Dear M. Kashif,

you deal with an interesting problem! However, FLUENT can not be the correct choice as long as you use it together with the k-eps option. k-eps is a semi-empirical turbulence model. It doesn't matter whether it is based on RNG or not. RNG even irritates here because it sounds as scientifically specially sound , because the math is complex, but k-eps as such is fundamentaly incorrect because although k = turbulent kinetic energy is fine, but eps is not fine, because it does NOT belong to the conserved mechanical variables.

Yes, many engineers still use k-eps in different formats (e.g. SST/RNG ...). I also used it in the Launder-Spalding version, e.g. recommended by Wolfgang Rodi, when I started with turbulence & mixing many years ago. There are meanwhile so many versions that every ambitious colleague tries to praise his own one, which is of course VERY good ("... we all are above average"  -

http://prairiehome.org/listen/podcast/).

The story is now that we have a real statistical theory of high-Re turbulence which is free of empirical parameters and even predicts the Karman constant as 1/SQRT(2*pi) = 0.399. You know that the international standard value is 0.40 and Princeton superpipe in 2014 gave: 0.40 +/- 0.02. The theory works nicely even for non-Newtonian fluids I recommend the colleagues in ANSYS/FLUENT to read and implement it.

I initially based it on Fokker-Planck equations (relative frequencies or, mathematically spoken: probabilities balanced in space and time) and learned later that it  has already found as so-called "b-omega" equations by Kolmogorov & Landau (1942). Mathematically it is identical with (today so-called) k-omega. Kolmogorov developed the idea also based on Fokker-Planck but by mathematicians it is called today "Kolmogorov forward equation" because K. developed some special mathematical features of Fokker-Planck equations. (Although once I saw in Moscow K. personally, I use further the name Fokker-Planck: they simply were earlier and because I am physicist ...).

Much later b-omega has practically been used as k-omega by Wilcox (https://secure45.securewebsession.com/dcwindustries.com/books/1928729088.htm), e.g. as a consultant for Boeing, but not fully understood because he still treats it as semi-empiricla case like k-eps. The detailed understanding started with Chapter 5 in the book MARINE TURBULENCE, Cambridge U. Press 2005, Chapter 5. Some points were still missing and have been completed for Re = \infty in one of the 2 attachments (Physica Scripta, Roy. Swed. Soc. 2013) and recently (attached) just for the case of finite Reynolds numbers in chinese industrial context, even for non-Newtonian fluids, on a  conference in Prague; also recently accepted for publication also in Physica Scripta). If you have specific questions on details which are possibly not interesting for the general audience, you may contact me directly by email.

Regarding the turbulence and Y+ with an enhanced wall function try to keep the Y+

Dear Maxwell thanks a lot for your informative response.

I tried my best to do so but i got the maximum error. The Yamagata experiment is about the heat transfer investigation of super-critical water.

I am to find the heat transfer coefficient of super critical water flowing vertically upward in a tube. So i decided to make it axisymmetric and did my analysis keeping Y+ ~1 but error was about 70% and above. I am interested to calculate area waited wall function heat transfer coefficient and not sure what to do please help me its my MS final year project and i am stuck. 

RNG K-epsilon is a modified form of Standard K-epsilon equation which is generally used to normalized or say overall effective results of all turbulent scales of motion. As in case of turbulence rather than only few length scales, many scales involved and to get the overall effect( production) of all scales RNG K-epsilon is preffered.

For further information visit following page

http://www.cfd-online.com/Wiki/RNG_k-epsilon_model

Dear all thanks a lot for your kind response.

I think that i am unable to convey my problem. Actualy i have met all the reuirements such as meshin with minimum skewness in my case maximum skewness is less than 0.1, aspect ratio is less than 20 in near wall cells. Picked the RNG, k-e turbulence model with enhanced wall treatment, in solution get the value of y+ almost 1. But when i check my results (in surface integrals, wall fluxes and wall function heat transfer coefficient or surface heat transfer coefficient ) got errors in the range above 70%. As a go on increasing Y+ results improve and give me best results at Y+=550 and above

I don't know what to do plz help me out

Thanks again to all of you.

Have you check mesh distribution?

thanks Mr. Shyu.

I no idea about mesh distribution so plz help me how to do that sir........

Mesh distribution means providing necessary inflation to those area where you need to capture the results. it also need to have equally arrangement of elements throughout your body. I don't know which tool you are using for meshing but there are many options specially in ICEM CFD where you can check your mesh quality by different parameters.

Dear Anand, I used inflation and edge sizing with biasing to have a finer mesh near the wall and got y+=0.013 for which a got about 100% error. The velocity vectors developed is attached for reference. As required by Mr. Abdul Aziz.

I am dealing with super-critical water at 24.52 M Pa and inlet temperature in the range of 600 K to 750 K. The inlet mass flow rate is 1260 kg/m^2s. the length of tube is 2000 mm with a dia of 7.5 mm. the flow is vertically upward with negligible pressure drop. The heat flux is applied at 1500 mm is 233 kw/m^2 and initial 500 is adiabatic for flow development.  

Dear M. Kashif,

you deal with an interesting problem! However, FLUENT can not be the correct choice as long as you use it together with the k-eps option. k-eps is a semi-empirical turbulence model. It doesn't matter whether it is based on RNG or not. RNG even irritates here because it sounds as scientifically specially sound , because the math is complex, but k-eps as such is fundamentaly incorrect because although k = turbulent kinetic energy is fine, but eps is not fine, because it does NOT belong to the conserved mechanical variables.

Yes, many engineers still use k-eps in different formats (e.g. SST/RNG ...). I also used it in the Launder-Spalding version, e.g. recommended by Wolfgang Rodi, when I started with turbulence & mixing many years ago. There are meanwhile so many versions that every ambitious colleague tries to praise his own one, which is of course VERY good ("... we all are above average"  -

http://prairiehome.org/listen/podcast/).

The story is now that we have a real statistical theory of high-Re turbulence which is free of empirical parameters and even predicts the Karman constant as 1/SQRT(2*pi) = 0.399. You know that the international standard value is 0.40 and Princeton superpipe in 2014 gave: 0.40 +/- 0.02. The theory works nicely even for non-Newtonian fluids I recommend the colleagues in ANSYS/FLUENT to read and implement it.

I initially based it on Fokker-Planck equations (relative frequencies or, mathematically spoken: probabilities balanced in space and time) and learned later that it  has already found as so-called "b-omega" equations by Kolmogorov & Landau (1942). Mathematically it is identical with (today so-called) k-omega. Kolmogorov developed the idea also based on Fokker-Planck but by mathematicians it is called today "Kolmogorov forward equation" because K. developed some special mathematical features of Fokker-Planck equations. (Although once I saw in Moscow K. personally, I use further the name Fokker-Planck: they simply were earlier and because I am physicist ...).

Much later b-omega has practically been used as k-omega by Wilcox (https://secure45.securewebsession.com/dcwindustries.com/books/1928729088.htm), e.g. as a consultant for Boeing, but not fully understood because he still treats it as semi-empiricla case like k-eps. The detailed understanding started with Chapter 5 in the book MARINE TURBULENCE, Cambridge U. Press 2005, Chapter 5. Some points were still missing and have been completed for Re = \infty in one of the 2 attachments (Physica Scripta, Roy. Swed. Soc. 2013) and recently (attached) just for the case of finite Reynolds numbers in chinese industrial context, even for non-Newtonian fluids, on a  conference in Prague; also recently accepted for publication also in Physica Scripta). If you have specific questions on details which are possibly not interesting for the general audience, you may contact me directly by email.

Hello M. Kashif,

I am not sure what you mean by (taking Y+=1-5 ... Y+=350). You do not explicitly force the Y+ values, these are computed fro you.

Also, the enhanced wall treatment in ANSYS FLUENT aims at alleviating the dependence of the solution on the Y+. The goal is to use blending functions so that the resulting wall-treatment becomes versatile (not sensitive to the Y+ value) and allows flexibility on the user’s adopted mesh resolution near the wall. The enhanced wall treatment for the momentum, energy, and species equations achieve this by blending the linear (laminar) and logarithmic (turbulent) laws-of-the-wall using a function suggested by Kader [Temperature and Concentration Profiles in Fully Turbulent Boundary Layers, Int. J. Heat Mass Transfer, 24(9):1541-1544, 1981].

It is not necessary that the RNG variant of the k-e model will always outperform the basic one. Wilcox provides a strong justification for using the k-omega model.

For k-e model check for y+ requirement, may be y+_min should be ~30. For near wall region use an appropriate wall function ( Start with std. wall function). Errors would be minimum

 The k-e model is not the physical law in the first ptinciples. When you solve an original problem first of all you must understand the phenomenon which lay

in the basis of it. We can use the programm packets for tipical case only.

Dear Jaafar

I have attached a table of results so you could see how the results are varying with wall Y+.

Mr. Helmut Ziegfeld Baumert

I am feeling blessed that you replied to my post and a lot of thanks for sharing your work. I am reading the paper and will contact you later for updates.

Thanks again Sir.

On the principle of independence of the boundary conditions of structure direction of turbulence

Lu Panming

Abstract

This is an introduction to the turbulence modeling theory of the present author, which can take the boundary conditions of turbulence structure into consideration ( the main contents have either not been published in normal journals or only published in chinese papers).   It is included that： (I)。Difficulty Problems Encountered in “Second-Moment-Closure” turbulence modelling ，i.e.  “Gao-Ge Anomaly” ;  (II)。The improvement  to the ”Second-Moment-Closure” turbulence modelling in order to allows the boundary conditions of turbulence structure direction could be prescribed;  (III)。An explanation to the principle of  independence  of  the boundary conditions of

turbulence structure direction ;  (IV)。Six suggestions to the possible future work directions;  (V)。 An explanation to the ”Gao-Ge Anomaly”.

------------------

4. The principle of the independence of the boundary conditions is not only to the turbulence modelling, but also suitable to the other subject, because it is frequently meet the equations are not easy to solve, so there is often a need of modelling or predigestion.  For example, both the D‘Alembert anomaly (~1752) and the Stokes anomaly (~1856), are due to breach the  principle of independence  of the boundary conditions, according to today`s point of view .This is because, first, by using the inviscid potential flow`s dynamic equations it is not possible to affiliate the slip-less condition of the real fluid at the wall, and  second, using the Stokes equation it is not possible to affiliate the boundary conditions both at the wall of cylinder and at the infinite to the cylinder.  The first anomaly lead to the discovery of the Prandlt`s boundary layer theory（1904）, and the  second anomaly  was solved by Oseen（1910）with introducing a modification. All these reflect the scientific worthiness and broad latency of the present principle   of the independence of the boundary conditions.

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above is an example paragraph,for more details or need the full text, please go to the end of this letter, where will be an web address existed.

http://staff.ustc.edu.cn/~pmlu/ 

 or

http://staff.ustc.edu.cn/~pmlu/%C2%C0%D6%F8%D5%D5%C6%AC%BB%E3%B1%E0/On%20the%20principle.pdf