SMALLEST LENGTH SCALE
 

HI GUYS, HOW CAN I FIND THE SIZE OF THE SMALLEST TUBULENCE IN MY BOX OF TURBULENCE. IT IS THE KOLMOGOROV SCALE I WANT BUT HOW DO I CALCULATE THIS. IS THERE AN EQUATION TO GIVE A GOOD ESTIMATE OF IT BEFORE DOING THE SIMULATION?

THANKYOU IN ADVANCE.

Re: SMALLEST LENGTH SCALE
 

Hi,

The relationship I have for Kolmogorov scale is

Kolmogorov scale = ((nu**3)/epsilon)**0.25

where nu is kinematic viscosity and epsilon is turbulence energy dissipation rate..

Tim

Re: SMALLEST LENGTH SCALE
 

Where can he get epsilon before starting a simulation?

Re: SMALLEST LENGTH SCALE
 

The Tennekes & Lumley book is good for these estimates. Typically you would estimate epsilon from the fluctuating velocity (u or k=1.5u**2) and the length scale of the turbulence (L): epsilion ~ u**3/L.

If the turbulence is stirred, so you know the rate at which you are supplying energy to it, then you could take epsilon as equal to this supply rate - the energy just cascades down from the large scales.

Re: SMALLEST LENGTH SCALE
 

The problem is that the fluctuating velocity or the kinetic energy varys from the position inside the boundary layer to the place outside of the boundary layer. The fluctuating velocity could be nearly zero in the viscous sublayer.Does that mean the length scale of the turbulence there is nearly zero ?

Could you enlighten me please ?

Re: SMALLEST LENGTH SCALE
 

Hi,

I found another, rather simpler, relationship for Kolmogorov scale...

Kolmogorov scale = d/(Red**0.75)

Where :

d is the charachteristic length,

Red is Reynolds number based upon characteristic length,

I am currently working on a channel flow case at Re = 32000, d = 0.01 therefore I get a Kolmogorov scale of 4.17E-6 M - does that sound resonable?

As for the comment about kolmogorov scale in the viscous sublayer - The viscous sublayer is a Laminar flow region - there are no turbulent eddies therefore there is not an applicable Kolmogorov scale.

Tim.

Re: SMALLEST LENGTH SCALE
 

Turbulence structures take their origine in the viscous sublayer region. So this region is very far from being laminar. The fact is that, in this region, most of the velocity oscillations are in directions // to the wall and turbulence structure looks like hairpin. Thus, from the mean average velocity point of view, this region looks laminar i.e turbulence doesn't act on it. But, for a DNS or LES this region is critical, turbulence structures appear there and there the velocity gradients are higher.

More over, in this region even if k and l tend to zero, the dissipation doesn't. It may mean that the turbulence spectrum glides to the very small scale.

Sylvain

Re: SMALLEST LENGTH SCALE
 

That's is really an insightful discussion. Back to the question, how could we evaluate the length scale then ? eta=(nu**3/epsilon)**0.25. What value of epsilon we should use here ?

Nearly the wall, epsilon=u_tau**3/0.41y, where u_tau=sqrt(tau_wall/density)

For channel flow, tau_wall=Cf*density*U**2/2, where Cf=0.0706Re**(-0.25), Re=U*H/nu, H is the channel height.

When y moves towards zero (the wall), epsilon will be towards infinite, the length scale eta will be towards zero.

Please correct me if I am wrong ?

Re: SMALLEST LENGTH SCALE
 

Remember that we're only talking about estimates of epsilon here. If we estimate that epsilon is u**3/L, then this doesn't confirm that epsilon is infinite at the wall. The most it tells us that epsilon has dimensions [L**2/T**3]. A good estimate in one part of the flowfield might be a very bad estimate in another part of the flowfield, where different physical effects dominate.

If you're particularly interested in epsilon at the wall, consider it's formal definition, 2*nu*<s_ij s_ij>. As it is a function of velocity gradients, which are finite at the wall, you'd expect espilon to be finite at the wall. From this finite value and the assumption that the velocity scale is u_tau, you could calculate the length-scale applicable at the wall, which is obviously nothing to do with the distance from the wall. But as you move away from the wall, it is reasonable to assume that the distance from the wall is the most important length-scale.