Is circulation real?

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

  1. Sailor Al
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    Sailor Al Senior Member

    Please, talk me through that process.
    At 5:08 Parcel A moves through the circled region and deposits some fluid on the surface.
    At 5:09 Parcel B moves through the circled region. Does it deposit some fluid over Parcel A's deposit?
    At 5:11 Parcel C B moves through the circled region. Does it deposit some fluid over Parcel A and Parcel B's deposit?
    What about the continuum of parcels between A and B, and between B and C? Does the fluid continue to deposit continuously?
    If the fluid is left to run for a long time, do these stationary layers build up?

    Or at 5:09 as Parcel B moves through the circled region, does it slide over the deposit of Parcel A? Is it retarded by contact with Parcel A's deposit?
    And at 5:11 as Parcel C moves through the circled region, does it slide over the deposits of Parcel A and parcel B? Is it retarded by contact with Parcel B's deposit?

    Is "The marker fluid is being stretched in the boundary layer" the result of your experimentation or is it to be found in a standard text?
    Surely if it is "being stretched", some of it has a non-zero velocity, contravening the no-slip condition?
     
  2. latestarter
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    latestarter Senior Member

    No disrespect was intended. Feel free to let off steam.
    Over the last few months on this and your other 2 threads it has seemed to be you against the rest of the world, it must be very wearing.
     
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  3. DCockey
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    DCockey Senior Member

    There appears to be some confusion about the non-slip condition and where it applies.
    The "no-slip" condition only applies at the surface. It does not say anything about the velocity a non-zero distance from the surface, whether that distance be 1 mm, 0.1 mm or 0.00000001 mm from the surface.
    So yes, the marker fluid has non-zero velocity except at the surface.

    Simple experiment of an analogous situation:
    Take a length of bungee cord and attach one end to the ground.
    Hold the other end in the hand with the cord vertical and taut.
    Walk forward.
    The end of the cord attached to the ground has zero velocity relative to the ground; in other words a "no-slip" condition.
    The remainder of the cord has non-zero velocity.
    The cord stretches and becomes thinner.
    If it could stretch indefinitely it would eventually become too thin to see.
     
  4. Sailor Al
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    Sailor Al Senior Member

    You are making this up as you go along!
     
  5. DCockey
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    DCockey Senior Member

    I do not see any reason to continue to engage with Sailor Al. He claims that he wants to learn about aerodynamics and then makes claims like the one above when someone tries to assist.
     
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  6. Sailor Al
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    Sailor Al Senior Member

    What I am trying to learn are the tricks and subterfuges that have to be employed to explain away the contradictions, fake physics and doubtful mathematics that are the foundations of aerodynamics.
    And now, this absolutely foundational concept, Prandtl's no-slip boundary, the breakthrough that resolved the century old impasse in fluid dynamics, is justified by reference to bungee cord being stretched indefinitely until it is too thin to see.
    • No reference to published text.
    • No description of experimental evidence.
    • No well established logical explanation.
    Indefinitely stretched bungee cord?

    On the contrary, @DCockey , your assistance has immensely nourished my desire to learn and is greatly appreciated.
     
  7. DCockey
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    DCockey Senior Member

    @Sailor Al, perhaps you should review the definition of an analogy. Here is one example: analogy https://dictionary.cambridge.org/us/dictionary/english/analogy
    You seemed to have difficulty in grasping how the velocity of a fluid could be zero at a surface and non-zero elsewhere. I thought a simple analogy would help with that understanding. Unfortunately it appears that either you did not take time to consider the analogy, or perhaps are someone for whom analogies have no meaning.

    I almost certainly just wasted time with this reply. But I'll hit send anyway. Perhaps it will be of some use to another reader in this forum.
     
  8. DCockey
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    DCockey Senior Member

    The above quotes of mine from May 2021 are applicable today.
     
  9. Sailor Al
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    Sailor Al Senior Member

    Indeed I do. At your suggested dimensions of 0.00000001 mm, a gas consists of molecules moving at around Mach 1. They will only be stationary at 0°K.
    For aerodynamics I think we need to work with gas theory which works at human scale, for which you don't need a microscope or a high-resolution camera.
    [EDIT] I suspect that even at your larger scales of 1 mm or 0.1 mm, experiments, even with "hot wires and laser anemometry" (#508), will struggle to demonstrate the presence of a no-slip boundary layer. But I will be delighted to review the evidence.
     
    Last edited: Nov 26, 2022
  10. baeckmo
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    baeckmo Hydrodynamics

    Actually, I think Sailor Al has a point here; for instance, the question about the non-slip situation is not quite clear with Prandtl. In his classical textbook “Führer durch die Strömungslehre”, 3:d edition from 1942, he just uses the image of two parallell surfaces, separated by a thin layer of fluid to explain the thinking behind the influence of viscosity. But as a fact, he does not give a reference or a validation to the statement that there is a non-slip condition at the boundary between a solid and a fluid.

    This means that if we accept the logic of fluid layers “sliding” over each other in laminar flow, then the same logic must apply to the limiting fluid layer close to the solid surface, and Sailor Al’s objection would be correct. So, were the old peers wrong then?

    To get a grip on the limit problem, we have to understand that there are two force systems at play here; the mass forces and the molecular forces. Their relative influence depends on the physical scale of the elements we study. In our “everyday life” scale, the mass forces are clearly dominant. However, as we approach the physical scale, where fluid and solid molecules influence each other across the boundary, then the molecular forces clearly outweigh the mass forces.

    As there are no absolutely flat solid boundaries, particularly not in microscopic scales, fluid particles in the microscale and ultimately in the molecular scale have to move transversely to the main flow direction, in and out of the boundary crevices. These movements obey the laws of mass force, but in this scale the molecular forces are dominating. The result is that the molecules in close proximity to the surface “stick” to the surface, and we get the “non-slip” boundary condition as a physical fact. The consequence of these physical events is that there is a logic fundament behind the theories used, even in the "human scale" that our sailor is searching.

    There are other phenomena in continuum mechanics that depend on this change of force system as well; boiling and cavitation are two; another is that if you get rid of the gas from water, for instance, the fluid can take strong expansion stresses.
     
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  11. DCockey
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    DCockey Senior Member

    The first assumption in fluid mechanics is the fluid can be considered as continuous, without needed to consider the individual molecules of the fluid. Length scales are much larger than the mean free path of the individual molecules. Properties such as velocity, density, temperature, etc at a location are considered to be the average of the properties in the vicinity of the point, with the average being taken over a size much larger than the mean free path of individual molecules but smaller than the size of any structures of interest.

    For length scales much larger than the mean free path of the individual molecules the "no-slip" condition when considered as the limit of the fluid velocity approaching a solid surface is valid. This is consistent with the velocity being continuous in a real fluid with viscosity. One exception to the continuity of velocity in a fluid is across a shock wave with the shock wave considered to have zero thickness. (In reality shock waves have thickness but it is small). Note that a shock wave cannot lie along a solid surface as there must be flow through a shock wave.

    An exception to the assumption that the fluid can be considered as continuous is rarified gas dynamics when the mean free path of the molecules is of the length scales of interest. Then the interactions of individual molecules and the associated statistics must be considered. For measurement and analysis of fluid motion associated with the water or air flowing past a boat the mean free path of the molecules is orders of magnitude smaller than length scales of interest.

    Back to the no-slip conditon. I'll copy part of a previous post #508: The no-slip conditions is valid until you look at length scales comparable to the mean free path of fluid molecules between collisions with other fluid molecules. At that level the general treatment of a fluid as a continuum also becomes invalid. The behavior of discrete molecules need to be analyzed. By the way the mean free path of molecules in air at sea level atmospheric pressure and density is around 60 nan0meters or 0.00006 mm, which is around 1 / 1000 of the diameter of a human hair. So in other words the no-slip condition is a valid approximation for virtually any purpose other than in very rarified conditions such as on the edge of space.
     
  12. Sailor Al
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    Sailor Al Senior Member

    Sure, no problem, why not? When you are looking at the flow within the fluid, that's a perfectly reasonable position. Within the fluid there should be no discontinuities.
    But why insist upon this condition where the fluid meets a solid boundary? There are two mediums (media?) behaving quite separately: the solid boundary, with its molecules madly vibrating with heat but firmly constrained in their lattice structure and the gas, with its molecules also madly vibrating but in addition, whizzing randomly around at Mach 1 and bouncing elastically off each other. Sure, deal with the gas as a continuous medium, but why does the gas have to come to rest at the interface?
    Where's a) the theory or b) evidence that it does?
    Why can't it slip over the boundary surface with its molecules bouncing off each other and off the solid boundary's molecules as well?
    You reject the argument at the molecular level that gas molecules only stop moving at 0°K, but still require that it does at the scale of 0.00000001 mm. You can't have it both ways!
    The whole theory of circulation, point vortices, lifting line, Kutta-Joukowski, Navier Stokes, etc., etc... the whole mad edifice of theoretical aerodynamics requires air to be stationary at the surface of the aerofoil.
    The theory is based on a fallacy.
     
    Last edited: Nov 27, 2022
  13. DCockey
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    DCockey Senior Member

    Many, many experiments have shown the general validity of the no-slip condition. If an individual wishes to believe it is not valid that is their choice.

    The velocity of a fluid is the average velocity of gas molecules at a point, not the average speed. Velocity is a vector quantity, speed is a scalar quantity and is the magnitude of the velocity vector. The average of a set of velocities can be different then the average of the speeds.

    The "0.00000001 mm" which Sailor Al repeatedly brings up in his attempts to rebut me originated post 513:
    The 0.00000001 mm distance was an arbitrary small number I typed as part of an explanation that the zero velocity of the non-slip condition only applies at a surface, not at any small distances from the surface. (Last phrase bolded because not understanding this appears to be a source of continuing confusion.)

    It should also be noted that I have already said the no-slip condition does not say anything about the velocity of gas molecules. Attempting to claim otherwise appears to be at the core of the attempts in this thread to discredit the no-slip condition.
     
  14. Sailor Al
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    Sailor Al Senior Member

    Please, can you provide a reference to one or two?
     

  15. DCockey
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    DCockey Senior Member

    Potential flow modeling has been at the core of theoretical aerodynamics for the past 100 years or so, in particular circulation, point vortices, lifting line, Kutta-Joukowski and so on. Potential flow modeling of a non-porous airfoil has absolutely no relation to the "no-slip" condition or anything conditions on the tangential component of velocity at the airfoil surface. The surface boundary condition used is zero normal velocity which is another way of stating that no flow goes through a solid surface.

    The no-slip condition is useful in understanding boundary layer behavior, but it is not essential or even used in most aspects of aerodynamic theory.
     
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