Hello,

I know that 2D LES is not a good thing to do. But since I was not interested in absolute values and wanted to do some fast calculations I took a turbulent 3D channel flow with LES and calculated it in 2D. Now it seems that by reducing the length of the spanwise direction my flow became laminar. However if I kept the same length in the spanwise direction than the ratio's of the dimensions of my cells (very big length in the spanwise direction) seemed to spoil my convergence. Is there anybody out there who has some experience in 2D LES and who could give me some advice?

Thanks in advance,

Jan Ramboer

Hi Jan,

It seems I can share some relevant experiences with you about performing 2-D LES. First, I did LES in a square duct. The initial velocity profile was set as a laminar flow (parabolic distribution on the cross-section of square duct) superimposed by some perturbation from the solution of Orr-Sommerfeld equation. Periodic condition was used in streamwise direction. In the flow evolution, the velocity profile was found to approach to a turbulent profile. The results can be found in my home-page. Then I reduced my 3-D program to 2-D and repeated the same calculation, I found the 2-D laminar velocity profile was not approaching to the expected turbulent distribution, instead, it stayed around the laminar one. It seems that 3-D calculation is a necessary condition for the flow to transit from laminar to turbulent. If you really would like to do 2-D LES, you have to extract the instantaneous velocity profile from a 3-D channel LES and use this as inlet condition to perform 2-D calculation. However, I am still doubting about how much turbulence physical information will be contained in such kind of simulation, or in another word, to what extent this simulation can reflect the relevant turbulence physics. That is just my opinion and experiences Thanks for your attention.

There is a reason that 2D LES is not a good idea for a duct flow: the initiation of turbulence from the boundary layer begins with the smallest scales of motion and requires the 3D bursts of horshoe vorticies (related to the slow-speed streaks) to get the correct qualitative and quantitative picture. Furthermore, the use of LES in the viscous sublayer region is problematic even in 3D - essentially, you must get DNS level resolution to get the correct spacing of the slow-speed streaks in the boundary layer. If you don't get the correct spacing of the slow speed streaks you will not get the correct turbulent bursts out of the boundary layer - from which it follows that you won't produce the large scale eddies that are necessary for the LES to work. Remember LES assumes that you have the large scale eddies correct. In a turbulent boundary layer, creation of the large scale eddies required that you get the physics of the burst/sweep mechanisms correct (i.e you must capture the small scales). There is no free lunch.

(1). I like your answer. (2). The other day, when I was running a 3-D flow through turbine passage with a low Reynolds number two-layer model, I decided to keep the mesh fixed and increase the Reynolds number of the flow. (3). The results was the resultant Y+ next to the wall became much larger than one. (4). And the previously captured secondary flow suddenly disappeared from the picture. (5).It was just amazing that it is hard to fool the mother nature.

Hello,

First thanks for answering. Another questions: did you try to investigate at which limits of the spanwise dimension your flow became laminar? I mean more or less which dimensions of the spanwise direction should you use to keep it turbulent?

Greetings,

Jan

To answer Jan;s question:

No, because my calculation is on square duct flow instead of Channel flow, the dimension sizes in the two cross-streamwise directions are same, as can be seen at http://mach.me.queensu.ca/~hongyi/. But it would be interesting to purposely make it a rectangular duct and to increase the dimension size in one direction. Probably that will answer your question.

To make some comments on Ben's response:

Based on my experience, I agree with Ben's first comment, that is the 3D bursts of horshoe vorticies play an important part in the transition from laminar to turbulent since when I started the calculation from perturbed laminar flow, I did observe a kind of ordered structure near wall and the corners of square duct and the corner regions was the most turbulence active region. Something I'd like to correct is that I tried to do both DNS and LES on 2-d channel, cause in 2-D case, the current capability of SGI workstation allows me to comfortably distribute enough grid points (500*256) into the turbulent sublayer region, the y+ of first grid point away from wall was about 0.1. Also, I tried to switch on and off the subgrid model (Smg SGS). The simulation did not show much difference, which means the grid was fine enough so that LES was basically approaching to DNS. Still I did not see any sign that the velocity profile evolve towards a turbulent one. The point is that turbulence burst is a 3-D phenomena which can not be well presented in 2-D. The grid resolution is not a critical issue. For instance, in the 3-D LES with grid (130*34*34), the transition phenomena can be clearly observed which may not be 100% digitally correct. However, in the 2-D DNS with grid 500*256, the transition was not found after 10,000 time step calculation.

(1). If we let u=U+u', v=V+v', and w=W+w', and substitute it into the continuity equation, (du/dx)+(dv/dy)+(dw/dz)=0, then we have, { (dU/dx) + (dV/dy) +(dW/dz) } + { (du'/dx) + (dv'/dy) + (dw'/dz) } =0. where U,V,and W are time averaged mean values, and u',v' and w' are fluctuating components. (2). We can assume that the mean flow also satisfy the equation, { (dU/dx) + (dV/dy) + (dW/dz) }=0. From here, for 2-D channel flow, one can assume that (dW/dz)=0, and the 2-D mean flow will satisfy the mean flow continuity equation of { (dU/dx) + (dV/dy) }=0. This is possible, because it is possible to make (dW/dz)=0, where W is a mean quantity only. (3). This leaves the fluctuating components to satisfy the equation of { (du'/dx) + (dv'/dy) + (dw'/dz) }=0. Where u'=u'(x,y,z,t), v'=v'(x,y,z,t), and w'=w'(x,y,z,t). It is difficult to make u'=u'(x,y,t), v'=v'(x,y,t), and w'=w'(x,y,t).(or (dw'/dz)=0 ) For this to happen, organized motion has to happen at any instant so that we can use { (du'/dx) + (dv'/dy) }=0 for 2-D simulation. This organized instantaneous motion, was not observed in the random turbulent motion of fluid. (4). As a result, the continuity equation can only be { (dU/dx) + (dV/dy) }=0 and { (du'/dx) + (dv'/dy) + (dw'/dz) }=0 for 2-D channel flow. That means the instantaneous components must always be 3-D transient. And the 2-D simulation will require the assumption of organized instantaneous fluid motion, which can not be classified as turbulent flow as is observed in nature.

The spanwise grid resolution is critical in obtaining the correct turbulent boundary layer. The slow speed streaks in a boundary layer generally are spaced at ~100 y+ units (observed in both laboratory and well-resolved DNS). These streaks are the initiation of the coherent motions and need on the order of 10 grid cells between the centers of the streaks to resolve the motion. Thus, if your spanwise resolution is ~20 y+ units, the streaks in a 3D LES will end up spaced about 200 y+ units. My experience shows the coarser spanwise resolution gives larger scale (and fewer) burst-sweep events. This produces a catch 22: if an LES model accurately captures the dissipation caused by the large scale motion, then the larger (and fewer) eddies in an under-resolved flow will not create enough global dissipation and the mean flow will be to fast. If an LES captures the correct mean flow then the dissipation computation by the LES must be incorrect: that is, since it has fewer eddies to work with, the LES must be computing an amplified dissipation for each eddy. Again, there is no free lunch. The fundamental premise of LES is that the larger scale motions are captured so that the smaller scales can be computed. However, when you don't create enough large scales you don't get the right smaller scales unless the model "fudges" the physics. This is why some 3D LES produce the correct mean flows and poor representations of turbulent statistics while other methods produce good turbulent statistics and poor mean flows. Your use of 2D LES has infinite grid spacing in the spanwise and cannot ever resolve the spanwise streaks. Thus you cannot produce the burst-sweep events that characterise boundary layer turbulence. 2D LES should only be used in flows that are actually 2D - i.e. it has successfully been used in atmospheric flows that model the atmosphere as a 2D space. Boundary layers have been and always will be 3D, thus, they require DNS level accuracy in the near wall region to capture turbulence. If you are trying to capture the effects of turbulence rather than the turbulence itself, then you should proceed with some kind of RANS modeling that accounts for the 3D physics that you are missing or underresolving. Alternatively, one could parameterize the 3D physics of boundary layers into a 2D LES (as far as I know, it hasn't been done). Simple application of any existing LES to a boundary layer in 2D cannot produce a good representation of the physics.

Ben

Hi, dear Jan,

Happy new year!

I just wonder whether you could kindly tell me where I can download a basic and, of course, free code for 2D-LES? My supervisor want me to dive into this subject, I am also very interseted, but I am afraid it will be too much for me to build up a palace from plain. Any hints would be highly appreciated. Thank you in advance!

Jan Xu