fredag 8 mars 2024

2nd Law vs Friction

Perpetual motion is viewed to be impossible because according to the 2nd Law of Thermodynamics (see recent posts)

  • There is always some friction.     (F)
Is this true? It does not appear to be true in the microscopics of atoms in stable ground state, where apparently electrons move around (if they do) without losing energy seemingly without friction, see Real Quantum Mechanics

But is it true in macroscopics of many atoms or molecules such as that of fluids? A viscous fluid in motion meets a flat plate boundary with a skin friction depending on the Reynolds number $Re\sim \frac{1}{\nu}$ with $\nu$ viscosity as follows based on observation:


We see that skin friction coefficient $c_f$ in a laminar boundary layer tends to zero as $Re$ tends to infinity (or viscosity tends to zero), which is supported by basic mathematical analysis. 

We also that there is a transition from laminar to turbulent boundary layer for $Re > 5\times 10^5$ with larger turbulent skin friction coefficient $c_f\approx 0.002$ with a very slow decay with increasing $Re$ with no observations of $c_f<0.001$. 

The transition to a turbulent boundary layer is the result of inherent instability of the motion of a fluid with small viscosity, which is supported by mathematical analysis, an instability which cannot be controlled in real life, see Computational Turbulent Incompressible Flow.

We thus get the message from both observation and mathematical analysis that (F) as concerns skin friction is true: Skin friction in a real fluid does not tend to zero with increasing $Re$, because there is always transition to a turbulent boundary layer with $c_f>0.001$.  

Laminar skin friction is vanishing in the limit of infinite $Re$, but not turbulent skin friction.

We can thus can rationalise the 2nd Law for fluids as presence of unavoidable skin friction from turbulent motion resulting from uncontrollable instability, which does not tend to zero with increasing $Re$ , reflecting presence of a non-zero limit of turbulent dissipation in the spirit of Kolmogorov.  

Connecting to finite precision computation discussed in recent posts, we understand that computational resolution to physical scale is not necessary, which makes turbulent flow computable without turbulence modelling. 

In bluff body computations (beyond drag crisis) it is possible to effectively set skin friction to zero as a slip boundary condition thus avoiding having to resolve turbulent boundary layers. In pipe flow skin friction cannot be set to zero.

PS1 A hope of vanishingly small laminar skin friction has been nurtured in the fluid mechanics community, but the required instability control has shown to be impossible, as an expression of the 2nd Law. 

PS2 One may ask if motion without friction is possible at all? Here we face the question what motion is, connecting to wave motion as an illusion. In Newtonian gravitation of a Platonic ideal world there is no dissipation/friction, but in the real world there is: The Moon is slowly receding from the Earth because of tidal motion energy loss. What then about the supposed motion of photons at the speed of light seemingly without energy loss from friction? Is this motion illusion, with necessary energy loss to receive a light signal? Computational Blackbody Radiationֶ  says yes! The 2nd Law can thus be formulated: 
  • There is no motion without friction. Photons in frictionless motion is illusion.
Do you buy this argument? Can you explain why? Instability? What is a photon in motion without friction? Illusion?

Why is there always some friction?


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