I had posted this message once before. I don't have any answer. I am posting it again hoping someone will throw some light.

For a submerged jet of a newtonian incompressible fluid having low Prandtl (~0.1), impinging on a wall, how should one model the flow near the wall for flow and energy solution. Pls. advice with ref. of books/journals

Hi,

Look for a paper by Wilcox. Really speaking the Wall functions cannot account for seperation because u need the distance of y+ =0.1 to predict seperation with fair accuracey. I remember reading paper by wilcox which includes streamwise pressure gradient p+ in wall function equation. There are other papers by Bradshaw too but modelling of seperation by wall function looks bit wary to me. BTW which model are u using? (Must be a High Re form )

Abhijit

Abhijit

Thank you for suggestions. We are using std. K-e model. To address the momentum boundary layer- near wall control volume was made a bit coarser and y+ <=11.6 std. wall function considered. For the thermal part Cebeci's model is used. Since it is a low Pr (~0.1) fluid, conduction is the dominating mode. With all these the results are reasonably matching with similar work done by others. We want to know how further refinement can be incorporated to capture the thermal effect of the flow separation. How will this pressure gradient situation influence the thermal behaviour of a low Pr. fluid.

I will look for Wilcox's & Bradshaw's papers as suggested by you.

rupa

Hi ,

yes u got it the Cebeci-Bradshaw model for HT. Thats ok. BTW do you mean y+>11.6, that's when the law of wall is valid. You will find more details in the book by Wilcox "Turbulence Modelling for CFD". Your normal wall function looks like U+ = 1/k*ln(Ey+). The modified Wall function looks like U+=1/k*ln(Ey+)-0.48(y+)*(p+) where p+=Vis/rho*U_tau* dp/dx. In flows where u model seperation, ie adverse pressure gradient flows dp/dx is important. U can derive the wall value of epsilon by integrating over the CV.Since u calculate Heat transfer from wall functions, The p+ should affect your calculations, How much I can't say bcos I have'nt sloved for fluids with low Pr No till now.

Hope This helps Abhijit

Hi there,

Please enlight me of the Cebeci-Bradshaw HT model? You are not refering to the algebraic eddy-viscosity model? Using a eddy-viscosity model, like the k-\eps, I don't think there is a need for anything more sophisticated than a simple constant Prandtl number HT model. There exists a number of improvements over the standard wall-function model (for the flow) - the first one is to eliminate y+ from your expression. The next one is to solve for k, and the third one is to improve the representation of the length scale. Launder have done some work on this. However don't expect any degree of accuracy for HT prediction using a wall-function type of model.

Regards Jonas

Dear Dr Jonas,

I don't need to enlighten you as ur a PhD. Well the Cebeci-Bradshaw models are nothing but modifications to wall functions so as to match the experimental Nu & St No distributions, (taken from their book "Turbulence" by Springer). I used p+ in my code & found good agreement in k & e and production terms in k equn with DNS data. As u know k-e model will over-predict HT in seperated flows, It leads to logically conclude that inculsion of p+ will lead to improvement in HT prediction (correct me if i am wrong) let me know your views /experience on HT prediction (in more elaborate manner if possible.)

Thanks Sir, Abhijit

Wall functions are not valid for separated flow region. You have to use integration to the wall. See Wilcox's book

(1). This again says that 99% of the time, we are getting the wrong CFD answers. (2). How many engineers world-wide are using Low Reynolds number turbulence models in their CFD analysis? Are you? Are your company?

(1) I agree 100% with you, Dr. John C Chien, that 99% [I have no figure to justify the 99% - I tend to believe it is close to 100% only !] results are wrong. (2) The issue is 'who is responsible ?' (3) We do not have any kind of benchmarks like : convergence criteria (it is everybody's intuition !), grid independence , and worst of it - when we come across publications with grid refinement at near wall region while employing high Re turbulence models !! (4) Please permit me to say that the wrong things are done not only in 'companies' - they are done and reported by others too. (5) Coming to the main topic, I refer to : Article # 6.6, p.184- "Two dimensional flows with pressure gradient" in the book 'Physical and computational aspects of convective heat transfer' by T. Cebeci and P. Bradshaw, Springer-Verlag Sudy ed.(1984). (6) If we go for Falkner-Skan transformation to address the seperation/stagnation region, derive the high Re k-ep eqns and arrive at the wall function - then how much wrong ('doing wrong' is a time-dependent phenomenon, I hope everyone agrees) we are - I will like to be enlightened.

I think that is what has been floated in this forum and some contributors have tried to convey the same.

It is easier 'said than done' that some particular eqn or set does not help - one should rather convey what should be done. I believe that should be the objective of this forum.

Thanks, mentioning that I personally gain very much from these discussions.

(1). When the low Reynolds number version of the two-equation k-epsilon model was published about 30 years ago, people should stop using the wall function approach. And I have started using the low Reynolds number model since early 70's. (2). But since the high speed computers were not readily available to researchers, the use of wall function was allowed in the published papers.(even though researchers have already convinced the limitations of the wall function) (3). There have been a lot of low Reynolds number turbulence modelling effort world wide since. (4). Unfortunately, in 90's, because of the release of commercial cfd codes, users have been limited by the time requirement in their project, therefore, the use of the low Reynolds number model and the mesh independent solution guidelines were ignored in favor of the quick answer. (5). So, the need to use a low Reynolds number turbulence model (including the Van Driest mixing length model) and the need to establish the mesh independent solution has long been recognized in 70's in the professional international conferences. (6). So, both the low Reynolds number model and the mesh independent issues are at least 25 to 30 years old. (7). It looks like that we are moving backward 30 years in time. (perhaps even further back into the Inviscid Era. )

[prapanj]

Hi

I am a novice to wall functions. But from the discussion above, can I also infer that for a steady state problem with flow separation, introducing a wall function will affect convergence? ( I mean no convergence at all).

I am trying to run a buoyancy driven flow around a hot object. The object has a complicated geometry. I just found that when I switch off wall functions, I get a converged solution, and when I switch on the walls( especially on the complicated geometry with many separation regions) the momentum residuals never reduce beyond a level. And I have run the case for ever to see if it would converge.

And I have read the pages in Wilcox's turbulence modelling that talks about the pressure term added to wall function ( I am using kOmega SST). By introducing this pressure term, can I expect convergence? Could someone explain in simple terms 'matching point'. By reducing y+ will be able to solve the issue without using the pressure term?

Thank you

Prapanj

[vishyaroon]

Originally Posted by Mukhopadhyay
;15461

(1) I agree 100% with you, Dr. John C Chien, that 99% [I have no figure to justify the 99% - I tend to believe it is close to 100% only !] results are wrong. (2) The issue is 'who is responsible ?' (3) We do not have any kind of benchmarks like : convergence criteria (it is everybody's intuition !), grid independence , and worst of it - when we come across publications with grid refinement at near wall region while employing high Re turbulence models !! (4) Please permit me to say that the wrong things are done not only in 'companies' - they are done and reported by others too. (5) Coming to the main topic, I refer to : Article # 6.6, p.184- "Two dimensional flows with pressure gradient" in the book 'Physical and computational aspects of convective heat transfer' by T. Cebeci and P. Bradshaw, Springer-Verlag Sudy ed.(1984). (6) If we go for Falkner-Skan transformation to address the seperation/stagnation region, derive the high Re k-ep eqns and arrive at the wall function - then how much wrong ('doing wrong' is a time-dependent phenomenon, I hope everyone agrees) we are - I will like to be enlightened.

I think that is what has been floated in this forum and some contributors have tried to convey the same.

It is easier 'said than done' that some particular eqn or set does not help - one should rather convey what should be done. I believe that should be the objective of this forum.

Thanks, mentioning that I personally gain very much from these discussions.

__________________________________________________ ____________

I have to agree with you all on this here. As a matter of fact. no turbulence model (to the best of my knowledge) has been formulated keeping in mind the flows with separation. RANS (steady or unsteady) may not be the way to go to analyse flows with separation. Even a case like the backward facing step case (which may not be as complicated as most of the industrial problems) has seen several turbulence models failing to predict the turbulence physics in the separation bubble and hence the reattachment downstream. The inaccurate results using the RANS models is something that the industry has to accept, unless it has the computational resources to perform a more time-accurate calculations (LES or at the least DES).

[mettler]

There is a good book, Computational Fluid Dynamics, by Roache. I have the 1982 edition (I had a prof retire and give it to me) that has excellent chapters on boundary conditions for different types of flow situations. Sorry, if Roache was already mentioned.