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Chemistry of Detonations - Kamlet M.J.

Kamlet M.J., Jacobs S.J. Chemistry of Detonations - Maryland, 1967. - 28 p.
Download (direct link): chemistryofdetonations1967.djvu
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Much to our surprise, however, it was also found that, although agreement between \0 and Pruby was indeed slightly poorer at the lower loading densities, the differences were still quite small and no trend could be discerned. At po~ 1.40 g/cc, differences averaged 2.4% (12 data sets); at 1.20 g/cc, differences averaged 2.1% (12 data sets); at 1.00-1.13 g/cc, differences averaged 2.0% (13 data sets). Further, in no case was the error as high as 5% at the lower densities.
3 The values of Pcaic included a correction step which involved subtracting 6% where 6'arb, the weight fraction of explosive going over to gaseous products, was greater than 0.93. See Appendix to Part I,
Such precision at 1.00 g/cc was most unexpected in the light of our earlier observation that at this low density 7Vrb, , and for underbalanced explosives may differ by as much as 10-20% from the corresponding ruby values. With TNT at 1.00 g/cc as an example:
^=0.0253 moles gas/g explosive, Nruby 0.0293,
difference^ 13.7%,
= 28.52 g gas/mole gas, MRUby = 26.38,
diff erence =+8.2%,
@art> 1282 cal/g, Qrtjby = 1104,
difference=+13.9%, but
P0aic=75.3 kbar, Pruby = 76.2,
difference = only 1.2%.
Similarly, with tetryl at 1.00 g/cc, N^b (0.0270) differs from ^Vruby (0.0323) by 16.5%, but Poaic (85.3 kbar) 4,. differs from Pruby (87.1) by only 2.1%. With picric acid at this density, # (0.0251) differs from A^ruby (0.0317) by 20.8%; Pcaic (84.4 kbar) differs from Pruby (87.9) by only 4.0%.
The results may be summarized as follows. Proper values of N, M, and Q in Eq. (1), e.g., ruby values or arbitrary values at the higher loading densities, lead to detonation pressures which agree well with ruby predictions. At the lower densities the H20-C02 arbitrary no longer provides proper estimates of N, M, and Q. This apparently makes little difference as concerns average agreement between Poai0 [Eq. (1)3 and Pruby, however, and we are faced with the seeming anomaly that input information which is known to be grossly incorrect leads to predictions from Eq. (1) which are very nearly correct.
The rationalization of this anomaly holds important implications about effects, of product compositions on calculations from Eq. (1). To whatever extent Eq. (1) successfully pkrallels ruby and the Kistiakowsky-Wilson equation of state, and to whatever extent the latter in turn successfully describe actual phenomena,, these Implications may also serve toward a better understanding of properties of explosives in real detonations and, eventually, certain types of damage effects.
III. BUFFERED EQUILIBRIA
It has been mentioned1 that product compositions in the Chapman-Jouguet condition and in the subsequent expansion of the detonation gases depend most strongly on the two important equilibria
2 C0*=>C02+C, AHo -41.2 kcal, (2)
+^+, ?Ä=-.31.4 kcal, (3)
and*that the H2O-CO2 arbitrary is simply a concise representation of the assumption that both equilibria
are predominantly to the right. From (H20/H2) ratios in ruby print-outs, it was shown that the computer predicts Equilibrium (3) to be far to the right for C-H-N-0 explosives at all loading densities under consideration. The computers (CO2/CO) ratios, on the other hand, indicate that it finds Equilibrium (2) to be predominantly to the right, i.e., (CO2/CO) > 15, only at loading densities above 1.70 g/cc (see(Table IV of Ref. 1 for specific data). At po<1.70 g/cc, ruby considers the 2 ^+ reaction to be in a regime of shifting equilibrium, and the increasing values of jVruby as loading densities and detonation pressures become lower are a reflection of rubys predicting greater amounts of carbon monoxide in accordance with Le Chateliers principle.
The resolution of the anomaly mentioned above has as its crux the fact that Equilibrium (2), whose shifting to the left at the lower densities engenders the changes in AWby, /ruby, and <2ruby, is buffered in the following sense: The number of moles of detonation gases per unit weight of explosive, their average molecular weight, and the amount of chemical energy which becomes available to heat and expand these gases do not vary independently of one another. As CO2 and solid carbon are replaced by successively increasing amounts of CO in the computer predictions (or in actual detonation mixtures), an inevitable increase in iVauBY (or actual N) is accompanied by equally inevitable decreases of comparable magnitude in rubys (or actual) M and Q.
Since at any po} P from Eq. (1) depends not on N, M, or Q alone, but on the quantity which we define by
=N^Pl2Q1|2, (4)
we Encounter the phenomenon of compensating errors which leads to an approximately correct result. In the previously cited instance of TNT at 1.00 g/cc, although arbitrary N, M, and Q differ from the corresponding ruby values by 13.7%, +8.2%, and +13.9%, respectively, (4.838) differs from ^ruby (4.998) by pnly -3.3%.
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