Flame Propogation Study

About

Before my days working for Chuck Wight, there was a student named Changwei Xiong (who still works with the program). One of the final things he noticed while on the quest for his Ph.D was an incongurence in the model's predition of lateral flame spread, and the actuallity measured in laboratories. According to Chuck, previous versions of the code have caused a pressure dependence depending on approximately P-0.2 where the measured version in literature [1] is P0.538.
Currently, simulations are running in order to reaffirm Changwei's findings, and find a solution. So far, the best progress came from identifying the fact that in the original input files, was set to constant as opposed variable. This changed the trend from a negative exponent to a positive exponent, if only by a very small amount. An image representing the trend of pressure dependence an be seen here. Note, there are two different runs, one with preheated gas above the entire length of PBX and one without. The preheated zone was originally tested to see if preheating cells in advance of the flame front could help with the pressure dependence. It did convert the exponent from positive to negative. But it caused one undesired effect, the increase of lateral spread rate. In the literature, spread rates are on average 100-1000 times slower than those in the simulation. The following table, taken from [1] shows measured flame spread rates for PBX.
Flame Spread Rates as a Function of Pressure
Pressure (MPa) Orientation Sf (cm/s)
17.1 Horizontal 4.4
7.9 Horizontal 2.4
3.4 Horizontal 1.7
1.4 Horizontal 1.3
0.49 Horizontal 0.57
0.21 Horizontal 0.37
0.077 Horizontal 0.23
17.4 Vertical 5.4
1.5 Vertical 1.3
Experimental Results from S.F. Son, et. al.

Current values simulated using sus reveal a different trend and a very different magnituted. The values are as follow:

Flame Spread Rates as a Function of Pressure
Pressure (MPa) Orientation Sf (cm/s)
17.1 Horizontal 441.2
15.0 Horizontal 449.5
10.0 Horizontal 469.4
7.9 Horizontal 485.1
5.0 Horizontal 473.7
2.0 Horizontal 450.1
1.5 Horizontal 480.9
1.2 Horizontal 483.4
0.7 Horizontal 463.1
0.49 Horizontal 424.8
Simulated results using sus: Revision 1
As such, we are now looking into a way to reduce the order of magnitude difference before addressing pressure dependence. To do this we are looking into using Unsteady Burn, and the scaling mass burn rate after a cell has been ignited.
At the moment, the best such method seems to be starting the the surface temperature gradient at a high value and letting it relax to a more reasonable value over time, which simulates a very short preheated zone in the PBX. Similarly, we are looking into cutting the intial burn rate that is set to a steady state value, as this is not the behaviour seen in nature. For more information, see page on magnitude.

Problem Setup

The problem is set up in a 2 dimensional domain consisting of 0.6 cm by 0.24 cm box. In the bottom 10% of the domain exists a block of PBX extending entire distance of domain. Z boundaries are symmetric to facilitate 2D behavior. A box of gas on the x- side of the domain (two cells thick by three cells long) at 600 K ignites the material. The x-, x+ and y- boundaries are also symmetric to prevent the PBX from moving around in the domain, as well as well as prevent the x boundaries from extinguising the flame.

Visual of Problem

These videos illustrate the simulation, though they were run in a much larger domain--one impractical for this study (at the moment).
First, we have a video revealing temperature detail of the gas above the PBX. The bottom column is the temperature, and the top is the particle mass.


Second, is a video detailing which cells with PBX are labeled as burning by the model (the only cells reacting).

Results - Revision 2

Results - Revision 1

Revision one consists of two sets of runs spanning 5atm to 171atm initial surface pressure. The first run is Changwei's original files with variable heat exchange on. It shows slightly better Pressure exponent than with var heat exchange off. However, the results cannot even be called close. It appears there is something fundamentally wrong with the way the model spreads flame. One possible cause is the fact that once Steady Burn flags a cell as burning, it starts to burn at full throttle. This may cause excessive heat at the flame front. This may expalin why there is a three order magnitude difference. What it does not account for is the incorrect pressure dependence. We are looking into slowing the flame down by three orders of magnitude before tackling the pressure dependence. As such, Revision Two is started. Data and information will be posted as soon as they become meaningful. The second run is Changwei's files with a one cell thick layer of 525 K gas. This, we hoped, would perhaps mimic Radiative heating, which we presume is why the flame spread is not of the correct pressure dependence. Results are still being looked at. Revision 1 Page

Burn Rate Test

The validity of Steady Burn as a model for normal burn rate has come under suspision with such a high (by 3 or more orders of magnitude) lateral flame spreading rate. As such, tests are being run, to test the theory. These consist of a 1x1x1 cm cell, 1/4 filled with PBX. The surface next to the gas is ignited by 600K gas, and the surface is allowed to burn away. Measurements will be taken and compared to literature value. Currently, the simulatiosn are running - 06/25/09. A video can be seen here.

References

[1] Son, S. F.; Asay, B. W.; Whitney, E. M.; Berghout, H. L.; "Flame Spread Across Surfaces of PBX 9501" In Proceedings of the Combustion Institute; Elsevier Inc.: 2007, Vol. 31, pp 2063-2070.

Misc.

All file linked to by this page can be found in this directory.
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Contact: josuf dot the dot uf at gmail

Updated: 06/18/09
Created: 05/21/09