Estimating Kolmogorov scale in LES

gotang · October 29, 2018, 11:08

Dear all,

I was hoping someone might be able to advise me on how best to estimate the Kolmogorov (length) scale in practical terms in CFX. I am running LES simulations using the WALE SGS, and am pretty new to running LES simulations at all.

So far, my best idea has been to follow the treatment from Pope's Turbulent Flows (section 13.3.3) which has:

$\epsilon \approx P_r = - \tau_{ij}^r \overline{S_{ij}}$

where:
$\tau_{ij}^r \equiv \tau_{ij}^R - \frac{2}{3}k_r \delta_{ij}$
$\tau_{ij}^R \equiv \overline{U_i U_j} - \overline{U_i}\; \overline{U_j}$
$k_r \equiv \frac{1}{2} \tau_{ii}^R \equiv \frac{1}{2} (\overline{U_i U_i} - \overline{U_i}\; \overline{U_i})$
$\overline{S_{ij}} \equiv \frac{1}{2}(\frac{\partial \overline{U_i}}{\partial x_j} + \frac{\partial \overline{U_j}}{\partial x_i})$

allowing $\epsilon$ to be calculated directly from the velocity/strain tensors (averaged appropriately and saved out as transient statistics), and then use $\eta \equiv (\frac{\nu^3}{\epsilon})^{\frac{1}{4}}$ to estimate the Kolmogorov length scale.

This doesn't seem like a particularly direct method to me though; is there a better/faster way of doing it?
Thanks in advance!

ghorrocks · October 29, 2018, 18:37

There are a whole bunch of ways to estimate epsilon, the Fluent manual lists a lot of them (http://jullio.pe.kr/fluent6.1/help/html/ug/node178.htm)

But note these estimates rely on knowledge of things like length scales, turbulent viscosity ratioes and so on, and these parameters can be difficult to determine as well. You will have to determine whether any of these approaches are going to work better than the direct (and more formally correct) method you describe.

gotang · November 1, 2018, 07:44

Brilliant - thanks! I'll have a look and see if any of those methods seem reasonable.

October 29, 2018, 11:08	Estimating Kolmogorov scale in LES	#1
gotang New Member Brian Join Date: Mar 2009 Posts: 17 Rep Power: 17	Dear all, I was hoping someone might be able to advise me on how best to estimate the Kolmogorov (length) scale in practical terms in CFX. I am running LES simulations using the WALE SGS, and am pretty new to running LES simulations at all. So far, my best idea has been to follow the treatment from Pope's Turbulent Flows (section 13.3.3) which has: $\epsilon \approx P_r = - \tau_{ij}^r \overline{S_{ij}}$ where: $\tau_{ij}^r \equiv \tau_{ij}^R - \frac{2}{3}k_r \delta_{ij}$ $\tau_{ij}^R \equiv \overline{U_i U_j} - \overline{U_i}\; \overline{U_j}$ $k_r \equiv \frac{1}{2} \tau_{ii}^R \equiv \frac{1}{2} (\overline{U_i U_i} - \overline{U_i}\; \overline{U_i})$ $\overline{S_{ij}} \equiv \frac{1}{2}(\frac{\partial \overline{U_i}}{\partial x_j} + \frac{\partial \overline{U_j}}{\partial x_i})$ allowing $\epsilon$ to be calculated directly from the velocity/strain tensors (averaged appropriately and saved out as transient statistics), and then use $\eta \equiv (\frac{\nu^3}{\epsilon})^{\frac{1}{4}}$ to estimate the Kolmogorov length scale. This doesn't seem like a particularly direct method to me though; is there a better/faster way of doing it? Thanks in advance!

October 29, 2018, 18:37		#2
ghorrocks Super Moderator Glenn Horrocks Join Date: Mar 2009 Location: Sydney, Australia Posts: 17,854 Rep Power: 144	There are a whole bunch of ways to estimate epsilon, the Fluent manual lists a lot of them (http://jullio.pe.kr/fluent6.1/help/html/ug/node178.htm) But note these estimates rely on knowledge of things like length scales, turbulent viscosity ratioes and so on, and these parameters can be difficult to determine as well. You will have to determine whether any of these approaches are going to work better than the direct (and more formally correct) method you describe. __________________ Note: I do not answer CFD questions by PM. CFD questions should be posted on the forum.

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November 1, 2018, 07:44		#3
gotang New Member Brian Join Date: Mar 2009 Posts: 17 Rep Power: 17	Brilliant - thanks! I'll have a look and see if any of those methods seem reasonable.