Zukoski number

[Corentin Macqueron]

Hello,

I have a question regarding Q*, the Zukoski number.

It is said to be ~1 for natural/typical fires, but how does CFAST deal with it?

From my understanding, even in the latest versions (we tried 7.7.3), we cannot ask CFAST to “target” a user specified valued for Q*.

It is up to us to determine a fire area transient profile, and that’s it? We can build this profile to “target” a specific value of Q* but it’s difficult because Q* depends on the HRR which can be O2-deprived and that’s a result of the calculation, and it also depends on the gas temperature, which is a also result of the calculation.

I guess CFAST could be programmed to dynamically adjust the fire area for a user specified Q*, right? Are there plans to do it ?

For the time being, what do you recommend?

I think we should always make a sensitivity study, for instance for Q*=0.25 to 2.5.

We are trying to do it but, again, as Q* depends on the calculation, it’s complicated.

Or maybe I am missing something and CFAST is already targeting Q*=1 ?

Thanks.

[Richard Peacock]

CFAST doesn't actually make use of Q*.  We do keep track of the oxygen available in the plume for combustion and limit the HRR to available oxygen (with a user-settable lower limit below which combustion does take place .. defaulting to 10% O2). Any unburned fuel is transported until it finds available oxygen to burn.

Still, CFAST doesn't track Q* or have it as an input parameter.

[Kevin McGrattan]

I think the question is whether or not CFAST could be easily programmed to adjust the fire area to achieve a desired Q*. Suppose someone specified an HRR curve with time,and also a constant value of Q*. Could CFAST then just compute the area for each time point.

[Corentin Macqueron]

Ok but we can link Q* to the imposed fire area, and this area dictates the flame height and it has an impact on radiation to targets, because the source point altitude is linked to one third of flame height, right?

Doesn't the fire area dictate plume temperature as well ?

In the end, the fire area (and hence Q* indirectly) has an impact on targets temperature so we have to carefully estimate the fire area, right ? 

So what would you recommend to estimate the fire area transient profile for, say, an electrical cabinet fire ?

[Corentin Macqueron]

Yes Kevin that's exactly the idea : give to CFAST a target value for Q* and let CFAST adjust the fire area to have this Q* value at any time.

[Kevin McGrattan]

The relationship between A, Q*, and Q are given by Heskestad's plume temperature and flame height correlations. Q is the most important parameter, and Q* and A are less important.

[Corentin Macqueron]

I understand that Q* is less important but it has an impact nonetheless and I think it would be interesting to be able to give it to CFAST as an input, especially since the CFAST documentation mentions it and says it should be around ~1.

In a broader view, I can't find guidelines to estimate the fire area profile. For a burner and a pool fire it is straightforward, but for a solid fire such as an electrical cabinet, I don't find it straightforward.

Le ven. 19 août 2022 à 20:22, Kevin McGrattan <mcgr...@gmail.com> a écrit :

The relationship between A, Q*, and Q are given by Heskestad's plume temperature and flame height correlations. Q is the most important parameter, and Q* and A are less important.

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[Kevin McGrattan]

If the fire emerges from one vent, the vent's area would be a good estimate of A. Then computer an equivalent D and then compute Q*

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[Reneke, Paul A. (Fed)]

For a given value of Q at a particular point in time you can choose your Q* by going to the equation with your Q and Q* and calculating the A to give you the Q*. I am not sure I see the advantage of setting the Q*. I suppose it would allow you to better control entrainment but is that a good thing to allow. It really isn’t something that happens in a real building with a real fire.

[Corentin Macqueron]

Yes Paul that's what we are doing to estimate A, but when the fire is O2 deprived we do not know a priori the real HRR. But ok it does not seem important for you.

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[Reneke, Paul A. (Fed)]

I am sorry. I did not mean to sound dismissive.

 

The more I think about it I can see some desire for the ability but it would take a significant effort. Not undoable but CFAST is just not organized to do entrainment that way so there would have to be a some rewriting. Also the accounting to be able to support that with everything else CFAST already does is not trivial. We would need a significant demand to consider it.

 

The code is available, if you can figure out how to do it then you could submit it to be considered for inclusion.

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[Corentin Macqueron]

That's ok Paul, no worry.

I have seen this parameter to have a huge impact on some targets in some cases but I also ask this forum because you are the experts and I value your views not matter what :)

I will continue to think about it. For the moment we have a way to work around it so I guess we'll keep going like that for a moment.

Best regards.

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[Kevin McGrattan]

Paul -- it should be possible to do this directly in CEdit without making changes to CFAST itself. Currently the user inputs an AREA for each HRR value. Suppose we just add a checkbox that says "Use Q*" or whatever that grays out the AREA column and replaces or adds a Q* column. If tis is done, the AREA can be easily calculated from the input Q*. CFAST will not have to do anything because it will still get the AREAs as it did before.

[Corentin Macqueron]

Kevin, that would be a simple pre-estimation, that work as long as the prescribed HRR finds enough O2. But if the fire is O2 deprived, the pre-estimated area will be flawed. No? I think it would need to be dynamically solved. Also, Q* depends in the gas temperature which is also a result of the calculation, so...

Le ven. 19 août 2022 à 22:26, Kevin McGrattan <mcgr...@gmail.com> a écrit :

Paul -- it should be possible to do this directly in CEdit without making changes to CFAST itself. Currently the user inputs an AREA for each HRR value. Suppose we just add a checkbox that says "Use Q*" or whatever that grays out the AREA column and replaces or adds a Q* column. If tis is done, the AREA can be easily calculated from the input Q*. CFAST will not have to do anything because it will still get the AREAs as it did before.

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[Corentin Macqueron]

And about the fire area of an electrical cabinet, we do not really have vents on our cabinets, we have scenarios where the doors are completely open. At peak HRR we can consider area = total height * total width but before and after peak, well... Usually we just do a prorata or we target some Q*. But again if the fire is O2 deprived, we have to first assess the O2 deprivation and correct our first guess. Maybe we are just overthinking this ? But we really observe huge impacts on some targets.

[Kevin McGrattan]

Yes, you are over-thinking it. In a zone model, you must specify Q(t). CFAST allows you to also specify A(t). You are then modeling a fuel flow rate from an orifice or burning item of some specified area. All I am suggesting is that if you want to replace the specification of A(t) with Q*(t), you are still doing more or less the same thing. Specifying Q*(t) is helpful if you do not really have a good idea of what the fire area is. For example, you might have a room filled with garbage and you are given a Q(t) and you can set Q*=1 and get a reasonable estimate of the area. 

Coupling all this with O2 would be a mess. This is beyond the scope of a zone model.

[Corentin Macqueron]

Ok, thanks. 

One less thing to worry about :)

I might try to show a use case where it has a somewhat important impact on some targets if I find the time.

Le ven. 19 août 2022 à 23:55, Kevin McGrattan <mcgr...@gmail.com> a écrit :

Yes, you are over-thinking it. In a zone model, you must specify Q(t). CFAST allows you to also specify A(t). You are then modeling a fuel flow rate from an orifice or burning item of some specified area. All I am suggesting is that if you want to replace the specification of A(t) with Q*(t), you are still doing more or less the same thing. Specifying Q*(t) is helpful if you do not really have a good idea of what the fire area is. For example, you might have a room filled with garbage and you are given a Q(t) and you can set Q*=1 and get a reasonable estimate of the area. 

Coupling all this with O2 would be a mess. This is beyond the scope of a zone model.

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[Reneke, Paul A. (Fed)]

I would be interested in use cases.

 

I don’t so much think that oxygen limited combustion is beyond the simple fire model in CFAST as I am not sure we have the kind of data that would be needed to do a significantly better job then we currently do. Unfortunately the kind of bench scale experiments needed for this work seems not to be of interest to the fire community.

 

While Kevin is correct that his suggestion would not require changes to CFAST it would require changes to CEdit, which might not be that easy. The current design of CEdit is being pushed and a new design would take, again, a lot of effort. I do think helping people better model the fire and specifically fire area would be useful. We will take this under advisement and figure out what is the best solution.

 

Thanks for the discussion. It has been useful.

 

Paul

 

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[dr_jfloyd]

Perhaps a little late to this discussion, but in nuclear PRA usage of CFAST while I was at JH we often looked to keep a fixed Q*. This wasn't difficult to do. We just used Excel with one column for Q and another column where A was computed using Q*. Then just copy and paste the columns into CEDIT. This might be a useful workaround for you if CEDIT isn't able to support this.

[Corentin Macqueron]

I also work for the nuclear industry and being able to target a user-specified Q* would indeed be appreciated.

Jason, I agree it's quite easy to do what you explain a priori when there is enough oxygen, but for O2 deprived fires one must first assess this deprivation otherwise the constructed Q* will be flawed.

I'm on vacation but when I come back I'll try to provide some real use cases where Q* has a quite significant impact.

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[dr_jfloyd]

In O2 deprived fires you may not have a fire plume as CFAST models it. Rather than a conical flame volume over the surface area of the pyrolyzing fuel (what CFAST's plume entrainment is based on), you may have burning along a 3D-surface where hot fuel rich gasses encounter oxygen rich gasses. I don't know that you can reliably make the claim that you get the best answer in O2 deprived fires by trying to define a fire area based on a Q* and the HRR due to available oxygen. If for an under ventilated fire, what you assume for Q* makes a difference in terms of damaged targets, then CFAST might not be the model you should be using.

[Corentin Macqueron]

Ok, thanks, interesting.

What kind of model should we use in those cases? We have many O2 deprived fires. Most of the time, electrical cabinets, and we use height*width as constant surface fire area for reference and then we do a sensitivity study.

But I rather had in mind a use case with excess of O2. I'll try to show it in a couple weeks. 

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[dr_jfloyd]

In the US typical practice for electrical cabinets is the fire elevation is the height of the upper vents in the cabinet or 1 ft below the top in the case where there isn't significant cabinet ventilation (NUREG/CR-6850), heat release rates from NUREG-2178 Vol 1, and the the fire area to limited the cabinet footprint. Generally speaking room sizes where there are PRA targets and electrical cabinets are large enough that a single electrical cabinet or two electrical cabinets (following spread rules in NUREG-2178 Vol 2) won't result in underventilation. It is when fires spread to cable trays that underventilation tends to be seen. 

One option is you could run any such cases with just enough ventilation to sustain the fire at its full size. Obviously this is conservative, but it eliminates the issue of trying to figure out what Q* is "correct". 

You could look at the actual room geometry, where the fire is, and where air is coming from and try to make an engineering assessment on a range of plausible Q* (I don't have any specific guidance on how to do that in a manner that would pass regulatory scrutiny) and then cases with that range and use the conservative results.

Another option is you use a CFD tool which can account for how the flame moves during underventilation.

[Corentin Macqueron]

Our electrical cabinets are always considered fully open to be conservative, i.e. the front face of the cabinet is completely open (our safety authority makes this mandatory). We hence use the 1 MW peak HRR as suggested in some NUREG documents (don't have it with me right now). And in thoses cases, in our 'small' rooms, we do have severe under ventilation, i.e. peak around 200 kW because of O2 instead of 1 MW. But we also have large rooms where 1 MW is fully sustained.

We used FDS (5.5.3, very old, I know) on these underventilated cases and the flame was 'teleported' from the cabinet to the inlet ventilation of the room when O2 was not completely sufficient.

To be somewhat assured that we did not do too many stupid things using CFAST and FDS on these cases, we compared CFAST to experimental electrical cabinets fires (AREVA/IRSN PICSEL experiments) in O2 excess and O2 deprived fires with height*width for fire area and the results weren't too bad. We also compared FDS and CFAST on those experiments and the results were quite the same.

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[dr_jfloyd]

The flame isn't teleported. Fuel can only burn where it meets oxygen. When a fire becomes underventilated, the fire can go out if not enough ventilation is present to sustain enough heat release to keep pyrolysis going. Or, as you can see in videos of under ventilated compartment fires where the fire is sustained, as the fire becomes ventilation limited that burning moves to the vent openings.

[Corentin Macqueron]

Yes, of course, I know it isn't teleported :)

We also have videos of this effect on some of our experiments.

But with FDS this happens almost all the time when the fire is underventilated, whereas in the concerned experiments the flame remained in the cabinet. By artificially increasing the O2 concentration in the room FDS keeps the flame in the cabinet.

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