# Is circulation real?

Discussion in 'Hydrodynamics and Aerodynamics' started by Mikko Brummer, Jan 25, 2013.

1. Joined: May 2006
Posts: 553
Likes: 70, Points: 28, Legacy Rep: 258
Location: Finland

### Mikko BrummerSenior Member

Bumped on an interesting paper in Sailing Anarchy http://www.newfluidtechnology.com.au/THE_COANDA_EFFECT_AND_LIFT.pdf. The paper is about Coanda effect, which is uninteresting when it comes to sails, but pages 4-14 talk about circulation and vorticity in an interesting way:

"Air possesses heat, humidity, pressure, density and the ability to transmit 2 kinds of pressure impulses. One is sound (acoustic) waves which propagate at the speed of sound with, across or against an air current flow direction. i.e. we can be heard upwind.

The second kind of pressure impulse is the type involved in lift. It also propagates within air that is flowing or still. Its speed is also exactly the speed of sound no matter how much force goes into its generation.
Sound waves are composed of many gas atoms in each wave or pressure peak. The pressure peaks may be different distances apart (different frequency past a fixed point) which determines the “pitch” of the sound.

The second type of pressure impulse is at the atom level and therefore has no frequency or pitch in the sense of the acoustic case. But it has direction and is termed Diffusion. An analogy: heat one end of an iron bar. The heat travels by diffusion along the bar. The atoms do not actually change their position but pass on their increased energetic state to the next atoms and so on. Similarly when air is disturbed, diffusion is also generated. The air atoms move at the speed of sound but only an infinitesimal distance to jostle the adjacent atoms. Diffusion therefore is a kind of relay from atom to atom."

Now, this second type of pressure impulse provides a mechanism on how circulation could work.

hoytedow likes this.
2. Joined: May 2006
Posts: 553
Likes: 70, Points: 28, Legacy Rep: 258
Location: Finland

### Mikko BrummerSenior Member

Circulation has intrigued me ever since I learned at school about the lifting line theory, simple and beautiful, yet predicting so uncanningly well the lift & drag of a finite wing, as shown in the test on elliptical wings of different aspect ratio by Ludwig Prandtl, the grand father of aerodynamics. That made me think already at the time that there has to be some physical connection to reality in it, more than just a mathematical theory. Yet the idea of air molecules actually circulating around the wing is ridiculous and clearly non physical.

3. Joined: May 2006
Posts: 553
Likes: 70, Points: 28, Legacy Rep: 258
Location: Finland

### Mikko BrummerSenior Member

Here's a mind experiment:
You are flying in an open cabin ultralight plane at low altitude above the sea. Out in the distance comes a sailboat sailing upwind on starboard tack. You turn towards the sailboat, flying at the speed and in the direction of the sailboats apparent wind.

In sailboat conjencture, apparent wind is defined as the sum of the true wind and the boat speed. In the lifting line theory, local velocity is defined as the sum of apparent wind and circulation.

Now, as you approach the sailboat it starts to influence air flow around your ultralight plane. When you travel at apparent wind speed and in its direction, you will feel a gentle wind on your face: At first when approaching on the windward side of the boat, you will feel a breeze on your left cheek - when flying past in front of the sailboat's mast, the gentle breeze will turn around your neck to your right cheek. The wind you are feeling on your cheek is circulation - if you add it to your own speed (the apparent wind), you will get the local velocity around the sailboat. Is it real or not?

While boat speed and true wind definitely are real, is apparent wind just fiction? For someone standing on the peer apparent wind is fiction, he only feels the true wind on his face. But for someone sailing onboard a high performance boat, the only thing that feels real is the apparent wind (actually it's local flow) - he can feel the boat moving (boat speed) and the apparent wind (local flow) on his face, but has no sensory perception of the true wind. An iceboat sailor cannot even see the wind on the water (ice), so for him only the apparent wind exists.

4. Joined: May 2004
Posts: 5,372
Likes: 255, Points: 93, Legacy Rep: 3380
Location: Italy (Garda Lake) and Croatia (Istria)

### daiquiriEngineering and Design

Hi Mikko,

Regarding your example of an airplane and a sailboat, I have a following objection to it.
The circulation is not defined as you did it in that example, i.e. it is not the wind (or fluid velocity) you can feel once you have taken away the upwind far-field velocity component.
The circulation is a mathematical entity, defined as the integral of the velocity over a closed line entirely contained in the fluid domain:

As such, you cannot feel it on your cheeks, since it is not a material entity.

The wind component which the pilot can feel on his cheeks in your example is evidently a material entity, but it is not the circulation around the sail. It is just an airflow induced by the boat's sail while it produces the lift force, and that airflow is mathematically represented through the velocity component called "induced velocity".

Cheers

hoytedow likes this.
5. Joined: May 2006
Posts: 553
Likes: 70, Points: 28, Legacy Rep: 258
Location: Finland

### Mikko BrummerSenior Member

6. Joined: May 2006
Posts: 553
Likes: 70, Points: 28, Legacy Rep: 258
Location: Finland

### Mikko BrummerSenior Member

Yes, I should have said velocity induced by circulation?

7. Joined: May 2004
Posts: 5,372
Likes: 255, Points: 93, Legacy Rep: 3380
Location: Italy (Garda Lake) and Croatia (Istria)

### daiquiriEngineering and Design

Which now creates another question: is the subject of this thread still the one in the title?

Because, as we have seen, the circulation is a mathematical entity and is not real in the material sense, but it's evidence is real in the material sense - and it is the lift force.

Cheers

8. Joined: May 2004
Posts: 5,372
Likes: 255, Points: 93, Legacy Rep: 3380
Location: Italy (Garda Lake) and Croatia (Istria)

### daiquiriEngineering and Design

Thanks, it now works.
However, it looks like a pretty layman's explanation of how things work. For example, this is the first time I hear about "two types of pressure impulses" in a fluid. My guess is that the author probably wanted to make a distinction between compressible and incompressible aerodynamics, but has imo chosen a pretty bad wording for that scope. The paper reportedly wanted to be an explanatory text for non-engineers and non-aerodynamicists, but with this story about different types of "pressure impulse", diffusion etc. it risks to just create more confusion, imo.
The rest, I just didn't have time and patience to read. I'll try again later, I promise.

Cheers

9. Joined: May 2006
Posts: 553
Likes: 70, Points: 28, Legacy Rep: 258
Location: Finland

### Mikko BrummerSenior Member

It is, in my books... first time I hear about the two types of pressure impulses, too. But his explanation has nothing to do with compressibility... rather with vorticity. So, if the hippies wandering to India in the in the 70s' used to sing "the whole universe vibrates complete" (referring to the sound of their music), maybe we can say the whole universe rotates complete, too .

Two reasons I would like to believe circulation is indeed physical and true:
- first the accuracy of the Prandtl lifting line prediction
- second the analogy of electromagnetism with fluid dynamics

10. Joined: May 2004
Posts: 5,372
Likes: 255, Points: 93, Legacy Rep: 3380
Location: Italy (Garda Lake) and Croatia (Istria)

### daiquiriEngineering and Design

Imo, it all goes down to what you intend by physical and true. As said previously, the circulation is not a material item. It is just a mathematical tool, defined through an equation. In that sense, it is as real and true as is any mathematical definition. However, it's definition is based on a real and physical quantity - the fluid movement (velocity).

Just like the velocity potential, for example. It is another mathematically defined quantity, which we physically do not sense or measure. Strictly speaking, it exists in the mathematical space only. But yet again, it is tied to the real world through it's related physical quantities: fluid movement and pressure. We can feel and measure the latter two, but we don't see or sense the potential. Hence, is it real? Again, it probably depends on the definition of "real".

The question can be essentially re-written in the following terms - if a quantity A is mathematically defined from a physical quantity B, can the quantity A also be considered physical and real?
I think that we are touching the basics of the philosophy of science here.

Cheers

1 person likes this.
11. Joined: Nov 2011
Posts: 252
Likes: 16, Points: 18, Legacy Rep: 117
Location: New England

### johneckSenior Member

In some sense it is real. However, lifting line theory brings it down to something that has no true physical reality to create an easily solvable problem. But the reality is that the fluid stream IS deflected and thus there must be circulation. The math doesn't care if it comes about because of a rotating cylinder, a flat plate or a wing or ...

12. Joined: Jan 2002
Posts: 2,696
Likes: 151, Points: 63, Legacy Rep: 2229

### Leo LazauskasSenior Member

IMO it is not very accurate for AR < 10, as shown in the attached graph.
And it is not a consistent low AR expansion, so it can not be relied upon to
give reasonable results for low AR wings.

#### Attached Files:

• ###### clslope.gif
File size:
19.8 KB
Views:
1,493
13. Joined: May 2006
Posts: 553
Likes: 70, Points: 28, Legacy Rep: 258
Location: Finland

### Mikko BrummerSenior Member

According to the paper, there is a physical (?) connection between molecules or atoms, and they communicate via vorticity:

"Diffusion spreads vorticity. It is by diffusion (the pressure impulse) that vorticity spreads from the point of generation. The pressure impulse does not radiate in all directions like acoustic waves, (acoustic waves however do possess vorticity, but it’s another subject) but instead rotates around a centre. “Nature prefers rolling over gliding” Osborne Reynolds. This is an energy conservation law as important as the other more well known energy conservation laws."

One molecule "nudges" the one next to it to tell it to react to the vorticity signal sent at the sound of speed from the wing, obeying biot-savart's law and therefore complying to the mathematical model of circulation. To understand better, one should probably read Hans Lugt, “Vortex Flow in Nature and Technology” - of course, the book could be as much non sense as the paper more or less based on it.

"When air actually flows as a breeze or fan generated airflow it is called Convection. “In contrast to diffusion, the transport of physical quantities by the moving fluid itself is called “convection”. Hans Lugt P 45."

So the "diffusion" does not involve physical motion of particles, like "convection".

14. Joined: May 2006
Posts: 553
Likes: 70, Points: 28, Legacy Rep: 258
Location: Finland

### Mikko BrummerSenior Member

Yes, but of course lifting line only has this one bound vortex on the whole span. When you spread it into a lifting surface with many horseshoe vortices like in VLM, the results get quite good (in potential flow), and it's still the vorticity doing the job.

15. Joined: Jan 2002
Posts: 2,696
Likes: 151, Points: 63, Legacy Rep: 2229

### Leo LazauskasSenior Member

And I would contend that VLM are flawed too.

There is a little known deficiency with VLM. It can be shown that there is a
by using more panels. Some researchers (like P.S. Jackson) use a fit to the
first three or four panels. D.W.F. Standingford came up with an elegant
solution in his PhD thesis for a panel method due to E.O. Tuck and which I
implemented in the lifting surface program (LSP) I posted on boatdesign.net.

It is difficult to see the "kink" I referred to, but if you remove the leading
-edge singularity it is very apparent. Sub-panelling can help a bit, but it still
persists. This kink is one reason that VLM tend to under-predict the induced
drag of thin wings.

There are actually several good arguments that VLM and other panel
methods are unable to capture the strength of the leading-edge singularity
and how its strength varies around the leading-edge and towards the tip for
curved planform wngs. The circular wing is a case in point and has been
discussed by, among others, Jordan, Boersma and Guermond in a variety of
papers.

1 person likes this.
Forum posts represent the experience, opinion, and view of individual users. Boat Design Net does not necessarily endorse nor share the view of each individual post.
When making potentially dangerous or financial decisions, always employ and consult appropriate professionals. Your circumstances or experience may be different.