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Independent Existence of Smallest Scale (Kolmogorov) Eddies 

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July 26, 2016, 13:19 
Independent Existence of Smallest Scale (Kolmogorov) Eddies

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If I understand it correctly, The smallest (microscale) eddies in a turbulent flow field are supposed to get their energy from the medium and or large scale eddies through the energy cascade notion of turbulent flow.
If no large or medium scale eddies exist in the flow (as evident from simulation results, assuming the mesh cell sizes are small enough to capture both the large and medium scales)  does that not indicate the lack of existence of microscale eddies in the flow? otherwise, where do they get their energy (to even exist) from? Any light shed on this topic is greatly appreciated. Thanks. 

July 26, 2016, 13:25 

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Filippo Maria Denaro
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July 26, 2016, 13:36 

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Thank you for your reply! 

July 26, 2016, 13:39 

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you can have large structures in laminar flow, immagine for example the backward facing step flow (Re<400) or the flow around a cylinder at low Re. The key is that they cannot transfer energy to smallest structures in an intertial way as the dissipation due to the viscosity acts at large length. 

July 26, 2016, 13:53 

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If a simulation conducted with a space and time resolution sufficient to capture large and medium scale eddies yields results that don't indicate any turbulent or transitional behavior (timeresolved curves of velocity and WSS at various points in the domain, for example, do not contain any high frequency fluctuations and resemble the inlet waveform of the problem)  I could conclude that further refinement of the simulation's resolution (down to the Kolmogorov scale) definitely won't yield results indicating turbulent phenomena? Thanks again! 

July 26, 2016, 14:00 

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Actually, before doing a CFD simulation you should be aware of the main physical features of the flow problem...Generally, the Reynolds number is the first indicator. Setting a grid size able to produce everywhere cell Re number O(1) is a guarantee to solve all the scales of the motion (DNS).
However, assuming in your case all the setup is correct, if you reach a steady solution it is for sure not turbulence. If you get an unsteady solution having one or very few and low wavenumber components it is laminar, too. 

July 26, 2016, 14:20 

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My problem has a pulsatile inlet, so by definition the solution isn't steady. Did you mean something else by 'steady solution'? Plus, can one conclude the lack of turbulence without evaluating the wavenumber, but only on the basis of temporal curves of the physical parameters (e.g. WSS and Velocity)? Thanks for your reply and your patience 

July 26, 2016, 15:12 

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I do not understand your sentence "I'm actually trying to justify not utilizing DNS by showing that the results that I have obtained using a coarse (relative to Kolmog. scale) mesh and time steps". If you already know that your grid size cut away the viscous part (and maybe also some part of the inertial?), this is already an indication you have a turbulent spectrum and you are performing a sort of LES without model. Refining the grid you will capture the part of the spectrum that can be relevant in your solution. You need to do a frequency analysis to see the extension of your energy spectra. 

July 26, 2016, 15:50 

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1. My model involves a pulsatile flow (transient) in a pipe that has a complex geometry (it is slightly curved, has a few fenestrations, etc.). The Reynolds number is ~1400. 2. I want to show that if I use a certain mesh cell size larger than the Kolmogorov length scale (in my case: cell_size =~ 5*Kolmog_length_scale) but smaller than the Taylor scale (Taylor_length_Scale =~ 4*cell_size), I can conclude that the flow field is laminar as long as the temporal curves of wall shear stress vs. time and velocity vs. time are 'smooth' and don't have high frequency fluctuations ('noise') riding on the low frequency waveform and are thus behaving like the velocity inlet waveform to my domain, which is 'smooth' and has a low frequency. 3. If this is indeed true, then there is no need to use DNS to find the smallest scale eddies in the flow field, because they would not exist. Are 2. and 3. indeed true? Thank you again for your help, I really appreciate it 

July 26, 2016, 16:11 

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Again, I do not understand... if you have an estimation of the Taylor microscale and Kolmogorov scale, that means you have estimation of turbulence characteristic scales therefore you contradicts that fact that the flow can be laminar...
in a laminar flow you have only the large integral scale, you can have some structures but no clear distinction between inertial and viscous ranges such to distinguish the viscous scales. In practice, the effect of the viscous term will dump any inertial range so that defining the Taylor microscale (the largest of the viscous one) makes no sense. For your Re number, being the geometry complex, I am quite sure you cannot have a laminar flow everywhere. Conversely, I can immagine more correct the question if the further resolving of the Kolmogorov scale would add something in the physics of the numerical solution. 

July 28, 2016, 16:26 

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Tags 
eddy lengthscales, energy cascade, kolmogorov, turbulence analysis 
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