Airfoil doubt

What makes the air, flow much faster on top of the airfoil, when compared with the bottom surface? In engineering terms, why is there a relatively higher rate of change in velocity over the top surface?
and is there any mathematical derivation/proof for coanda effect?

is my question so stupid that no one can answer?

russ_watters
Mentor
You asked on a weekday morning....

http://en.wikipedia.org/wiki/Coanda_effect

The simplest part of the explanation is that if the flow didn't stay connected to the airfoil, there would be a vacuum, so it is that vacuum that pulls the air down against the airfoil.

dude russ,
I personally feel that coada effect is a function of the velocity of the fluid stream,(in other words rate of shear) and the radius of curvature of the cylinder, spoon, airfoil.
And I am sure that there is much more to the story. Wikipedia doesn't give any mathematical/physical derivation, but explains the physical aspect of it.
So I need some heavy derivations. Is it patented?

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I believe the velocity difference is caused by the Kutta condition:

For an airfoil with positive angle of attack, the downstream stagnation point will be on top of the airfoil. This is impossible to maintain in a viscous fluid because there would be an infinite change in velocity around the trailing edge of the airfoil. The stagnation point moves to the trailing edge via an induced circulation about the airfoil.

http://en.wikipedia.org/wiki/Kutta_condition
http://en.wikipedia.org/wiki/Circulation_(fluid_dynamics)

ive only had one fluid mechanics class so correct me if im wrong on some of these things

so there's no mathematical/scientific derivation for coanda effect?

Does the Kutta condition ever apply to propellers?

http://en.wikipedia.org/wiki/Kutta_condition
The Kutta condition is a principle in fluid dynamics, especially aerodynamics, applied at sharp corners such as trailing edges of airfoils in steady flow. It allows an aerodynamicist to incorporate a significant effect of viscosity while neglecting viscous effects in the underlying conservation of momentum equation. It is important in the practical calculation of lift on a wing.

Besides wing stall, what might be another example of "unsteady flow"?

The upper surface of the aerofoil must be viewed as half-venturi-tube. thus, the point where maximum thickness of aerofoil exists, it behaves as the throat of a venturi tube. here, Velocity is max and pressure is min. When flow comes out of throat and flows towards the trailing edge, where the venturi opens up, velocity decreases and pressure increases.
So, the answer to your question is, the chamber of the aerofoil makes it behave like a venturi, resulting in variation of velocity and pressure. Lower surface of an aerofoil are generally flat.

Gold Member
The guy farther up talking about the Kutta condition was on the right track. Kutta explains why the air above moves faster.

Kutta condition just explains CIRCULATION. It expalins the position of the rear stagnation point, it does not explain the velocity profile of air on an erofoil. Kutta also expalins the reason for starting vortices. To the best of my knowledge, it no where comes close to explain velocity profile

Gold Member
Kutta explains why the air up top is accelerated. Without that, conservation laws wouldn't be satisfied. The upper surface is NOT a half-Venturi tube and there is no such thing as "equal transit time", another common explanation for why the flow on top is accelerated.

Potential flow theory would show that at positive angle of attack, the rear stagnation point would be on top of the airfoil and that the air on the bottom would bend around the trailing edge and meat the top air at that stagnation point. On an airfoil, which has a sharp trailing edge, that would require an infinite velocity while turning around that edge. In a real, viscous fluid, this is impossible. The viscosity of the fluid essentially forces that rear stagnation point to be located at the trailing edge, meaning the top flow is much faster than the bottom flow in order to satisfy continuity.

That is the real cause of the flow over the top of the foil being so much faster than below. The higher speeds means that the airfoil has a net circulation when at steady-state, and that circulation can translate into lift through the Kutta-Jukowski theorem. You could also just take the actual velocity profile and do Bernoulli on it.

The important thing is that the Kutta condition is exactly what explains the accelerated flow over the top of the airfoil. Of course, I would love to hear your competing argument for why it doesn't explain the phenomenon.

Kutta condition states that the circulation over an aerofoil is such that the rear stagnation point is at trailing edge. Movement of stagnation point from above the aerofoil surface to the trailing edge is accompanied by STARTING VORTEX. This no way explains why air should move faster to relocate the rear stagnation point.

Ok, as per BONEH3AD statement, once the stagnation point is relocated at trailing edge, the job is done, and air should stop accelerating. But this is not the actual case. Kutta condition just explains circulation and starting vortices. This no where explains why air flows faster on upper surface.

Gold Member
You are seriously going to argue this? I do aerodynamics for a living.

You still haven't explained adequately how I am wrong. That, of course, is because I am not wrong.

gmax137
You are seriously going to argue this? I do aerodynamics for a living.

I don't know if you're right or not, but this kind of appeal to authority just doesn't cut it here. Nobody is really interested in what you do for a living.

Gold Member
I suppose I probably could have taken a different route, but this guy has no point. He is stating the Kutta condition as it is applied in potential flow theory. However, there is a physical basis for that application, and that is the driving factor for why the air on top moves more quickly. It must. Physics forces the location of the stagnation point to be on the trailing edge and conservation laws force the flow on top to move faster. That IS the explanation.

I don't know if you're right or not, but this kind of appeal to authority just doesn't cut it here. Nobody is really interested in what you do for a living.

It gets my attention.

The Coanda effect has to do with the viscosity of air and what happens when the air shears in the boundary layer. (See Gersten and Schlichting: "Boundary Layer Theory.") The mathematical problem is that the "fluid approximation," which is basis of fluid dynamics, is not valid. See this paper (mine ):

http://arxiv.org/abs/nlin/0507032

I believe the velocity difference is caused by the Kutta condition:

For an airfoil with positive angle of attack, the downstream stagnation point will be on top of the airfoil. This is impossible to maintain in a viscous fluid because there would be an infinite change in velocity around the trailing edge of the airfoil. The stagnation point moves to the trailing edge via an induced circulation about the airfoil.

http://en.wikipedia.org/wiki/Kutta_condition
http://en.wikipedia.org/wiki/Circulation_(fluid_dynamics)

ive only had one fluid mechanics class so correct me if im wrong on some of these things
You're confusing cause and effect. The Kutta condition is an effect. The phenomenon is air molecules flowing by and interacting with the molecular structure of an airfoil.

http://arxiv.org/abs/nlin/0507032

Basic flow comes from displacement. For field integrity there must be an aft mass flow equal to the forward displacement. In an ideal flow there would be equal flow above and below for no lift. With Kutta in real flow, circulation moves the forward stagnation streamline down equivilent to the aft. More (most) of the displaced air is diverted over the top, with increased velocity.

You're confusing cause and effect. The Kutta condition is an effect. The phenomenon is air molecules flowing by and interacting with the molecular structure of an airfoil.

http://arxiv.org/abs/nlin/0507032

It's been a while so forgive me if there are inconsistencies in this but I believe ccrummer is correct. Kutta is based on circulation and if I remember correctly, circulation originates from viscous effects and boundary conditions on the airfoil. This being the case, the flow must bend to create a transition region of some sort behind the camber causing a low pressure region speeding up the original flow.

Gents you have my attention. Reading arxiv.org. It will take some time to ratioalize it with "fluid approximation".

Sorry that i am re-entering this zone after a long time.
Firstly, kutta condition is not a cause for air flowing at a greater speed over the airfoil. It is an effect of it.
The cause comes from the fact that airfoil in air, behaves like half venturi tube, which can explain all the features of the airfoil.
It can explain why air flow is faster on the upper surface