Flat Plate with tripping
 

Hello!

I am currently working on my masterthesis in Aeroacoustics of Airfoil. For now, I am running an LES Simulation(WALE Subgrid Scale model) of a flat plate with tripping. The results seem to be laminar before and after tripping (see fig, there is also a comparison between RANS and LES Simulation). I used a Tripping Geometry (triangle with base 0.2mm and heigth 0.4mm) at x=4cm (calculated from Rex = 1e5 for transition on flatplate). My surface mesh is NOT highly resolved. My y+ is ~1 and x+ ~100 (LES requires x+<= 40). I used a coarser surface mesh as students before me had good enough results with x+ ~100.

I am not sure how I have to go forward now. I have following ideas

1. Critical Reynolds number for flow over Flat Plate is around 5e5. That could be the problem.
2. Refine surface mesh and try.
3. I could not find any relavent literature for deciding on the trip geometry. If you could point me towards proper literature or suggest me a way to get the right geometry, I would be thankful!

My masterthesis duration is limited and it would save me some time if you could shed some light on where the problem could be and why the flow is not transitioning.

Thanks!

PS: I plotted Wall Shear Stress and not skin friction coefficient because I forgot to time average the skin friction coefficeint in my simulation, and only averaged wall shear stress. For theoretical values, I calculated the wall shear stress from the theoretical skin friction coefficient equation and used it for the plots.

yes, your grid is too coarse for such problem both for y+ and dx+... what about the dz+?
I doubt you can have enough computational power to solve on a reasonable grid for such problem. DO you have the good results by the person you cited?





I suggest to plot directly along Re_x axis, this way we can see the region of O(10^5).

Thank you for your reply. I am using Polyhedral meshing in star-ccm+, x+ and z+ have roughly the same value.

I have access to HPC. I will try refining the mesh and compare the solution.

I am aware my x+ is coarse. Is my y+ coarse, too? Isn't y+ of 1 near the wall not enough for LES? or does the tripping here call for more refined prism layers?

Yes, to resolve the BL you need a refined distribution of y+.
But how do you compute your y+ in your case? How do you evaluate u_tau?

Star-CCM+ has an in-built Wall y+ function. I tried going through the documentation to see how it is defined but it is not mentioned.

For prism layer meshing, I calculate my wall distance (first layer height) using flow velocity, dynamic viscosity, reference length and density, so that my y+ is a little less than 1

For plotting u+ vs y+ curves, I calculate y+ the following way.

From the simulation results, I get the value of wall shear stress(time averaged in case of LES) in the flow direction at the point on plate (this point is the point of intersection of the plate and the line along which I plot u+ and y+). Using this wall shear stress value, I calculate u_tau as,

=

and then y+ as

Ok, thus your y+ is strongly depending on the wall stress you compute but, of course, the wall stress you compute is strongly depending in your grid resolution.
You see why you need to check the consequences of a refinement along y.
Usually, such kind of problems require a DNS resolution in the normal to wall direction. In other words, you need to have several nodes having y+<1 to describe the viscous sublayer and computing accurately the wall stress.

Okay, that makes sense. I will refine the prism layers and compare the results. Thank you for your help! :D

A short update if anyone comes back to this thread again with the same issue.

I simulated a flat plate with a coarse LES mesh (x+~100, y+~1), and a fine LES mesh (x+~40, y<1) and the case with fine LES mesh does give a turbulent profile.

The simulation was done with an inlet, outlet, periodic boundary conditions on either side of the plate. The plate is rounded at the front (NOT sharp).