The Unsolved Problem of Turbulence

Discussion in 'Hydrodynamics and Aerodynamics' started by Earl Boebert, Mar 28, 2019.

  1. Earl Boebert
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    Earl Boebert Senior Member

  2. Dejay
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    Dejay Senior Newbie

    Thanks, great article!

    So do you believe there is a true theory of turbulence? To me it sounds like trying to find a theory of the ballpit. It's all emergent behavior of chaotic interactions that resolves into patterns with certain probabilities, but is fundamentally unpredictable except by simulating the exact state of every single particle involved.

    So you could only find equations and models to estimate and predict it within limits, but never to explain the mechanism of how flow changes (since it's dependent on minute states of molecules).
     
  3. Earl Boebert
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    Earl Boebert Senior Member

    Actually, I haven't a clue :)

    Cheers,

    Earl
     
  4. Dolfiman
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    Dolfiman Senior Member

    Now that we are aware of the interactions complexity at atomic to molecules sub scales, one can be intrigued not by the turbulence itself but reversely by the possible existence of laminar flow at our macro scale : what are the damping mechanism in action when the speed is slow enough that could lead to such uniform flow, e.g. exchange of energy between close molecules so that the molecule at speed+ gives some energy to the molecule at speed- ?
    And is the Navier-Stokes equation fit for such purpose, able to render such phenomena if any ?
     
  5. DCockey
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    DCockey Senior Member

    One school of thought links turbulence to chaos theory. Chaotic systems are deterministic but very small perturbations in initial conditions can produce very different results.
     
  6. jehardiman
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    jehardiman Senior Member

    Actually all the data I have ever taken from real bodies points to multiple bifurcation points. If you start looking at Poncaré maps of speed vs drag of "ship shaped" bodies in random waves, you notice that there are energy sinks that are strange attractors. I think that there is a doctorate sitting in there somewhere, but for real engineering 3D cases it is just a matter of "the ITTC line plus a little" as I said in an old post.

    Dolfiman, always remember that the Navier-Stokes equation is a mathematical contrivance that hangs its hat on the condition that there is no change in internal energy (i.e. specific continuity and boundary conditions) and therefore patently false. Useful, but false.
     
  7. DCockey
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    DCockey Senior Member

    jehardiman, could you elaborate on that statement? I'm confused because my understanding is total energy is conserved within the fluid, not internal energy. Also there can be a flow of energy across a boundary, and the equations can be modified to account for energy changes within the flow field, for instance by combustion.
     
  8. jehardiman
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    jehardiman Senior Member

    Yes, but the only energy that is counted is the energy that makes a difference to the specific continuity and boundary conditions. The energy internal contained as turbulence within the specific del unit is not known at the boundary, it can only be expressed as a tensor over the space. This means that if you want to account for the specific internal energy of turbulence you already have to know its distribution over the space before you begin. This turns the problem into a self-licking ice cream cone. Go see Leo Lazauskas's old "Skin-Friction Formulas" thread in the software forum.
     
  9. Dolfiman
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    Dolfiman Senior Member

    Well I am not expert neither user of related numerical tools, but just interested to understand and I mostly rely on this document, an introduction lesson on turbulence done in schools of engineers, that is well balanced with not too much math, a lot of explanations and illustrations, insights on current obstacles and research. The chapter 2 introducing the Navier-Stokes and the Reynolds number is very good, introducing the 2 mechanisms of the quantity motion transport in action : diffusion (which is at macro scale a coherent statistic representation of the molecular interactions), convection (speed itself transporting the motion quantity). Diffusion is linear with speed and favors laminar flow (flow stays parallel). Convection is non-linear with speed and leads to vortex. And the Reynolds number, which appears from an adimensional form of the Navier-Sokes equation, can be interpreted as the ratio of convection effect / diffusion effect. (I hope my translation/simplification is correct :) )
    The document is in French with no translation available unfortunately, but helpful I think because the author keeps the "introduction to" objective all along the text while dealing with all the complexities of the subject :
    https://hal-ensta.archives-ouvertes.fr/cel-01228137/document
     
  10. Mikko Brummer
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    Mikko Brummer Senior Member

    Here's some simulated turbulence... and leech vorticity ("tip vortex").


    Turbulence.png Leechvorticity.png
     
    Dolfiman, CT 249, Erwan and 2 others like this.
  11. daiquiri
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    daiquiri Engineering and Design

    Mikko, those pics are impressive! May I ask what was the computation time, and on what hardware?
     

  12. jehardiman
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    jehardiman Senior Member

    Dolfiman, that's what I mean, a "simulated turbulence" input at the boundary is all you can do. You will never know the "real" turbulence at the boundary. You have to avoid both 'cherry picking' and also the 'butterfly effect'.
     
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