torsdag 14 juli 2022

Nature of Turbulence vs Euler CFD

What makes Euler CFD into a parameter free model or Theory of Everything ToE for slightly viscous incompressible flow is:
  1. Finite rate of turbulent dissipation effectively independent of Reynolds number $Re$ after transition to turbulence. 
  2. Slip serving as effective boundary condition for $Re$ beyond drag crisis at $Re\approx 500.000$.
Here 1 reflects the nature of turbulence as an energy cascade from large to small scales,  developing from shear or opposing flow instability in slightly viscous incompressible flow,  into a smallest scale $h \sim Re^{-0.75}$ where the energy is dissipated into heat with an amount which is determined by large scale features. This is the essence of classical qualitative turbulence theory stating independence of rate of turbulent dissipation for $Re$ beyond transition to turbulence, which could be at $Re\approx 10^3$ with $h\approx 10^{-2}$ which opens to capturing mean values such as drag in bluff body flow balancing turbulent dissipation in computations with $10^6$ mesh points, to be compared with unreachable $10^{14}$ to resolve smallest scales if $Re =10^6$ common in aerodynamics of vehicles (largest DNS reaches $10^{11}$).  

Turbulence is thus uncomputable to smallest physical scales for $Re >10^6$ in any foreseeable future, but mean-value quantities such as drag and lift are computable today with desk top power, because of the nature of turbulent flow. Turbulent flow is thus in its details uncomputable but readily computable as concerns mean-values for large variety of problems of great practical interest.  This is very remarkable as an answer to a basic open problem in fluid mechanics.

Further 2 reflects that it is not necessary to resolve thin no-slip boundary layers scaling with $Re^{-0.5}$ asking for $10^{13}$ mesh points, since slip does not generate any boundary layers and thus the above millions of mesh points suffice.  Specifically, main stream turbulence is not mainly generated from no-slip boundary layers as the core element of Prandtl's boundary layer theory dominating modern fluid mechanics making CFD into an impossibility. 

Altogether 1 and 2 express the basic nature of turbulent flow, which makes it possible for Euler CFD as best possible solution to the Euler equations to serve as a quantitative ToE for slightly viscous flow meeting the NASA 2030 CFD Vision. Listen to the breakthroughs Parviz Moin believes (time 18.21) are needed to reach the Vision, which have now been reached by Euler CFD. 

Note that Euler CFD can be seen as a form of Large Eddy Simulation LES with a turbulence model which is automatically generated from a principle of best possible solution to the Euler equations and slip as wall model.

Note also that slip can be seen as the most basic and simple wall model expressing zero friction between fluid and wall as an expression of observed very small skin friction, to be compared with complex wall models supposed to capture thin turbulent boundary layers arising from no-slip asking for computational resolution beyond reach.      

 

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