift"

How does this explain the constant Lift generated by planforms with tapered ends.
(P.S: I am in agreement of your explanation and I also have the opinion that Johnson's theory has many flaws, however, I also think His theory shold not be dismissed by a wave of a finger, rather it should be examined in the light of the fundamentals of physical laws)

 

[rb1957]

"How does this explain the constant Lift generated by planforms with tapered ends."

sorry aeroafrix2 but i don't get you you're referring to, care to explain.

and i welcome all comments about this, though i too didn't see anything new in Johnson's "theory" which seemed to me to be plots of CFD ... but maybe i missed something ?

 

[vortexman]

Hi aeroafrix2,

I'm not sure I understand what you mean by "constant lift of planforms with tapered ends", but I assume you mean a constant spanwise distribution of lift. Tapered wings don't necessarily have constant spanwise lift distributions, and I don't think anything I said has a bearing on that issue.

Regarding Johnson's "theory", there may or may not be many flaws, but there seems to be one huge one, recognized by examining it in the light of the fundamental laws of physics. That flaw is that he attempts to "disprove" so-called "circulation theory by means of an incorrect observation. His observation is that the lift generated by a wing doesn't vary with circulation as "circulation theory" would predict. His huge mistake is that he uses stream vorticity rather than circulation around the wing. Dismissing his theory on this basis doesn't constitute "the wave of a finger".

vortexman

 

[aeroafrix2]

Hello Vortexman,
sorry I was refering to the spanwise lift distribution of tapered planform.

If I may ask which Johnson are you refering to? the C. Johnson or the A.D. Johnson (the popular aerodynamis text author?)

I did ask that question because C. Johnson justified his circulation theory explaination of Lift by infering that the reduction of the chord in tapered planform accounts for the constant spanwise lift distribution in tapered planforms (elipitical wings)! What got me thinking was his assumption that if very "complex mathemtaics stuff" is used to solve his 3D model of Lift generation by circulation using his 2D model as a basis the conclusion arrived at would be the same as for the constant spanwise distribution of Lift seen on tapered planforms.

 

[rb1957]

as i understand it, tapered planforms don't have a constant airload distribution ... elliptical ones are supposed to (won't mention the Spitfire as 1/2 the world believes that the planform was chosen to accomodate the machine guns, as opposed to aerodynamic efficiency)

 

[btrueblood]

Err...I learnt it that the ideal (most efficient) lift distribution is elliptical, and the elliptical plan gives this most effeciently (in terms of metal weight required). Other planes use varying section and varying AOA across the span to achieve the same results...

 

[KENAT]

Hmm, I was taught ellipse is most aerodynamically favorable, but has a structural mass penalty; inverse ellipse (not sure that's quite the right term) was structurally most efficient but with aerodynamic draw backs; variations on 'tapered' are a compromise between the 2 extremes.

As to the Spit, nah, it was for the steam cooling of the Goshawk;-).

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[aeroafrix2]

@rb1957,
I thought tapered planform was a compromise between aerodynamic efficiency and structural (i.e. weight)penalty? at least that was what we were told some years ago in our aerodynamic lectures!

As for the source of lift being justified through the circulation theory, do we agree that C. Johnson's explanation are in order? Mathematical formulation of the theory appears o be order, though some of the assumptions might be questionable, but then, can anyone come up with reasons why this theory shouldn't be?

 

[rb1957]

yes, it is (a compromise) ... it only came up as people started talking about tapered planforms having constant lift (spanwise distribution) ... which i think we agree it doesn't.

as for Johnson's "theory", i don't think (IMHO) we agree it's in order, or that it's much of a theory ... scanning the posts i see a theme that there isn't much new in it (just seemed to be a bunch of CFD plots). clearly your take is different, what do you see in his paper ?

 

[btrueblood]

I agree with vortexman:

That flaw is that he attempts to "disprove" so-called "circulation theory by means of an incorrect observation. His observation is that the lift generated by a wing doesn't vary with circulation as "circulation theory" would predict. His huge mistake is that he uses stream vorticity rather than circulation around the wing. Dismissing his theory on this basis doesn't constitute "the wave of a finger".


IRstuff wrote:

The problem with circulation is that there is no physical mechanism by which it can occur, nor by which it can be observed.

I think I disagree here. There is a very significant, and measurable, pitching moment coefficient generated by a wing, or even a 2d foil section, and the pitching coefficient varies pretty much proportionately to the lift coefficient, both in circulation models and in real airfoils (why else do airplanes need tails or other pitch control surfaces?). The airfoil pitching moment is also in the correct direction to counteract the circulation predicted by theory, and from what I gather, is one of the reasons the potential flow plus circulation theory for airfoils has been around so long. A lot of the NACA profiles, esp the low-drag laminar profiles, were generated using potential flow models as the basis for the shapes, backed up by subsequent wind tunnel testing.

 

[rb1957]

well not really (again, IMHO) ...the pitching moment is only due to the convention of having the lift act at 1/4 chord.

it's really 6 of one, 1/2 a dozen of another ... whether you fix the position of the lift force and add a moment to adjust, or let the lift act where the cp would have it; but i think we've gone down the fixed force approach for long enough.

 

[btrueblood]

Umm. No, the center of lift is at the 1/4 chord point, for ANY airfoil producing lift - even a flat plate or a perfectly elliptical section. You can do a moment analysis to figure that out, the pitching moment minimizes when the counter torque is applied at the center of lift...

But, the pitching moment, even on a flat plate, is non-zero at any non-zero angle of attack, and it doesn't matter where you restrain it. The pitching moment acts to return the airfoil to a zero-lift position, which is why tailplanes produce negative lift.

 

[IRstuff]

There is no physical mechanism for getting air to move forward against the flow of the atmosphere across a wing. You might get half of a circulation, but that's just the normal flow. A counterflow cannot physically exist.

TTFN

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