Which is the correct explanation for lift?

[Robin04]

Hi,

I read several approach to the explanation of aerodynamic lift. Bernoulli, Newton, Kutta-Joukowski. I found a topic about discussing Bernoulli and Newton, and the conclusion was that they are both valid individually. But what about the Kuttaa-Joukowski theorem? And are these approaches all valid in the same fluid model (inviscid) or they can be applied in a different one?

Thank you for your answers! :)

 

[rcgldr]

Are you asking how to create a mathematical model to calculate lift and drag versus air foil, wing size, air speed, angle of attack, ... , or are you asking for a somewhat simple explanation of how wings generate lift. For the simple case, here is an example web page:

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

Newtons third law always applies: forces only exist in equal and opposing pairs, the wing exerts a force onto the air, air exerts an opposing force onto the wing. For Newtons second law, the force a wing exerts onto the air results in a pressure differential and/or an acceleration of the air. The pressure differential in the immediate vicinity of the wing contributes to acceleration of air beyond the immediate vicinity of the wing.

For Bernoulli, there are airfoil modeling programs that split up the surfaces of a wing into a large number of small squares, then calculate the relative flow speed just outside the boundary layer for those squares. This is complicated and usually based on some variation of Navier Stokes to determine the flow fields. Once the flow speeds are calculated, I assume Bernoulli can be used to calculate pressure based on those relative air speeds. The air curves as it flows over the top surface of a wing, and Bernoulli doesn't apply to curved flows since acceleration perpendicular to flow coexists with a pressure differential perpendicular to the flow, but there's no change in speed for perpendicular acceleration, just a change in direction. I assume each of the large number of squares is small enough that curved flow isn't an issue for using Bernoulli. These pressures are summed up to produce a net pressure differential and force on a wing. Commercial aircraft travel at mach 0.75 to mach 0.90, and combined with a wing loading a bit over 1 pound per square inch, the density of the air changes, but there's a form of Bernoulli for compressible flow. I don't know if there are any other adjustments made to Bernoulli to provide more accurate results with this type of modeling (the flow speeds could be adjusted from their actual speeds to make Bernoulli work if needed). One issue is the flow generally detaches from the upper surface of a wing before reaching the trailing edge, and I don't know how this is handled. There are other issues, but you'd need more of an expert on this stuff to explain it.

 

[Robin04]

So if I understand right, the article tells that Bernoulli is just one part of the story. If we try to calculate the lift using only Bernoulli we'll get a wrong result. In order to get a correct answer we have to combine Bernoulli, Newton and Kutta Joukowski. Until now I thought that these approaches are all correct individually, they just point out different important facts about lift, for example Bernoulli helps us to design efficient airfoils, the Kutta-Joukowski helps to explain wing tip vortices... If the correct explanation of lift is the combination of these 3 approaches why don't they unite them? Why is everybody talking about them separetly?

 

[boneh3ad]

If that's what the article says then it's wrong. If you know the velocities ahead of time then Bernoulli will give the right answer. You just need some other means of calculating or measuring the velocity.

Newton is always correct but is impractical for calculation. It's very difficult or impossible to measure the change in momentum in the flow due to the action of the wing.

The Kutta-Joukowski theorem is beautiful and useful mathematically but may not always be practical and still requires knowing the flow field through some other means in order to get the correct answer.

One of the simplest solutions to the problem of finding the actual flow field are a class of methods called panel methods. They replace the wing by a series of point singularities (sources/sinks or vortices) and use them with the no penetration condition and Kutta condition to get a flow field based on potential flow theory. It is quit simple and can be made more accurate in a number of ways that are still fairly simple, such as in XFOIL. Otherwise there are various models of increasing complexity based on the Navier-Stokes equations that can be solved on a grid to get the flow field, though that is computationally intensive.

 

[Robin04]

If that's what the article says then it's wrong. If you know the velocities ahead of time then Bernoulli will give the right answer. You just need some other means of calculating or measuring the velocity.

So if somebody says that Bernoulli is wrong then it is right indeed (Bernoulli), just the velocity calculation was wrong?

Newton is always correct but is impractical for calculation. It's very difficult or impossible to measure the change in momentum in the flow due to the action of the wing.

If I understand it right, Newton is only used for a simple explanation for "laymen" but there is no developed mathematical method to use this principle to fully describe the lift.

The Kutta-Joukowski theorem is beautiful and useful mathematically but may not always be practical and still requires knowing the flow field through some other means in order to get the correct answer.

So the Kutta-Joukowski therorem is equivalent with Bernoulli?

Sorry if I have stupid questions, I learned all these during my pilot training and I'd like to get things cleared in my head. :)
Although I want to be a aeronautical engineer so I'll have to learn these later. :D

 

[boneh3ad]

So if somebody says that Bernoulli is wrong then it is right indeed (Bernoulli), just the velocity calculation was wrong?

No, it just means they don't understand Bernoulli's equation, it's limitations, and it's requirements for use.If I understand it right, Newton is only used for a simple explanation for "laymen" but there is no developed mathematical method to use this principle to fully describe the lift.[/QUOTE]

That's probably pretty accurate. If you have the requisite information to calculate lift via Newton, there are almost certainly easier methods that you've passed along the way. Mathematically it is pretty simple: whatever momentum is directed down by the wing must be matched by an upward force. That's just not all that practical for calculations. For example, you again need the whole flow field first anyway, and at that point you can get there more easily with Bernoulli. However, Newton always applies, Bernoulli does not.

So the Kutta-Joukowski therorem is equivalent with Bernoulli?

Not equivalent, just similar in requiring to already know the flow field from some other means. That's is the common thread here. Fluid dynamics is a complex topic and there generally are no easy answers, and when there are, they are of very limited applicability.

 

[A.T.]

If I understand it right, Newton is only used for a simple explanation for "laymen" but there is no developed mathematical method to use this principle to fully describe the lift.

Newtons 3rd Law fully accounts for the force on the wing and the math is simple conceptually, but computationally extremely expensive, and thus not practical. You have to differentiate between a physical explanation and a feasible method of quantitative prediction.

 

[Nidum]

http://www.pilotsweb.com/principle.htm