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Backlayering and changes with grid resolution
The problem I am dealing with is a tunnel. I am looking at a case where I get some smoke spread upstream against the airflow. The extent of this backlayering length is 12 m on a 0.4 m grid. If I go to 0.2 m grid I get 34 m backlayer, 0.1 m I get 55 m. I know FDS over-predicts the velocity I need to control smoke. But what I am struggling with specifically here is the backlayering length and convergence (of some sort) with grid refinement. I would simulate a 0.05 m grid but 0.1 m is at the limit of what I can feasibly do (and most of the time in practice I see grids 0.4 m to 0.2 m - in this study there was not much difference in downstream temperatures between 0.1 m and 0.2 m grids).
I have tried a lot of different thigns. I thought maybe this was tied to the turbulence model, and near-wall conditions. I tested numerous models, even fixed the near-wall viscosity. It did not seem to perturb things at all. I have tested flat versus arched ceilings, but am not seeing much change either. It might still be this, but I am less convinced this is the problem.
The hot plume spreading upstream against the incoming airflow is a difficult flow regime to resolve. But what I struggle with is that as the grid is refined each time, the extent of the upstream spread increases. It suggests to me that maybe there is something going on with the plume from the fire, and the peak temperatures. As the grid gets finer perhaps temperatures increase, thereby increasing the vertical momentum of the plume and thus the backlayering extent (since the horizontal jet has more momentum).
I have thought about implementing a PID controller and tuning the upstream velocity to just stop backlayering. That will, I think, show a similar result in the upstream velocity needed continuing to increase with each grid refinement. My reasoning here is that if the velocity was just enough to stop backlayering, at the next grid refinement step (based on experience) we will see backlayering, and so on.
Could this also be tied to the pressure tolerances and perhaps I need to run a tighter tolerance to catch this? Any other ideas what could be happening?
I have developed a simple case, 4 files, with grid resolution at 1 m, 0.5 m, 0.25 m, 0.125 m (A, B, C, D) - I ran A through C and have attached slices showing the extent of BL (A has no BL, BL then increases with refined grids - did not get to run the finest grid yet, but expect trends would be the same).
GridA.fds.txt
GridD.fds.txt
GridC.fds.txt
GridB.fds.txt
I'll take a look. One thing I'll check is if the fire itself plays a role; that is, does the fire's plume and temperature profile change affect the backlayering. Simple way to check this is to make the fire a fixed volume heat source. The other issue would then be the treatment of the near-wall stresses, boundary layer, etc.
Thanks. I think it is connected to the fire plume. I looked in Section 6.5 of the validation guide and there are some vertical velocity profiles in there. I suspect as the grid gets finer the model is predicting a higher plume vertical velocity, and this affects backlayering.
Yes, but we expect higher plume velocities up to a point. That is, a really crude grid smears out the hot plume leading to lower vertical velocity. As the grid is refined, the plume velocity should converge. Still, I'll consider this and the near-ceiling viscosity, etc. I have confirmed your initial findings.
I've tried a few things related to the NEAR_WALL_TURBULENCE_MODEL, but nothing showed up as glaringly wrong. Try setting NO_SLIP=T on the SURF line that defines the walls. I have found that this tends to slow the progression of the backlayer and seems to better define the gravity current. I'll run more cases over the weekend.
I tested some very simple models of a pool fire and found that with a finer grid. The finer grid case tended to get an increased vertical centerline velocity. Attached two models FYI. I suspect if the plume centerline velocity was at convergence, then we would probably start to see the same on backlayering. Maybe the fire plume nears tighter near-fire resolution. Plume2.fds.txt Plume1.fds.txt
I think you're right in the sense that the fire is the thing to look at. I added a vertical slice 7 m upstream of the fire in which I recorded the 'AREA INTEGRAL' of 'ENTHALPY FLUX X'. That is, the amount of energy flowing in the upstream direction (hence the negative sign). You'll see that this quantity is not yet converged for Grid D (12.5 cm). What makes this tricky is that this energy (approx. 1 MW) is a very small fraction of the total HRR of the fire (50 MW). But even so, that extra energy sustains the back-layer for a greater distance upstream in the fine grid case.
It has quite an impact then, for such a small amount of heat.
Have you looked at the momentum flux at all? That might be a bigger differential.
I took a slightly different approach here. I simulated a 30 kW pool fire (based on a paper you co-authored - CFD Fire Simulation Using Mixture Fraction Combustion and Finite Volume Radiative Heat Transfer). Files attached and see image for results. This converged fairly well (though the finest grid case does need to run longer, though hard to see that the results would change at all). Input files attached for info.
This was only 30 kW, but I wonder if the result here is a clue to what is going on? The simulation needed a finer grid to really capture the plume centerline velocity. Maybe if the plume is resolved on a 0.05 m grid in the tunnel models, but a coarse grid is used further away, we end up with better grid convergence. Would be a big model, even if the 0.05 m region is kept near to the fire. Maybe the backlayering will still be more relative to experiment still, or perhaps the more well-resolved plume has effectively less vertical momentum overall and thus can capture backlayering closer to the test. I do want to try repeat this current exercise with a larger pool fire and see how it compares to the McCaffrey correlations.
Also, I tried changing turbulence model and flux limiter (dyanamic LES and central differencing) - results got worse relative to plume correlations.
PX-1-2.fds.txt PX-1-1.fds.txt PX-1-3.fds.txt
I added an even finer mesh, 6.25 cm. I also added animations of the centerline temperature field (20 °C to 1000 °C) for Cases C (25 cm) and E (6.25 cm). I think that this points out the problem with the notion of convergence in LES. As the case is refined, the fire exhibits greater turbulent motion, but also has a different "structure". The animations demonstrate this better than words.
https://user-images.githubusercontent.com/11333911/223181023-8469b314-1e28-4292-96f5-9131ce53d7c0.mp4
https://user-images.githubusercontent.com/11333911/223181102-25e7932c-d270-4618-a4b0-cf6b269a6c2c.mp4
Yes, the animations show the change in plume structure very well. The plume seems to be the critical thing here, though I am still not quite sure what the path forward to resolving this is.
Matt, One of the things I'd like to do is create a series to model the Alpert and Heskestad/Delichatsios correlations for steady plumes. One of the problems I see is that we don't really know whether the fine calculations are converging to the correct solution. (I'd like to think so, but comparing with the correlations will be good.)
We should see a similar trend, and from there we ought to be able to develop a solution to this problem.
Hi Randy, I agree, that should show us something. I posted a little while back about the McCaffrey plume predictions on the centerline, and was getting results trending toward a converged result (pasted below). I am testing a model to look at the horizontal ceiling plume as well. I will share results when I get them. I would think if we could get the vertical part converged, and the horizontal, that would give us confidence in what is going on, or expose the problem perhaps. It might be too that the grid we need to resolve the plume well becomes too fine for practical use in tunnel fire simulations.
I ran a simpler case in which I created a thermal plume of about 10 MW. Shown are cases with 25 cm and 12.5 cm resolution, time-averaged over 10 s. The result is shown at 300 s. As in the fire case, there is a slight difference in the energy flow upwind that sustains the gravity current for different distances.
Fundamentally the same result then with just the thermal plume.
I have been looking at ceiling jets a bit here. I found that a simulation over predicted the jet maximum velocity by around 60 to 70%. There was some work out of Lund a few years back that got a similar outcome. See below. This might be a key to solving this - if we can get the ceiling jet velocity right perhaps things will start to work better. I am currently running a fine grid case here of the ceiling jet. Will post results when available.
https://lucris.lub.lu.se/ws/portalfiles/portal/5660006/4246970.pdf
I ran a case modeling the horizontal ceiling jet. Image below, three different grids. The maximum plume velocity is typically more than the correlation. There is some sensitivity to the grid, but not drastic. Still, the finer grids do show higher plume velocity, which would support the observed behavior of more backlayering. Why? Hard to say for sure, though it points to turbulence I think. Would be somehow related to the prediction of the jet and entrainment.
I ran this thermal plume case at 50 cm, 25 cm, 12.5 cm and 6.25 cm. Shown here are 25, 12.5, and 6.25. Curiously, the 12.5 cm resolution has the longest back-layer and greatest enthalpy flow upstream. The plume dynamics in this case are noticeably different than the other three, with much more "puffing" contributing the upstream gravity current. This suggests that the dynamics of the plume are undergoing different transitions as the grid is refined.
In your case, there at least appears to be convergence. Obviously, the same amount of energy flows in all directions, eliminating that as a complicating factor. I think in the case of the tunnel fire under longitudinal ventilation, the changing fire plume dynamics complicate the convergence study.
Matt, How are you measuring the max velocity? I wonder if we are just seeing the effect of resolution on the velocity fluctuations and the correlation is looking at the "mean" -- that is, the statistical expectation. It can be difficult to tease out the mean from an LES, especially if there is a transient to the mean.
Hi Randy - I used a time average statistic on a grid of points...like this:
&DEVC XBP=0.00,0.00,0.0,0.0,1.5,2.0,QUANTITY='U-VELOCITY',ID='velP-01',POINTS=20,STATISTICS_START=30.0,STATISTICS_END=260.0 /
Files are attached. PX-1-6.fds.txt PX-1-7.fds.txt PX-1-5.fds.txt
Matt, I don't see any problem there, except that we are getting the time average of the resolved (filtered) velocity field, which should change as the grid resolution changes. What I think we want is the mean of the "true" or "dns" velocity field, u. Here I'll use <u> to indicate the mean applied to the dns velocity field. And I'll use U to indicate the LES resolved velocity field. So, what we really want is <u> = <U+u'> = <U> + <u'>.
We might want to add 'SUBGRID KINETIC ENERGY' to the output. If you assume isotropy, then you get the u' from
u' = sqrt(2/3 k_sgs)
which is used, for example, in the denominator of the mixing time scale model (tech guide, eq. (5.15) for tau_u). In theory, this value goes down as the filter width (grid spacing) is reduced.
I think this will all still point to FDS over-predicting the max ceiling jet velocity, but it might help with the interpretation of the grid dependence.
Here I'll use to indicate the mean app
A kind remark here. I see the boundary is applied as concrete. I have seen cases where a working mechanical smoke extract system failed after 600 s (arbitrary time) because of the walls being heat up (increased temp => increased gas volume). In this example as well, as the walls heat up, the thermal conditions of the plume might change even with a constant HRR fire.
I suggest to setup a benchmark with a fixed wall temperature.
Good point. Either fix the wall temperature or you can set TIME_SHRINK_FACTOR to something like 10, which effectively lowers the specific heat of the wall material by that factor, speeding up the time to steady state.
HI - I am wondering if this issue is tied to the pressure equation and tolerances. Per the User Guide there is the pressure tolerance that has a default of 20 / dx^2 and velocity tolerance with a value dx/2. As the grid resolution changes, these solver tolerances change. This might at least explain some of what we see, with different behaviour at changing resolutions. Some previous work discussed how the baroclinic term affects backlayering (Fire Dynamics Simulator (Version 4.0) Simulation for Tunnel Fire Scenarios with Forced, Transient, Longitudinal Ventilation Flows), which is what prompted me to look at this. I am running some cases here, but my current computer capability is limited so it is taking a while. I added this line to my cases, to force the solver to use the same tolerance each time:
&PRES TUNNEL_PRECONDITIONER=.TRUE.,VELOCITY_TOLERANCE=0.0001,PRESSURE_TOLERANCE=1.0,SUSPEND_PRESSURE_ITERATIONS=.FALSE.,CHECK_POISSON=.TRUE.,MAX_PRESSURE_ITERATIONS=100 /
I would think that the pressure tolerance would be the one to look at. The tighter the pressure tolerance, the better the model computes this baroclinic term. The velocity tolerance is more relevant for mesh to mesh pressure continuity. In these tunnel cases, that is largely handled by the preconditioner.
Tested this (pressure tolerance) on a few cases, but did not see anything of significance. I circled back to the wall functions. The wall shear stress decreases as the grid is refined. This might be a factor. The y+ values for a typical tunnel simulation are large, but to hit anything within O(y+~100) needs a grid that is prohibitively fine for these sorts of tunnel simulations. Have tried a few different wall functions too, but nothing worth noting has been found. I did try a no slip BC and that did something with slightly different backlayering, but this may be a two wrongs making a right. Is there maybe another wall function or approach (perhaps not implemented in FDS) that is better suited to situations like this?
Look at the fire or plume itself. Do you see qualitative differences as you change the grid? My last look at this (above) suggested that changes in the grid size can lead to changes in the fire or thermal plume that then affect the backlayer. I thought of adding a baffle or obstruction upstream of the fire to disrupt any grid-related pattern that might form at the leading edge.
I would like to confirm the previous assessment that this effect has nothing to do with the pressure tolerance. In the meantime I have run the cases with the inseparable UScaRC solver resulting in a velocity error of 1E-16 and a pressure error of 1E-8. Nevertheless, similar images are obtained, see the results for GridB and GridC (the latter is currently not yet finished):
I tested the grid resolution aspects a bit more. Below is the summary. Note - I only ran these out to 120 s, but by this time things were starting to settle down.
My take-away is that the backlayering extent seems to be better predicted with the finer grids, y+ around 250 or less. The cases all show variation, though there is some trending in backlayering length at finer grids (e.g., A2 versus A4 and A5).
Case: 10 m wide, 5 m high, 50 MW fire, 30% radiative component, upstream velocity 2.25 m/s, fire geometry 1.2 m high, 4.2 m wide, per NFPA 502 2014 Vc = 2.1 m/s (free stream) and 2.3 m/s (local to fire)
Short summary: Grid resolution appears to be a key component of the backlayering – need y+ in the order, using V/Vc = exp(-0.054 Lb/H) gives Vc = 2.6 m/s (13 m backlayer) which is +25% (in line with other runs)
Details: Grid A: 0.5 m throughout, 6.5 m backlayer (BL), y+ (in BL region, rough order) ~ 1000 Grid A1: 0.25 m around and up to 4.5 m upstream of fire, 0.5 m elsewhere, 8.5 m BL, y+ (in BL region) ~ 500 Grid A2: 0.25 m throughout, 12 m BL, y+ (in BL region) ~ 250 Grid A3: 0.125 m around and up to 4.5 m upstream of fire, 0.5 m elsewhere, 4 m BL, y+ (in BL region) ~ 160 (abrupt y+ change at grid change) Grid A4: 0.125 m around and up to 14.5 m upstream of fire, 0.5 m elsewhere, 12 m BL, y+ (in BL region) ~ 200 Grid A5: 0.125 m around the fire, 0.0625 m near upper wall up to 14.5 m upstream of fire, transition from 0.125 to 0.25 m from 14.5 m to 15.5 m upstream of fire, 13 m BL, y+ (in BL region) ~ 160
Grid A
Grid A1
Grid A2
Grid A3
Grid A4
Grid A5
GridA.fds.txt GridA1.fds.txt GridA2.fds.txt GridA3.fds.txt GridA4.fds.txt
A3 is curious. What do you suspect is the cause of that backlayer being considerably less than the others?
Suspect it is the grid interface, see here...probably I need to run these a bit longer too, but I think there are some trends coming through
An additional update - previous models had a slight problem on the inlet BC (the velocity surface did not cover the whole face so the net inlet velocity was a little lower than quoted). I reran the model with 10 m wide, 5 m high, 50 MW fire, inlet velocity 2.25 m/s. Reran models with:
GridA2: 0.25 m = no backlayer GridA3: 0.125 m around the fire and 5 m upstream, 0.5 m elsewhere = no backlayer GridA4: 0.125 m around the fire and 15 m upstream, 0.5 m elsewhere = 6.0 m backlayer GridA5: 0.125 m around the fire, 0.0625 m near the upper wall (for about 15 m upstream), then out to 0.25 m = 6.5 m backlayer
Images below. The y+ values in the upstream region (about 5 m or so upstream of the fire) were around 200 or less for models where backlayering was seen. The take-away appears then that near-wall resolution is key to this issue. I am testing a finer grid (0.0625 m throughout) but the number of cells is huge so it is taking a while to run. I think if that result shows a similar amount of backlayer to what we see here (6 to 7 m), then it might be possible to close this issue on the basis that the grid resolution near the wall needs to be such that y+<200 to get grid convergence. Will post that result when it is available.
I expect the convergence of the back layering is related to the energy budget within the ceiling jet. Why is the backside boundary of the tunnel wall modeled as insulated? That will increase the degree of backlayering since you are minimizing the loss of energy from the ceiling jet.
I would also be curious to see if the convergence were better if you used a fixed heat transfer coefficient. As you refine your grid, FDS is moving the free stream gas temperature used in the convection calculations closer to the wall. It would be interesting to see if your convergence correlates to a converged convective heat flux/gas temperature at the wall as well.
On Wed, May 17, 2023, 2:07 AM mattbilson76 @.***> wrote:
An additional update - previous models had a slight problem on the inlet BC (the velocity surface did not cover the whole face so the net inlet velocity was a little lower than quoted). I reran the model with 10 m wide, 5 m high, 50 MW fire, inlet velocity 2.25 m/s. Reran models with:
GridA2: 0.25 m = no backlayer GridA3: 0.125 m around the fire and 5 m upstream, 0.5 m elsewhere = no backlayer GridA4: 0.125 m around the fire and 15 m upstream, 0.5 m elsewhere = 6.0 m backlayer GridA5: 0.125 m around the fire, 0.0625 m near the upper wall (for about 15 m upstream), then out to 0.25 m = 6.5 m backlayer
Images below. The y+ values in the upstream region (about 5 m or so upstream of the fire) were around 200 or less for models where backlayering was seen. The take-away appears then that near-wall resolution is key to this issue. I am testing a finer grid (0.0625 m throughout) but the number of cells is huge so it is taking a while to run. I think if that result shows a similar amount of backlayer to what we see here (6 to 7 m), then it might be possible to close this issue on the basis that the grid resolution near the wall needs to be such that y+<200 to get grid convergence. Will post that result when it is available.
[image: Backlayer] https://user-images.githubusercontent.com/15055988/238849183-f6e57090-8f62-4568-be61-a724e56bb646.png
GridA2.txt https://github.com/firemodels/fds/files/11494614/GridA2.txt
GridA3.txt https://github.com/firemodels/fds/files/11494615/GridA3.txt
GridA4.txt https://github.com/firemodels/fds/files/11494621/GridA4.txt
GridA5.txt https://github.com/firemodels/fds/files/11494626/GridA5.txt
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