Integral length scale in DFMethod - ParsaTInflow

[JustinBonus]

Hi,

I hope that this message finds you very well.
I have a question regarding the integral length scale calculation in Digital filter method.
I run a test case (sort of similar to the homogeneous turbulence available in the tutorial), and plot the mean value, rms of velocity fluctuation on the center-line of the box.
I calculate the cross correlation function for a specified point on the inlet. The value of the correlation is equal to one when Ruu(0) and is equal to zero when Ruu(inf) (Which make sense).
Now my concern is: In the majority of experimental work, the value of the integral length scale is equal to the integration of the correlation function when its value is equal to zero. What I mean is: The correlation function should be integrated from Ruu(0) until Ruu(..) = 0.
In the simulation, I set the value of longitudinal integral length scale to 1 (mm), and by calculating the length scale with the above methodology, I end of getting a value of equal to 2 (mm).
I tested this for a couple of more models and the results are the same!

Please advice me on this issue.

Regards,
Parsa

• ParsaTInflow, February 23, 2021

[JustinBonus]

Hello Parsa

Sorry for the late reply. May I ask for more details regarding the your numerical simulations? Such as what are the boundary conditions for the lateral boundaries in your computational domain?

If your numerical simulations are similar to the homogeneous turbulent flow tutorial as you have mentioned. Please verify that if you have employed the periodic boundary conditions for the lateral boundaries. If this is the case, due to the situation that the generated synthetic turbulence is periodic in the lateral directions, you should integral the correlation functions from the point of interest (at which its length scales are computed) to a point that is half-wdith of the lateral dimension of the computation away from the former point. Otherwise, you will get length scales twice as large as the desired ones, which happens to be the issue you encounted. If this is not case, can you please share me with your case files and related results so that I investigate your issue? Thanks.

Again I'm sorry for this late reply and I hope that this can resolve your issue.

Best regards,
Jiawei

• jwan1, June 04, 2021