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MaxManus
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Why does the air flow faster over the wing? In my fluid mechanics course we used streamlines and a half body to show that the air flow faster over a half circle, but I do not understand why it does so.
K^2 said:On the other hand, the fact that air over the wing travels faster isn't directly related to the lift. It does tell you that you have positive circulation, which means the air is deflected downwards, which is how you really compute lift, because you can now use momentum conservation (Kutta Joukowski Theorem). But lift itself is caused by pressure at the boundary, and the air speed at the boundary is zero all around the wing. So you cannot use it as an explanation of lift.
K^2 said:No, it doesn't. Kutta condition merely tells you that the streams meet, but because of the separation layer between them, it doesn't tell you anything about their relative velocities. In other words, Kutta condition doesn't tell you that the stream over the top of cambered wing has to travel faster.
On the other hand, the fact that air over the wing travels faster isn't directly related to the lift. It does tell you that you have positive circulation, which means the air is deflected downwards, which is how you really compute lift, because you can now use momentum conservation (Kutta Joukowski Theorem). But lift itself is caused by pressure at the boundary, and the air speed at the boundary is zero all around the wing. So you cannot use it as an explanation of lift.
K^2 said:No, it doesn't. Kutta condition merely tells you that the streams meet, but because of the separation layer between them, it doesn't tell you anything about their relative velocities. In other words, Kutta condition doesn't tell you that the stream over the top of cambered wing has to travel faster.
On the other hand, the fact that air over the wing travels faster isn't directly related to the lift. It does tell you that you have positive circulation, which means the air is deflected downwards, which is how you really compute lift, because you can now use momentum conservation (Kutta Joukowski Theorem). But lift itself is caused by pressure at the boundary, and the air speed at the boundary is zero all around the wing. So you cannot use it as an explanation of lift.
Yes, that is true.Andy Resnick said:DrDu,
I'm having a hard time parsing your post- the Kutta condition requires the velocity to be *bounded*, not *continuous*.
MaxManus said:Thanks, but now I'm not sure if I understand. It might be that I misunderstood my fluid mechanic course, but I believe we used the fact that the air flows faster over the wing and the bernoulli equation to show that there will be a lift. I have read the links and see that there are other things that create lift too, but is it wrong to say that that faster flow over the wing creates lift?
DrDu said:The flow at the end of the wing has to fulfill the so called Kutta Joukowski condition. I. e., the steam lines from above and below the wing have to be parallel and of equal velocity. That determines the degree of circulation around the wing and the difference of velocity below and above wing.
DrDu said:I cannot follow your argumentation that the lift cannot be calculated from the air speed as the air speed vanishes at the wing. The vanishing of the velocity is due to friction.
Bernoulli only applies when friction can be neglected. But this is the case already at distances small compared with the dimesnion of the wing.
DrDu said:The amount of circulation is fixed by the Kutta condition. My point is that after the wing the velocity of the fluid elements passing above and below the wing at the line (or surface) where they meet has to be equal as pressure must be a continuous function.
DrDu said:Yes, that is true.
I doubt on physical grounds that in sub-sonic stationary systems a shock wave with discontinuous velocities or pressure can pertain.
In the real world, depending on air foil, angle of attack, wing loading, ..., the flows aren't quite equal, there's turbulence and vortices at the trailing edge, as differences in velocity and pressure exist at the trailing edge where the flows merge. Wing tip vortices also significantly interfere with the flow on a typical aircraft (high end gliders with 80+ foot wing spans would be an exception).DrDu said:After the wing the velocity of the fluid elements passing above and below the wing at the line (or surface) where they meet has to be equal as pressure must be a continuous function.
Andy Resnick said:This is all fine, but what does it have to do with an airfoil? The conformal mapping of a cylinder to an airfoil results in a solution that (excluding stall) has negligible boundary layer separation. However, the *inviscid* flow pattern- a limiting flow pattern- around a bluff body has, AFAIK, remained resistant to solution by either theory, calculation, or experiment.
DrDu said:Well, thank you for your pacience. I am enjoying very much this discussion.
Andy Resnick said: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 said:But you still avoided my primary question. Is the velocity behind a streamlined object continuous or not?
http://en.wikipedia.org/wiki/Venturi_effectAccording to the laws governing fluid dynamics, a fluid's velocity must increase as it passes through a constriction to satisfy the conservation of mass, while its pressure must decrease to satisfy the conservation of energy. Thus any gain in kinetic energy a fluid may accrue due to its increased velocity through a constriction is negated by a drop in pressure. An equation for the drop in pressure due to the Venturi effect may be derived from a combination of Bernoulli's principle and the continuity equation.
russ_watters said:in other words, it's an inside-out venturi tube.
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.russ_watters said:airfoil ... it's an inside-out Venturi tube.
rcgldr said:
rcgldr said: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?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.
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: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.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.The theory is based on an analysis of a Venturi nozzle. But an airfoil is not a Venturi nozzle. There is no phantom surface to produce the other half of the nozzle. In our experiments we've noted that the velocity gradually decreases as you move away from the airfoil eventually approaching the free stream velocity. This is not the velocity found along the centerline of a nozzle which is typically higher than the velocity along the wall. [emphasis added]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.The Venturi analysis cannot predict the lift generated by a flat plate. The leading edge of a flat plate presents no constriction to the flow so there is really no "nozzle" formed.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.This theory deals with only the pressure and velocity along the upper surface of the airfoil. It neglects the shape of the lower surface.
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 said: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
russ_watters said:Do you have any links to diagrams that show flow that isn't nearly parallel to the nearest airfoil surface?
DrDu said: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 said:for a flat surface, the thickness 'd' of the boundary layer a distance 'x' from the leading edge is given by d/x =5* Re^0.5, where Re is the local Reynolds number at the distance 'x'.