Is circulation real?

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

  1. Alan Cattelliot
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    Alan Cattelliot Senior Member

    SailorAI, you picked my curiosity. Considering only what i've been teached, or what I have learned, the only thing that pops into my mind is : Superfluids.

    Superfluids do behave as if they were inviscid. With regards to the subject of the talk, I"ve made a quick research. Here is my though : The circulation theory applies on inviscid flows. The fact that the minimization principle reduces to the Kutta condition in the special case of a sharp-edged airfoil, wedded to the fact that this principle is an inviscid principle (equivalent to Euler's momentum equation), imply that the classical Kutta-Zhukovky lift over an airfoil with a sharp edge is both computed and explained from inviscid consideration. So, is there some evidence that lift can be generated around a profile by a superfluid flow, in the absence of viscosity ? What causes the lift ? I 've found this interesting publication, showing that lift can indeed be observed around a 2D profile, in an inviscid flow. https://davideproment.github.io/research/assets/papers/PhysRevLett.123.154502.pdf

    The authors of the study precise : "the current result provides a convincing argument about the mechanism behind circulation development over the airfoil. It is simply a momentum conservation mechanism; the Hertz principle of least curvature is one of its variational analogues."

    Which could indicate that nor the compressibily, nor the viscosity, nor any 3d effect is responsible for lift generation. The lift coefficient in laminar flows appears to only depend on the shape of the boundaries.
     
  2. Sailor Al
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    Sailor Al Senior Member

    I am delighted that one of my posts has piqued interest, not scorn, derision or abuse!
    The article was far too complex for me to study, but, if your summary is correct, it would appear to disprove J.D. Anderson's assertion (Sect 4.5.1):
    "However, if we lived in a perfectly inviscid world, an airfoil could not produce lift. Indeed, the presence of friction is the very reason why we have lift."
    Which is anyhow obviously and patently absurd!
    And anyway it wasn't a physics experiment, they were playing with a simulator :
    "Using simulations of the Gross-Pitaevskii equation"
    However, your post doesn't really address my question which is "could an acceleration of a gas ever be isentropic", even in an ideal world of inviscid, calorifically ideal gases? Never mind the practice, is it theoretically possible or, as in the case of time travel, flying pigs or negative gravity, logically impossible?
     
    Last edited: Sep 29, 2022
  3. Alan Cattelliot
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    Alan Cattelliot Senior Member

    I couldn't make my hand on the original article. Is it the one that Mikko Brummer cited in his thread ? The assertion that in an inviscid world, no lift could be produce by an airfoil is a particular case of the D'Alembert paradox. https://en.wikipedia.org/wiki/D'Alembert's_paradox. No drag = no lift (the notation here denote an bijective relation, ie no lift = no drag is also true, according to D'Alembert). Prantl's work on the boundary layer could be interpreted as a solution to the paradox, by introducing the "non-slip condition". However, if the boundary layer is indeed physically observed in the real world, Kutta and Joukowski proved that even in an inviscid flow, even without requiring that V = 0 at the boundary, lift, hence induced drag, can always be obtained (where bolt characters, here, express a vector) . D'Alembert hypothetis leads to the resolution of the equation of continuity.
    ΔΦ = 0, with V = gradΦ
    V.n = 0, where n is the boundary's normal
    V → V∞ upstream
    Kutta and Joukowski showed that besides solutions given by the continuous functions Φ0 that gives a null circulation, it exists also some non-trival solutions. They also showned that, for "rounded" bodies, the value of the circulation in any continuous solution to the problem of D'Alembert is not determined. Any values of the circulation are solutions to the "non lifting problem". Finally, they introduced the "Kutta-Joukowski" condition (for subsonic regimes) to demonstrate that the circulation can be determined around 2D profiles with a sharp trailing edge, demonstrating also the existence of solutions to the "lifting problem".



    It is really hard to create true insviscid flows.To my knowledge, only superfluids flows are known to exhibit this propertie, and it should be noted that the superfluidity have also other properties that are not understood today. I couldn't find any experiment on real profile in inviscid flows. Just theorical and numerical evidence. It's maybe why the the D'Alembert paradox has no accepted solutions today, and is still the matter of numerous and "heavy" discussion. As a consequence, the cause of lift is unknown today, but more and more evidence pile up, showing that the viscosity by itself may be dismiss. If you read the conclusion to this paper, in attachement, you will find this assessment, that differs from the ones from my previous post :

    "We have presented evidence that correct drag/lift can be obtained by computing turbulent solutions of the Euler equations with slip boundary conditions. We have thus shown that drag/lift mainly results from the turbulent nature of the flow and only to a small part from viscous boundary layers."

    I was teached the boundary layer theory as The Best Theory Explaining Lift and Drag, by one of the best and famous expert in the world. My mind has strong issues when reasonning outside of this theory. But I have also a scientist mind. Regarding the work that i've done when working on appendages and sailplanes, correlating numerical results with laboratory testing and true performances - ie on the water - , I being amazed that the Kutta Joukowski theory combined with the Prantl's lifting line theory always give amazing results that's fit well with the reality if turbulence intensity is around 9% (external flows). Results obtained with the tenth of effort compared with Navier-Stokes codes, and with the hundredth of the effort compared with tank or wind tunnel.

    Sorry, Sailor AI, I tried to find experiments on such isentropic acceleration of gases, but I've failed for now. My idea that, maybe, superfluids could help doing this is a failed attempt. In a recent study, I discover that even superfluids convey entropy when moving. That disqualified them as usable medium to be used to directly prove the possibility of an isentropic acceleration of gases. I can make a few steps back, and consider the wind tunnel apparatus that you've showned, together with my remarks about isentropic transformations, I would imaging a dynamic control of the temperature and the pressure in every locations of the appartus, including the temperature and the pressure of the gas in movement. This could be extremely hard, or maybe impossible... I worked on hypersonic experiments in wind tunnels, like the one you presented, for the Mars Pathfinder mission, and to characterize atomic emissions in interstellar media. To be able to make our experiments, we used costfull materials, cooling systems, molecular pumps, designed custom nozzles, brackets, trying to control the temperature and pressure effects in the tiny portion of the circuit where measurements were done. A the cost of a tremendous energy consumption, to balance the losses we yet minimized with all our efforts. So, even with this theoretical idea that we could, indeed, realize an isentropic acceleration of gases, I am not sure that, in the absence of a brand new theory of the matter and its states, we are able to fully realize it. Our current technology is essentially based on the use of non-isentropic effects, we make our gain in the variation of the entropy. A technology able to produce some gain of isentropic effects should be totally disruptive, and could perhaps make pigs fly ;) I would'nt say that such a technology is impossible. We shall be patient, and keep our mind open.
     

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  4. Sailor Al
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    Sailor Al Senior Member

    I was talking about the article you posted in your thread #361 just now.
    As for the rest... I don't know what to say. I asked a simple question ("could an acceleration of a gas ever be isentropic", even in an ideal world of inviscid, calorifically ideal gases? Never mind the practice, is it theoretically possible or, as in the case of time travel, flying pigs or negative gravity, logically impossible?) and you reply with many paragraphs of complex arguments.
    I am not asking about experiments, I am asking about theory!
     
  5. Alan Cattelliot
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    Alan Cattelliot Senior Member

    In short, my answer would be yes. Isentropy is absolutely defined for system outside equilibrium, so acceleration may not be an issue for isentropy, in theory.
     
  6. Sailor Al
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    Sailor Al Senior Member

    So, to support your claim, please provide a sketch of the imaginary apparatus that Anderson is asking us to imagine to achieve the isentropic acceleration of a gas. Make it as ideal as you like.
     
  7. Alan Cattelliot
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    Alan Cattelliot Senior Member

    We are turning in circle here, SailorAI. All the appartus cited below are theorically isentropic. I think that the reason why we turn in circle is because you ask an real apparatus for something theorical. Is there any contradictions in your question ? Trying to avoid this contradiction, MC-RASH and I put efforts in answers to make the distinction between practical and theorical. But i didn't give you satisfaction. Putting in question the underlying assumptions of the classical theory will not be an evidence sustaining your claim that compression & decompression of air around a sail is responsible for lift and drag. What about water around a moving daggerboard ? if we put this daggerboard in the air, do its lift coefficient will change ? Again, could you please consider in your thought the notion of dynamic pressure ? It may be some help to you, because I think that you have an intuitive and correct notion of what is causing the lift, only lacking some technical terms. Technical terms are not so important if your purpose is to sail a boat or a plane. Some of the greatest F1 pilots are very poor mechanicians, but they still know how to drive.
     
    Last edited: Oct 1, 2022
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  8. Sailor Al
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    Sailor Al Senior Member

    Yes, and all are theoretical experiments. But none of them describe an experiment like , as Anderson requires: "Consider a fluid element initially at rest, say, an element of the air around you. ... Let us now accelerate this fluid element isentropically to some velocity V and Mach number M, say, by expanding the air through a nozzle."
    That is the theoretical experiment I'm asking you to describe.

    What is contradictory about my asking for such a theoretical experiment?
     
  9. mc_rash
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    mc_rash Junior Member

    You ask something and after answering your question you redefine your question in a manner that anybody never could proper answer any of your questions.
    That is the answer on your last question, what is contradictory about your asking.
     
  10. gonzo
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    gonzo Senior Member

    That is incorrect. Atoms will vibrate at a larger amplitude when the iron is heated, so they are in fact changing position. Therefore the bar expands with heat. It is very different from heating a gas where there is convection, a phenomenon not present in solids. That is a terrible analogy.
     
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  11. Alan Cattelliot
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    Alan Cattelliot Senior Member

    I agree with Gonzo about the analogy. It is not the best attempt to explain the terms that are summed in the Navier-Stokes equations...

    SailorAI, have you tried this website ? I just google isentropic flows. I find this link interessant. First, it may give you a practical example of isentropic acceleration of gas. Second, it indirectly explains why the space launchers have multiple rockets, an "old" technologie that could have been already replaced by aerospikes engines. It's another subject...
    Isentropic Flow Equations https://www.grc.nasa.gov/www/k-12/airplane/isentrop.html
     
  12. Sailor Al
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    Sailor Al Senior Member

    Yes, But I couldn't get past the first sentence of the explanation:
    "As a gas is forced through a tube, the gas molecules are deflected by the walls of the tube. If the speed of the gas is much less than the speed of sound of the gas, the density of the gas remains constant and the velocity of the flow increases"
    The highlighted phrase is presented as a fact without any explanation. Why is it so? Is it true?
     
  13. mc_rash
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    mc_rash Junior Member

    Basically it means the density of the gas within the tube does not change if the speed is much less then the speed of sound. If the speed aproaches speed of sound things change and also when the gas flows faster than speed of sound. Mach number gives the ratio of local speed vs speed of sound. Properties of flow change with mach number and are depending on speed of sound.

    Why should the highlighted phrase NOT be true?
     
  14. Sailor Al
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    Sailor Al Senior Member

    No, the question is why is it true? It is presented as a statement of fact: like the sun will rise tomorrow, or gravity is a force of attraction, or the speed of light is absolute. There is an infinite number of reasons why these statements may be false, but they aren't, and there are scientific reasons for that.
    I am asking for the scientific reason behind the stated fact.
     
    Last edited: Oct 1, 2022

  15. Alan Cattelliot
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    Alan Cattelliot Senior Member

    Let's begin with the definition :
    upload_2022-10-2_9-40-8.png
    If we maintain the mass constant, like in this closed tuben we establish the relation between the variation of density and the variation of volume.
    upload_2022-10-2_9-46-42.png
    So can we re-write the compressibility as the variation of density when a pressure is applied.
    upload_2022-10-2_9-55-39.png
    There is two way to compress a gas ( or a solid ) : Slow compression and fast compression. The slow compression is called isothermal compression. Real compressions are made somewhere between these two theorical cases. The fast compression is called isotrenpic compression. The isothermal compression happens when the gas temperature remains constant when the gas is compressed. Using a bicycle pump, the temperature rises if your stroke rate is high, and it's difficult. If you go slowly, it's easier, and the temperature does not rise. The isentropic compression happens when the energy has no time to be transfered among the gas. It is the case in the Laval nozzle, described in the link from NASA Glenn Center.
    upload_2022-10-2_10-0-34.png
    The equations for the isothermal cases are most simple than the equations for the isentropic case, with identical conclusions, but with additionnal parameters. So we can focus on the isothermal case .

    upload_2022-10-2_10-15-39.png
    From the gas law, we can establish that the isothermal compressibility is the inverse of the pressure. For a given gas, the higher the pressure is, the smaller is its compressibility. So air at water level is much much much less compressible than air in the outer atmosphere. The variation of density being proportionnal to the variation of pressure times the compressibility, small variations of pressure will only cause small variation of density.

    upload_2022-10-2_12-1-11.png

    For instance, at sea level, when the upstream speed is small, the variation of pressure is small, as seen in the image below, so the difference of the momentum calculated with the Bernouilli equation for incompressible flow and the momentum calculated with the Bernouilli equation for compressible flow is small, and thus can be neglected the density variation in the force calculations.
     
    Last edited: Oct 2, 2022
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