In the field of CFD I am a novice (I'm a researcher in experimental fluid-dynamics) and I apologize if mine is a trivial question. I would like to know how to determine inlet boundary conditions of turbulent dissipation (epsilon = e) using LDA experimental data on length scales, for a CFD code with a two equations k-e turbulence model applied to a duct flow (with square section preferably). I think I could use the relation e = C*(k^1.5)/l, where e is the turbulent viscous dissipation, C is a constant, K the turbulent kinetic energy (I can evaluate it) and l the integral length scale of the flow. The problem is how to quantify C, with regards, I suppose, to the experiment (i.e. duct flow) and to the turbulent Reynolds number ul/ni (in my case 238: when is it defined high?), where u is the rms flow velocity and ni the kinematic viscosity of the fluid (air). Other expressions for e, as in example those formulated in "Tennekes/Lumley A first course in turbulence" or in "McComb The physics of fluid turbulence", give very different results.

Thanks in advance for any suggestion.

Hi Massimiliano

Firstly, I can be considered a novice as I have only worked with CFD packages for less than a year. I apologise if my contribution does not help you solve your problem.

There are 2 ways to set inlet b.c.: 1. set hydraulic diameter and turbulence intensity if there is this option in the dialog box.

2. set k and e if you insist or tere is no other option.

Integral or turbulence length scale l is a physical quantity related to the size of the large eddies that contain the energy in turbulent flow. Since these eddies cannot be larger than the duct, the integral length scale is equal to 0.07L, by experimental result. The factor 0.07 is based on the max. value of the mixing length in a fully-developed turbulent pipe flow. L is usually denoted as the hydraulic diameter of te pipe.

I hope this will help. Good luck.

Lam

Your suggestion it's no doubt helpful for me, and I'm very grateful to you for it, but my primary need it's to know a relation between boundary conditions and experimental data specific for the case studied.

Hi Massimiliano

Sorry for not able to help out the last time. I hope that this may help.

Based on the past experience with the CFD package from Fluent, the epsilon is given as (C^0.75)*(k^1.5)/l; where C is an empirical constant, k for kinetic turbulence energy and l for turbulence length scale. For k-e model, all I know is that C is equal to 0.0845 by default. I am afraid that I cannot tell you more about C.

If you are running a CFD package, there may be other options like defining the hydraulic radius and the turbulence intensity; or kinetic turbulence energy and the characteristic length. If there is these options, then you may simplify that in the inlet b. c. dialog box.

As for the turbulent Re nos., the nos. you had showed, may be the cell Re nos.(if it is from the CFD simulated results). If that is true, then you may find that these nos. are calculated from cell-cell boundary. The question is rather hard to give you a proper answer, as I have not been analyzing these nos. at the time I was helping out in the research work. This is because it was not the main criteria at that time and also not what we are targetting during that period.

Hope there is something you can find in this email. Good luck again.

Hi Massimiliano,

you don't need do apologize, im working on cfd and turbulence sine one and half year and i have similar problems.

But now to your Problem: The formular you suggested is an emperical one. I think it isn't very accurate.

Perhaps there is an alternative way to get epsilon.

If your turbulence is decaying. (there is no shear or other source for production of turbulent kinetic energy) then you can say that

epsilon = - U * dK / dx

U is mean velocity.

see Journal of Fluid Mechanics 1996 vol 312 pp 373-407

especially page 380

Brown, Bilger

An experimental study of a reactive plume in grid

turbulence

greets

Roland

First of all, thank You very much for Your suggestion, which is useful for my study. Anyway my formula to calculate epsilon seems to be the same relation used in the cited article to get the integral length scale (l) with the constant C = 1. Thank You again and goodbye.