CFD Online Logo CFD Online URL
www.cfd-online.com
[Sponsors]
Home > Forums > General Forums > Main CFD Forum

Model constants in k-epsilon model

Register Blogs Members List Search Today's Posts Mark Forums Read

Like Tree6Likes
  • 1 Post By opaque
  • 2 Post By Opaque
  • 2 Post By ZubenUbi
  • 1 Post By Goutam

Closed Thread
 
LinkBack Thread Tools Search this Thread Display Modes
Old   December 15, 2006, 02:46
Default Model constants in k-epsilon model
  #1
Sachin T
Guest
 
Posts: n/a
Hi all,

I have a doubt regarding what is the criterion to select/adjust the model constants in standard k-epsilon model? Also, for which flow situations/geometries this model won't wor`k?

Thanks a lot,

Sachin
 

Old   December 15, 2006, 11:38
Default Re: Model constants in k-epsilon model
  #2
opaque
Guest
 
Posts: n/a
Dear Sachin,

Those model constants are not meant to play with.. They have been refined over years based on several flow conditions.. They are not perfect, but they satisfy a lot of consistency checks..

If you change one of them, you must revisit each one of them in order to satisfy a few physical contrains..

You should read a few turbulence modeling papers (usually the older ones) where this consistency checks are better explained. Newer papers assume the reader already knows about.

Some books:

Mathematical models of turbulence 1972 1972, B. E. Launder and D. B. Spalding. London: Academic Press Inc. (London) Limited. Paper, 169pp., #2.50

Turbulence Models and Their Application in Hydraulics. By W. RODI. International Association for Hydraulic Research, Delft, 1980. Paperback

Check early publications by Launder, Rodi, Leschiner, Rotta, Hanjalic, Speziale and if you want to go far in time.. Try the seminal paper by Harlow and Nakayama

Harlow, F.H., and P.I. Nakayama, "Turbulence Transport Equations," Phys. Fluids, Vol. 10, pp. 2323Ç2332, 1967.

I do not recall if the popular book by Wilcox discuss the origin of the constants..

Turbulence modelling for CFD. By D.C. Wilcox

good luck

Opaque
jiez likes this.
 

Old   December 17, 2006, 17:56
Default Re: Model constants in k-epsilon model
  #3
Purkmeisster
Guest
 
Posts: n/a
Dear opaque,

Could you briefly describe the consistency you talk about and the physical constrains.

I have toyed myself with the coefficients, for instance if I want more turbulence dissipation I would change the Ceps2 to a lower value. In this case what physical constrains would this violate?

Best Regards
 

Old   December 17, 2006, 23:55
Default Re: Model constants in k-epsilon model
  #4
Opaque
Guest
 
Posts: n/a
Dear Purkmeisster,

It has been quite a few years since I read those papers where the equation constraining Ce2, Ce1, and C_mu was discussed.. Usually in turbulence papers in the late 60's and early 70's..

However, the physical consistency of the model constants must satisfy a few simple turbulent flows. The following is taken from a presentation by Dr. K. Hanjalic (University of Delft)

"... The terms have the following physical meanings:

P - production of k (of turbulence!) due to mean-flow deformation (work of turbulent stresses associated with the mean flow deformation, or transfer of energy from the mean motion to turbulent fluctuations by the action of Reynolds stresses); (note that usually u&prime;iu&prime;j < 0 when &part;Ui/&part;xj > 0 so that in most flows P > 0).

&epsilon; - dissipation of k into heat by viscosity (Note &epsilon; > 0 always!)

D - diffusive transport of k (viscous, by fluctuating velocity and by fluctuating pressure,respectively)

...

a) energy decay in homogeneous turbulence -> U1 &part;k/dx1 = âˆ'&epsilon;

b) rapid distortion: Uj &part;k/dxj = P

c) convection-diffusion equilibrium (pure transport): Uj &part;k/dxj = D

d) local turbulence energy equilibrium: 0 = P âˆ' &epsilon;

e) diffusion-dissipation equilibrium: 0 = D âˆ' &epsilon;

a). In the absence of production (no mean-rate of strain, nor body force) in a homogeneous turbulent flows, the turbulence kinetic energy will freely decay and will ultimately be dissipated by viscosity. This is a natural, irreversible process. In the initial period, while the turbulence Reynolds number is still high, the process occurs by energy cascading towards smaller and smaller eddies, independent of viscosity. At a later stage when the Reynolds number becomes sufficiently small, the decay is governed by viscosity. Experiments show (confirmed by DNS) that both, the initial and final periods of decay can be expressed approximately by exponential law, k &prop; tâˆ'n (or &prop; xâˆ'n), with n &asymp; 1.2 in the initial period, and n &asymp; 2.5 in the final period.

This decay law can be used to determine the coefficient associated with the sink term of the scale-providing equation.

b) If a turbulent flow is subjected to a sudden mean-rate of strain, the dissipation can be neglected as compared with the imposed turbulence production term. Such is a flow subjected to a sudden contraction, free turbulent flow encountering a solid wall parallel or inclined to the flow direction, or a change in the wall topology, or a boundary layer flow over a stagnant wall encountering transversely moving wall, e.g. turbine rotor. Useful information for modelling and model validation (particularly of second-moment closures) can be obtained by analyzing the response of turbulence to rapid distortion, since the uncertainties in the model &epsilon; equation can be ignored.

c) At the free edge of a turbulent flow both production and dissipation can be neglected as compared with the convection and diffusion which are roughly in balance.

d) The local energy equilibrium prevails in the inner zone (logarithmic region) of a wall boundary layer at zero or weak pressure gradients. Both the convective and diffusive transport are here small in comparison with the production and dissipation which balance each other locally. This energy balance has a number of additional implications: the shear stress can be regarded as approximately constants, mean velocity obeys the semi-logarithmic law and the characteristic turbulence length scale increases linearly with the wall distance. All these features are exploited in tuning the the coefficients in a turbulence model.

e) This last case is encountered e.g. in the central zone of a fully developed pipe or channel flow, where the production can be neglected (weak or no mean rate of strain) and convection is zero by definition. Locally dissipated turbulence is supplied by diffusion from other regions in the flow. Although not crucial for most engineering application, satisfying these conditions is often a challenge for a turbulence model.

..."

Hope the information is somehow useful ..

Regards,

Opaque
jiez and sadjad.s like this.
 

Old   December 18, 2006, 07:50
Default Re: Model constants in k-epsilon model
  #5
Purkmeisster
Guest
 
Posts: n/a
Thank you for a very good answer (perhaps good for the wiki?).

May I continue to ask some follow up questions:

What I'm thinking of is an applied engineering point of view. That is, in this case, trying to fit the model to a range of experimental data. If a change in a model constant results in a better experimental fit, then what are the pitfalls of the approach, aside from that the constants found are might only be valid over the system investigated (and even only the range investigated)?

Best Regards
 

Old   December 18, 2006, 09:11
Default Re: Model constants in k-epsilon model
  #6
ZubenUbi
Guest
 
Posts: n/a
What you have to take care about is the interdependance of the constant values one to each other.

Suppose you start with the decay of homogeneus turbulence, then you can fix the value of c_eps2.

From the homogeneus shear flow, you can show that c_eps1 depends of c_nu and c_eps2.

c_nu is fix from the log law, as for sigma_eps. But sigma_eps also depends on c_nu,c_eps1, c_eps2 and the Karman constant.

Finally, sigma_k is given by the value of sigma_eps and c_eps2, so it depends on all the previous test case.

So, as an exemple, if you want to change c_eps2, without changing the behaviour of your model in the lag law region, then you also have to change all the other constant to keep the good behavior.

I can give you a PDF file - I have written but not finalized and which is in french - which explains all this relationship.

ZubenUbi

jiez and Ximena Delgadillo like this.
 

Old   December 20, 2006, 03:11
Default Re: Model constants in k-epsilon model
  #7
Purkmeisster
Guest
 
Posts: n/a
Dear ZubenUbi,

My email is: cfduser@gmail.com
 

Old   December 28, 2006, 10:29
Default Re: Model constants in k-epsilon model
  #8
sachin T
Guest
 
Posts: n/a
Thanks a lot for ur info.!!!
 

Old   December 28, 2006, 10:45
Default Re: Model constants in k-epsilon model
  #9
sachin T
Guest
 
Posts: n/a
Dear ZubenUbi,

Can I too get the file from you? Also, can I translate it readily into english? My email is: sachintarkunde@yahoo.com

 

Old   January 17, 2010, 11:15
Default model constants in standard k-epsilon model
  #10
New Member
 
Yogini Patel
Join Date: Jan 2010
Location: Finland
Posts: 15
Rep Power: 16
Yogini is on a distinguished road
Hello ZubenUbi,

I have some confusion regarding to the model constants in standard k-epsilon model.So can you give me the pdf file ?
My email is yogi.msu@gmail.com

Thank you!!

Yogini.
Yogini is offline  

Old   January 18, 2010, 19:32
Default
  #11
jet
New Member
 
Join Date: Nov 2009
Posts: 12
Rep Power: 16
jet is on a distinguished road
Hi everybody,

would it be possible that anybody could send me the file concerning the model constants, too (sekran@web.de) ?

Would be great!

Thank you!
jet is offline  

Old   February 18, 2010, 08:39
Default model constants in standard k-epsilon model
  #12
New Member
 
Vitor Manuel M. G. da Costa Gomes
Join Date: Feb 2010
Posts: 1
Rep Power: 0
il-Vec is on a distinguished road
Dear ZubenUbi

Can I too ask you for the said pdf? thanks in advance!

Regards
il-Vec is offline  

Old   March 15, 2011, 15:59
Default
  #13
New Member
 
James
Join Date: Mar 2011
Location: GTA Canada
Posts: 1
Rep Power: 0
aerospace_GT is on a distinguished road
Dear ZubenUbi

Sorry to bother you, but can I also have a copy of this PDF.
aerospace_GT is offline  

Old   June 23, 2011, 20:37
Default
  #14
Member
 
Join Date: Apr 2011
Posts: 55
Rep Power: 14
Ruonin is on a distinguished road
Dear ZubenUbi

Sorry to bother you, but can I also have a copy of this PDF.

I have been studying the K Epsilon model constants effect on pipe flow.

My email is rsilva@eq.uc.pt

Thank you.

Cheers.
Ruonin is offline  

Old   March 19, 2012, 08:39
Default Pdf copy
  #15
Senior Member
 
Goutam Saha
Join Date: Dec 2011
Location: UK
Posts: 131
Rep Power: 14
Goutam is on a distinguished road
Can I also have a copy of this PDF (English version).
I have been studying the K Epsilon model constants effect on pipe flow.

My Email is g.saha.1@research.gla.ac.uk

Thank you.

Cheers.
brunopvaneli likes this.
Goutam is offline  

Old   November 21, 2014, 09:30
Default Pdf from Mr ZubenUbi
  #16
New Member
 
Join Date: Nov 2014
Posts: 1
Rep Power: 0
Adjgs is on a distinguished road
Dear all,

Could anyone send me the file of Mr. ZubenUbi?, does not matter if it is in French.

Thank you very much in advance

(a.gonzalez.sanchez@gmail.com)
Adjgs is offline  

Old   December 4, 2014, 09:13
Default
  #17
Member
 
Qureshi M Z I
Join Date: Sep 2013
Posts: 79
Rep Power: 12
m zahid is on a distinguished road
hi

i am working on RANS modeling i have some confusion about constants. could anyone send me the file of Mr. ZubenUbi? english or in french,

Regars

email. mziqureshi@hotmail.com
m zahid is offline  

Old   July 18, 2016, 15:35
Default
  #18
New Member
 
Ximena Delgadillo
Join Date: Jul 2016
Posts: 2
Rep Power: 0
Ximena Delgadillo is on a distinguished road
Does anyone have the document of Zuben Ubi you could send me ?

A lot of thanks

ximena_ax20@hotmail.com
Ximena Delgadillo is offline  

Closed Thread

Thread Tools Search this Thread
Search this Thread:

Advanced Search
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are Off
Pingbacks are On
Refbacks are On


Similar Threads
Thread Thread Starter Forum Replies Last Post
about Subgrid-scale model impecca OpenFOAM Running, Solving & CFD 4 December 20, 2013 11:36
SimpleFoam k and epsilon bounded nedved OpenFOAM Running, Solving & CFD 1 November 25, 2008 21:21
selection of model constants sachin T CFD-Wiki 3 May 22, 2007 05:14
derivation of epsilon equation of k-epsilon model Ricardo Rezende Main CFD Forum 5 May 1, 2007 06:38
changing model constants in k-e turbulence model Sunil CFX 3 October 3, 2006 13:12


All times are GMT -4. The time now is 00:45.