måndag 11 juli 2022

Why Euler CFD is a Zero-Cost Parameter Free ToE

The fact that for slightly viscous incompressible bluff body flow with Reynolds number $Re>500.000$, Euler CFD with slip boundary condition (without boundary layers) serves as a parameter-free essentially zero-cost computational model without dependence on Reynolds number as a Theory of Everything ToE in the spirit of Einstein, depends on two key circumstances:

  1. Finite rate of turbulent dissipation effectively independent of $Re$ after transition to turbulence (e.g $Re >200$ in isotropic turbulence) (reference).
  2. Slip serving as effective boundary condition for $Re > 500.000$ (NACA0012 previous post).
Here 1. reflects Kolmogorov's conjecture and means that a mesh size of around 1/200 of gross dimension is sufficient to capture turbulence. Further, 2. reflects that Euler CFD with slip can capture drag and lift with little dependence on $Re$ beyond drag crisis around $Re=500.000$.  

Altogether, Euler CFD can capture drag and lift beyond drag crisis with a mesh size of around 1/200 of gross dimension thus at essentially zero computational cost (because no thin boundary layers have to be resolved). 

The fact the drag and lift coefficients do not include dependence on $Re$ (with $Re =\frac{UL}{\nu}$,  $U$ typical flow speed, $L$ typical length scale and $\nu$ typical viscosity) and yet can serve as measures of drag and lift for $Re$ beyond drag crisis, gives observational evidence that indeed drag and lift have a very weak dependence on $Re$ beyond drag crisis, as shown in the previous post (see reference showing drag independence for $Re>10000$ for a collection of blunt bodies).  Also recall that drag and rate of turbulent dissipation balance, and so observed independence of drag beyond drag crisis supports 1.   

   

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