open TELEMAC-MASCARET The mathematically superior suite of solvers

Thanks for your input!

I am only interested to compute it in order to have an idea of the turbulence levels in specific areas of my model (eg. downstream of piles). I don't need to calibrate anything against measurements. So which equation I use is therefore not that important (although the difference between the two estimations is approx. 20%) but it would be good to know which one fits the best...

With sqrt(k)/U I get rather high values directly downstream of my piles (approx 0,3-0,6 up to 1,0 at the very maximum) so maybe sqrt(2/3.k)/U is more in line with classical values found in the litterature.

I don't have a lot of experience with k-epsilon, but I think that this concept of turbulence intensity can be really useful in order to prescribe boundary conditions for k-epsilon. It sounds attractive to set k and epsilon based on a given r0 corresponding to the expected turbulence level at the model entrance (to be tuned according to how the actual turbulence develops downstream, of course). But I might be wrong!

Best regards
PL

Hello PL,

"...it would be good to know which one fits the best..."
since the k-epsilon model assumes isotropic turbulence, u'=v'=w', with k=0.5*(u'^2+v'^2+w'^2) and the magnitude of the turbulent intensity TI is defined as sqrt(1/3*(u'^2+v'^2+w'^2)) you get TI=sqrt(2/3*k), therefore I recommend to use this relation. Turbulent intensities of nearly 1 means that the standard deviation of the flow velocities or to say the mean value of the velocity fluctuations is nearly equal to the mean flow velocity, and this is really high.

Actually the boundary conditions implemented in Telemac perform good since they reflect the turbulence quantities distributions in free surface flow. We compared them also with other relations from Nezu and Nakagawa (1993) and got more less the same needed length in order to reach developed turbulence. Using these relations instead of specifying KMIN and EMIN, one can shorten a little bit the needed length, but be aware that the required length still can be amazing. Furthermore the needed length is especially a function of the used / assumed velocity profile at the inflow boundary condition.

Best regards,
Clemens

Hello Clemens,

OK, then it makes sense that sqrt(k)/U is valid in 2D while sqrt(2/3.k)/U is valid in 3D since the RMS of the turbulence intensity magnitude is sqrt(1/2*(u'^2+v'^2)) in 2D while it is sqrt(1/3*(u'^2+v'^2+w'^2)) in 3D, as you wrote. I am running a 2D case at the moment.

Regarding the boundary conditions, my comment was just to point that one can hint KMIN and EMIN by assuming a given TI at the model entrance. TI can be estimated roughly using tables based on assumed flow conditions, a bit in a similar way than friction coefficients. Before comparing with how does the turbulence evolve inside the model.

Best regards
PL

Hi PL,

ah, 2D simulations and yes. The simulated depth-averaged TKE doesn't necessarly reflect the post processed mean value coming from a 3D calculation and can be e.g. much higher. I think maybe due to the additional semi-empirical production terms appearing in the depth-averaged transport equations.. but everyone can correct me.

Before you step into it.. TEL2D uses the boundary conditions for k and epsilon as described in Jean-Michel Hervouet's book and other books, and they work good. In 2D you need almost no inflow length for turbulence development in comparison with 3D since in 2D you don't have the dependency on the assumed velocity profile over the depth (constant or logarithmic).

Best regards,
Clemens

Hi Clemens,

Thanks for your reply and comments.
In my current model I got turbulence intensities of approx. 0,15-0,20 in the mean channel for a relatively high discharge and a Strickler coefficient of 25. This is pretty much in line with the expected turbulence I would say. I got up to 0,5-0,8 directly downstream of piles in a pile raw that is located in the channel parallel to the main flow direction. Here again I found this being rather ok, maybe a bit high but not unrealistic as far as I can judge.

As a side note, I read from "The influence on soil erosion" (Gijs Hoffmans) that for uniform flows we can assume that sqrt(k) = 1,2 x u* (u* : friction velocity). By comparing k and u* in my model (u* correspond to a Strickler coefficient of 25) I saw that the coefficient was rather 1,7 than 1,2 (I don't have a true unifrom flow though, only stationary). This seems to go in line with your comment on a higher k in 2D than 3D? Just a guess.

Interesting to play a bit with k-epsilon. I hope I can dig a bit more into it and in 3D in the future.

All the best,
PL