# Y+ value for Large Eddy Simulation

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 August 22, 2011, 21:05 Y+ value for Large Eddy Simulation #1 New Member   Join Date: Dec 2010 Posts: 11 Rep Power: 15 Hello there I would like to know if someone could give me a clear explanation about 2 things. 1) Why Y+ in LES must be equal to 1 or below. 2) What would happen in term of scale size modelisation if Y+ is greater than 1 (between 9 and 25) I have spent hours and even days on internet looking for a clear explanation but it does not look like there is one. Or I don't understand it maybe (I am French and quite everything is in English about CFD modelling. I'm not too bad in English after 3 years spent in UK but it's obviously still not like if I was native ) Hope someone could give me a little explanation. Thank you very much

 August 24, 2011, 01:56 #2 Senior Member   Raashid Baig Join Date: Mar 2010 Location: Bangalore, India Posts: 135 Rep Power: 16 I too have this doubt. Can someone give a conclusive answer/reference ? Thanks in advance, Raashid

 August 24, 2011, 15:26 #3 Senior Member   cfdnewbie Join Date: Mar 2010 Posts: 557 Rep Power: 20 Here's my attempt: y+=1 is somewhere in the laminar sublayer, i.e. the layer that determines your du/dy at the wall and thus all the nasty things like wall friction and heat exchange. Thus, if you want to capture the physics going on there, you need some resolution in that range, unless you are using wall functions (which were invented to circumvent this type of resolution requirement). this might not be all there is, tough.... any turbulence experts here?

 August 24, 2011, 17:31 #4 New Member   Join Date: Dec 2010 Posts: 11 Rep Power: 15 I agree that Y+=1 or below is definately in the viscous subayer but does that mean that the smaller y+, the more small scales size behaviour we catch? And then does it also mean that the bigger y+, the less small scales behaviour we catch but it will not change anything about the results obtained on the bigger scales size?

August 24, 2011, 18:09
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Quote:
 Originally Posted by yannossss I agree that Y+=1 or below is definately in the viscous subayer but does that mean that the smaller y+, the more small scales size behaviour we catch?
yes, at least in the viscous sublayer. The size of your grid cell (or the number of points per unit length) determine the smallest scale you can catch on a given grid. From information theory, the Nyquist theorem tells us that we need at least 2 points per wavelength to represent a frequency (we need to be able to detect the sign change). However, 2 points per wavelength is just for Fourier-type approximations. For other schemes like O1 FV you need a lot more, maybe 6 to 10 to accurately capture a wavelength. Let's assume that you have the same grid in all of the flow (i.e. high resolution everywhere, no grid stretching or such). Then the smallest scale you can capture is determined by your grid and scheme, the better/finer, the smaller the scale.

OF course, most grids will coarsen away from the wall, so the smallest scale will "grow bigger" away from the wall as well

Quote:
 And then does it also mean that the bigger y+, the less small scales behaviour we catch but it will not change anything about the results obtained on the bigger scales size?
Ha, that's the crux of LES of course, the bigger y+, the fewer the small scales you will catch, but does that change the result of the bigger scales?

The answer is not straight forward, but I'll try to make it short:

Let's talk about NS-equations (or any non-linear conservation eqns). The scales represented in the equations are coupled by the non-linearity of the equations, i.e. what happens on one scale will (eventually) reach all other scales (also known as the butterfly effect). So the NS eqns represent the full "nature" with all its scales and interactions. We now truncate our "nature" by resolving only the larger scales, since our grid is too coarse.... what will happen? Will the large scales be influenced by the lack of small scales?

Hell, yeah, they will. We are lacking the balancing interaction of the small scales, since we don't have these scales. We are also lacking the physical effects that take place at small scales (dissipation).... so we have production of turbulence at large scales, the energy is handed down through the medium scales but is NOT dissipated at the small scales, since they are simply not present in our computation. Will that influence the large scales? Definitely!

That's why LES people add some type of viscosity (effect of small scales) to their computations, otherwise, their simulations would very likely just blow up!

hope this help!

cheers

 August 24, 2011, 19:10 #6 Senior Member   Julien de Charentenay Join Date: Jun 2009 Location: Australia Posts: 231 Rep Power: 18 Hi Yann, I think that you need to distinguish 2 cases: 1) Cases where the turbulent fluctuation are generated by the shear at the wall (think channel flow, pipe, flow detachment over a smooth curvature); 2) Cases where the turbulent fluctuation are generated by flow shear (think detachment at sharp edges, mixing layers). The nature of the development of the turbulent structure is quite different in the two cases. This makes the later (detached flow at sharp edges) well suited for Detached Eddy Simulation (DES) and, imo, LES that do not require y+ of 1 at the wall (but you would need an appropriate wall function to get a "correct" velocity profile). For the former (wall generated turbulence) it is paramount that you capture appropriately the generation of the turbulence at the wall, hence the requirement for y+ of 1. This would allow your LES model to capture the transition from the viscous layer to the developed layer with the appropriate turbulent energy transfer. To answer the second part of your question: what happens if LES is not well resolved at the wall: For wall generated turbulence, it is going to be harder to trigger the turbulence due to locally high numerical and sub-model viscosity (in my opinion - I can not back it up with paper). If your case is close to the turbulence transition you may find that a "coarse" mesh may predict a laminar solution whilst a "finer" mesh may predict a turbulent one. For the sharp edge, the solution in the wake/mixing layer should remain reasonable provided that the velocity profile is adequate. On another note: One need (in my opinion) to be careful with the y+ output by the CFD software when running LES. As the y+ is calculated based on the velocity in the cell adjacent to the wall, the y+ will vary at each iteration. The relevant y+ for meshing purpose is in my opinion the one based on the velocity average (which can only be known when the simulation is complete or can be guessed on the basis of a RANS turbulent one). Caution: I have not done any LES for the last few years but I did have a fairly good theoretical grasp. I hope it helps. Kind regards, Julien cfd_newbie, pfhan, chivaee and 16 others like this. __________________ --- Julien de Charentenay

 August 24, 2011, 19:58 #7 New Member   Join Date: Dec 2010 Posts: 11 Rep Power: 15 Thank you very much for the replies lads I really appreciate it and yes it does help My case of study is on one hand a square cylinder and on the other hand a circular cylinder. Both are studied in LES with water and have a diameter/side length of 0.04m. The particularity of my study is that a shear flow has been applied. but not a shear flow as most of the study and I would even say as all of the study where a shear flow is applied, because in all research papers and journals I found, the only kind of shear flow applied has the shear parameter K applied in the crosswise direction. My study deals with the fluid velocity evolving along the spanwise direction. Both square and circular cylinders are tested with K=0, 12.5 and 25 which gives a uniform velocity of 1m/s when K=0, and a velocity evolving between 1 and 2m/s when K=12.5 and between 1 and 3m/s when K=25. Also in the case of the circular cylinder 3 constant non-dimensional rotation rates are applied for each of the different shear flow. α=0, 1 and 2. Because of computational power I have been allowed by my supervisor to have a y+ of 10 which is obtained for the case where K=0 but i didnt think it would increase when K=12.5 and 25 but it obviously did as soon as the velocity or the averaged velocity increase too. But anyway results I obtained are not too bad (when I compare the case where K=0 with other papers). Furthermore I'm still only a student and this is a first approach for this kind of study....it has probably been studied before but nothing dealing with this kind of shear flow has been published, or it is well hidden. so it should be fine for me Thanks again for the quick replies, byebye Matt1986 likes this.

 January 16, 2014, 08:42 LES modeling for wind farms #8 New Member   Ava Join Date: Nov 2013 Location: UK Posts: 17 Rep Power: 12 Julien de Charentenay Thank you so much for your explanation here. I have another question. I am doing wind farm assessment of the atmospheric boundary layer in an urban arean with building and trees and I am going to use LES. My question is that do you think that this case falls in the second category i.e. "Cases where the turbulent fluctuation are generated by flow shear"? I am asking this because I am trying to find the suitable y+ for my case and I have not find anything in the literature up to now. The thing is that the area of the site that I am doing the simulation is about one kilometre so I need to use as course mesh as possible. Thank you, Ava.

 January 19, 2014, 06:06 #9 Senior Member   Julien de Charentenay Join Date: Jun 2009 Location: Australia Posts: 231 Rep Power: 18 Hi Ava, Thanks for reading my old posts. Your situation is quite challenging. In order to have the "right" wind profile in an open area in LES you would need to resolve the boundary layer (i.e having y+ of around 1). Considering that your situation is an urban area, it may be acceptable to under-resolve the boundary layer. My advice would be to: 1) monitor the profile in the boundary layer area ahead of your area of interest to ensure that the inlet profile does not evolve to something too different; 2) Assess the sensitivity of the results to the boundary layer refinement (which can be an expensive exercise). You may want to compare your LES results to RANS. If the velocity average are consistent, it could help you build some confidence... Julien AvaShahrokhi and piu58 like this. __________________ --- Julien de Charentenay

 January 19, 2014, 06:53 #10 Senior Member   Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,793 Rep Power: 71 I can suggest that the type of refinement close to the walls is also depending on what is the relevant variable you want to measure... AvaShahrokhi likes this.

January 22, 2014, 01:16
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Julien:
Quote:
 I think that you need to distinguish 2 cases: 1) Cases where the turbulent fluctuation are generated by the shear at the wall (think channel flow, pipe, flow detachment over a smooth curvature); 2) Cases where the turbulent fluctuation are generated by flow shear (think detachment at sharp edges, mixing layers).
Thanks for the great answers julien.
One thing how would you know which case is applicable for your analysis? My flow is over a wing and I should be expecting turbulent fluctuations generated by the shear at the wall as well as the shear flow.

 January 23, 2014, 19:21 #12 Senior Member   Julien de Charentenay Join Date: Jun 2009 Location: Australia Posts: 231 Rep Power: 18 Here are my 2 cents worth about your case: If the region of interest in the flow is dominated by the development of the velocity profile around the wing and particularly flow detachment from the wind profile, there it is clearly a cases (1). The flow shear as in the wake of the wing would fall under cases (2), but the wake of the wing need to be accurately predicted. In my quote for cases (2), I explicitly nominate detachment at sharp edges (in other words, where the detachment point is well known and dominated by geometrical features). In my opinion flow over a wing would be a case (1). Julien __________________ --- Julien de Charentenay

March 19, 2017, 01:44
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Hegel
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 Originally Posted by julien.decharentenay Hi Yann, I think that you need to distinguish 2 cases: 1) Cases where the turbulent fluctuation are generated by the shear at the wall (think channel flow, pipe, flow detachment over a smooth curvature); 2) Cases where the turbulent fluctuation are generated by flow shear (think detachment at sharp edges, mixing layers). The nature of the development of the turbulent structure is quite different in the two cases. This makes the later (detached flow at sharp edges) well suited for Detached Eddy Simulation (DES) and, imo, LES that do not require y+ of 1 at the wall (but you would need an appropriate wall function to get a "correct" velocity profile). For the former (wall generated turbulence) it is paramount that you capture appropriately the generation of the turbulence at the wall, hence the requirement for y+ of 1. This would allow your LES model to capture the transition from the viscous layer to the developed layer with the appropriate turbulent energy transfer. To answer the second part of your question: what happens if LES is not well resolved at the wall: For wall generated turbulence, it is going to be harder to trigger the turbulence due to locally high numerical and sub-model viscosity (in my opinion - I can not back it up with paper). If your case is close to the turbulence transition you may find that a "coarse" mesh may predict a laminar solution whilst a "finer" mesh may predict a turbulent one. For the sharp edge, the solution in the wake/mixing layer should remain reasonable provided that the velocity profile is adequate. On another note: One need (in my opinion) to be careful with the y+ output by the CFD software when running LES. As the y+ is calculated based on the velocity in the cell adjacent to the wall, the y+ will vary at each iteration. The relevant y+ for meshing purpose is in my opinion the one based on the velocity average (which can only be known when the simulation is complete or can be guessed on the basis of a RANS turbulent one). Caution: I have not done any LES for the last few years but I did have a fairly good theoretical grasp. I hope it helps. Kind regards, Julien
Hi julien
your answer was very helpful for me. recently i`m researching LES`s application. could you give me some materials about LES? i`m confused by it... thank you very much!

March 19, 2017, 01:46
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Hegel
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 Originally Posted by julien.decharentenay Hi Yann, I think that you need to distinguish 2 cases: 1) Cases where the turbulent fluctuation are generated by the shear at the wall (think channel flow, pipe, flow detachment over a smooth curvature); 2) Cases where the turbulent fluctuation are generated by flow shear (think detachment at sharp edges, mixing layers). The nature of the development of the turbulent structure is quite different in the two cases. This makes the later (detached flow at sharp edges) well suited for Detached Eddy Simulation (DES) and, imo, LES that do not require y+ of 1 at the wall (but you would need an appropriate wall function to get a "correct" velocity profile). For the former (wall generated turbulence) it is paramount that you capture appropriately the generation of the turbulence at the wall, hence the requirement for y+ of 1. This would allow your LES model to capture the transition from the viscous layer to the developed layer with the appropriate turbulent energy transfer. To answer the second part of your question: what happens if LES is not well resolved at the wall: For wall generated turbulence, it is going to be harder to trigger the turbulence due to locally high numerical and sub-model viscosity (in my opinion - I can not back it up with paper). If your case is close to the turbulence transition you may find that a "coarse" mesh may predict a laminar solution whilst a "finer" mesh may predict a turbulent one. For the sharp edge, the solution in the wake/mixing layer should remain reasonable provided that the velocity profile is adequate. On another note: One need (in my opinion) to be careful with the y+ output by the CFD software when running LES. As the y+ is calculated based on the velocity in the cell adjacent to the wall, the y+ will vary at each iteration. The relevant y+ for meshing purpose is in my opinion the one based on the velocity average (which can only be known when the simulation is complete or can be guessed on the basis of a RANS turbulent one). Caution: I have not done any LES for the last few years but I did have a fairly good theoretical grasp. I hope it helps. Kind regards, Julien
my e-mail: shihaijian90@163.com thank you again

 March 19, 2017, 05:57 #15 Senior Member   Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,793 Rep Power: 71 I think that a reading of the y+ in terms of a local computational Reynolds number can help to understand better. The key is that any numerical discretization that works at O(1) would solve locally the turbulent scales.

March 21, 2017, 23:41
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Hegel
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 Originally Posted by FMDenaro I think that a reading of the y+ in terms of a local computational Reynolds number can help to understand better. The key is that any numerical discretization that works at O(1) would solve locally the turbulent scales.
Thank you professor. I have read the help of ANSYS. It explains LES elaborately.

 Tags large eddy simulation, les, y+=1

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