Kolmogorov microscale for a check valve
 

Hello!
I try to estimate the Kolmogorov microscale for a hydraulic check valve. I attached a schematic of the valve.
The Kolmogorov microscale is defined as

where is the average rate of dissipation of turbulence kinetic energy per unit mass and is the kinematic viscosity of the fluid.

It is the smallest scale in turbulent flow in which viscosity dominates and the turbulent kinetic energy is dissipated into heat. The Kolmogorov microscale can be expressed with the Reynoldsnumber Re as

with the chracteristic length scale l.

Now my questions: What is the characteristic length scale in may case of the check valve? Can I use the hydraulic diameter of the valve?
I look in serval book, but I never found a satisfactory answer.

The Re-number of the valve is

with the flow rate Q, diameter of the valve and the viscosity .


Thank you for an answer!
Regards,
Christoph

what about the magnitude of the velocity inlet?

The highest velocity is at the edge of the valve and is


For typical values the velocity at the edge is in the range of u = 0 ... 25 m/s.
At the inlet the velocity is a little bit lower.

So you have Re=O(10^3). It's quite small to try working in DNS/LES formulation. The kolmogorov scale is about 10^-4m

Thank you for the answer!

But 0.1 mm is quite large for the small valve: 0.5 mm plate stroke and the diameter of the inlet is 2 mm.
What is the right characteristic length for this valve? I took the hydraulic diameter which is 2*h (plate stroke) = 1 mm.

I performed different simulations in OpenFoam (DNS, LES one equation eddy visosity, and RANS k-omega SST) with the assumption of an axisymmetric flow problem. I know with turbulence it is not exactly true, but it was only a try. The differences in the flow rate between the three simulation runs were small.

A rapid estimation is obtained by considering that at the Kolmogorov lenght scale you can set Re_eta=1 -> eta=ni/U.
You cannot assume the axisymmetry if you want to use DNS/LES

ok, thanks.
So, it is not impossible to perform a DNS simulation maybe from a quarter of the check valve with the corresponding boundary conditions.
With this rough estimation arount 500 000 to 3 000 000 cells are necessary for a DNS simulation.

you cannot simulate a quarter of valve

If I have time (and the workstation), I will try a DNS for the whole, half and quarter geometry and compare these simulations against each other. Because I am not sure, how large the error is.

Thank you again for your advice!

it's not an error issue, other than the whole domain is simply wrong ...
you can use that only in RANS.

I know that from literature.
But I found a lot of papers dealing with axisymmetric direct numerical simulations for high Re-numbers. I did not find any comment in these papers, why it is possible.

So, I tried it for my check valve example. Simulation is still running - but the first results show nearly no difference between DNS in 3D and 2D.

that's not possible... no 2D DNS can give a physically meaningful solution of the real 3D turbulent flow around a valve.
I am not aware of any relevant publication in the DNS/LES community of an axisymmetric DNS study.

I suspect:
1) the 3D case has not yet developed the fully developed unsteady flow.
2) your code has a lot of numerical viscosity
3) you are using a too coarse grid

Thank you for the very fast answers! :)

One of these papers is:
http://www.sciencedirect.com/science...96890412002981
The pressure difference through the valve is up to 80 MPa, so in my opinion with the given dimension a high trubulent flow.

I am using about 500 000 cells, but I will increase the number further.
Maybe it could be the numerical viscosity, but how can I check it?

regards,
Christoph

I don't want to be offensive but such a paper would not be published in any good fluid mechanics journal...

Do you have suggestion for good Journals?

Journal of Fluid Mechanics, Journal of Computational physics, Physics of Fluids, Int.J. Numerical Methods in Fluids, Computers & Fluids, Theor.Comput. FLuid Dynamics, Journal of Turbulence...

just as example, see

https://www.researchgate.net/publica...iston_assembly

Thank you!
With the results in this paper it is quite clear that it is not recommendable to use DNS in 2d.
In my case the results are not so impressive and clear.
Now, I have an other question:
I performed two 2d simulation of the valve. Once with the k-omega-SST turbulence model and the second time without using a turbulence model. I found only minor differences between both simulations. But I do not know why the differences so small; maybe I resolve the larges eddies of the flow (but it should be not possible in 2d)?

regards,
Christoph

First, You cannot compare the RANS solution directly to the DNS solution. This latter must be statistically averaged. But if you do a 2D DNS there is no physical meaning in the solution you get, so the statistics are not relevant.
If you have numerical viscosity that depends on the type of discretization of the convective term. Generally upwinding or flux-limiters are the sources such error.

I performed some additional analysis of the results. And now I see clearly that the axissymmetric assumption for DNS simulations is not correct. In the attached figure I depicted the pressure iso-surface and the velcoity magnitude in the background.

You helped me a lot to understand turbulence simulation a little bit better!

Attachment 50517