Hi, i am working with LES of fully developed turbulent pipe flow problem. I am using periodic boundary conditions. my domain size is 5D*D. Re_tau is 390 and Re_bulk is 5600. I am ending up with laminar flow, even after giving initial perturbation in the flow field. Can you please tell me the better methods for introducing initial perturbation in to the initial flow field. please tell me if there is any better approach.

thanks in advance. by rajani

Hi Rajani,

for an approach with initially reduced viscosity or gradually Re_tau reduction see:

Eggels J.G. M. "Direct and Large eddy simulation of turbulent flow in cylindrical pipe geometry" PhD thesis Delft University of technoloy

Eggels J. G. M. et al "Fully developed turbulent pipe flow: a comparison between direct numerical simulation and experiment" J. Fluid Mech. Vol. 268 pp. 175-209, (1994)

Dear Rajani,

I sincerely believe that it is not the initial condition that is the problem in your case. Although random perturbed field is not a very "scientific" way of setting up a turbulent flow, as long you evolve the flow enough long time it will inherently become turbulent, e.g. it will become

- 3 dimensional - random, - vortical, - dispersive, - diffusive, - etc.

What is of bigger importance here is the accuracy of your numerical scheme and the subgrid stress (SGS) model you are using. Smagorinsky model may be to dissipative slowing down or even inhibiting transition. Try a dynamic model (Germano, Lilly, scale similarity, etc.) or the "selective" Smagorinsky model by Sagaut. These models behave better in your transitional/turbulent flow situation. The numerical scheme should be at least second order (in this case, a central scheme is recommended instead of a second order upwind scheme) accuracy. Higher order (compact) schemes are definitely recommended. But second order (central)schemes work for "engineering" LES problems!

Hope these will help you!

Doru

Dear Doru,

You said: " a central scheme is recommended instead of a second order upwind scheme ",

Can you tell me the reason why upwind scheme is not preferable ? What do you think about Roe, Osher, Van Leer's Riemamn solver + MUSCL scheme for LES ?

Regards

Li Yang

Hello Li,

About the suitability of the second order upwind schemes for LES as compared with the central second order scheme you can check the site at CTR Stanford. They investigated the matter and draw the conclusion that second order central schemes (end "enough" resolution I should add) are better that second (and even higher) order upwind schemes, when LES is in concern. A comment for these second order upwind schemes: if you look in the proceedings of ICCFD1 held in Kyoto (2000) you will find an article by an Italian professor who investigated the suitability of state of the art FV schemes for wall bounded flows. (Sorry I don't have the proceedings with me and I don't remember his name or the title of the article). His conclusion is … "shocking" in a way: from all the classical FV schemes, it is only the flux difference splitting by Roe that gives reliable solutions in all the cases he investigated (laminar viscous flows, so he does not include the "inaccuracies" of the turbulence modeling in the results). Interesting isn't it?

It was previously known that the flux vector splitting scheme by Van Leer while gives nice smooth and accurate solutions for transonic and supersonic INVISCID flows with shocks, it is too dissipative and more to be applied for viscous wall bounded flows.

About the Roe scheme: If you modify the flux formula like :

F=(Fr+Fl)/2+eps*|A|(Ul-Ur)/2

And you use eps=0.1-0.2 instead of 1 you can still use this scheme for LES (T. Bui from NASA Langley did this to study the turbulent flow in a pipe and he got nice results).

I strongly suggest you to look into Multidimensional Upwind Residual Distribution schemes, these are more accurate, have a compact stencil, easy to design a parallel algorithm, etc. as compared with classical FV schemes. If you want further details, I can send you some references.

Hope these helps,

Doru

Please read "..not to be applied .." instead of ".. more to be applied .." in the sentence about the VanLeer FV splitting scheme !

The upwinding will definitely lead to dissipation. This may be the major problem in LES. Too much dissipation will mash the subgrid model. Several papers have addressed this problem, e.g. JCP, V153, p273, 2001.

Dear Doru,

Thank you very much indeed.

I have got a multiblock NS code based on Roe scheme. I am quite interested in the Multidimensional Upwind Residual Distribution schemes if they can be good for LES. Will it be very difficult to implemente such kind of schemes in a code based on Roe's scheme? I would really appreciate it, if you could provide me some references and give me some advice.

Kind regards

Li

Dear Li,

You can still use your code for LES, provided that you use the modification I sugested you for the flux computation ( with the Roe FDS scheme) :

F=(F_l+F_r)/2+eps|A|(U_l-U_r)/2 where eps=0.1-0.2 instead of 1 (or even smaller depending on your grid resolution, e.g. the bigger resolution->the smaller you have to take eps). Multidimensional Upwind RD schemes work on simplicials (triangles in 2D and thets in 3D), thus are not that easy to implement in your code.

A good reference for the new compact 3rd-order Multidimensional Upwind Residual Distribution schemes, please check: AIAA-2001-2547 "A Parallel Multidimensional Upwind Algorithm for LES", 15th AIAA CFD conference June 2001, Anaheim.

Sincerely, Doru

Dear Doru,

You are right. That is probably an easier way. Thank you very much indeed.

Best wishes

Li

Hi capi, thank you very much for your help. i have refered the paper. it seams my code is working now. once again thank you. by rajani

Dear Duro,

if I am not mistaken, the original Roe scheme is only of first order. With MUSCL interpolation, the scheme becomes third order. I wonder what is the accuracy will be after the scheme is modified as following: F=(F_l+F_r)/2+eps|A|(U_l-U_r)/2

where eps=0.03-0.05. I also would like to know what the physical meaning of this expression is. I am alos worrying if it would be too expensive to do LES if I want to simulate a transonic flow around a wing section of about one million grid points.

Regards

Li

Hello Li,

Your scheme order will be 2nd order, simply because by doing MUSCL you consider that the solution has a linear variation over the cell(s). The resulting scheme I sugested you is an upwind biased scheme (not an upwind anymore).

If you want to do LES with shock-waves, things are much more complicated then that! You have to use a limitter which will add extra dissipation in the shock region while keeping a reduced dissipation in the "smooth" regions! The usual shock detector used in the Jameson scheme(central scheme+2nd and 4th order Artificial Dissipation terms) works.

Try it!

Best regards, Doru

Dear Doru,

Thank you very much indeed,

>> The resulting scheme I sugested you is an upwind biased scheme (not an upwind anymore).

Can I say that the scheme actaully becomes a second order central difference scheme F=(F_l+F_r)/2 plus the artificial viscosity eps|A|(U_l-U_r)/2. Therefore, the difference between Jameson's scheme and this modified Roe's scheme lies in the different artificial viscosity expressions used.

In that sense, it means that the scheme will not be able to handle supersonic flow (for example, Mach number > 2) very well, which is a drawback of Jameson's scheme.

I would very much appreciate it, if you could let me know your opinion on this issue.

Kind regards

Li