Is circulation real?

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

  1. daiquiri
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    daiquiri Engineering and Design

    You are correct. The lines shown are curved, so they are not simple vectors. I have not payed attention to that particular in the video. So the video actually shows two mathematical operations, one is the Vfoil = V - Vx, and the other one is the construction of streamlines of this fictitious vector field Vfoil.

    Anyways, I wouldn't be so rigorous to call it an error. Streamlines are an excellent visual tool for representing a velocity field, just like colors are used to illustrate stress values in a mechanical component. The important thing is to always bear in mind what we are actually looking at.

    Cheers
     
  2. DCockey
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    DCockey Senior Member

    My apologies to Leo if anyone interprets my comments as meaning that he is not an applied mathematician. Leo certainly is an applied mathematician, the type which engineers and others concerned with practical concerns find useful. :cool:
     
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  3. DCockey
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    DCockey Senior Member

    Here's a link to a short video showing particle paths past a lifting airfoil from a reference frame fixed to the airfoil. Note that particles which originate under the dividing streamline do not have large vertical motion, and do not travel "forward" relative to the airfoil.
    http://www.youtube.com/watch?v=x1Lut0PlSik
     
  4. Leo Lazauskas
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    Leo Lazauskas Senior Member

    It's all just a convenient artifice, Slavi. We could be having this same discussion
    about whether there are "real" waves travelling in all directions at some point
    behind a ship.
     
  5. Leo Lazauskas
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    Leo Lazauskas Senior Member

    No apology necessary, David. From what I have read over the years, you don't
    have a mean bone in your body.
     
  6. Ad Hoc
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    Ad Hoc Naval Architect

    You mean...there are no real waves???!! :eek::eek::eek:
     
  7. Leo Lazauskas
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    Leo Lazauskas Senior Member

    I'd go one extra step. For some applied mathematicians a task is complete
    when an integral (or some other) equation has been written down. For me
    it's just the start. And then it's all just a very amusing, diverting game with
    high scores and low scores corresponding to speed and accuracy.
    The reality, or otherwise, of circulation, vortices etc is peripheral to the task at
    hand.
     
  8. Leo Lazauskas
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    Leo Lazauskas Senior Member

    Of course there are. There are long waves, short waves, and the occasional tearful farewell at a railway station.
     
  9. Ad Hoc
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    Ad Hoc Naval Architect

    Railway station!!!???...bugger...that's where I've been going wrong. Ive always been at the quay side!! :eek:

    Indeed, very succinctly summarised.
     
  10. philSweet
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    philSweet Senior Member

    This is the nature of self-induced circulation. And it behaves very nicely most of the time. The circulation that is induced by the foil is proportional to the free stream velocity and thus the lift, being proportional to V x C, is proportional to V^2. And self induced circulation scales geometrically with the foil.

    Contrast with a Flettner Rotor. Not so nice. Circulation scales with what, exactly? The circulation is not self induced in the same way. Energy has to diffuse into the cast-off wake in a manner that allows the wake to induce usable circulation.

    The only sense I can make of the original question is that "sound" represents the isentropic, reversible aspect of the process and "diffusion" represents the entropic, nonreversible component.

    <edit> Never mind, went back and read the entire article. He's just not very comfortable with presenting superposition. His diffusion vortex is just one that doesn't have a captive patch of material. Nothing to to with entropy. Which is a misuse of the term diffusion IMO.
     
  11. DCockey
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    DCockey Senior Member

    I suspect that sometimes when a mathematician says the solution is trivial what they really mean is they don't know how to generate a numerical solution.

    As an undergraduate I had a course taught by Mike Greenberg on applied math for engineers. One of his truisms was that one of the best ways to prove a solution actually existed was to show a solution.
     
  12. DCockey
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    DCockey Senior Member

    I suspect the common use of the term "induce" as in "The circulation that is induced by the foil is ..." is the origin of much confusion in aerodynamics. It can be tempting to assume that the airfoil is somehow "inducing" circulation in a manner analogous to a magnet "inducing" an electric current in a moving wire. Unfortunately actual fluid flow vortex "magnets" are not available, only mathematical idealizations.

    There are mathematical analogies between a magnetic field and fluid flow once the fluid flow is either approximated by a potential function governed by Laplace's equation which is only valid for high Reynold's number. However the underlying physics of magnetism and fluid flow are fundamentally different and thus the analogy can be mis-leading in understanding the physical mechanisms of fluid flow.

    (Interestingly there is also an analogy possible between 2D magnetic fields and very low Reynold's numbers creeping flow between parallel plates as in a Hele-Shaw apparatus.)
     
  13. Ad Hoc
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    Ad Hoc Naval Architect

    Analogies are a very important tool, whether correct or incorrect is often immaterial.

    Where very complex mechanisms and/or maths come into play there is a need to put the "numbers" or "theory" into general understanding, so that those not well versed in the subject can get a "crash" course. Thus, the analogy serves its purpose in conveying the message. One should not get too hung upon on the accuracy of an analogy, except that, does the analogy help convey the understanding of "it"..what ever 'it' may be....if the answer is yes, then job done!
     
  14. DCockey
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    DCockey Senior Member

    My experience is the analogy between magnetic fields and fluid flow can be useful in explaining the characteristics of flow around airfoils and similar flows, but can be mis-leading in understanding the physical mechanisms causing those characteristics. When that occurs the analogy goes from being useful and doing its job to being counter-productive.
     

  15. DCockey
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    DCockey Senior Member

    Enigma of the Aerofoil by David Bloor, 2011 provides an excellent though lengthy history of airfoil theory development including the prominent role played by the concept of circulation. http://press.uchicago.edu/ucp/books/book/chicago/E/bo12024403.html The Cambridge based "mathematical physicists" had great difficulty in accepting what is now the standard theory, in part because it appeared to them to conflict with their equations and theorms.
     
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