Fluid mechanics, why does the air flow faster over the wing?

DrDu

I think I have a good understanding on how a boundary layer forms. In old times I even wrote a paper on multiple scales techniques (although in QM, not fluid mechanics).

I also saved a copy of Prandtls collected works from the library which is here on my shelf.

I am confused. I thought the *inviscid* flow pattern to be known, at least for a cylinder?
What is a "bluff" body? I can't find a really fitting translation into German.

I always thought that after a wing ideally there is no von Karman street, only the vortex formed when starting? But maybe that is an (over-)idealization.
In a von Karman sheet, the direction of the vortices alternates. So I would expect that at least on the mean the velocity above and below the street is equal.

Well, thank you for your pacience. I am enjoying very much this discussion.

Andy Resnick

Me, too!

I only have a moment to respond, I can do more later:

1) 'Bluff' bodies are the opposite of slender bodies, 'blunt' may be a more descriptive term:

http://www.princeton.edu/~asmits/Bicycle_web/blunt.html

2) I am unaware of a complete and general solution for Re -> 00 flow past a solid body. I haven't pored over the literature lately, tho.

3) We haven't considered airfoils of finite length yet- it turns out the dominant mechanism of vortex shedding from a finite airfoil is from the ends, not along the length.

http://pilotsweb.com/principle/art/v_sheet.jpg

More later...

DrDu

ad 1) ok, so the contrary of streamlined
ad 2) naively, I thought that inviscible is the same as an ideal fluid. However, the limit Re-> infinity (or nu->0) is a singular limit and so it will not coincide with the nu=0 case.
However, I have no good idea how this will lead to turbulence.
ad 3) that I know. In 3d, the vortex lines are closed.

But you still avoided my primary question. Is the velocity behind a streamlined object continuous or not?

Andy Resnick

I don't know about 'avoided', but in general, no. The velocity is not continuous in the general case.

Edit: Schlichting's book "Boundary-layer theory" has some detailed information. To summarize, for flow past a circular cylinder, boundary layer separation occurs at 4 < Re < 40, and the separated flow remains laminar until around Re > 10^5, at which point it becomes turbulent separated flow.

After laminar boundary layer flow has separated from the body, the flow evolves into free shear layers downstream (the wake). In the limit Re -> 00 , the free shear layers resolve to line and point discontinuities.

russ_watters

My own understanding proved somewhat misguided in a recent thread and through that, I figured a simpler way to explain it:

The airfoil provides an obstruction that the air has to travel around, which squeezes it - but due to conservation of mass and the fact that it doesn't compress much, it has to travel a lot faster to get past the bigger obstruction (the top surface of the airfoil). In other words, it's an inside-out Venturi tube. http://en.wikipedia.org/wiki/Venturi_effect

Andy Resnick

like! :)

rcgldr

Part of an ongoing debate between web sites. Nasa link explaining that an airfoil does not behave like a Venturi, but doesn't offer an alternate explanation.

http://www.grc.nasa.gov/WWW/K-12/airplane/wrong3.html

In a Venturi, other than transitions through constriction points, the flow is uni-directional. In the case of an airfoil the direction and speed of flow varies with distance from the airfoil, following the boundary layer in the immediate vicnity of the airfoil, and as vertical distance from the airfoil increases, the flow is more downwards and perpendicular to the surface of the airfoil.

In a Venturi, the pipe restricts the flow of air. On a cambered airfoil (or the cambered stagnation zone on a flat airfoil), there's a Coanda like effect where the air tends to follow the cambered surface to fill in what would otherwise be a void.

Andy Resnick

I think this model is too simple, and gives an incomplete answer.

First, they only consider half of the flow: the accelerating part, as the flow is constricted. They neglect the second half, when the flow expands. Second, this is inviscid flow.

Adding viscosity back makes the second half of the flow region more important, because the second half of the flow region takes fluid from a low pressure region back to a high pressure region- the air is moving *against* the pressure gradient.

For inviscid flow, this is no problem- no energy is lost during the acceleration phase, and so all the energy is recovered as the flow slows down. Viscosity results in the loss of some energy. Viscous effects are important primarily in the boundary layer.

Thus, any fluid that has lost too much energy by viscous dissipation is then unable to move back to the high pressure region behind the airfoil, resulting in the boundary layer separating from the airfoil. And this is what is observed- boundary layer separation at some angle of attack.

russ_watters

[QUOTE=rcgldr;2943946]Part of an ongoing debate between web sites. Nasa link explaining that an airfoil does not behave like a Venturi, but doesn't offer an alternate explanation.

http://www.grc.nasa.gov/WWW/K-12/airplane/wrong3.html
I've never heard that before. Do you have any links to diagrams that show flow that isn't nearly parallel to the nearest airfoil surface?
You can make a venturi tube have flow separation if the curve isn't right and the coanda effect would play a role in that as well. Either way, though, the basic Venturi effect isn't the only thing affecting the lift on a wing, but it does explain a lot of it and the question in the OP wasn't about lift, it was just about the speeding up of the air. Anyway, from the link you posted: The fact that it is inside-out is obviously a difference and since it is just an analogy, it can't be expected to perform perfectly, but I'm wondering if the size of the Venturi has any impact on the velocity profile.....I think it must. Basically, it seems to me that the further away the two halves of a two-dimensional Venturi, the more like an airfoil it would behave. "Typically" doesn't imply "always" to me. Agreed. The Venturi analogy would not seem to work for a flat plate. The flat plate minimizes/eliminates that component and I would think makes downward deflection and coanda effect the only active parts. Agreed - but the OP only asked about an example (a half circle) where the lower surface is essentially a zero angle of attack flat plate.

In short, there are few if any scientific theories that can be explained in 5 words. They are always more complicated than that and in the case of lift, there are several different principles at work. I don't think it is fair to say that the idea is wrong, just incomplete for fully explaining lift. More importantly, few people have a problem with the idea that a flat plate with a positive angle of attack can deflect air downards and create lift regardless of what is going on above it. It seems to me that understanding the velocity increase is the biggest problem and this explanation isolates and deals with only that piece.

rcgldr

If you look at any diagram of streamlines over an airfoil, from the point of upwash to near the peak of the cambered surface, they constrict as velocity increases and pressure decreases (mass flow within streamline is constant). The inner streamline follows the airfoil surface (actually the boundary layer), but as you get further away from the airfoil surface, the outer streamlines have less of a upwash component and more of a component perpendicular to the leading portion of the airfoil surface where the streamlines contrict, otherwise a void between streamlines would be created. Once past the peak, velocity decreases, pressure increases, the streamlines expand, and as you get further away from the airfoil, the less the streamlines follow the surface. The net result is that the higher above the airfoil, the less the flow follows the surface of the airfoil, eventually reaching a point above the airfoil where the air is virtually unaffected.

http://www.youtube.com/watch?v=7jTeiz_f1iY

http://www.youtube.com/watch?v=6UlsArvbTeo

This web site includes a photo as well as an animation of how a parcel of air is affected by a wing passing through it from an air based frame of reference.

http://www.avweb.com/news/airman/183261-1.html

DrDu

Andi, just a question. When you say inviscid, do you mean lim Re -> infinity or nu=0?
I think the case nu=0 gives Euler equations which are rather trivial to solve in comparison with the Navier Stokes Equations for low Re.
I see no reason why the limit should converge to the latter.
However, sometimes inviscid and ideal are used interchangeably.

Andy Resnick

That's a very insightful question.

Hopefully you can see that setting [itex] \mu = 0 [/itex] is very different than lim Re -> [itex]\infty[/itex]. I am unaware of what the 'official convention' is, and in fact one way I distinguish good texts and bad is based on how clearly they make this distinction.

AFAIK, "Inviscid" simply means that viscosity effects are unimportant. While this may be true for the far-field velocity distribution of a fluid, it neglects the boundary layer. Setting the viscosity = 0 negates the boundary layer, while lim Re -> [itex]\infty[/itex] maintains it.

Andy Resnick

I erred- the thickness goes as Re^-0.5, not Re^0.5.

SDEric

Could one of you physics gurus answer this one. There was an answer to this question posted early in this thread, but I'd like to make sure it reflects the consensus opinion.

If you had an airfoil that was half a cylinder, with the flat bottom at a zero angle of attack (that is, parallel to the direction of flow), would lift be generated?

It wouldn't even have to be an entire half a cylinder; any section of a cylinder would work for the thought experiment. The point being, if you had an airfoil that was symmetrical front to back, and at a zero angle of attack, would lift be generated?

The NASA program "foilsim" says lift would be generated. If this is true, I would love an explanation.

I understand the mechanics of air being deflected down by both the top and the bottom of a wing, and the whole idea of "turning" air flow. I am curious whether the Bernoulli effect alone creates lift.

MaxManus

My post is a year old, and I don't remember the equations but yes the there will be generated lift with zero angle of attach. But Im not sure of your last question. If you agree on the bernoulli effect, then why not agree in an ideal example where you haven't taken the mass of the into the problem?

rcgldr

One of the links from one of my earlier posts is broken now. There's an archived version of it, but most of the images are gone:

archive_/~weltner/Mis6/mis6.html

As far as a true half cylinder goes, you might be able to generate the 2d coordiantes of a half cylinder based air foil and use XFOIL to calculate the polars (lift and drag versus AOA, Re, ...).

http://web.mit.edu/drela/Public/web/xfoil

A true half cylinder would generate a lot of drag. If the air foil was made of a thin slice of the upper part of a cylinder, a flat bottom and a circular arc of a few degrees on the top, it might work in theory, but actual examples appear to need a non-zero angle of attack to produce lift. A frisbee is similar to this, except the bottom surface is hollow so is similar in shape to the upper surface, and from what I recall, a frisbee needs an angle of attack to generate lift. An aerobie is a flying ring that combines a special triangular outer spoiler rim with an airfoil section similar to a thin slice of a cylinder for the inner shape, but it still needs some non-zero angle of attack to produce lift. The spoiler rim is designed to keep the center of lift near the center of the ring over a reasonable range of angle of attacks to eliminate pitch torque which would result in a roll due to gyroscopic precession.

http://aerobie.com/about/ringscientificpaper.htm

SDEric

Thanks! I can easily see how a slice of a cylinder would create lift if it were at a non zero angle of attack. The angled bottom would deflect air down, and the curved top would turn the upper air stream down. The net effect would absolutely be to push air down. Probably the optimum angle of attack would be with the initial portion of the upper surface tangential to the airflow, but that's just a guess.

I just cannot see how lift would be generated at a zero angle of attack. Sure, the air following the rear portion of the curve would be turned down and would lift the back portion of the cylinder section. But the exact opposite effect would take place at the front of the cylinder section. It seems to me that the net effect would be to only apply torque to the cylinder section.

NASA's Foilsim program seems to say that a cylinder section would have lift at a zero angle of attack. But that is a simulator, and may or may not be completely correct.

Here's the "Misinterpretations of Bernoulli's Law" paper you were attempting to link to above: http://plato.if.usp.br/2-2007/fep0111d/Bernoulli.pdf