Bernoulli's Principle and Airflow

[Hckey2477]

I was teaching Bernoulli's relationship to lift during a CFI stage check yesterday and came across the topic of airflow flowing faster over the top of the wing (low pressure) than the lower. I was then asked the question as to why. The only thing i could come up with was because the airflow travels a further distances and tries to meet up with the air below the wing. He told me this was correct but again asked why does this happen. I didn't have a clear explanation, and he didn't have a clear answer. He just said he wanted to know if i knew it. I passed the stage check, did a little research and still could not come up with an answer other than a physics equation. Any help?

 

[NickH]

tgrayson in 3... 2... 1...

Ah he's late...

How about this: http://www.boundvortex.com/ReadArticle.aspx?ArticleID=53

 

[tgrayson]

How about this: http://www.boundvortex.com/ReadArticle.aspx?ArticleID=53

Thank you.

Note the above explanation is considered orthodox and is in all the better aerodynamics books, as well as books dealing with fluid dynamics. In other words, I'm not making it up, although it sounds bizarre.

 

[B767Driver]

The only thing i could come up with was because the airflow travels a further distances and tries to meet up with the air below the wing. He told me this was correct but again asked why does this happen. ?

This is not correct...but is the popular explanation in pilot circles...and is actually distributed in FAA publications.

The best, most concise and correct answer is that lift is produced by a pressure differential between the top and bottom of the wing.

This pressure differential is caused by two laws of physics in action...1) the Continuity Principle and 2) Daniel Bernoulli's Principle.

The Continuity Principle states that mass cannot be created or destroyed and is represented by A1V1=A2V2 (area and velocity). As camber or an angle of attacked is introduced...the top side of the airfoil reduces the Area (A2) for the mass airflow to go. Therefore, the velocity must increase to fit the mass airflow into the reduced area. (i.e. the "free stream flow" area has been restricted by the airfoil.)

Now, Bernoulli gets involved. Bernoulli states that as velocity increases, pressure decreases. The pressure on top of the wing is reduced more than the pressure on the bottom and the lift force is created.

The airflow over the top and the airflow over the bottom have nothing to do with each other and "like" particles do not "meet" at the trailing edge.

Now...you know the simple truth.

Continuity Principle + Bernoulli = Lift.

 

[tgrayson]

The Continuity Principle

Doesn't explain how the quantity of air going over the top vs the quantity around the bottom is determined and so can't explain the net pressure differential. Only circulation can do that.

 

[B767Driver]

Doesn't explain how the quantity of air going over the top vs the quantity around the bottom is determined and so can't explain the net pressure differential. Only circulation can do that.

Circulation explains how friction allows the boundary layer from breaking down...and is probably the most important part of the process...and probably should be introduced in explaining lift production...but ignoring a breakdown in the boundary layer...the continuity principle definitely determines the quantity of the mass airflow. Remember...you can't create or destroy mass...(you know that)...so the mass flow is the same...it's all about how fast it travels.

You must be talking about whether the mass flow will adhere to the trailing edge.

 

[tgrayson]

the continuity principle definitely determines the quantity of the mass airflow.

Yes, but that only tells us what's going on with the wing *as a whole*. More specifically, though, we need more air going above the wing vs going below, so that we can get a greater velocity increase. Otherwise, we have the same level of suction on the bottom of the wing vs the top, and that does us no good.

 

[B767Driver]

Yes, but that only tells us what's going on with the wing *as a whole*. More specifically, though, we need more air going above the wing vs going below, so that we can get a greater velocity increase. Otherwise, we have the same level of suction on the bottom of the wing vs the top, and that does us no good.

I believe you can use the Continuity Principle to determine this...a thicker wing produces more lift, right? Start at the forward stagnation point. Divide the upper and lower airflow. Either camber or AOA...or a combination of both will determine the amount and velocity of air in both locations.

Increase the AOA and the stagnation point lowers on the airfoil...and more air goes over the top.

I understand how the magnus effect can create lift in a spinning object like a golf ball...but that circulatory effects in an airfoil are used to overcome an adverse pressure gradient that escalates past the point of maximum thickness.

 

[B767Driver]

TG...

Here's something else to think about.

In a spinning object like a golf ball...the only source of lift is the magnus effect...there is nothing else there to induce lift. So here, circulation is the sole source of the normal force.

But how is circulation induced in an airfoil? It doesn't spin. Circulation is introduced by the design of the trailing edge....the sharp trailing edge. And this doesn't have any bearing on the amount of air flowing over the top of the airfoil.

So in an airfoil...the design of the leading edge, camber, and angle of attack all play roles in the pressure distribution. In an airfoil, circulation is introduced to ensure the airflow is consistent over the entire chord and fights the adverse pressure gradient towards the trailing edge.

Also, what happens if the airflow separates prior to the trailing edge? You still have some lift being produced over some parts of the airfoil...just not enough to sustain flight. Which is why circulation is the critical component.

 

[tgrayson]

And this doesn't have any bearing on the amount of air flowing over the top of the airfoil.

It does. The circulation moves the front stagnation point to the underside of the airfoil and moves the rear stagnation point to the trailing edge. Were this not so, the airflow would experience the same acceleration on the top of the airfoil as it did on the bottom and no net lift would be generated.

Start at the forward stagnation point. Divide the upper and lower airflow.

Yes, but circulation determines where that front stagnation point is.


Look at page 170 in Carpenter's book. He remarks that this is related to d'Alembert's paradox.

 

[B767Driver]

Yes, but circulation determines where that front stagnation point is.


Look at page 170 in Carpenter's book. He remarks that this is related to d'Alembert's paradox.

I just read over that chapter. I only see where circulation affects the trailing edge. The drawings (which don't mean a lot) only show the rear stagnation point moving to the trailing edge...my book shows the forward stagnation point in the same place. Furthermore, the text mentions a change in the rear stagnation point, but makes no mention of a change to the forward one.

I don't recall studying anything that mentions a change in the forward stagnation point. Do you have a more specific reference in this regards?

 

[tgrayson]

I only see where circulation affects the trailing edge. The drawings (which don't mean a lot) only show the rear stagnation point moving to the trailing edge...my book shows the forward stagnation point in the same place. Furthermore, the text mentions a change in the rear stagnation point, but makes no mention of a change to the forward one.

I don't know if Carpenter explicitly mentions it (others do), but look at his diagram on page 169, where he has the splitter plate. Where he puts it on the rear of the cylinder clearly shows the leading edge stagnation point below the midpoint of the cylinder. Same thing for the magnus effect cylinder on page 165.

In my book "Fluid Mechanics" it says:

Figure 15.9 shows the irrotational flow pattern around an airfoil for increasing values of clockwise circulation. For gamma = 0, there is a stagnation point A located just below the leading edge and a stagnation point B on the top surface near the trailing edge. When some clockwise circulation is superimposed, both stagnation points move slightly down.
​

Note that Carpenter does say explicitly that without circulation, no lift occurs, which shows that the continuity equation and Bernoulli alone cannot do it.

 

[B767Driver]

In my book "Fluid Mechanics" it says:

Figure 15.9 shows the irrotational flow pattern around an airfoil for increasing values of clockwise circulation. For gamma = 0, there is a stagnation point A located just below the leading edge and a stagnation point B on the top surface near the trailing edge. When some clockwise circulation is superimposed, both stagnation points move slightly down.
.​

Are you sure this doesn't mean downstream? Anyway, it seems like the slight movement of the stagnation point is trivial vs. the Area carved out by the airfoil.​

 

[B767Driver]

[/INDENT] Note that Carpenter does say explicitly that without circulation, no lift occurs, which shows that the continuity equation and Bernoulli alone cannot do it.

Yep, I agree with that...because without trailing edge separation, you'd never overcome the adverse pressure gradient.

And basically, that's my understanding of circulation...while it will produce a force due to the Magnus Effect...it's basic job in lift production is to ensure that the adverse pressure gradient is defeated and trailing edge separation is assured.

And while it's necessary for lift...it's not the primary reason lift is produced.

 

[tgrayson]

it's basic job in lift production is to ensure that the adverse pressure gradient is defeated and trailing edge separation is assured.

I think you have a misunderstanding there. The role of circulation is to ensure that the air moves faster over the top of the airfoil and slower on the bottom, which produces the net pressure differential that produces lift.

The quantity of circulation that is established is whatever is necessary to produce a smooth flow off the trailing edge. Circulation is fundamental to the production of lift.

Carpenter says it in bold letters on page 178:

Lift is generated by the production of circulation around the wings, by which some velocity is added to the stream-wise velocity over the top of the wing, and some is subtracted from the velocity beneath the lower wing surface. By Bernoulli's principle the resulting speed difference produces a lower pressure on the top surface than on the bottom surface, and the consequent pressure distirbution produces lift.
​

Nothing there of the continuity principle.

 

[tgrayson]

Are you sure this doesn't mean downstream?

It means moving down on the airfoil, but that is effectively downstream too.

Anyway, it seems like the slight movement of the stagnation point is trivial vs. the Area carved out by the airfoil.

The area cut out by the airfoil is completely meaningless unless you can carve out more from the top than from the bottom. If you catapulted a semi into the air, it would carve out a formidable amount of air, and the continuity principle would operate around it too, but it would not generate lift.

As for whether it's trivial, how could you know? You don't know what "slight" means nor do you know what a slight increase in air volume moving over the airfoil would produce. The pressure reduction over a wing per cubic foot is pretty small.

 

[Superfly7XAF]

I found this interesting:

http://www.grc.nasa.gov/WWW/K-12/airplane/wrong1.html

A little simplistic I know (esp. for the guys posting above me) but I thought it breaks down the misconceptions of lift fairly well.

 

[B767Driver]

As for whether it's trivial, how could you know? You don't know what "slight" means nor do you know what a slight increase in air volume moving over the airfoil would produce. The pressure reduction over a wing per cubic foot is pretty small.

I think you are ignoring an important part of lift production. I already stated that I agree with you that circulation is necessary to produce a lift force.

But how do you increase and decrease circulation?

By varying camber, angle of attack, etc. and all of the factors pertinent to the inviscid flow.

The ability of the trailing edge to accelerate (circulate) the air is fixed by the mass and velocity of the source flow...so the only way to increase circulation would be to provide it with an airflow of a higher value. And in doing so, the continuity principle definitely applies.

 

[tgrayson]

And in doing so, the continuity principle definitely applies.

All I said was that it wasn't sufficient to explain the pressure differential, because without circulation, there is none.

There are three essential concepts to explaining lift:

1. Continuity Equation
2. Bernoulli Equation
3. Circulation

 

[Hckey2477]

Thanks for all of the insight on this topic, It seems there is a lot of speculation. I will take all your info and try to put it all together. Hopefully I don't get asked this on my FAA checkride lol. Thanks again.