LES Quality Measures

[JWilliamson]

This is a continuation of a previous discussion started in:

http://groups.google.com/group/fds-smv/browse_thread/thread/bcc91ccdd404022e

Randy (rmcdermo) suggests a quantity called the Measure of Turbulence
Resolution (MTR) to quantify the quality of the LES resolution of
turbulence. He defined the quantity based on the turbulent kinetic
energy (k) as:

MTR(x,t) = k_sgs/(k_les + k_sgs)

which is always between 0 and 1, and "good" values should be less than
0.2.

I consider this to be a good quantity to describe turbulence. However,
it was brought up during the Annual BFRL Fire Conference that there
may be several of these quantities based on the physical behavior of
interest. I have been thinking of what might be useful for evaluating
sub-grid models and here is my current list of concepts:

Turbulence: MTR
Combustion: MCR
Convective Heat Transfer: MCHTR (ie. to solid obstructions,
sprinklers, etc.)
Radiative Heat Transfer: MRHTR (This would be nice to combine with
Convection, but I will keep it separate for now)
Spray or Droplet Motion: MSR

If you have ideas for other quantities, please post them.

Obviously, it is challenging to derive any of these quantities in a
way that can be easily implemented in FDS. I have an idea that I think
could work for Combustion. It's simply a comparison of the local
reaction rate per unit area produced by FDS compared to the analytical
solution for a laminar flamelet. The idea here is that your combustion
is well resolved in a grid cell if the combustion resembles a single
laminar flamelet (counterflow flame). The quantity can be defined like
this (it can only be defined in grid cells where combustion takes
place):

MCR(x,t) = (q"_fds - q"_fl)/q"_fds

q"_fds = [max(rho*Y_F; s*rho*Y_O2) * DH * (dx*dy*dz)^1/3] / tau
(equation 9.2 User Guide, multiplied by the LES grid size)

q"_fl = const * (Y_F * chi_st^1/2) / (1-Zst)
const ~ 200 kW/m^2 for methane in air
chi_st is the scalar dissipation rate, which could be approximated
from tau

What do you think? I haven't convinced myself that this gives us any
more information than MTR, but I would like to hear some of your
thoughts.

Justin

[rmcdermo]

Justin,

Thanks for starting this discussion. This subject is a HUGE can of
worms, but it is something we must start to think about.

Before I comment on your suggested MCR, I wanted to mention that I was
contacted by Simon Gant of Heath and Safety Lab in the UK and he has
reservations about MTR that he describes in a paper "Grid Resolution
Issues with Large-Eddy Simulation" which he has submitted to Flow,
Turbulence, and Combustion. I quote, "The fundamental problem with
methods involving the resolved turbulent kinetic energy is that
[k_les] can be higher in an LES solution than the total turbulent
kinetic energy from DNS. Whereas one might expect [k_les] to increase
as the grid is
refined, it has been shown that in mixing layers, jets, wakes and
channel flows [k_les] can actually decrease [14, 23]."

14. Celik, I.B., Cehreli, Z.N., Yavuz, I.: Index of resolution quality
for large eddy simulations. J. Fluids Eng. 127, 949-958 (2005)

23. Klein, M.: An attempt to assess the quality of large eddy
simulations in the context of implicit filtering: Flow, Turbul.
Combust. 75, 131-147 (2005)

Here also is a reference for other LES quality measures.

7. Celik, I.B., Klein, M., Freitag, M., Janicka, J.: Assessment
measures for URANS/DES/LES: an overview with applications. J. Turbul.
(2006) doi:10.1080/14685240600794379

In the end, Simon and I sort of agreed (I think) that MTR may be the
most practical measure for FDS at the moment, but the jury is still
out.

Ok, I like the list you have compiled! Though for different problems
these measures may not be independent, as a start I think I agree with
you that it would be good to separate them as much as possible and try
to find validation cases which are as focused as possible on the
phenomenon of interest. For example, the helium plume case completely
avoids the issues of combustion, convective heat transfer, and
radiation. We are left with determining whether we have sufficient
resolution for turbulence and scalar transport.

So, this brings to mind that you are basically proposing to substitute
MCR for MYR (you have reserved MSR for "spray", so I use Y for mass
fraction). For MYR I had in mind that we would do something with the
scalar dissipation rate computed at two different length scales. Your
proposal looks interesting, but I need to study my flamelet equations
and think about this before I comment further. One issue I can see
arising is that if dx --> 0, q"_fds .ne. q"_fl. So, how would we know
we have sufficient resolution? A prerequisite for obtaining LES to
DNS convergence is that all the models converge. So, this is not a
knock on your approach to MCR, as much as it may point out that we
need to think about the convergence characteristics of our combustion
model.

Cheers,
Randy



On May 7, 8:43 am, JWilliamson <williamson.justin.w...@gmail.com>
wrote:

> This is a continuation of a previous discussion started in:
>

> http://groups.google.com/group/fds-smv/browse_thread/thread/bcc91ccdd...

[clauten]

The relevant length scale for scalar dissipation, which controls
turbulent combustion, is the Batchelor scale which I believe is
proportional to the Kolmogorov scale multiplied by the inverse square
root of the Schmidt number (don't quote me on that). Since for air the
Schmidt number is close to 1, I would think that a calculation that is
well-resolved from a hydrodynamic standpoint would also be well-
resolved from a chemistry standpoint.

On May 7, 5:43 am, JWilliamson <williamson.justin.w...@gmail.com>
wrote:

> This is a continuation of a previous discussion started in:
>

> http://groups.google.com/group/fds-smv/browse_thread/thread/bcc91ccdd...

[Ofodike A. Ezekoye]

This is generally true, but the only concern here is that the reaction zone (100 micrometer and less) can be (and is often) buried inside the Batchelor scale. I guess it depends on what one means about resolving chemistry. Flamelet models work for the reason that detailed descriptions of the reaction zone are sometimes not required.

[JWilliamson]

I agree with Randy and Ofodike. The challenge with MCR will be in how
we define DNS. Do we have to resolve the chemistry (~0.1 mm grid or
smaller)? or is it sufficient to stop at the flamelet level where we
can obtain an analytic solution (~1 mm grid)? I think as far as the
application of FDS is concerned, the flamelet level will suffice.

I also agree with Chris (clauten) that resolving the turbulence will
go a long way toward resolving the combustion. I'm not sure that the
MCR will tell us anything more than MTR can already. The way I
pictured it is that the flame sheet can wrinkle several times in a
single grid cell. The more the flame sheet wrinkles within the grid
cell, the harder it is for us to capture all of the sub-grid scale
interactions (radiation absorption/emission, species diffusion,
thermal diffusion, etc.). I'm not quite sure if MCR is necessary, but
it could be interesting to compare MCR and MTR.

Randy suggested a MYR quantity for species resolution. This seems to
me to be mostly captured by turbulence and combustion. The exceptions
that I can think of are near a surface undergoing pyrolysis, or an
evaporating droplet (this issue has been identified for simulations
with sprinkler sprays tracking too few droplets). Did you have
something different in mind?

Thanks for the comments!

Justin


On May 7, 10:18 am, "Ofodike A. Ezekoye" <dezek...@mail.utexas.edu>
wrote:

[rmcdermo]

Justin,

Consider a flow with steady, uniform velocity (MTR=0), but with a step
function in mass fraction. If we based our grid on MTR we would
completely under-resolve the scalar field.

R

On May 7, 11:57 am, JWilliamson <williamson.justin.w...@gmail.com>
wrote:

[Kevin McGrattan]

Check the User's Guide for a description and examples, if they exist.