Length Scale Plot

$ \sigma = MAX(min(\cfrac{k^{\frac{3}{2}}}{\varepsilon},\kappa \delta),\Delta) $

Why has this formulation been chosen? The $ k-\omega $ and many others turbulence models define the length scale as $ L=\frac{k^{3/2}}{\varepsilon} $.

The lower limit is set to depend on the LES grid refinement (which must be conditioned by the size of the near wall structures) rather than Kolmogorov length in order not to leave its estimation entirely to the RANS model.

The upper limit is defined as a geometrical characteristic of the flow because of the lack of accuracy of RANS predictions in free stream edge.

PROBLEM: the definition here reported allows eddies not to be totally contained into the inlet domain definition, although they are totally inside the eddy box!! ( mind the difference between eddy box and domain!!!) Shouldn't the length scale and the eddy box definition consider such a problem? I personally think that this is an important lack at least when a WALL boundary condition is defined!


Eddy length scales higher than the green line will generate eddies not completely contained into the domain!!

NOTE and QUESTION : where must $ \sigma $ be calculated? In the SEM formulation we define the fluctuating velocity component as:

$ \mathbf{u}(\mathbf{x}) = \mathbf{U}(\mathbf{x})+\cfrac{1}{\sqrt{N}}\sum_{k=1}^{N} A \boldsymbol{\varepsilon} f(\mathbf{x}-\mathbf{x}^k) $

Do $ \sigma $ have to be calculated at $ \mathbf{x} $ or at $ \mathbf{x}^k $ position? Since it is an eddy length scale, I would assume that it should be a function of $ \mathbf{x}^k $, BUT N.J. in his subroutines chose it as depending on the $ \mathbf{x} $ position (resulting that a single eddy has several lengths scale) .

Neverthless, the new DF-SEM requires compulsorily the eddy length scale to be constant within the eddy!!

Eddy Animation


A small picture which shows the eddy movement. The eddy box is defined as: -0.41 < x < 0.41; -0.41 < y < 2.41; -0.41 < z < 3,52. The eddies pass through the inlet surface (which lies in the centre of the eddy box) and are recreated when they are eventually convected outside the box. At the present stage all the eddies are convected with the same velocity, but some tests will be available in future to see the influence of convective speed to the inlet quality.

Cf comparison


Pressure Fluctuation



A qualitative visualization of the pressure in the SEM (left) and the DF-SEM (right) suddenly highlights the new DF-SEM decreased the pressure fluctuation to almost the natural size of turbulent ones. Obviously a quantitative analysis which considers pressure root mean squares may define more accurately this behaviour!

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Topic revision: r5 - 2010-10-25 - 16:49:46 - RuggeroPoletto
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22 Jul 2018


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