[syavash]

Dear Foamers,

I have been studying the spatial growth of ZPG boundary-layer using OpenFOAM LES. I have performed some simulations but the results are not very satisfactory.
I wanted to share my results and my experience, hopefully someone will be interested and provide some hints to improve the results.
In the first figure, a snapshot of the developing boundary-layer is observed (instantaneous x-velocity).
I have used the Lund Recycling method, shared by Joachim on the forum:


Lund Recycled Method for LES (flat plate)


As for boundary conditions, for "U" I have applied inletOutlet and advective conditions at the top and outlet boundaries, respectively. For "p" I have applied a zeroGradient at both the inlet and outlet boundaries, as well as at the solid wall. At the top boundary, I have applied an outletInlet condition.
I have used the dynamic version of Smagorinsky SGS model developed by Alberto Passalacqua:


Improved implementation of dynamic Smagorinsky


In the second figure, I have provided the evolution of friction velocity obtained through two distinct solvers: native pisoFoam and an explicit fractional-step method RK4. The friction velocity at the ref. station (shown by dash-line) is 0.0478 and 0.049 for piso and RK4, respectively. These values are overpredictions when compared to DNS at a similar Reynolds Number based on momentum thickness.

piso solver: Re_theta = 1150 u_tau = 0.0478
RK4 solver: Re_theta = 1190 u_tau = 0.049
DNS (Jimenez et al, JFM 2010): Re_theta = 1100 u_tau = 0.0462

The domain length is 26,5,1.3038 in streamwise, wall-normal, and spanwise directions, respectively.
As it is evident from the table above, the problem is the overprediction of friction velocity (u_tau). Also, shape of the mean velocity profile is different than DNS for both solvers. Of course, this correlates with the overpredicted friction velocity.
I have tried to consider reasonable values for grid spacing as follows:
dx+=50
dy+=1.0 with a growth ratio of 1.057
dz+=15
Now, to improve the results I have tried a combination of different stuff. Most notably was:
1-Double the size of spanwise domain, while keeping the dz+ the same--> no real improvement achieved
2-Double the size of spanwise domain with the same number of grid point (dz+=30)-->I have got better results. The friction velocity has reduced, but still away from DNS.
3-Double the number of streamwise grid points (dx+=25)--> Virtually the same results as step 2, i.e. an improvement was achieved and the friction velocity has reduced.
According to my examination, the friction velocity (thus mean velocity profile) shows a dependency on the grid aspect ratio of dx/dz. This finding however needs to be confirmed by some other observations.
Now, I would like to ask other people to share their opinions on this subject. Hopefully, a framework could be established based on which satisfactory boundary-layer LES will be carried out.
Regards,
Syavash

[syavash]

Well, I wanted to provide some update.


In the first figure attached, the normalized velocity profile at the same station marked by the dash-line in the original post (delta=0.84) is presented.

Also, the normalized velocity profile is compared with two DNS studies in similar Reynolds numbers. It can be seen that the profiles substantially deviates from DNS in the log-law region.


In the second figure attached, the same diagram is presented but for the refined mesh-in streamwise direction-with dx+=25. It can be observed that the results has significantly improved. I have not got the results for RK4 yet, so at the moment I can only upload the results for native pisoFoam.


I hope these results will provide some hints for people who do LES using OpenFOAM.


Regards,
Syavash

[syavash]

To provide a closure, I have attached the local mean velocity profile, as well as RMS of velocity fluctuations.

I have only provided the results of pisoFoam, as RK4 explicit solver has shown slight difference with data of DNS.

Regards,
Syavash

[luofq_SYSU]

Thank you for shearing. Could you please introduce how to extract momentum thickness in OpenFOAM postProcessing?

[syavash]

Originally Posted by luofq_SYSU

Thank you for shearing. Could you please introduce how to extract momentum thickness in OpenFOAM postProcessing?

This was cumbersome task, but before I developed a tool for it!
You may find it on my GitHub repository TurbLab.

Regards

[luofq_SYSU]

Originally Posted by syavash

This was cumbersome task, but before I developed a tool for it!
You may find it on my GitHub repository TurbLab.

Regards

Thank you for your work. I found it.
https://github.com/syavash20/TurbLab...egralThickness

Best Regards

[luofq_SYSU]

Originally Posted by luofq_SYSU

Thank you for your work. I found it.
https://github.com/syavash20/TurbLab...egralThickness

Best Regards

Dear Ehsan,

I have compiled your code "integralThickness" in OF10, and it is functioning properly. However, I have two further questions that I'd like to inquire with you about.

1. Does the input field "Uvec" means "UMean/mag(U_0)"?

2. The theta result in my case has presented a negative value, which is most likely due to the fact that (1-Ux/U_0) is negative above the boundary layer.
Therefore, what is the upper limit Y of the integration? may be the wall distance when U_x=U_0?

Best regards.

[syavash]

Originally Posted by luofq_SYSU

Dear Ehsan,

I have compiled your code "integralThickness" in OF10, and it is functioning properly. However, I have two further questions that I'd like to inquire with you about.

1. Does the input field "Uvec" means "UMean/mag(U_0)"?

2. The theta result in my case has presented a negative value, which is most likely due to the fact that (1-Ux/U_0) is negative above the boundary layer.
Therefore, what is the upper limit Y of the integration? may be the wall distance when U_x=U_0?

Best regards.

Sorry for the late reply,

Glad to know that the code is compiled on newer versions!
In response to your questions,

1. Uvec is the span-wise averaged of UMean. If you have a long-enough time-averaged UMean, you can use it instead.

2. Note that both free-stream velocity and the integration height are hard-coded. The former is 1 and the latter was something like 2.xx! I guess this is why you are getting negative values. You may modify them as you see fit.

Kind regards
syavash