Estimation of Flammability Limits of Selected Fluorocarbons with F(sub 2) and CIF(sub3) Page: 23 of 78
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used to compute the values on the right hand side of the equation and then to solve for AT (and
hence Tf) on the left hand side. The new value for Tf is used for the next guess and the process
is repeated until the guess and the solution converge to a common value. Once Tf is found, Pf
will be determined by the ideal gas law. The resulting final values are presented in the models as
the "final" results under the heading of "adiabatic case."
As in the original spreadsheet series, a "detonation pressure" is estimated as simply twice the
calculated adiabatic pressure per the Langweiler approximation (see ref. 3, p. 172). Langweiler
also approximated the detonation temperature as:
T2 = 2y/(y+1)Tf
where Tf is the adiabatic temperature attained by combustion and y is the heat capacity ratio
cPlcv. It is not clear at what temperature y is to be calculated, but the result will not vary a great
deal with this choice. The spreadsheet models calculate y for this purpose at Tf. The
temperature immediately behind the shock front, T2 is also listed in the "adiabatic model" under
Throughout this and the previous section, several distinct physical environments should be
defined. The initial condition is user specified, and is generally near room temperature and
atmospheric pressure. It is designated by the subscript "i" in the adiabatic calculations and "1"
(following both the Lewis and von Elbe  and Jost  notation) in the detonation model. The
adiabatic endpoint, designated here by the subscript 'f' (final), is the endpoint reached if the gas
simply reacts to the specified final products and is heated by its heat of reaction. The
"detonation" or "shock" condition is that which applies immediately behind a fully developed
shock wave. It may take some time and distance for an initiated flame to accelerate to a shock,
especially when the reactant mix is barely within the region of compositions permitting
explosions. The shock conditions will persist locally only briefly, being dissipated behind the
shock at what must be about the local speed of sound. The shock condition represents both a
moving compression wave and physical movement of the gas at the shock front, pushed by the
flame and explosion immediately behind the front. This leads to a final pressure-like term called
the impulse, which is the momentary force per unit area exerted by the combination of the
post-shock pressure plus the momentum of the moving gas. This impulse will persist for the
duration of the passage (or arrival) of the shock front, which will be moving at supersonic speed
(relative to sound speed in the unburned gas). The momentum portion of the impulse is
directional, exerting force in the direction of the bulk motion of gas in the shock but not
perpendicular to that motion.
Texts by Jost  and by Lewis and von Elbe  discuss detonation waves in burning gas
mixtures in similar same terms. The notation used here follows that of Lewis and von Elbe ,
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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/m1/23/: accessed May 23, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.