# DNS of square duct at Re_tau = 600

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 July 4, 2012, 14:33 DNS of square duct at Re_tau = 600 #1 Senior Member     Paolo Lampitella Join Date: Mar 2009 Location: Italy Posts: 742 Blog Entries: 17 Rep Power: 21 Sponsored Links Dear all, i'd like to have some opinions about a not very recent work which i was trying to use for comparisons with LES. I'm referring to the DNS data of Huser and Biringen for the turbulent square duct at Re_tau=600 (based on hydraulic diameter): Huser, Biringen (1993): Direct numerical simulation of turbulent flow in a square duct. J. Fluid Mech 257 My concern about their data is on the numerical method and the grid. More specifically, they use a 5th order upwind for convective terms and 4th order central/spectral discretizations for the diffusive and pressure terms in the wall-normal/streamwise directions. The grid is 96x100x100 leading to dx+=40 (!!!) and 1.2

July 4, 2012, 14:58
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Quote:
 Originally Posted by sbaffini Dear all, i'd like to have some opinions about a not very recent work which i was trying to use for comparisons with LES. I'm referring to the DNS data of Huser and Biringen for the turbulent square duct at Re_tau=600 (based on hydraulic diameter): Huser, Biringen (1993): Direct numerical simulation of turbulent flow in a square duct. J. Fluid Mech 257 My concern about their data is on the numerical method and the grid. More specifically, they use a 5th order upwind for convective terms and 4th order central/spectral discretizations for the diffusive and pressure terms in the wall-normal/streamwise directions. The grid is 96x100x100 leading to dx+=40 (!!!) and 1.2
what kind of scheme where they using? finite difference?

If the dns is fully resolved, there's no need not trusting an upwind formulation, since the dns is -by definition- numerics-free. Just getting there requires more effort (in terms of degrees of freedom) with a dissipative scheme....

 July 4, 2012, 15:22 #3 Senior Member   cfdnewbie Join Date: Mar 2010 Posts: 557 Rep Power: 13 I just looked at the paper, it is available for free online. I dont see anything wrong with it, even for the coarse grid there is very litle aliasing, and the results for the fine and coarse grid are very close.

 July 4, 2012, 16:08 #4 Senior Member     Paolo Lampitella Join Date: Mar 2009 Location: Italy Posts: 742 Blog Entries: 17 Rep Power: 21 Yes but, as i said, they use a 5TH ORDER UPWIND scheme for the convective terms and the grid spacings in wall units are (x: streamwise, y-z:duct section): dx+ = 40 (!!!!!!!!!!!!!!!!!!!!!!) 1.2 < dy+,dz+ < 10.5 This does not seem to be a well resolved DNS, i would doubt it even if a centered scheme was in use (which can't probably be the case due to the very coarse stream-wise resolution). Of course, they show that there is no great difference among the two grids, but the other grid is even coarser and they still use an upwind scheme. Indeed, they show some energy spectra (at some very weird wave numbers, as they do not cover the whole available spectral space in x) which have a clear numerical effect due to the upwind (the dissipative range is fully covered already at scales with dx+=85, seriously?), which can be somehow inferred by comparison with the plane channel spectra of Moser et al. However, i'm not saying that this DNS is wrong by principle, still i was wondering if anyone has tryied to replicate such a DNS with some more accurate approach (e.g., a fully spectral code and a decent resolution).

July 4, 2012, 16:21
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 Originally Posted by sbaffini Yes but, as i said, they use a 5TH ORDER UPWIND scheme for the convective terms and the grid spacings in wall units are (x: streamwise, y-z:duct section): dx+ = 40 (!!!!!!!!!!!!!!!!!!!!!!) 1.2 < dy+,dz+ < 10.5 This does not seem to be a well resolved DNS, i would doubt it even if a centered scheme was in use (which can't probably be the case due to the very coarse stream-wise resolution). Of course, they show that there is no great difference among the two grids, but the other grid is even coarser and they still use an upwind scheme. Indeed, they show some energy spectra (at some very weird wave numbers, as they do not cover the whole available spectral space in x) which have a clear numerical effect due to the upwind (the dissipative range is fully covered already at scales with dx+=85, seriously?), which can be somehow inferred by comparison with the plane channel spectra of Moser et al. However, i'm not saying that this DNS is wrong by principle, still i was wondering if anyone has tryied to replicate such a DNS with some more accurate approach (e.g., a fully spectral code and a decent resolution).
Hm, how did you find the y+ values to be so high? Figure 6 in their paper shows u down to about 1, that confuses me....

 July 4, 2012, 16:33 #6 Senior Member     Paolo Lampitella Join Date: Mar 2009 Location: Italy Posts: 742 Blog Entries: 17 Rep Power: 21 Which is what i'm saying, it is almost 1.2. I'm saying this because i tested the grid stretching described in the paper with the parameter used by them, also there are no actual points in the graph, it is a full line which can't be interpreted that straight (still, the solid curve of case A is certainly stopping at y+>1). I have to correct myself on the spectra i cited before, as they are shown for the worst resolution (case A, nx = 64), so the spectrum shows a dissipation range at scales with even higher dx+ than what i said before.

 July 4, 2012, 16:39 #7 Senior Member     Paolo Lampitella Join Date: Mar 2009 Location: Italy Posts: 742 Blog Entries: 17 Rep Power: 21 Just in case someone esle want to jump in, we are talking about this work: http://www.cfmbyexample.com/resources/JFM_Duct.pdf

July 4, 2012, 16:45
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 Originally Posted by sbaffini Which is what i'm saying, it is almost 1.2. I'm saying this because i tested the grid stretching described in the paper with the parameter used by them, also there are no actual points in the graph, it is a full line which can't be interpreted that straight (still, the solid curve of case A is certainly stopping at y+>1).
yes, sorry, I see, I was confusing the dy and the dx before. Sorry, it's a little late here....

Quote:
 I have to correct myself on the spectra i cited before, as they are shown for the worst resolution (case A, nx = 64), so the spectrum shows a dissipation range at scales with even higher dx+ than what i said before.
Well, I honestly don't know where the dissipation range would be at the Re_tau, but the spectra do clearly show such a range.... One could argue (what you are doing, if I understand you correctly) that the scheme dissipation is creating this range, although the physical dissipation should happen at higher wavenumbers...
The aliasing at the tail clearly shows that this is not a DNS, but still underresolved.... it's a shame that they didn't show the spectrum for the case B, that would have helped us answer the question...

You are right, it's hard to tell what is numerical and what is physical dissipation in this case...

too bad we don't have a higher resolution solution...

July 4, 2012, 16:46
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 Originally Posted by sbaffini Just in case someone esle want to jump in, we are talking about this work: http://www.cfmbyexample.com/resources/JFM_Duct.pdf

well, the one guy (biringen) has his email on the website, maybe just write him and ask about it? I found most of these guys to be really friendly and helpful...

 July 4, 2012, 17:32 #10 Senior Member     Paolo Lampitella Join Date: Mar 2009 Location: Italy Posts: 742 Blog Entries: 17 Rep Power: 21 That is exactly what i was arguing, you understood correctly. Of course i don't know where the dissipation range should be in your same way. But it being at scales with delta+ around 100 does not sound very good. Sadly, there are no published spectra on the square duct which i am aware of and to compare with. Also, i am not aware of other works using this one as reference, except similar ones (upwind, same coarse resolution), the ones from Huser and Biringen themselves, a work from Patterson Reif (RANS, v2f) and an LES (Metais, if i'm not wrong). No other reliable DNS at the same Re_tau. Asking Biringen himself is probably going to be my next shot, but i was hoping that maybe someone is already aware of this work or some other work with less questionable choices... you know, before bothering a Professor about a work done by some Ph.D. student 2 decades before. Again, i am not arguing about the work itself but if my life would depend on this DNS (and hopefully my life is never going to depend on a DNS)... well, i would ask for a second opinion. The fact is that, today, you can find fully spectral DNS at lower Re_tau and much higher resolution (relative and absolute as well), but they are relatively useless for LES.

 July 5, 2012, 06:18 #11 Senior Member   Filippo Maria Denaro Join Date: Jul 2010 Posts: 3,412 Rep Power: 39 http://onlinelibrary.wiley.com/doi/1....200410307/pdf you see that the cited DNS is also very old ....

 July 5, 2012, 06:23 #12 Senior Member   Filippo Maria Denaro Join Date: Jul 2010 Posts: 3,412 Rep Power: 39 perhaps the necessary resolution for DNS is discussed here http://www.dtic.mil/dtic/tr/fulltext/u2/p013672.pdf

 July 5, 2012, 07:54 #13 Senior Member     Paolo Lampitella Join Date: Mar 2009 Location: Italy Posts: 742 Blog Entries: 17 Rep Power: 21 Indeed, i'm now considering the work cited therein (Gavrilakis) as a reference for the resolution. Still, i can't use it for comparisons with LES as the Re_tau is pretty low.

September 29, 2012, 04:04
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Quote:
 Originally Posted by FMDenaro perhaps the necessary resolution for DNS is discussed here http://www.dtic.mil/dtic/tr/fulltext/u2/p013672.pdf
It just gives the total no of nodes, no information for dx, dy and dz

 September 29, 2012, 04:06 #15 Super Moderator   Sijal Join Date: Mar 2009 Location: Islamabad Posts: 4,331 Blog Entries: 6 Rep Power: 45 is it possible to perfom the DNS and LES for this test case using Fluent and comuter with i7 processor and 24 GB RAM ?

 September 30, 2012, 16:54 #16 Senior Member     Paolo Lampitella Join Date: Mar 2009 Location: Italy Posts: 742 Blog Entries: 17 Rep Power: 21 It depends on which of the two you are referring to. For Gavrilakis, the reference cited by Filippo is indeed a good one (all you need to know is in the paper); also, the one of gavrilakis is actually performed by a 2nd order method too. So you can replicate those two DNS with Fluent, it being of comparable accuracy. Also, your RAM is surely enough. The number of processors is however making the difference in the amount of time you will need to get your solution. We are still talking about few mln cells, which i would put on more than 10 or even 20 processors. For what concerns the Huser reference, well, the situation is quite different. An actual DNS would require a lot more cells than the one used in the reference... we are talking about 20-30 Mln cells. Using less cells but still more than the reference is not enough for a DNS in Fluent and you will need the same resolution of the previous case (which leads to my previous estimate). So, i'd say it's not affordable in fluent This is for what concerns DNS. LES is much more affordable in both cases (i had fine results with 400K cells for the huser case). Still, a single i7 processor coul be a limiting factor if time is an issue. No problem for the RAM.

 November 18, 2012, 18:28 #17 Super Moderator   Sijal Join Date: Mar 2009 Location: Islamabad Posts: 4,331 Blog Entries: 6 Rep Power: 45 Did you take the length 1?

 November 19, 2012, 05:42 #18 Senior Member     Paolo Lampitella Join Date: Mar 2009 Location: Italy Posts: 742 Blog Entries: 17 Rep Power: 21 The parameters i used for the rectangular channel (H heigth of the channel, W span of the channel, AR=W/L) are: rho=1 mu = 1/Re_tau_H/2 H = 1 W = AR * H dp/dx = – 8 * (1+1/AR) In this case, spatial and temporal steps scale like: dx+ = 2 * dx * Re_tau_H/2 dt+ = 4 * dt * Re_tau_H/2 Where: Re_tau_H/2 = rho*u_tau*H/2/mu and u_tau is the average friction velocity over the section

 November 19, 2012, 06:48 #19 Super Moderator   Sijal Join Date: Mar 2009 Location: Islamabad Posts: 4,331 Blog Entries: 6 Rep Power: 45 What is the value of W and L is then? Is L is the length along x axis? and W=H? What about the viscosity? Where we do apply the pressure gradient? The two faces (inlet and outlet) are taken as periodic boundaries right? How to impose the given pressure gradient?

November 19, 2012, 14:41
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This is the pic of mesh and some initial results. Used instantaneous initialization for the LES available in Fluent.
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