Estimation of Flammability Limits of Selected Fluorocarbons with F(sub 2) and CIF(sub3) Page: 24 of 78
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and the equation numbers are those found in that reference (Chap. VIII, p. 524ff). The theory of
gas detonations is based on Hugoniot curves, which relate preburn and postburn pressures and
specific volumes under shock and nonshock conditions. Key points of this detonation model are
repeated here. Two equations
2i (l' vv n T
v - 1+ + T = 0 (21)
V2 I I x zx
V2 ~72V2 n2T272
(Cv) (T2-T,) - AE - . - -1 Jn2T+nITi v) = 0 (22)
must be solved for the two unknowns v2 and T2. The definitions of some of these variables are
not what one might first imagine. The variable v is the volume of a unit mass of gas at condition
1 or 2, the pre-shock and shock condition, respectively, while n is the number of moles per unit
mass of the gas at condition 1 or 2. Therefore AE and ( Cv )(T2 -T,) must be in units of energy
per gram of product gas. The factor (Cv ), intended to mean the average Cv between T and T2 of
the product gas mix, is variously taken as the linear average of Cy(T) and Cy(T2), as the integral
of Cv dT from TI to T2 divided by (T2 -Tj), or sometimes (for ease of calculation) simply as
Cy(T2). The integral form, the most accurate and defensible, is used in these models.
These equations are solved iteratively by a convergence technique. Using an initial guess for T2,
Eq. (21) is solved for the ratio v/v2. It may have two branches, one corresponding to a
supersonic shock, and the other to a slow flame. The solution.of interest here is the higher value.
Inserting this value for v1/v2 in Eq. (22), we solve for T2. This becomes our next guess. New
values for temperature-dependent parameters are computed from the new T2 (i.e., ( Cv ) and Y2)
and we iterate through Eqs. (21) and (22) until the value of T2 converges.
Once v2 and T2 have been determined, other parameters are derived. The parameter P2 is
obtained from the ideal gas law, which for the variable definitions used here, is
P2 v2/n2 R T2= P, v,/n1 RT . (23)
The detonation velocity, D is obtained from
D = V 72n2RT2 . (24)
The shock impulse is given by
i = (P2- P)v/v2 , (11)
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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/m1/24/: accessed May 26, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.