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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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As is discussed in the Appendix ruby’s estimate of the position of Equilibrium (5) is strongly influenced by the input heat of formation of carbon; similar considerations are likely to apply as regards Equilibria (2) and (3). Thus, the possibility exists that ruby’s estimates of N, M, Q, and the various N{ bear little relationship to the values of these quantities in actual detonations.
It follows that the H2O-CO2 arbitrary must be considered similarly suspect as regards estimates of actual N, M, and Q. In consequence of the buffered equilibria, however, this arbitrary may nevertheless be completely adequate for the estimation of actual ô, and hence actual detonation pressures and velocities.
B. Computer-Based Methods of Calculation
We have already questioned ruby’s input assumptions regarding the AH/ of carbon, the ki of the “minor”
10 Dr. E. Lee, Lawrence Radiation Laboratory (private communication). The referee has pointed out to us that Mader experimented with a positive Ä#/ in the course of his BKW studies. While using a positive Äß/ for carbon was a help in calculating P and D, it caused troubles in calculations involving the isentropic expansion of the detonation products, perhaps because it was not allowed to change during this process.
detonation species, and the parameters in the K-W equation (Appendix Ñ of Ref. 1). Other of the input data may be at least as suspect in that they are based on inherently inexact measurements or involve extrapolations to pressures far beyond experimentally accessible ranges.
In seeming contradiction, however, ruby does in fact succeed in predicting detonation pressures over a limited range of compositions and loading densities, which accommodate the body of inherently inexact and often contradictory measurements about as well as might be expected of any computational method. Further, the computer's estimates of detonation velocities show reasonably good agreement with more accurate experimental information over the same limited range of compositions and densities.
Again we feel that a rationale for “correct” results from “incorrect” input information may be found in the phenomenon of compensating “errors” such as have already been shown to minimize the effects of differences between arbitrary and ruby N, M, and Q in Eq. (1). It is no less likely that, even where the computer grossly misjudges the AVs, the buffered equilibria may introduce mutual cancellations which also tend to lessen the effects on ruby’s pressure and velocity of “errors’* in the various quantities which interact to produce these predictions in the computer’s multi-iterative machinations. Thus relatively large differences between ruby values and actual values of pj, Pk (or Vg), T, the Äß/s, 2^», CvdT, N, Q, Ej—Eo, y, etc., may offset one another and lead to values of /ruby and Z>rt7by which are very nearly “correct.” In consequence, ruby’s P and D predictions maty parallel those of Eq. (1) in being insensitive to exact product compositions and hence to inaccuracies in large segments of the input information.
ruby and Eq. (1) probably both reflect the fact that, as is discussed in the next section, actual mechanical properties of detonations are also insensitive to exact product compositions. It is also possible that the success of the K-W equation of state with other parameters and covolumes,4-7,11 other equations of state,12 and other computer-based methods over limited ranges of explosive composition and density may be attributed to similar buffering phenomena. A necessary corollary is that, as has already been pointed out in part by Jones,u good agreement between predicted and experimental P and D do not necessarily justify, (a) the form of the equation of state, (b) the equation-of-state parameters except over limited ranges of composition,
(c) covolume factors of the detonation products, (d) assumptions regarding the form and properties taken
IJ R. D. Cowan and W. Fickett, J. Chem. Phys. 24, 932 (1956).
12 For a review of the various equations of state, see S. J. Jacobs, ARS (Am. Rocket Soc.) J. 30, 151 (1960).
18 H. Jones, Third Symposium on Flame and Explosion Phenomena (The Williams and Wilkins Co., Baltimore, 1949), pp. 590-594.
by carbon and other solid products in the detonation, (e) other input information, and (f) predictions of other detonation properties which are not subject to experimental verification.
C. Actual Mechanical Properties of the Detonation
From an analysis of computer results not unlike our own, Johansson and Persson14 have recently suggested that detonation pressures might vary with the square of the loading density, i.e., for individual explosives
P=ApoK, K = 2.0, (6)
where A is a constant depending on the nature of the explosive.15 The proportionality was demonstrated for five materials over the important range 1.0<po<1.6 g/cc.
The results in Table VI and Fig, 1 of Ref. 1 confirm quite clearly that the K-W equation with Mader’s parameters (as reflected in ruby2) accommodates a P—Api relationship exceedingly well and extends the applicable density range to 1.00-1.96 g/cc. Our many comments regarding possible inadequacies of ruby should markedly weaken the significance of this observation, however, if based on the computer results alone. The suggestion that the P-po2 relationship may be real is therefore made primarily on the basis that, as will be discussed in Paper III of this series,1* the total body of available experimental information on detonation pressures of C-H-N-0 explosives also supports K=2.0 in Eq. (6).
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