Expand TGA_ANALYSIS to Easily Reproduce Isothermal TGA Runs

[TristanHehnen]

Is your feature request related to a problem? Please describe.
Rates of pyrolysis reactions are often described by two main terms, the rate constant $k(T)$ and the reaction model $f(\alpha)$:

$\frac{d\alpha}{dt} = k(T) ~~ f(\alpha)$

Keeping the sample temperature constant allows one to assess the reaction profile and thus facilitates the choice of the reaction model.

In terms of FDS this can be used to assess if the chosen model fits to the behaviour of the sample, recorded during isothermal TGA experiments.

Describe the solution you'd like
It would be nice if the functionality of the existing simplified TGA model TGA_ANALYSIS could be expanded such that isothermal TGA runs can easily be replicated.

Two extra parameters need to be added for the isothermal conditions, for example:

• ISO_TEMP, provided in °C, the target temperature of the isothermal run (or maybe use TMPA similar to the initial temperature when using the constant heating rate)
• ISO_T_END, provided in seconds, used to stop the simulation, since they could run for long times at low temperatures when running for completion
• [optional] TIME_STEP, provided in seconds, to have some control over the resolution of the output

The output should basically be a CSV file like the existing one, providing time, sample temperature and the sample mass.

[drjfloyd]

The current model starts at TMPA and goes to TGA_FINAL_TEMPERATURE using TGA_HEATING_RATE. Does just using a really slow heating rate and TGA_FINAL_TEMPERATURE just a little larger than TMPA do what you need? The parameters below would give 150 C for 5 hours with 1000 lines of output. For E=10000 the change in reaction rate would be 0.05 % and at 100000 the error would be 0.5 %.

TMPA=150, TGA_FINAL_TEMPEATURE=150.01,TGA_HEATING_RATE=3.3333E-5,TGA_DUMP=1E-5.

[TristanHehnen]

Ah, that is a good idea!
I'll try it out.

Thank you!

[TristanHehnen]

I did some testing and found some strange behaviour with TGA_ANALYSIS and how the pyrolysis reaction kinetics are defined in FDS-6.10.1-0-g12efa16-release. In some cases the computing time increases massively.

I've used the PMMA from the NIST_NRC_Parallel_Panels and adapted one of the WUI needle verification cases to create a TGA baseline case. This baseline is compared with the performance of TGA_ANALYSIS.

When reducing the heating rate in TGA_ANALYSIS, the computing time strongly increases for values below about 1K/min. The solid lines in the following plot are from TGA_ANALYSIS, the dashed lines from the respective baseline case. The legend contains the heating rate of each case and the wall time of the simulation. It is interesting to observe that for the heating rate of 0.01 K/min TGA_ANALYSIS is significantly slower than the stripped down FDS simulation of the baseline.

Now to the isothermal simulations. Three setups are investigated (legend shows wall time per case):

• (TGA_Iso_01) the baseline, but TMPA is set to 320°C and there is no RAMP or any sort of heating involved, just a constant ambient temperature (blue)
• (TGA_Iso_02) TGA_ANALYSIS, from TMPA at 320°C to TGA_FINAL_TEMPERATURE at 320.01°C (green)
• (TGA_Iso_03) the baseline, but RAMP_TMP_GAS_FRONT is used to heat up from 320°C (TMPA) to 320.01°C (orange)

Again, a significant increase in computing time is observed for TGA_ANALYSIS. The orange case could be reduced to 1s or wall time, by removing the time step restriction (&TIME T_END=18000, WALL_INCREMENT=1, RESTRICT_TIME_STEP=F /). This was not possible for the blue case, it leads to funky results, thus DT=0.2 was used instead.

A colleague tried to verify the above findings and picked one of her material parameter sets of a different project (TGA_Fictitious). Surprisingly, in this case the isothermal TGA_ANALYSIS concluded in less than a second. Even though the material parameters are fictitious, they are not impossible. I noticed that one difference was that she defined the parameters of the pyrolysis reaction with REFERENCE_TEMPERATURE, PYROLYSIS_RANGE and HEATING_RATE. Using instead A, E and N_S=1 from the CHID.out, that FDS computed, and running the same simulation, the wall time increases to 4140 s.

Thus, it seem there is some issue between TGA_ANALYSIS and how the decomposition reaction kinetics are defined.
Attached are a couple of the files described above.

TGA_Iso_01.txt

TGA_Iso_02.txt

TGA_Iso_03.txt

TGA_Fictitious.txt

[drjfloyd]

In the code, the number of steps used in the TGA analysis is inversely related to the heating rate. The expectation is that the time should be proportional to the number of steps which is inverse to the heating trate and that seems to be what your plot legend is showing.

10 K = 1 s
1 K = 3 s (approximately 10 times 10 K)
0.1 K = 30 s (~10 times 1 K)
0.01 K = 294 s (~10 times 0.1 K)

If the use of a very slow TGA heating rate is making cases run too long, then you can also just do a TGA equivalent analysis without invoking the TGA model. Use a very small sample thickness (TGA_ANALYSIS forces 1E-5), a high heat transfer coefficent (TGA analysis forces 100) , turn off radiation, set TMPA to the isothermal temperature, and you can output the surface density of the different materials plus the convective heat transfer. WIth those you can get normalized mass loss and heating rates.

[TristanHehnen]

As written above, I did run cases with the TMPA - these are referred to as "baseline".

This does not explain however, why changing

• from REFERENCE_TEMPERATURE, PYROLYSIS_RANGE
• to A, E and N_S=1

the computing time increases by a factor of about 4140 for TGA_ANALYSIS.

[drjfloyd]

Which two input files show this?