Hi everyone, I am a new one in les. I have a problem in the wall boundary condition treatment. I read several papers on this topic, but no detail information, it says that I should use the wall function. I want to know how to use the wall function.

1. In my case, turbulent flow around square cylinder, wall function suggested by Werner and Wengle is used. (Large-eddy simulation of turbulent flow over and around a cube in a plate channel, Proceedings of 8th symposium on turbulent shear flows, 155-168).

2. The results are reasonable. Time averaged drag, lift coefficients, Strouhal number agree well with experimental data.

3. Phase averaged flow fields are also match well with experimental data.

4. In my calculation, Standard Smagorinsky model is used.

5. The problem of applying Werner&Wengle's wall treatment : Wall boundary condition is described based on the time averaged terms. However, in LES, filtered N-S equations are different from the time averaged viewpoint. So the unknown terms in LES can not be expressed by the time-averaged terms.

6. Grid Scale (or filtered) terms are necessary to be applied in Wall boundary condition of LES.

7. Anyway, there are some minor problems in my LES technique, the overall results are very good.

I'm really appreciate you so much for you to provide me such useful information. But there are still some questions that I have to ask you.

I have not found the original paper. (Large-eddy simulation of turbulent flow over and around a cube in a plate channel, Proceedings of 8th symposium on turbulent shear flows, 155-168). I only found a similar reference on which the Werner-Wengle wall function was used. It says "Tub=2*Mu*|Up|/dy",here, Tub is the stress on the wall, Mu is the viscosity coefficient, Up is the velocity on the first grid off the wall and the dy is the distance. The problems are:

[1] The wall stress has its direction including Txz,Tyz. Which direction is it(Tub) stand for? In my understand, they take the same law in the two direction. That is there is Tvb in another direction. Is it right?

[2]In the filtered Eq, the unknowns are the Reynold stress. Are they replaced by the Tub and Tvb on the wall?

1. Werner & Wengle's wall function is a kind of two layer model. It uses linear and power law according to the distance from the wall.

2.[1] The wall stress has its direction including Txz,Tyz. Which direction is it(Tub) stand for? In my understand, they take the same law in the two direction. That is there is Tvb in another direction. Is it right?

Yes. you're right.

3. [2]In the filtered Eq, the unknowns are the Reynold stress. Are they replaced by the Tub and Tvb on the wall?

I'd like to explain based on my calculation. I use non-dimensionalized filtered N-S equations and standard Smagorinsky model. After some algebraic manipulations, the Rey. stress terms (= tau_ij,j ) and diffusion terms are combined and expressed as (1/Re+nu_turb)(u_i,j +u_j,i),j = T_ij,j

T_ij=(1/Re+nu_turb)(u_i,j +u_j,i) is considered to be the stress terms generated from turbulent flow. 1/Re is from the fluid itself and nu_turb is from turbulent flow itself.

Near wall, wall shear stresses (Tub and Tvb) obtained from wall function can be used as the value of (1/Re+nu_turb)(u_i,j +u_j,i)

Here, u is the filtered velocity.

Kim.

Hi, Jongdae,

Thangk you again for you help. I'll try it.

I want simulate a example in the paper "AIAA j. Vol34. No.6 1996,PP1111-1119" wroten by Elias Balaras and Carlo Benocci. There is a problem. That is Ret, the Reynolds numbers based on the friction velocity Ut. they simulate an example of plane channel flow and the Ret=200-2000. when given this Ret, how does the initial and the inlet boundary define ? Moreover, before we get the flow field, we don't know the friction velocity.

^_^£¬i'm a beginer too.<large eddy simulation for incompressible flows>Pierre Sagaut edit.i use no-slip conditions at wall.

Hi,

First of all about the BC (if I understood correctly your question) : The plane channel flow test case is given for periodic boundary conditions in the x and z directions. So you do not need a specific BC for inlet.

But you need to introduce a source term to conserve the flow rate and balance the pressure drop due to the walls, otherwise the flow will go to zero !

About the Re_tau :

Here I don't understand your question ! You talk about Ret=200-2000 : is the turbulent reynolds number equal to 200 ?

Anyways, if U want to reproduce a channel flow simulation, you need to do it at the same turbulent reynolds number as it was done. But you need to know the flow rate (and therefore the flow rate or bulk velocity) corresponding to that Re_tau, right ?

And here comes into action the Dean Correlations ! They say that for an incompressible flow you have the following correlation :

Re_tau = 0.123 (Re_c)**(7/8)

Where Re_tau is the turbulent Reynolds number and Re_c is the Re based on the initial Poiseuille profile in the Channel flow with the velocity at the centerline, or related to :

Re_c = 1.5*Re_b where this formula is more general since Re_b is the bulk Reynolds number and it's always verified either for laminar or turbulent flows.

Re_c = U_centerline*h/nu Re_b = U_b*h/nu Re_tau = U_tau*h/nu

U_b = 2/3*U_c

For example, if you want to reproduce a simulation that gave Re_tau=180, you need a Re_c = 4145, and Re_b = 6218.

Now if your viscosity nu is 1e-5 and the half-height of the channel flow is 1, then the bulk velocity is : U_b=6.218e-2 m/s. Now you now what should be your initial condition and the flow rate you need to conserve along the simulation in order to obtain a Re_tau equal to 180.

Hope it helps.

Alexandre Chatelain. PhD Student, LES of Heat Transfer. CEA Grenoble - LEGI/MoST Team FRANCE.

Hi, Alexandre,

Thank you so much. However I still have some question.

In Elias Balaras' paper(AIAA j. Vol34. No.6 1996,PP1111-1119), The friction Reynolds number is Re_tau=U_tau*h/nu, Here U_tau is friction veolicity. Do you think the friction Reynolds number is the turbulent reynolds number? If yes, it is ok. when we know Re_tau, we can know Re_c ,Re_bother. If no, what should i do?

Thank you again.

Yes of course : the turbulent Reynolds number is strictly the same as the friction Reynolds number ! It's just a matter of how you call it.

So everything is fine then ! Regards.

Hi Jongdae Kim and Alexandre , I got the figure. Thank you so much for you help. Regards.