Secondary Flow in Square Duct
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Good day.
I'm running LES in a square duct case to test the effect of various inlet boundary treatment. The first thing I tried is the uniform inlet boundary. However, I can't get the correct secondary flow pattern. The parameter of the simulation: Geometry: Square duct, dimension 1.0x0.05x0.05m (aspect ratio 20) Inlet velocity: 0.2 m/s Reynolds number: 10,000 Simulation time: 20s (4 throughflow) Time step size: 1e4 s No. of grid cells: ~1 million Turbulence model: Smagorinsky SGS Solver: OpenFOAM (pisoFoam) After 20s simulation time, I tried to view the secondary flow by extracting velocity vectors from the cross section and yields something like this: Attachment 15561 (actual grid density is higher) I'm not sure why the velocity vector direction is reverse direction from what I've seen in literature. Does anyone have suggestions? Your help is much appreciated, thank you. 
first, the inflow you used is not physical and is not congruent to an LES approach...
I suggest to set the case of a periodic inflow/outflow and run until an energy equilibrium is reached. Then you can store a timesequence of velocity on a plane and use it as inflow for your simulation second, have you used the dynamic Smagorinsky or the static one? If you use the static one you get probabily too much dissipation Third, hwo about the clustering of the grid near the wall? are you resolving th BL? 
Hi Denaro, thanks for taking the time to reply.
I'm using velocity inlet boundary condition because the objective of our study is to determine the performance of several turbulent velocity inlet boundary conditions designed for LES, including uniform velocity, random white noise and other attempts to impose a reasonable amount of fluctuations. If it is the effect of the unphysical inlet as you've explained, perhaps extending the duct length will help? I'm currently using static Smagorinsky model. In terms of grid clustering, I did set the grid up such that the ratio of the walladjacent grid size to the domain centre grid size is roughly 1:5 ratio. The y+ was reported to be about the value of 4.5 at maximum (for 95% of the duct length, excluding the inlet region). Velocity profile seems reasonable. Thanks again for your suggestions. I'm planning to rerun the simulation with Dynamic Smagorinsky, extended duct length and slightly increase the grid density and hope it yields something better. 
Some suggestions:
 use only the dynamic Smagorinsky model;  the grid must be refined furhter near walls, ensure that 2  3 point are within y+=1; 1 milion of cells for Re=10^4 is too coarse. Perhaps you could try at lower Re number..  Try also to run the simulation without any SGS model (so called LES nomodel) to see the effect of the model on the fluctuation  Control the total kinetic energy in time As you probably know, many studies were done to specify a suitable way for inlet conditions in LES. 
Thanks for the pointers.

Dear Lee,
Have you got the correct secondary flow pattern? Recently I am also doing the simulation of the square duct flow based on some anisotropic turbulent models and Reynolds stress turbulent models using OpenFoam. But I got the totally inverse secondary rotating direction to the experimental observation. If you have found the problems, could you please give me some hint about that. Thank you in advance. 
Hi Hellen,
Sorry to say that I haven't really worked out the problem at this time (I've been putting this matter in the background while I worked on some other things, since I couldn't resolve it). Just to describe some modifications I made and didn't really work, I changed the LES model to dynamic Smagorinsky, almost doubled the number of elements, and tried a periodic boundary condition. So far, still having the same issue. One thing I suspect is that the flow is still developing and therefore attempts to visualize the secondary flow will be affected by the development of the mean flow. Perhaps the simulation time needs to be longer (unfortunately our workstation is running something else, so I can't really try that). All the best in your attempts. Do tell me if you succeed! 
Hi, Lee.
Thank you very much for the reply and the information. I have not solved this problem either. These days, I have checked the code of the different turbulent models. It looks no problem on the equations. Besides, I have also tried the longer ducts but met the same problems. And now I begin to suspect that the processing of the wall boundary conditions at the corners in OpenFoam. But now I do not know how to modify it. Also DO tell me if you have some progress. Best regards 
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