CFD Online Discussion Forums - WHAT TURBULENCE ENERGY INPUT SHOULD I USE?

From simple turbulence theory, the turbulence energy input which enters the problem on the largest scale is given here just usinng the velocity of the airfoil (or wind tunnel?), and that kinetic energy of the flow, as the flow develops turbulent regions, is fedding the turbulence and cascading to the smallest scales where it dissipates due to the viscosity. So if your Rey=6x10^6, then somewhere on scales of the order of 10^-6 of the size of your airfoil, one will have Rey=1, and these are the dissipative scales. The energy that enters the turbulence is the same that dissipates on the smallest scale as no energy get lost in the cascade process.

So I would expect that if you run a time dependent simulation, then the turubulence should develop all by itself.

PUting numbers into this. Say you are computing a domain or airfoil of size D, and the wind or wing speed is V. The largest size of the turbulence (Eddies) is D and the velocity within the Eddies is of the order of the velocity change of the flow over a distance D, which here is probably V, as the flow stops at the airfoil. The turbulent energy say E is in unit of ergs per second per gram (energy per unit of time and unit of mass) is given by the quantity:

E=(V^3)/D , where ^3 means to the power 3. This is so because the change of the velocity is from V to zero as it reaches the boundary layer of the airfoil on a scale of size D. This same energy cascades to smaller scale L < D but its value does not change, so that if the smaller scale L have a velocity (Eddy velocity) U, where

V^3/D=U^3/L all the way down to the dissipative scale where Rey=1.

So the turbulent energy input has to be the same as this one, namely

E=V^3/D ergs/sec/gm

I hope this helps.