# Is circulation real?

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

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### daiquiriEngineering and Design

Strictly speaking, "circulation" is defined as a closed-circuit line integral of the velocity field, as have been said several times by now. So it is not a velocity, it is an integral of the velocity.

Arvel Gentry in his famous paper about origins of lift uses the term "circulation flow", which is different, the difference being made by the word "flow". This could be the cause of the confusion in nomenclature which has been created, and is what imo the the perturbation field you guys are talking about. English is not my first language, so perhaps I am about to say a nonsense here, but had he used the term "circulating flow" instead of "circulation flow" he would have avoided this ambiguity, imo.

Or perhaps I'm just being too pedantic here...

Anyways - yes, when you subtract the uniform flow from the velocity field created by an airfoil, you are left with what closely reminds of a circulating flow. These videos show graphically what does the velocity field around airfoils look like when the uniform inflow is subtracted:
http://youtu.be/j_J8kNodgBQ
http://youtu.be/rLuJYHdWBJ8

And yes, since the closed-line integral of the uniform flow is always zero, it means that the circulation around an airfoil is due to the integral of just this circulating flow component shown in the videos.

Cheers

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### Mikko BrummerSenior Member

Thank you, Tom. Did you have a time to look at the coanda-paper:

"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."

What do you think about these 2 types of pressure impulses, do they exist? Are you familiar with the book of Hans Lugt, “Vortex Flow in Nature and Technology”?

I found this from the same guy, with a billiard ball analogy http://www.terrycolon.com/1features/fly.html

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### Mikko BrummerSenior Member

Thanks! These videos save me from doing the simulation myself. Now, if I'm ballooning from left to right above the airfoil, at first I will feel a breeze in my right cheek, then in my neck, and somewhere after mid chord in my left cheek - just as I anticipated at the beginning of the thread.

You guys are amazing - you find the answer to the most bizarre problems one can think of. Next I expect you to finally give us the definition of planing.

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### daiquiriEngineering and Design

We'll need a help from Superman for that one.

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### baeckmoHydrodynamics

Citation, Leo:

.............In fact, mathematicians are not appreciated these
days. (I nearly cried then, but I managed to hold it in.)

Interesting discussion here! First my dear Leo, I don't think mathematicians are less adorable/annoying than the rest of us. Speaking for myself, it is rather the Lady Math herself that is a demanding mistress. I really wish I had payed her more attention when my brain was receptive enough, but there were other ladies to satisfy back then, prompting for acute action..... So, while the sharper brains here have passed on to discuss applications, I keep dwelling on the first notes in this thread, still feeling there are a few observations to make regarding Mikko's original question, and the article he is referring to.

Going back to the origin of the "circulation" theme, I believe lord Kelvin (or was it Ludwig Prandtl?) did not refer to fluid circulation when settling for the word. It is rather expressing a special case of a line integration of the product velocity times distance. We call the product "potential" (also velocity or stream potential). The "special" is that it is a closed integral; the mathematical procedure of integration will "circulate" in a loop.

The possible meaning, as I can see it, of the closed integration (circulation) is an isopotential surface, connecting all loci having the same potential, and we have no organ that is sensitive to this. But we are certainly sensitive to its gradient, namely velocity.

It is tickling to my mind, that the "twin" phenomena of potential and circulation are developed from the pure non-viscous potential flow context, and they do add an element of the "missing link" to the mathematical treatment of non-viscous flow; they both have the dimension "m2/s", same as found in the kinematic viscosity. Here is the beauty of Lady Math; she can provide us tools that make it possible to study a process all the way from negative to positive infinity, and by integration the complete domain can be treated.

As an (Eulerian?) experimentalist, I can only study a very limited physical domain. Whatever influences coming from outside that domain are lumped together in a white noice. But this limitation doesn't worry our Lady, and for this we are in debt to Leo and his collegues, who know how to make her reveal her secrets.

So, the flapping of a butterfly wing outside a window in Queensland, Australia (or is it a mackerel tail, considering the raining?) is travelling some eleven hours, before the first wave front reaches my ears. It takes roughly six more hours until all the air molecules in the atmosphere have got the message. Unfortunately, by then it is so dispersed, that it drowns in the noice; I cannot register it, but Lady Math can.

Which leads to the concept of two different "pressure pulses" that Mikko found in the paper cited. To me, that is sheer nonsense, there is only one mechanism by which the information about a change of status in a continuum can take place, and that is by the propagation of a wave travelling with the critical speed in the substance, i.e. the speed of sound. What may have lead to confusion in the article is what happens when the change of state happens faster than it can be "reported to the entire mass" by wave propagation, because then we have a phase lag between velocity and pressure.

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### Leo LazauskasSenior Member

It was just a joke, Baekmo. I am actually a bit tougher than that
I'm afraid I don't have much to contribute because
(1) there's nothing to solve or calculate, and
(2) circulation can be viewed, as Tom Speer said, a book-keeping
convenience. I'd add the Kutta condition into that category as well. Whether
they are real or or not is completely uninteresting to me.

Shut up and calculate! - N. David Mermin.

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### daiquiriEngineering and Design

I am reading this as "compressibility" (shock waves, to be precise), am I doing right? It would then be the same way I had interpreted that odd story about pressure impulses - see my post #8.

Nice post, Baeckmo. Almost poetically written.

Cheers

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### markdrelaSenior Member

That's an excessively strong definition of "2-dimensional". It would invalidate classical finite-wing theory, for example, which is certainly solid.

A better definition of 2D flow is:
* spanwise flowfield variations are small compared to chordwise variations
* velocity field of wake vorticity is nearly uniform (not zero!) over the chord

This does not rule out 3D wing effects, and it also does not rule out sweep. A high-aspect ratio swept wing has locally 2D flow if we align "spanwise" and "chordwise" axes with the wing, not with the freestream. The "spanwise" velocity is then everywhere constant, and does not affect the lift, which is the same as the lift of the 2D flow projection in the plane perpendicular to the wing.

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### DCockeySenior Member

Section removed.

The perturbation flow of an airfoil, what remains when the uniform flow is subtracted from the velocity field of the airfoil, does is not always close to the circulatory flow. The perturbation velocities include both the circulatory flow portion (if there is lift) as well as portions due to thickness and camber. As the lift decreases for a real airfoil the parts of the circulatory flow due to thickness and camber can become the primary portions of the perturbation flow.

Consider an airfoil (other than an infinitely thin flat plate) generating zero lift. The velocities close to the airfoil will differ from the uniform flow. This is true for a symmetric airfoil at zero angle of attack, a cambered infinitely thin plate at the angle of attack which generates zero lift, and the general case of an airfoil with thickness and camber at the angle of attack which generates zero lift. As the angle of attack of any of these changes and lift is generated a circulatory flow will be generated with amplitude proportional to the lift. The portion of the perturbation flow due to thickness and camber will change but its amplitude will remain essentially the same.

Those familar with thin airfoil theory may say that the effects of angle of attack, camber and thickness are independent. This is correct in thin airfoil theory with the zero normal velocity boundary condition applied on a straight line/plane. In reality there is coupling between the effects of angle of attack, camber and thickness on the perturbation flow field. Its even true for potential flow when the boundary conditions are applied at the airfoil's surface.

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### DCockeySenior Member

The locations of where the spanwise circulation distribution is at the maximum and where the spanwise flow is at the minimum and the flow as horisontal as possible on both sides of the sail will depend on how close the foot of the sail is to the deck, the shape and twist of the sail, mast bend, etc.

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### DCockeySenior Member

There is a theorm applicable only to two dimensional, simply connected regions that circulation is the integral of the vorticity in the region bounded by the curve along which the circulation is calculated. I underlined applicable only to two dimensional, simply connected regions because the simply connected part can be the source of considerable confusion. It was involved in the rejection of airfoil theory by the Cambridge University mathematical physicists at the beginning of the 20th century.

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### DCockeySenior Member

Circulation in a potential flow with a line/surface across which the surface is discontinuous equals the jump in potential where the curve along which the circulation is calculated crosses the discontinuity. Without a discontinuity in potential circulation is zero in potential flow.

The definition of circulation as the path integral of the tangential component of velocity along a closed curve is equally valid for non-potential flows, and occasional useful when considering such flows.

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### JoakimSenior Member

That is quite unusual therminology. Pressure is just pressure. Maybe they are trying to describe incompressible and compressible flows? In fluid dynamic modelling the sound waves are often neglected by defining the flow as incompressible (even for air, which still can have local density based on pressure and temperature).

Pressure has no diffusion, but other flow variables like velocity (viscosity), temperature (conductivity) and concentrations do. Diffusion can also be neglected as is done e.g. in panel methods. As you know, panel methods can predict lift and circulation, thus they are not caused by diffusion.

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### Mikko BrummerSenior Member

This makes sense. Thanks.

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### PetrosSenior Member

I think describing the it as two types of pressure is not helpful. A sound wave is a an energy input into a medium (a fluid) that causes a spike in pressure in that medium. Nature of sound transition is related to the ratio of specific heats of that medium. The temperature of the fluid changes the speed of the sound, but not the nature of the energy in it (as in the volume of the sound).

The other type of pressure is actually the acceleration of the mass of the air. The pressure changes with either changes in that acceleration (on a sail, the amount of camber on the surface or the speed of the flow over the curved surface), or in changes is the mass of the fluid (as affected by temp or barometric pressure for example. The effect of the pressure is actually the cumulative effect of the mass of each particle or molecule of air being accelerated, or curved, over that surface.

Quote "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."

This is just confusing, it has nothing to do with the atom, but with mass, it has nothing to do with diffusion, it has to do with F=ma. A force over an area is the definition of "pressure", mass times acceleration equal a force. Where does diffusion come in here? Are they inventing a new term? or are they just illiterate? Atoms do not even enter into this calculation, it simple is a question of mass and acceleration. This is not helpful in trying to understand the process of lift generation.

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