tgrayson
New Member
What is your understanding of how the trailing edge induces circulation? (I can't tell that you explicitly said in your post.)
Coanda effect
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What is your understanding of how the trailing edge induces circulation? (I can't tell that you explicitly said in your post.)
B767Driver
New Member
Carpenter just states that placing a sharp edge at the aft stagnation point produces the rotational flow...with accompanying illustrations showing the streamlines. He doesn't provide math...but streamlines based upon experimention based upon different locations of the TE. He does state that the rotational flow behaves just like flow in a weather system...or water going down a drain.
The speed is inversely proportional to the radius of the circle. As the flow nears the trailing edge...the radius gets smaller and the flow accelerates (accel = mV^2/r). He states that as the air flows to the trailing edge point...where the radius of the circle is the smallest...the acceleration required to make the turn is too great....leading to separation.
So I suppose, by the decreasing radius of the effective circle????
The speed is inversely proportional to the radius of the circle. As the flow nears the trailing edge...the radius gets smaller and the flow accelerates (accel = mV^2/r). He states that as the air flows to the trailing edge point...where the radius of the circle is the smallest...the acceleration required to make the turn is too great....leading to separation.
So I suppose, by the decreasing radius of the effective circle????
tgrayson
New Member
That's kinda what I remember from Carpenter. He does a good job setting up for the touchdown and then drops the ball on the one yard line.
The reason that the sharp edge sets up circulation is very important. I'll post on that when I get home. I'd like to be able to reference the diagrams in Carpenter's book to show that the material that I add is consistent with his model.
B767Driver
New Member
I never did glean from him separation from the bottom - up. I'd be interested to hear your take on this.
tgrayson
New Member
Ok, Carpenter shows what the airflow would look like with no viscosity:
As you can see, there is a normal stagnation point on the leading edge, but the rear stagnation point is on the top. In order for the rear stagnation point to be there, the airflow must be like this:
Carpenter's text agrees with this drawing, as on page 172:
Now, I'm going to move from Carpenter's book to some content from "Fluid Mechanics", by Kundu & Cohen. The actual descriptions they use, however, come from John D. Anderson's "Fundamentals of Aeordynamics.".
They say:
They continue, and this is the most important part:
So, whereas Carpenter seems to imply that the starting vortex is a result of circulation, according to this text is is the cause of it.
The end result is a closed system of vortices:
As you can see, there is a normal stagnation point on the leading edge, but the rear stagnation point is on the top. In order for the rear stagnation point to be there, the airflow must be like this:
Carpenter's text agrees with this drawing, as on page 172:
Figure 7.9 shows the flow smoothly flowing around the trailing edge towards a stagnation point on the upper surface.
However, except at very low airspeeds, the flow around the trailing edge cannot happen.Now, I'm going to move from Carpenter's book to some content from "Fluid Mechanics", by Kundu & Cohen. The actual descriptions they use, however, come from John D. Anderson's "Fundamentals of Aeordynamics.".
They say:
Within a fraction of a second (in a time of the order of that taken by the flow to move one chord length), however, boundary layers develop on the airfoil, and the retarded fluid does not have sufficient kinetic energy to negotiate the steep pressure rise from the trailing edge toward the rear stagnation point. This generates a back-flow in the boundary layer an a separation of the boundary layer at the trailing edge. The consequence of all this is the generation of a shear layer, which rolls up into a spiral form under the action of its own induced vorticity. The rolled-up shear layer is carried downstream by the flow and is left at the location where the airfoil started its motion. This is called the starting vortex.
Here is their picture:
They continue, and this is the most important part:
The sense of circulation of the starting vortex is counterclockwise in Figure 15.10., which means that it must leave behind a clockwise circulation around the airfoil.
Here's my image of what just happened:
So, whereas Carpenter seems to imply that the starting vortex is a result of circulation, according to this text is is the cause of it.
The end result is a closed system of vortices:
B767Driver
New Member
It sure seems that they are both saying the same thing to me. As I read the passages from Anderson...I don't see any appreciable differences from what Carpenter is saying. He actually, reinforces what I learned from Carpenter.
The trailing edge is definitely a player in circulation...and it appears to me the starting vortex is simply the result of the boundary layer separation...and not the cause of anything. Expand on this if you think differently.
From Anderson's illustrations...I can see how it looks like the air separates from underneath. But...it shows the starting vortex curling up rapidly after the intial downward momentum that causes that illusion.
Back to Coanda....do you feel this is any part of that effect?
The trailing edge is definitely a player in circulation...and it appears to me the starting vortex is simply the result of the boundary layer separation...and not the cause of anything. Expand on this if you think differently.
From Anderson's illustrations...I can see how it looks like the air separates from underneath. But...it shows the starting vortex curling up rapidly after the intial downward momentum that causes that illusion.
Back to Coanda....do you feel this is any part of that effect?
tgrayson
New Member
The Anderson material says that the starting vortex starts the circulation:
Anderson: ...The sense of circulation of the starting vortex is counterclockwise in Figure 15.10., which means that it must leave behind a clockwise circulation around the airfoil.
<<The trailing edge is definitely a player in circulation...and it appears to me the starting vortex is simply the result of the boundary layer separation...and not the cause of anything. Expand on this if you think differently.>>
There would be no circulation if there were no separation. It's what starts the circulation happening. This is what causes the Kutta condition to be true. A vortex forms to change to circulation in whatever way is necessary to ensure that the airflow leaves the trailing edge smoothly. This is a form of stability. Any change in AOA generates a new starting vortex.
<<From Anderson's illustrations...I can see how it looks like the air separates from underneath. But...it shows the starting vortex curling up rapidly after the intial downward momentum that causes that illusion.
>>
The flow cannot separate from the top, because it is the bottom flow that is trying to move around the trailing edge, and it will continue to do so until the separation causes the quantity of circulation to be such that the rear stagnation point reaches the trailing edge. The top flow never reaches the trailing edge until the Kutta Condition is satisfied.
And I'm not asking you to rely on the picture, but to rely on the text that describes what the picture shows. If the flow were coming from the top, the starting vortex would rotate in the opposite direction.
Carpenter also says that the flow separates from the bottom going to the top, so they both agree on this. Separation happens before circulation.
Nope. Carpenter himself says:
This centripetal force mV^2/r which is required to get the particle of air round the corner can only be provided by a pressure force from the air in streampaths further out--it could not be provided by viscous forces since these would be tangential to the flow.
B767Driver
New Member
Associated with illustration 7.10, Carpenter states that separation occurs cleanly at the trailing edge. 7.9, I believe is only a starting condition...where the stagnation point is on the upper surface of the wing. Once the airflow begins...the stagnation point changes to the trailing edge where separation occurs. Do I have this wrong?
Also...your point about the vortex causing circulation...not the trailing edge. Wouldn't this be like a wake? A wake doesn't "drag" the airplane down. The adverse pressure forces on the wing drag the airplane down. The wake is an effect of the cause.
How is the vortex the cause of circulation and not an effect of it? Once it leaves the surface...I don't see how it's causing the circulatory flow?
B767Driver
New Member
I'm confused on this, then. The circulatory flow is clockwise. So, to me, the clockwise flow continues in streampaths around the radius of a circle....the center of the circle a point known as the trailing edge. As the radius of the circle gets smaller...and eventually reaching the aft stagnation point, the trailing edge...wouldn't the air on top keep trying to accelerate and make the turn towards the lower surface?
Is it the higher pressure air from the lower surface that dominates the confrontation...causing the lower surface flow to separate?
tgrayson
New Member
Not quite. He says "Very rapidly the stagnation point moves rearwards from its starting point [on the upper surface] until the flow separates totally from the sharp trailing edge."
The reason the stagnation point is moving is due to circulation. The airflow is already separating as the bottom layer moves around the sharp edge.
No, but I'm thinking that Carpenter's use of the word "separation" is a bit sloppy here. Most books talk about the airflow leaving the trailing edge "smoothly" or "cleanly".
Agreed, the starting vortex trailing the aircraft is not relevant. What is relevant is where the starting vortex was when it begin. Newton's third law states that for every action there is an equal an opposit one; this is why the starting vortex creates another vortex in the other direction. But once the vortex is created, it will continue until something stops it. It doesn't need the starting vortex any more. The only time a new vortex is needed is when the circulation must change.
tgrayson
New Member
Initially, there is no circulation. When the airfoil starts moving, the air flows around the airfoil almost as if their is no viscosity. This is when the rear stagnation point forms on top of the airfoil, as Carpenter describes on p. 172, last paragraph. Only once a certain speed is reached does the airflow start to separate around the trailing edge. THAT establishes the circulation that moves the stagnation point to the trailing edge.
[This is a difficult discussion to have online; I need books and whiteboards.
Coming to Memphis anytime soon?]
B767Driver
New Member
I should pick up Anderson's text and read it.
Like you said...Carpenter didn't expand much on how the trailing edge induced circulation. But, you are saying that the lower surface airflow flows up around the trailing edge and mixes with the upper surface flow...and creates a vortex. It's this vortex....somewhere on the upper surface....that actually induces the circulatory flow...and separates at the trailing edge leaving behind the starting vortex...trailing off into wherever land of irrelevance.
If that's it....I think I got it.
Like you said...Carpenter didn't expand much on how the trailing edge induced circulation. But, you are saying that the lower surface airflow flows up around the trailing edge and mixes with the upper surface flow...and creates a vortex. It's this vortex....somewhere on the upper surface....that actually induces the circulatory flow...and separates at the trailing edge leaving behind the starting vortex...trailing off into wherever land of irrelevance.
If that's it....I think I got it.
B767Driver
New Member
[This is a difficult discussion to have online; I need books and whiteboards.
You did a good job.
The text, while explaining the concept well, left me with a big void in understanding the nuts and bolts of how the TE induced the circulation. Now, I see exactly what's going on.
And I'd have to agree....no Coanda Effect here. As the circulatory flow requires some type of lower flow to induce a vortex.
tgrayson
New Member
Hmmm.....lots of vector calculus. There are only a handful of sections that I found useful. This is "Fundamentals of Aerodynamics", not his more accessible "Introduction to Flight." I could probably photocopy these sections, if you like.
<<Like you said...Carpenter didn't expand much on how the trailing edge induced circulation. But, you are saying that the lower surface airflow flows up around the trailing edge and mixes with the upper surface flow...and creates a vortex. It's this vortex....somewhere on the upper surface....that actually induces the circulatory flow...and separates at the trailing edge leaving behind the starting vortex...trailing off into wherever land of irrelevance.
If that's it....I think I got it.
>>
That sounds like pretty much it. I would change "lower surface airflow flows up around the trailing edge" to "lower surface airflow separates at the trailing edge and curls up into a vortex". That vortex then induces an equal and opposite vortex around the airfoil. (the bound vortex)
caliginousface
Frank N. Beans
Alright just so I have this clear, doesn't the Coanda Effect say a fluid will follow a convex surface? So not really critical to the development of lift, but just charactertistic of fluids in general.
tgrayson
New Member
You could always ask if circulation is "real" or just a mathematical method that just happens to provide the right answers.
tgrayson
New Member
Yes.
The most careful statement would be that there is no evidence that the Coanda Effect is necessary for the production of lift, since lift is explained accurately through analytical methods which do not rely on the Coanda Effect.
Realms09
Well-Known Member
I spent some more time at the library today looking through Schlichting's "Boundary Layer Theory" which appears to be a classic reference on the subject. Once again, it did not have any specific reference to Coanda effect. I then found a book that was a collection of papers on circulation and boundary layer control, which did have a few references to the effect. I also did a search of an online aerospace paper database. In all cases these papers were regarding jets of air being blown near the leading edge or trailing edge to achieve various performance goals.
From "Experimental and Computational Investigation into the Use of the Coanda Effect on the Bell A821201 Airfoil," Gerald Angle Il, et. al:
The key here is that anywhere in the technical literature where Coanda effect is mentioned, it is directly referring to a jet of air in air. In other words, this is a small stream of air moving quickly relative to air flowing around it that encounters a surface. There are no such jets on a normal wing, so it does not make sense to talk about this effect regarding lift production.
My speculation and incomplete thought is that it is not fundamentally different than how a boundary layer and corresponding flow outside of it develop as any fluid flows over a body, but it just caught the attention of investigators because they were dealing with jets.
From "Experimental and Computational Investigation into the Use of the Coanda Effect on the Bell A821201 Airfoil," Gerald Angle Il, et. al:
The key here is that anywhere in the technical literature where Coanda effect is mentioned, it is directly referring to a jet of air in air. In other words, this is a small stream of air moving quickly relative to air flowing around it that encounters a surface. There are no such jets on a normal wing, so it does not make sense to talk about this effect regarding lift production.
My speculation and incomplete thought is that it is not fundamentally different than how a boundary layer and corresponding flow outside of it develop as any fluid flows over a body, but it just caught the attention of investigators because they were dealing with jets.
tgrayson
New Member
Yep, I have that and didn't find anything, as I recall.
<<As the boundary layer is entrained, the local pressure in the boundary layer is reduced>>
Why would that be? The increased velocity does not come from the boundary layer itself (as in static pressure), so the Bernoullli principle would seem not to apply.