help with wall functions
 

hello.
I am trying to implement k-e model with wall functions. Model equations are solved alright but I am having difficulty how to go on with wall functions.
Versteeg (eq.3.39) gives equations for u+, k and e to be used close to walls when 30 < y+ < 300. My questions are
a) Do I apply k & e close to wall as Dirichlet bc with those formulas?
b) Do I apply the log-law for all cells which fall in the range of the log law ? what if a boundary cell is equally adjacent to two walls ? Or i use unstructured mesh.
c) Are wall functions necessary for the k-e model ? Because right now it can solve some problems with relatively low Re number but diverges when i go over 10^4. If i avoid solving k&e it goes much more higher, but obviously to the wrong solution.
Thanks in advance for any hints
Daniel

it should be noted that turbilence models like k-e are devided into two groups from view point of near wall treatment: 1-high reynolds numbers 2-low raynolds number models. when you are concerned will high reynolds ones you should make these modifications(i.e. application of wall function) only to wall adjacent cells. not all the cells lying in range of 30 to 300. in this case the width of wall adjacent cell will be selected such that its y+ lies in the range named above.
generally speaking, concept of y+ is only meaningful in wall adjacent cells.
on the other hand, low reynolds models does not need any wall function.but cells width in near wall region should selected such that Y+ falls well below 10 for adjacent mesh and this increases number of meshes and consequently the run time.
then firstly, you should select your turbulence model.
if you use standard k-e model, be informed that this model is a high reynolds number one.
you can refer to UMIST university .pdf files about wall functions and their application. it can be easily found in internet.

Thank you very much for taking the time to reply.
I wrongly thought that for standard k-e ( high Re model), I could avoid
using wall functions as long as i use very fine mesh near walls.
But I now understand the model coefficients are correct only with the use of
wall functions.
thanks again. I am on to googling the UMIST publications.

Wall functions Turbulence Model
 

Hei,

to answer you question a):
1) Explicit Time Discretization:
-k: add the whole wall function term to the source term
-e: Dirichlet BC

1) Implicit Time Discretization:
-k: split the wall function term, the part which includes k goes to the ap coefficient, the rest into the source term
-e: either Dirichlet BC or add to the ap coefficient and multiply the wall function term with and add it to the source term

Cheers
Hans

Dear Hans,
Thank you for the hint. I have found a detailed discussion of wall boundary condition treatment in a late chapter of versteeg, basically same as what you mentioned here. One minor doubt i have is about the use of 10^30 which is larger than (1 / Machine epsilon) ? I will use 10 ^ 15 instead to avoid truncation errors.
regards,

Looks like 10^30 is ok as the largest double precision number is 10 ^ 307.
Anyway now everything is working fine except that I do not have something to compare my results to.
I took the source term linearization for the k-e model from here http://staffweb.cms.gre.ac.uk/~ct02/research/thesis/node54.html#eq4:24
phoenics's I suppose. I am using the third one. I was able to linearize the k-source term using Picard's method and get same results when the Cd = 2.
I suppose this parameter is tunable, am I correct ?
But using the same method for the epsilon source term linearization gives me something completely different.
My result looks more like the one given for method 2 ?? Can anyone enlighten me on how the linearization is done ?

regards,

Dear Mr Daniel,

I have cfd code for laminar flow (channel flow) with colocated grid arrangement. I have implemented k epsilon turbulence model in to this. Now if i see my velocity profile (coming as expected) i found that it is more peakier than that of a laminar profile. Also the pressure at the inlet increasing like anything.

My boundary conditions : Velocity inlet, pressure outlet and wall (top and bottom).

And I have followed the book versteeg and malalasekara. Also I have compared my laminar flow results with FLUENT code and found it is matching but i am getting this peculiar problem for turbulent flow. Please tell me your valuable suggestion.

thanks in advance

jyothish