Estimation of Flammability Limits of Selected Fluorocarbons with F(sub 2) and CIF(sub3) Page: 16 of 78
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5. Use approximations from flame and detonation theory to estimate the (brief) pressure pulse
generated in a fully developed shock.
Though the results of these models were used in prediction of flammability limits, nothing in the
model explicitly speaks to whether or not a gas mix would be flammable. The postcombustion
temperature was used outside the context of the spreadsheet and compared with a correlation
between reaction temperatures for gas mixtures known experimentally to be flammable.
Most spreadsheets postulated two bounding chemical reactions with different oxidizer/fuel
ratios. For a starting gas mixture with an oxidizer/fuel ratio between that of the two reactions,
the reactants are distributed between the two reactions so that complete consumption of both fuel
and oxidizer occurs. Initial gas mixtures outside the bounding ratios were not valid for that
particular spreadsheet. A few spreadsheets used a single reaction (those valid for very high or
low reactant ratios), treating excess reactant as a diluent.
A heat of reaction is associated with each reaction in the spreadsheet. In some versions, this heat
of reaction is embedded in algebraic formulae in the spreadsheet, and in others it was calculated
from a table of heats of formation of each participating species. The heat of reaction for the
particular mix being run, along with the change in composition upon reaction, is used as an input
to a flame propagation model.
Only limited documentation of the model's physical chemistry basis was found . An
examination of the mathematics of the spreadsheets indicates that they are an application of a
standard model of the burning of a premixed flammable gas in a spherical chamber. This
constant volume spherical flame propagation model is discussed in both Jost  and Lewis and
von Elbe . The notation and format used most closely follows that of Jost , Chap. IV. It
should be emphasized that this theory is not for detonations (supersonic shock propagation) but
rather for subsonic flame front propagation. The model of an expanding spherical flame front in
a fixed volume spherical chamber should, to the extent that the energetics of the reactions are
representative of the actual flame process, give a reasonably accurate depiction of the final
pressure attained when all the gas is burned. During burning, the flame velocity generally
increases, possibly eventually running up to sonic, then to supersonic velocities, at which point
this model must be discarded in favor of a direct model of fully developed detonation waves.
Since the gas volumes of usual concern in GDP operations are neither spherical nor likely ignited
in the center, flame velocities and local pressures may well exceed those predicted by the
spherical flame propagation model. For this reason, a "detonation pressure" is estimated in the
spreadsheet models, in addition to the static, pseudo-adiabatic final pressure. This detonation
pressure is estimated simply as twice the final flame pressure, based on an approximation
proposed by Langweiler . The shock pressure is the local pressure within a moving, fully
developed shock wave moving with the advancing flame front.
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Trowbridge, L.D. Estimation of Flammability Limits of Selected Fluorocarbons with F(sub 2) and CIF(sub3), report, September 1, 1999; Tennessee. (https://digital.library.unt.edu/ark:/67531/metadc623234/m1/16/: accessed May 25, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.