Estimation of Flammability Limits of Selected Fluorocarbons with F(sub 2) and CIF(sub3) Page: 46 of 78
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not, except in extreme cases, tell if the system can actually accomplish these events successfully.
In extreme conditions, the model may yield results in which the impulse is lower than the
detonation pressure. In such cases, gas movement is calculated to be in a direction opposite to
the direction of propagation of the shock, hardly a condition conducive to development of a
shock. The true boundaries of explosivity of the gas mixture lie well beyond such conditions,
however. The model will compute detonation pressures for conditions where, in fact, no
detonation would actually occur in a practical case. The flammability prediction in the
detonation pressure model spreadsheets does not derive from the detonation theory itself, but is
an empirical correlation based on the thermochemistry of the system.
The 1992 explosion'pressure models used a subsonic flame propagation theory to estimate
pressure of a gas mixture as it burns in a closed vessel. That model of combustion computes
pressure as a function of the fraction of gas burned but does not compute the rate of flame
propagation during that process. To do that would require calibration with experimental flame
speed data. An approximation was employed to estimate the potential detonation (i.e., fully
developed shock) pressure from the final gas pressure. Again, no real criterion existed in that
model (nor in the present versions) to determine if such a detonation would occur for a given gas
mix. The potential detonation pressure was subsequently used in various analyses of GDP
systems to evaluate safety or potential hardware integrity in gas explosion scenarios. A factor
not included in those analyses is the "impulse," which is a pressure-like term that includes not
only the detonation pressure (the local pressure in the shock wave) but also the effect of the
forward motion of that shock wave.
In interpreting effects of potential detonations, it is important to consider the short durations
involved. Assuming it forms in the first place, the shock wave may be traveling at several
hundreds of meters per second, but the zone of combustion may be on the order of millimeters
broad, and the postshock high pressure region some multiple of this. The pressures generated
may be very high, but are present for a very short time, which limits the energy that can be
transferred to the walls confining the explosion. Naturally, treating the detonation pressure (or
impulse) as though it were a static pressure is conservative, but may well be excessively so. If
such a treatment suggests that costly counter-measures should be taken, it may be wise to
examine the time-dependent effects more closely.
During the modification and development of the models discussed here, it became apparent that
some of the weaknesses and limitations of the two models could be minimized by a
comprehensive approach combining elements of each. Both models, but more particularly the
detonation pressure model, are limited to consideration of gas mixtures containing a single fuel
and single oxidizer. In real applications, it is likely that a combination of such species will be
present. A second problem with the detonation pressure model as currently constituted is the
difficulty of considering dissociation and other high temperature chemical effects. These
difficulties could in large measure be eliminated by use of the thermodynamic equilibrium
calculation for determining the reaction endpoint rather than resorting to specific defined
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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/m1/46/: accessed May 20, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.