In turbulence they do often say flow with wide range of length scales and often say like epsilon equation tends to convect too large length scales ,what is this length scale and why do they relate it with epsilon like terms ,what is the importance of it

Read the introduction of tuebulence.

What *causes* turbulence? What *sustains* turbulence? What *aggrivates* turbulence?

What *is* turbulence?

Answer those questions & you may well have answered the original length-scale question...

diaw... (Des Aubery)

thanks friend's but can u suggest where to read introduction by the way my question is what is the advantage of using length scales cant we proceed or describe turbulence phenomenon without mentioning scales .

Read CFD-Wiki, here is a direct link:

http://www.cfd-online.com/Wiki/Turbulent_length_scale

Turbulence is characterised by "eddies" of various sizes, ranging from large, determined by the physical boundaries of the flow, to very small, determined by the viscocity of the fluid. The kinetic energy of the turbulence travels from the large eddies pretty much conserved until it reaches the smallest eddies where it is dissipated by viscous effects.

Under equilibrium, the turbulent kinetic energy produced is equal to that dissipated. So, if we can estimate the scale of te large energy-containig eddies, we can use that scale (under equilibrium) to estimate how much is dissipated.

I think one reason why one gets an over-estimated dissipation (length scale) is that there is really a lag between energy showing up at the larger scales and then dissapearing (to heat) at the small scales. So, if you use the "length-scale" (big) to estimate the dissipation (small) you get an over-estimate.

I hope my rambling is not confusing.

What *causes* the eddies to form in the first place?

The exact production term in k equation is -uu.dU/dX. It's show that turbulence grows under the effect of shear stress.

If the question is : why uu is not always equal to zero - which is a solution of Reynolds Average Navier Stokes Equation - I am afraid that no one can answer.

ZubenUbi

To complet Pennysworth's message :

k-Eps, as any other 1 point model, is build over the hypothesis of turbulence under equilibrium.

In fact, at the beginning, turbulence energy is produce at large scale by the velocity gradients.

Then this energy is transfer to small scall, throught what is called the Energy cascade.

After that, the energy is dissipated by small scales.

1 point models used to consider that the amount of transfered energy by time unit and the amount dissipated energy by time unit are equals - which happen at equilibrium. This is obvious if we consider the production term in the Eps equation : it is proportional to the k production term.

From another point of vue, that's mean that the dissipation in 1 point model is not the amount of energy dissipated by time unit, but is the amount of energy transfered by time unit.

In shear region, the amount of energy transfered by time unit overestimates the dissipation, in shearless region, it underestimates the dissipation.

3 equations "k_Eps_Phi" models have been developped to correct this, where Phi could be a time scale build over k/Eps and dUdX.

Multiscales models also correct this.

As Pennysworth, hope this is not to confusing,

ZubenUbi

Thanks Pennsworth ,ZubenUbi , Jonas , diaw and Q thanks for u r participation in making this clear to me ...regards bajjal