Wall shear stress in channel flow
 

Dear All,

I am solving a 2D channel flow of wind in simpleFoam (kEpsilon model). I use a double-graded domain (Domain.jpg). There is a uniform wind flow of 1.53 m/s in the x direction.

I am currently doing a mesh refinement study, with number of cells in both directions doubling with each simulation (see Results.jpg). In this figure, the velocity profile at the centre of the channel in the z direction and the wall shear stress profile at the bottom wall of the channel (z=0) are shown. As you can see, with increasing mesh refinement, the wall shear stress is clearly not overlapping. The wall shear stress has been calculated using the magwallShearStress utility.

The residuals have been set very low (10e-15) and have converged, so that is not the issue. The coefficients used are Cmu=0.09, C1=1.44, C2=1.92 and SigmaEps=1.3. kqRWallFunction and epsilonWallFunction are used. The yplus values at the bottom wall calculated using the yPlusRAS utlity are between 0-3 for the four cases.

In the future, the bottom wall will be heated and so the heat flux at the bottom wall, and thereby the wall shear stress there, is of the utmost importance. Can anyone tell me why the wall shear stresses are not overlapping even though the number of cells are most probably more than adequate for resolving accurately a 2D channel flow?

I have also attached the entire case (zip and tar formats) for easy reference.

Thank you in advance for your time.

Not sure about your case, but the wall shear stress for me is usually a "value", not a "function".

So I dont know what you have plotted on the right side of your chart. When it is the shear stress, you can see that the behaviour near the wall in your 3 finest meshes is nearly the same. This could be a point, that thoses meshes are fine enough to resolve the wall shear stress, while the coarse one (red) shows another trend which correspsonds to the velocity profile of the red curve.

I also cant find the OpenFOAM utility magwallshearstress on GitHub. And I am unsure about the wall functions. You have low y+ values (shouldnt it be z+?). Why do you also use a wall function? Maybe you can decrease z+ to 1 and neglect the wall functions? What turbulence model do you use? (people like me dont wanna download zip files to look in cases, so just write them in starting post next time ;))

What you could do:
clarify what kind of stress is plotted. Calculate the wall shear stress by this: http://www.cfd-online.com/Wiki/Wall_shear_stress
Plot the velocity profile normalized with the wall shear stress velocity in a log chart. That is usually a good way to analyse the velocity profile because the "important" areas are resolved better.

Just my thoughts.

Dear Hans,

Thank you for your reply. The graph that confused you is the wall shear stress at the different cells starting from the inlet all the way to the outlet. Of course, for a fully developed flow, the wall shear stress is a constant value.

I apologize for the typo earlier. The utlity that I used is wallShearStress. As mentioned in the opening line of the post, I used a kEpsilon turbulence model. I was also thinking along the lines of switching off the wall functions since the z+ value is close to 1. Thank you for your suggestion.