[gu1]

Hi,

With the intention of performing LES in a multiphase flow, I first want to perform URANS to later import the information and thus perform LES.

An important aspect that is much discussed in the literature is to calculate the integral length scale and divide it by the cell volume. Since this value is greater than 5, we then have good mesh agreement for LES. Well, that was my understanding.

However, how should the length scale for multiphase be calculated? Since in an E-E approach we have two fluids. Using a model based on kEpison, I calculated according to the literature (L = k^1.5/epsilon) for water. I'm not sure if I did it correctly.

Thanks.

edit1: In fact, because it is multiphase (dispersed and continuous phase - bubble injection), does the equation used and referred to, L, need to be changed?

[Severus]

Hello,

The way to calculate the integral length scale is to use the autocorrelataion of the velocity fluctuations. The method to do it with OpenFOAM (that I can now think of) is to have probes at different locations, measure the velocity signals over time. See probes in OpenFOAM.
Then you can collect a long enough temporal signal and use this signal and compute the fluctuations. With the resulting fluctuations you can calculate the autocorrelation of velocity fluctuations.
Finally you have to integrate the autocorrelation to find the integral time scale. From that get the integral length scale.
You can refer to any turbulence book for more information about the same.

The above mentioned approach works well with DNS/LES data or experimental data.
In your case, since you do URANS, computing the integral length scale from this approach may not be accurate. You can get Urms or U' from the URANS simulation but here the turbulence is modelled and the way U' is calculated assumes isotropic turbulence.

Solution to your question:
Now, since you mention that you plan to use Euler-Euler method with LES, you have to note that your grid size requirement has an upper limit.
It is called the Milelli criterion. (depending on the bubble diameter). So you can use that criterion to estimate the grid size requirements.

For more information about Milelli criterion you can see
Ničeno, B., Dhotre, M. T., & Deen, N. G. (2008). One-equation sub-grid scale (SGS) modelling for Euler–Euler large eddy simulation (EELES) of dispersed bubbly flow. Chemical Engineering Science, 63(15), 3923-3931.

Milelli, M. (2002). A numerical analysis of confined turbulent bubble plumes (Doctoral dissertation, ETH Zurich).

Thanks

[gu1]

Originally Posted by Severus

Hello,

The way to calculate the integral length scale is to use the autocorrelataion of the velocity fluctuations. The method to do it with OpenFOAM (that I can now think of) is to have probes at different locations, measure the velocity signals over time. See probes in OpenFOAM.
Then you can collect a long enough temporal signal and use this signal and compute the fluctuations. With the resulting fluctuations you can calculate the autocorrelation of velocity fluctuations.
Finally you have to integrate the autocorrelation to find the integral time scale. From that get the integral length scale.
You can refer to any turbulence book for more information about the same.

The above mentioned approach works well with DNS/LES data or experimental data.
In your case, since you do URANS, computing the integral length scale from this approach may not be accurate. You can get Urms or U' from the URANS simulation but here the turbulence is modelled and the way U' is calculated assumes isotropic turbulence.

Solution to your question:
Now, since you mention that you plan to use Euler-Euler method with LES, you have to note that your grid size requirement has an upper limit.
It is called the Milelli criterion. (depending on the bubble diameter). So you can use that criterion to estimate the grid size requirements.

For more information about Milelli criterion you can see
Ničeno, B., Dhotre, M. T., & Deen, N. G. (2008). One-equation sub-grid scale (SGS) modelling for Euler–Euler large eddy simulation (EELES) of dispersed bubbly flow. Chemical Engineering Science, 63(15), 3923-3931.

Milelli, M. (2002). A numerical analysis of confined turbulent bubble plumes (Doctoral dissertation, ETH Zurich).

Thanks

Thanks.

Without a doubt, I even read both articles mentioned and am respecting the indicated criteria (d_b/Delta > 1,5).

However, I still have doubts about how to calculate the scale length to later use the Niceno model (NicenoKEqn in OpenFOAM). Could you guide me?!

[Severus]

Hello,
I wouldn’t recommend you continuing with the first approach I mentioned for the same reasons I have given in my first response.

Now, coming back to what you exactly want, you mention using KEpsilon model and your question is if you can use the expression for length scale. Firstly, since you are performing Euler-Euler RANS, you have to use a model that includes bubble induced turbulence (BIT). The inclusion of BIT is important to get a more accurate length scale, as you want to model the eddies as accurately as possible.

I did some searching in the source guide and for KEpsilon for multiphase, you can see the following options,
https://cpp.openfoam.org/v7/mixtureK...8H_source.html
https://cpp.openfoam.org/v7/LaheyKEp...8H_source.html

As you can see in the description, both of them include BIT. You can also read the references to see the expression used for the length scale which is the same as what you intend to use (just multiplied with Cmu coefficient).

Take a look at this function object (turbulenceFields):
https://www.openfoam.com/documentati...nceFields.html
https://www.openfoam.com/documentati...8H_source.html
See the description too. This can output the turbulent quantities you need.

Hope this helps
Thanks

[gu1]

Originally Posted by Severus

Take a look at this function object (turbulenceFields):
https://www.openfoam.com/documentati...nceFields.html
https://www.openfoam.com/documentati...8H_source.html
See the description too. This can output the turbulent quantities you need.

Hi,

Many thanks for the reply. I apologize for taking so long to respond to your comments.

I tried this function, very useful, however, for the multiphaseEulerFoam it does not work.

I'm even trying to get the wallShearStress from my study.
If you can help me with this...

Thanks

[Severus]

Hello,
If it doesn't work for multiphaseEulerFoam, the best way is to try to code it inside the solver by making appropriate modifications.

From the code I see that it should be possible to implement. You can try it for v9.
https://www.openfoam.com/documentati...8C_source.html
(Lines 88 to 104)

Good luck!

[gu1]

Originally Posted by Severus

From the code I see that it should be possible to implement. You can try it for v9.
https://www.openfoam.com/documentati...8C_source.html
(Lines 88 to 104)

Thank you very much.

I believe integral length scale is important only for RANS, correct?