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Old   December 15, 2006, 02:46
Default Model constants in k-epsilon model
Sachin T
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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,


Old   December 15, 2006, 11:38
Default Re: Model constants in k-epsilon model
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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. 23232332, 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


Old   December 17, 2006, 17:56
Default Re: Model constants in k-epsilon model
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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
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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 = '&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 ' &epsilon;

e) diffusion-dissipation equilibrium: 0 = D ' &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; t'n (or &prop; x'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 ..



Old   December 18, 2006, 07:50
Default Re: Model constants in k-epsilon model
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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
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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.


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Old   December 20, 2006, 03:11
Default Re: Model constants in k-epsilon model
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Dear ZubenUbi,

My email is:

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

Old   December 28, 2006, 10:45
Default Re: Model constants in k-epsilon model
sachin T
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Dear ZubenUbi,

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


Old   January 17, 2010, 11:15
Default model constants in standard k-epsilon model
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Yogini Patel
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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

Thank you!!

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Old   January 18, 2010, 19:32
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Hi everybody,

would it be possible that anybody could send me the file concerning the model constants, too ( ?

Would be great!

Thank you!
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Old   February 18, 2010, 08:39
Default model constants in standard k-epsilon model
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Vitor Manuel M. G. da Costa Gomes
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Dear ZubenUbi

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

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Old   March 15, 2011, 15:59
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Dear ZubenUbi

Sorry to bother you, but can I also have a copy of this PDF.
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Old   June 23, 2011, 19:37
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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

Thank you.

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Old   March 19, 2012, 08:39
Default Pdf copy
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Goutam Saha
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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

Thank you.

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Old   November 21, 2014, 09:30
Default Pdf from Mr ZubenUbi
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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

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Old   December 4, 2014, 09:13
Qureshi M Z I
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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,


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Old   July 18, 2016, 14:35
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Does anyone have the document of Zuben Ubi you could send me ?

A lot of thanks
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