Fuel surface temperature and HRRPUA

[Alexandre]

Hi,

I simulated a heptane pool fire, based on the fire_whirl_pool model. The idea was to reproduce the simulation with a specified HRRPUA instead of using the pyrolysis model, as I would like to model more complex fuels later for which I would know HRR evolution but with limited knowledge on their properties.

So what I did is remove BOILING_TEMPERATURE and HEAT_OF_REACTION on MATL line. I added a HEAT_OF_VAPORIZATION on SURF line to compensate, I assume, the removal of HEAT_OF_REACTION.

As explained in the user guide, "if a MATL line is invoked by a SURF line containing a specified HRRPUA, then that MATL ought to have only thermal properties". So I ran 2 simulations, with more or less information on the MATL line just to be sure we would not lose information there.

--- Results ---

Obviously we have about the same results for HRR and MLR since it was made to fit the simulation with pyrolysis model. But the fuel surface temperatures are really different from each other, about 90°C with pyrolysis model and 350°C with specified HRR (and still increasing at the end of simulation at 150 s), which is a problem, not only because of the discrepancy with the former model but because it is way higher than the boiling temperature (98.5°C) which, I believe, cannot be taken into account as a maximum temperature when using a specified HRR.

My first question is: did I forget some parameters I should have specified ? And if not, is there a known reason or a solution for these discrepancies, not only between the two models but with boiling temperature ?

Thank you in advance.

[dr_jfloyd]

With pyrolysis being computer you are removing heat from the surface in order to evaporate the fuel.  With pyrolysis not being computed, you are not removing that heat; the result is a higher surface temperature. Instead of specifying material properties, just set TMP_FRONT to be the boiling temperature.  

[Alexandre]

Am I not removing that heat by using heat_of_vaporization on surf line ?

Also, my goal is to simulate fuel surface temperature as good as possible but using HRRPUA like I said in the original post. In that regard, I am not sure TMP_FRONT will help me so much. That is why I wondered if there was a way to take boiling temperature into account while using HRRPUA, either with FDS in its current state or with a few modifications in the source code.

[dr_jfloyd]

Sorry, misread your post.

Ultimately the temperature of the fuel pool in your case is going to be determined by the heat flux into the pool surface, the heat conduction through the pool, and the energy removed by vaporization. Errors in any of these will result in errors in the pool temperature. In your case, by prescribing the HRRPUA, you have decoupled the energy removed by vaporization from the heat flux into the pool surface and the heat conduction through the pool. You have some combination of over predicting the heat flux to the pool surface and under predicting heat transfer through the pool (the literature value for conductivity does not account for any convection). Since you know that pool surface temperature will be approximately the boiling temperature, you an avoid the compounding effects of any errors by just specifying TMP_FRONT to be the boiling temperature.

[Alexandre]

Thank you for your detailed answer.

I may have been short on explanations for my issue, sorry for that.

Unfortunately, fixing TMP_FRONT would not solve my issue because I would like to simulate not only the max steady-state temperature but also the evolution of MLR with fuel temperature or, in this case, fuel temperature with MLR since we specify it through HRRPUA. 

The ultimate goal is to write a suppression model that will use this evolution during a possible fire suppression phase (by using water application and cooling the fuel below fire point). Not with heptane obviously but first I wanted to check the capability to reproduce connection between fuel temperature and MLR by using HRRPUA with a well known liquid.

That is why I was/am wondering if there was something to be done to better simulate liquid fuel temperature even when we lack information on fuel properties and with awareness on assumptions we have to make due to the problems you mentionned in your last post.

[dr_jfloyd]

If you are going to be prescribing the HRRPUA, it will be difficult to obtain the correct surface temperature. Any errors in the heat feedback to the pool surface and / or conduction into the pool will manifest as a surface temperature error. Conversely, if you were predicting everything, the fact that you are seeing too high of a surface temperature suggests that you would see too large of an evaporation rate. At this point in time, the prediction of pyrolysis / evaporation of liquid fuels puts you in the realm of research use of fds. For liquid pools, FDS does not model either convection in the pool (each grid cell of the pool is completely independent of that others) or losses to the walls of the fuel pan (only the bottom). 

[Alexandre]

Thank you again for your answer. 

The motivations there are clearly research-oriented so I feel good being in the realm of research use of fds.

I just would like to be sure I understood the issue.

When you say 

"For liquid pools, FDS does not model either convection in the pool (each grid cell of the pool is completely independent of that others) or losses to the walls of the fuel pan (only the bottom)."

I understand this is the case when we use either the pyrolysis model or a prescribed HRRPUA. In this case, even if there is room for improvement regarding calculation of liquid fuel temperature, that would not explain the difference between the results we get using these two models.

What I understand from our discussion is that the discrepancy, as you said earlier, would be essentially due to the decoupling of the energy removed by vaporization from the heat flux into the pool surface when using HRRPUA. Am I wrong ?

If that is the case, my question is: do you believe there would be a way to modify calculation of liquid fuel temperature when using HRRPUA to take into account, at least, effects of boiling temperature ? I would just like your opinion on this before I look deeper into the code.

Another question which is actually of greater importance for us: what would be your opinion on a suppression model that would use fuel surface temperature as a parameter to calculate MLR decrease ? The idea would be something close to the Arrhenius law but while using HRRPUA on the free burning phase. It has been coded already and we have a some comparisons with experimental results. Should you be interested, I'd be happy to discuss it further.

[Kevin]

How is your proposed model different from those already in FDS? For example, there is a water suppression model that leads to an exponential decay of HRRPUA as a function of water mass per unit area. There is also the full pyrolysis model that fully couples water cooling and surface heating/pyrolysis. Have you tried these?

[Alexandre]

Yes I have tried these. The model was meant to "replace" the exponential decay of HRRPUA as a function of water mass per unit area. I have tested this exponential decay quite some time ago on tests we performed during my PhD thesis and it was part of what I presented in the last Interflam conference. From what we have tried, I understand the full pyrolysis model works fine, but its use will be limited to the fuels on which we have a very good knowledge.

Since suppression in the gas phase has evolved not long ago, the idea was to be able to model suppression by fuel cooling. What we wanted was to be able to do predictive simulations, which is not really possible, if not impossible with the current model since we need an extensive knowledge on the fire scenario to define E_COEFFICIENT.

The only hypothesis is that for one fuel surface temperature there is one and only corresponding MLR whether we are in the free burning phase or in the fire suppression phase, which is an hypothesis used in the Arrhenius law actually. We had several ideas to model it so we have tried 3 more or less complex models (including the Arrhenius law).

To use the model properly, what the user would need is a decent knowledge on MLR evolution and fuel properties to have confidence in the temperature of the fuel surface during the free burning phase (hence this topic in the beginning). Then, once water systems are activated, the model calculates MLR based on the fuel surface temperature and the results on free burning phase for MLR as a function of fuel surface temperature.

[Kevin]

I don't think that your basic hypothesis is correct, that the fuel surface temperature uniquely defines the burning rate. This would only be true if the pyrolysis were confined to a very narrow layer at the surface. What about materials like wood? Wood burns at different rates as the pyrolysis front moves through the solid, leaving a relatively hot char layer in its wake.

Can you cite a reference that supports your hypothesis?

[Alexandre]

I completely agree with you, I should not have phrased it this way.

Indeed, using fuel surface temperature implies that the pyrolysis is located at this very surface and the model is expected to reproduce physics for these applications. We worked mainly on pool fires for which we have experimental data which seem to confirm this hypothesis for this application (thanks to a local measurement of temperature in the pool close to fuel surface). As for connection between fuel temperature and reaction rate, it is commonly used through the Arrhenius law for all kind of materials, including those for which we have in-depth pyrolysis. Maybe I should have talked about "local temperature" (which may be inside the material) and not "surface temperature".

But then I wonder, can we currently take into account the depth at which pyrolysis occurs with a prescribed HRRPUA? Because as written in the technical guide, “the desired HRR is translated into a mass flux for fuel at a given solid surface, which can be thought of as the surface of a burner”. So it would seem pyrolysis will be assumed to occur at fuel surface even during the free burning phase.

Also, I checked the way it is done with the full pyrolysis model. Equation 7.28 p71 in technical guide involves a term Ts which is a solid temperature I guess. But where is it taken? I checked in the source code and I understand ONE_D%TMP(I) is a surface temperature, am I wrong? 

[Kevin]

In the full pyrolysis model, the solid is divided into discrete layers and the temperature and reaction rate are calculated for each layer by solving the one dimensional heat conduction equation. There is a unique T_s in each layer, and a corresponding reaction rate which is a function of the layer temperature and fuel mass fraction.

[Alexandre]

Thank you for your quick answer. I must have misread the loops.