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 NIK May 17, 2004 13:06

LES.. Basic Questions

Hi, i am trying to switch from Fortran based RANS code to LES for my FVM code. Q1. I am bit stuckup with the use of space fiter..how to actually use it in Navier Stokes equations? Q2.In what respect i shall be switching from my time averaged Navier Stokes eqautions? I have studied it theoratically but am not still clear about how to implement it actually in the code. Q3. From where are we inputting the unsteady velocity and pressure etc as in comparison with time averaged ones in RANS? I highly appreciate you for your comments

 Hall May 17, 2004 15:25

Re: LES.. Basic Questions

I am working with LES now, but use FDM and spectral method. Here is my understanding, not sure if it is suitable to your case.

Like RANS, in LES, the equations you try to solve is already filtered N-S equations (people called it LES equations). So there is no explicit filtering needed. But it may come in due to the subgrid scale (SGS) modeling (e.g. similarity models) on the right hand side. By comparing RANS and LES equations, you can see the only difference is the Reynold stress term. Also remember the definition of velocity is different. That's it.

Choicing RANS or LES dependents on your research purpose. For application in engineering, RANS is widely used. Right now as I know LES is still limited to pure research purpose, especially turbulence at high Reynolds number where DNS is not avaible. Maybe in the future, LES will dominate industry also because it is believed to be more general which can be applied to different types of flows. Any model of RANS is limited to a small range of flows because of the constants in the model. It need to be modified to appy to other type of flows.

Q3 is Good question. I don't know also. What we doing is at the beginning of simulation, we add some small pertubation by random function.

 Brian. May 17, 2004 18:19

Re: LES.. Basic Questions

Hello..I wonder how you mean the velocity is different in LES to RANS? What is the velocity that is presented in LES papers? How does it relate to actual velcity? How do I compare actual velocity (say, from experiment)to LES velocity (whatever that may be). Thank you.

 Hall May 17, 2004 19:40

Re: LES.. Basic Questions

Assume the originally velocity is called full velocity. in RANS, velocity is the averaged full velocity, time average, space average and similarity average. Usually time average is used. In LES, velocity is the filtered full velocity. Actually it is kind of space averaged. For comparing with experiment data, we need to filtering the experiment data to get filtered velocity. Say if we use tophat filter, uf_i = 1/6( u_{i-1} + 4. u_i + u_{i+1} ), i is the index for space points. Or you can restore the full velocity from les velocity by solve the reverse equation above (so for tophat filter, you need to solve a tridiagonal matrix). The space average of RANS is not same as the LES at most time. For example, for 1 dimension case, RANS will use all the points, i.e. u_mean = 1/n (u_1 + ... + u_n). While LES will only use part of the points. Maybe it is more clear if we transfer the v to spectral sapce. In spectral space, RANS only u_mean, while LES has u_mean + some large scales components. The filtered velocity only loss small scales components. Find a book, any turbulence book, it is more clear than what I say. Hope this help! Good luck

 NIK May 18, 2004 06:28

Re: LES.. Basic Questions

Thanks..it is really helpful Now plz comment on what i have understood...as if i am right or not... once i solve the LES equations explicitly (4rh order Runge Kutta method of inviscid terms) and upwinding for Viscous terms..and the solution i get will give me the updated variables. It is just like time avg (RANS) except the spatial switch to give me the subgrid term as my velocity if now spatially filtered...So is there anyother difference? AS i only forsee that i just need to add one switch that if grid reduces to certain limit (subgrid) just dont compute but put the value of modeled varibles (subgrid terms)?

 Lionel Larcheveque May 18, 2004 09:48

Re: LES.. Basic Questions

Hi,

First, RANS is formally related to an ensemble average, neither a time or space one. Nonetheless, using the RANS equation and invoking ergodicity, several computational approaches can be used, according to the problem to solve:

0, 1, 2 or fully 3D (related to the possible homogeneous directions of the flow)

steady or unsteady (for unsteady computation, one can consider that only the 'random' turbulent structured are modelled and that the 'coherent' (various definition) ones are solved).

In contrast, LES is always 3D (except for very few cases related to true 2D turbulence like stratified flows) and unsteady.

The relation between the instantaneous "real velocity" and the LES velocity computed at each timestep is quite complex. Maybe the better approach is to consider the instantaneous LES values as related to an ensemble average of numerous realizations of a flow that differ only by their subgrid parts.

Comparisons between LES and DNS/experiments have to be performed in some statistical level. Therefore at each timestep you need to accumulate data. At the end of the computation, you will perform time averaging and space averaging if homogeneous direction(s) is(are) available.

If you compare LES results with DNS one, you also will have to filter DNS data using an low-pass filter prior to the comparison. In fact, the more your LES is coarse, the more this stage is desirable because a higher turbulent kinetic energy part has been filtered out in your computation. For comparison with experimental data, such a filtering is generally not required because the cutoff frequency of the LES is commonly higher than the cutoff frequency of the measurement devices.

Concerning the inflow data, you basically need to use a steady mean profile with added unsteady fluctuations. The difficulty is to set realistic fluctuations that closely mimic the turbulent one. It's a LES very hot topic, (have a look to the in AIAA J. 42(3), 2004: there is a special section dedicated to the subject).

Eventually, two general references dedicated to LES:

Short course by U. Piomelli (http://www.glue.umd.edu/~ugo/research/figs/CFD01.ps.gz ): good start for newcomers in the field.

Book by P. Sagaut (http://www.cfd-online.com/Books/show...hp?book_id=247 ): to go deeper with a rigorous mathematical approach

Hope this helps

Lionel

 Hall May 19, 2004 16:11

Re: LES.. Basic Questions

Hi,

This first part is right. I am not sure what do you mean 'when grid reduce to ...'. Do you mean you change the grid number all the time during calculation? As I know the grid points usually is fixed. And I don't think there is such spatial switch. The grids are always much less than the required. ... For example, consider a series expansion: exp(x) = 1 + x + x^2/2 + ...... when x -> 0 The expansion has infinite terms. No matter how many terms you take, you can't get exact exp(x), only approximation. But in most time, the first few term is good enough, let's say 3 terms. Then the truncation error is expressed as O(x^3), i.e. exp(x) = 1 + x + x^2/2 + O(x^3) This is the same thing for LES. For real flow (high Reynolds number), we need huge number of grids to capture all the scales of turbulence, which is beyond the ability of computer. So we only compute the large scales (like the three terms above), cut off the small scales and modeled them (like above O(x^3)). No matter how many grids you have, you only have part of the scales and still need to model the rest. SGS model means model the scales which are not represented by the grid.

By the way, I stongely suggest you read some LES book, it is much clear for such basic questions.

Good luck!

 Li Yang May 19, 2004 17:14

Re: LES.. Basic Questions

"I stongely suggest you read some LES book, it is much clear for such basic questions."

Well, I am obviously confused who should read some LES books. I would read the following papers first:

Turbulent inflow conditions for large-eddy simulation of compressible wall-bounded flows, Sagaut P, Garnier E, Tromeur E, Larcheveque L, Labourasse E, AIAA JOURNAL 42 (3): 469-477 MAR 2004

Large-eddy simulation of a compressible flow past a deep cavity Larcheveque L, Sagaut P, Mary I, Labbe O, Comte P PHYSICS OF FLUIDS 15 (1): 193-210 JAN 2003

 Li Yang May 19, 2004 18:24

Re: LES.. Basic Questions

Sorry Hall, my previous response was due to a mistake.

Li

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