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New method for predicting detonation velocities of aluminized explosives
Combustion and Flame 142 (2005) 303–307 www.elsevier.com/locate/combustflame
Brief Communication
New method for predicting detonation velocities of aluminized explosives Mohammad Hossein Keshavarz ∗ Department of Chemistry, Malek-ashtar University of Technology, Shahin-shahr, P.O. Box 83145/115, Islamic Republic of Iran Received 8 June 2004; received in revised form 6 February 2005; accepted 29 March 2005 Available online 27 April 2005
Abstract A simple procedure for determining detonation velocities of aluminized explosives, which have significantly nonideal behavior, is introduced. It is shown how only the atomic composition and condensed phase heat of formation of explosives, as compared with complicated computer programs, are sufficient for reliable, simple prediction of detonation velocity. Detonation velocities can be predicted by assuming that aluminum powder, based on oxygen content and the different pathways of decomposition of explosives, partially interacts with detonation products. Detonation velocities calculated by this procedure for aluminized nonideal explosives are in good agreement with experimental values, that is, results computed using BKWS-EOS. 2005 The Combustion Institute. Published by Elsevier Inc. All rights reserved.
1. Introduction Detonation parameters such as detonation velocity and detonation pressure are performance parameters and represent the effectiveness of different explosives; they can be calculated using different computer programs, e.g., BKW [1], RUBY [2], TIGER [3], CHEQ [4], and CHEETAH [5]. The heat of formation and density of the explosive substance and the equation of state (EOS) of the detonation products are usually needed for the calculations. There are several EOSs, among which BKW-EOS is used extensively to calculate detonation properties [1]. BKWC-EOS [5], BKWR-EOS [6], and BKWS-EOS [7] are three different parameterizations of BKW-EOS. * Fax: +98 0312 522 5068.
E-mail addresses: [email protected], [email protected].
Aluminum powder is used in explosives to enhance air blast, increase bubble energies in underwater weapons, raise detonation temperature, and create incendiary effects. It increases the heat of detonation and acts as an intermediate sensitivity agent. For many years, researchers have investigated the role of aluminum powder in explosives with the goal of producing utilitarian explosive mixtures containing aluminum powder [8–14]. Aluminized composite explosives are classified as nonideal explosives: the amount of material reacted may be a function of reaction zone length. The degree of heterogeneity and the secondary exothermic reactions occurring in the detonation products expanding behind the detonation zone are two important characteristics of nonideal explosives. Partial equilibrium rather than a complex reaction mechanism can be used to predict the detonation properties of nonideal explosives by specifying the initial amount of aluminum assumed to react. As physical separation
0010-2180/$ – see front matter 2005 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.combustflame.2005.03.011
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M.H. Keshavarz / Combustion and Flame 142 (2005) 303–307
of the fuel and oxidizer in aluminized explosives results in extension of the chemical reaction zone, they are often poorly modeled by Chapman–Jouguet theory. Thus, a nonideal explosive can have Chapman– Jouguet detonation pressure and velocity significantly different from those expected from equilibrium and steady state calculations using a computer program such as BKW [1]. Fairly accurate data are highly desired in the calculation of the various detonation parameters of ideal and nonideal explosives. There is a continuing need for simple, reliable prediction of detonation performance rather than complicated computer programs. This study had as its original purpose the development of a simple, reliable method, as compared with complex computer programs, for calculating detonation velocities of aluminized explosives with nonideal behavior. A new equation is introduced to correlate detonation velocity with elemental composition and condensed-phase heat of formation, as well as the initial density, of the explosive. The calculated detonation velocity is then compared with measured values and the predictions of BKWS-EOS using full and 50% interactions of aluminum with detonation products. It should be noted that the predicted results are comparable to the output of complex computer programs, and accuracy is not necessarily enhanced by greater complexity.
2. Detonation velocities of aluminized explosives Some empirical equations have been developed for predicting Chapman–Jouguet (C-J) detonation pressures and velocities of pure explosives and mixtures of different classes of explosives [15–27]. Detonation velocity is one the most important detonation parameters and can be measured directly with high accuracy to within a few percent at various charge diameters and extrapolated to an “infinite diameter.” Various studies show that the detonation velocity of aluminized explosives depends on elemental composition, oxygen balance, heat content, and initial density of the mixture. The heat of formation is a measure of the energy content of an energetic material and usually enters into the calculation of explosive properties such as detonation velocity and pressure. Condensed-phase heats of formation of explosives can be calculated for some classes of explosives [28–31]. All chemical bonds present in the reacting explosive are broken, resulting in the formation of monatomic species, which subsequently recombine to form stable products. For mixtures of highly volatile aluminum explosives, significant difficulties lie in the uncertainty in the amount of aluminum oxidized at the Chapman–Jouguet point. Because it is
not clear to what degree the aluminum is oxidized at the Chapman–Jouguet point for aluminized composite explosives, thermodynamic calculations of detonation parameters were carried out by assuming a specific degree of oxidation of aluminum [32–35]. Detonation pressure and velocity increase with an increase in the amount of gaseous products, prevention of oxidation of aluminum causes an increase in the number of gaseous molecules. On the other hand, complete oxidation of aluminum can force oxygen to react with oxygen rather than carbon, producing hot gas phase as a result of the large negative heat of formation of Al2 O3 . Experimental values reported for the detonation velocity of TNT/Al demonstrate that increasing the percentage of aluminum does not result in an appreciable change in the detonation velocity values. Because TNT is very oxygen deficient, it can be assumed that the least amount of aluminum can react with the detonation products of TNT. Some pathways for decomposition of ideal and less ideal explosives recently suggested [22] depend on the oxygen content of the explosive. It can be assumed that partial oxidation of aluminum will occur in any mixture of aluminum with Ca Hb Nc Od explosives based on the oxygen balance of the explosive. Different aluminum oxidation pathways can be introduced under the following conditions: 1. If d a, only 10% of Al reacts. 2. If d > a and b/2 > d − a, only 25% of Al is oxidized. 3. If d a + b/2 and d 2a + b/2, only 50% of Al reacts. It is possible to represent the detonation velocity of an explosive as a function of its composition on the basis of an approach proposed earlier, e.g., by Stine [26,27] and Rothstein and Petersen [24,25], to define and evaluate in a fairly simple and straightforward manner the detonation velocity at theoretical maximum density. The presence of a higher percentage of aluminum in the mixture increases the initial density and, in most cases, decreases the detonation velocity. To express the detonation velocity of nonideal aluminized explosives as a function of basic parameters, namely, elemental composition, oxygen balance, heat content, and initial density of the mixture, various combinations of the parameters mentioned were studied and optimized with experimental data. The results show that the detonation velocity of aluminized explosives is reliably predicted by D (km/s) = 2.693ρ0 − 0.2391a + 0.2810b + 0.4750c + 0.8382d − 0.2765e × OxAl − 0.0045Hf ,
(1)
M.H. Keshavarz / Combustion and Flame 142 (2005) 303–307
where ρ0 is the initial density of the mixture (g/cm3 ), Hf is the condensed-phase heat of formation of the mixture (kcal/mol), and OxAl is the amount of oxidized aluminum based on the above-described conditions. a, b, c, d, and e are the numbers of moles of carbon, hydrogen, nitrogen, oxygen, and aluminum, respectively, in 100 g of mixture. The procedure of Kamlet and Hurwitz [18], for determining adjustable
305
parameters, was used to find constants for the suggested correlation. The heat of formation and other necessary data for calculations are listed in Table 1. Detonation velocities calculated for aluminized explosives are listed in Table 2 and compared with the results obtained with BKWS-EOS using full and partial equilibrium as well as measured values. Only 50% of the aluminum is
Table 1 Parameters used in calculations Explosive
Chemical formula
% Al
Condensed-phasea Hf (kcal/mol)
H-6 HBX-1 HBX-3 HMX/Al (90/10) HMX/Al (80/20) HMX/Al (70/30) HMX/Al (60/40) RDX/Al (90/10) RDX/Al (80/20) RDX/Al (70/30) RDX/Al (60/40) RDX/Al (50/50) TNETB/Al (90/10) TNETB/Al (80/20) TNETB/Al (70/30) TNT/Al (89.4/10.6) TNT/Al (78.3/21.7) TNT/Al (67.8/32.2)
C1.89 H2.59 N1.61 O2.01 Al0.74 Ca0.005 Cl0.009 C2.06 H2.62 N1.57 O2.07 Al0.63 Ca0.005 Cl0.009 C1.66 H2.18 N1.21 O1.60 Al1.29 Ca0.005 Cl0.009 C1.216 H2.432 N2.432 O2.432 Al0.371 C1.08 H2.16 N2.16 O2.16 Al0.715 C0.944 H1.888 N1.888 O1.888 Al1.11 C0.812 H1.624 N1.624 O1.624 Al1.483 C1.215 H2.43 N2.43 O2.43 Al0.371 C1.081 H2.161 N2.161 O2.161 Al0.715 C0.945 H1.89 N1.89 O1.89 Al1.11 C0.81 H1.62 N1.62 O1.62 Al1.483 C0.675 H1.35 N1.35 O1.35 Al1.853 C1.399 H1.399 N1.399 O3.264 Al0.371 C1.244 H1.244 N1.244 O2.902 Al0.715 C1.088 H1.088 N1.088 O2.539 Al1.11 C2.756 H1.969 N1.181 O2.362 Al0.393 C2.414 H1.724 N1.034 O2.069 Al0.804 C2.090 H1.493 N1.896 O1.791 Al1.193
20 17 35 10 20 30 40 10 20 30 40 50 10 20 30 10.6 21.7 32.2
−0.81 −2.54 −2.53 5.44 4.83 4.22 3.63 5.95 5.29 4.63 3.97 3.31 −27.75 −24.66 −21.58 −5.91 −5.17 −4.48
a Heats of formation of pure explosives were obtained from [7].
Table 2 Comparison of detonation velocities calculated using the new correlation, Eq. (1), those obtained using BKWS-EOSa , and measured values [7] Name
ρ0 Dexp (g/cm3 ) (km/s)
Dnew (km/s)
% Deviation (new)
DBKWS-EOS % Deviation (km/s), BKWS-EOS, full full
H-6 HBX-1 HBX-3 HMX/Al (90/10) HMX/Al (80/20) HMX/Al (70/30) HMX/Al (60/40) RDX/Al (90/10) RDX/Al (80/20) RDX/Al (70/30) RDX/Al (60/40) RDX/Al (50/50) TNETB/Al (90/10) TNETB/Al (80/20) TNETB/Al (70/30) TNT/Al (89.4/10.6) TNT/Al (78.3/21.7) TNT/Al (67.8/32.2)
1.75 1.71 1.84 1.76 1.82 1.86 1.94 1.68 1.73 1.79 1.84 1.89 1.75 1.82 1.88 1.72 1.8 1.89
7.39 7.30 7.06 8.25 7.97 7.62 7.40 8.03 7.72 7.43 7.12 6.81 8.25 7.99 7.70 7.08 6.98 6.93
6.44 0.17 0.80 0.59 4.02 4.73 3.92 0.00 0.60 1.93 1.09 0.00 −1.55 0.01 1.82 −0.47 0.97 1.70
7.22 7.18 6.27 8.32 7.93 7.27 6.86 8.02 7.60 7.03 6.42 5.78 7.85 7.53 6.99 7.02 6.59 4360
7.9 7.31 7.12 8.3 8.3 8 7.7 8.03 7.77 7.58 7.2 6.81 8.12 7.99 7.84 7.05 7.05 7.05
−8.6 −1.8 −11.9 0.2 −4.5 −9.1 −10.9 −0.12 −2.2 −7.3 −10.8 −15.1 −3.3 −5.8 −10.8 −0.4 −6.5 5.94
a Using full and partial (50%) interactions of aluminum with detonation products.
DBKWS-EOS % Deviation (km/s), BKWS-EOS, partial partial 7.49 7.38 6.91 8.41 8.22 7.82 7.46 8.08 7.81 7.49 6.93 6.02 7.91 7.73 7.43 7.12 6.94 −15.7
−5.2 0.96 −2.9 1.3 −1.0 −2.3 −3.1 0.6 0.5 −1.2 −3.8 −11.6 −2.6 −3.3 −5.2 1.0 −1.6 −4.8
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assumed to interact with combustion products in the case of partial equilibrium. As indicated in Table 2, the new manually calculated detonation velocity surprisingly agrees very well with experimental data, as compared with that calculated using the complicated EOS, namely, BKWS-EOS. Comparison of the calculated results with experimental data and BKWS-EOS results listed in Table 2 may be taken as appropriate validation of the simple correlation introduced for use with aluminized explosives.
mentally or estimated by theoretical methods, the results of this work are remarkable.
Acknowledgment I thank the research committee of Malek-ashtar University of Technology (MUT) for supporting this work.
References 3. Conclusions The equilibrium composition of detonation products can be determined from the condition of total isobaric–isothermal potential minimum at the condition of elements mole number conservation. Partial equilibrium rather than a complex reacting mechanism can be used to predict the detonation properties of nonideal explosives if the initial amount of aluminum that is assumed to react is specified. During detonation transformation of nonideal explosives, powdered aluminum can participate in chemical reactions proceeding inside the detonation wave. The present method is exceedingly simple and, at the same time, gives results that are comparable to values predicted using other methods involving equations of state of the products. Taking into consideration the few percent deviations generally attributed to experimental measurements, the agreement between calculated and measured temperatures is also satisfactory. The motivation behind this work was to propose a procedure that could be used to determine the detonation velocity of aluminized explosives. A simple correlation complementing the computer output was introduced for manual calculation of the detonation velocities of aluminized explosives using the condensed-phase heat of formation and atomic composition of mixed explosives. Given the chemical formula of a real or hypothetical mixture of aluminum and CHNO explosives, one can estimate the detonation velocities of aluminized explosives to within a few percent. Because the contribution of |Hf | in Eq. (1) is small relative to the elemental composition of aluminized explosives, this permits a simple calculation of the detonation velocity of explosives even when the condensed-phase heats of formation are relatively uncertain. As indicated in Table 2, excellent agreement is obtained between measured and calculated values for detonation velocity for all aluminized explosives, as compared with values computed using BKWS-EOS. As the data necessary for this method comprise only the approximate heat of formation of CHNO explosive, which can be determined experi-
[1] C.L. Mader, Numerical Modeling of Explosives and Propellants, second ed., CRC Press, Boca Raton, FL, 1998. [2] H.B. Levine, R.E. Sharples, in: Operator’s Manual for RUBY, Report UCRL-6815, Lawrence Livermore National Laboratory, Livermore, CA, 1962. [3] M. Cowperthwaite, W.H. Zwisler, in: TIGER Computer Program Documentation, SRI Publ. 2106, Stanford Research Institute, 1973. [4] A.L. Nichols, F.H. Ree, in: CHEQ 2.0 User’s Manual, UCRL-MA-106754, Lawrence Livermore National Laboratory, Livermore, CA, 1990. [5] L.E. Fried, W.M. Howard, P.C. Souers, in: CHEETAH 2.0 User’s Manual, Lawrence Livermore National Laboratory, Livermore, CA, 1998. [6] M. Fringer, E. Lee, F.H. Helm, B. Hayes, H. Hornig, R. McGuire, M. Kahara, M. Gudiry, in: Proceedings of the Sixth Symposium (International) on Detonation, Coronado, CA, Office of the Chief of Naval Operations, Washington, DC, 1976. [7] M.L. Hobbs, M.R. Baer, in: Proceedings of the Tenth Symposium (International) on Detonation, Boston, MA, 1993. [8] A. Maranda, Propellants Explosives Pyrotech. 15 (1990) 4. [9] A. Maranda, S. Cudzilo, W. Trzci´nski, J. Nowaczewski, in: Proceedings of the Twenty-Seventh International Annual Conference OICT, Karlsruhe, 1996. [10] S. Cudzilo, A. Maranda, J. Nowaczewski, W. Trzci´nski, Combust. Flame 102 (1995) 64. [11] A. Maranda, J. Nowaczewski, W. Trzci´nski, in: Proceedings of the Sixth International Seminar EuroPyro ’95, Tours, 1995. [12] A. Maranda, in: Proceedings of the Fifth International Seminar Euro-Pyro ’93, Strasbourg, 1993. [13] A. Maranda, Propellants Explosives Pyrotech. 16 (1991) 5. [14] A. Maranda, Propellants Explosives Pyrotech. 16 (1991) 6. [15] M.J. Kamlet, S.J. Jacobs, J. Chem. Phys. 48 (1968) 23. [16] M.J. Kamlet, J.E. Ablard, J. Chem. Phys. 48 (1968) 36. [17] M.J. Kamlet, C. Dickinson, J. Chem. Phys. 48 (1968) 43. [18] M.J. Kamlet, H. Hurwitz, J. Chem. Phys. 48 (1968) 3685. [19] M.H. Keshavarz, M. Oftadeh, High Temp. High Press. 34 (2002) 495.
M.H. Keshavarz / Combustion and Flame 142 (2005) 303–307 [20] M.H. Keshavarz, M. Oftadeh, Bull. Korean Chem. Soc. 24 (2003) 19. [21] M.H. Keshavarz, M. Oftadeh, Indian J. Eng. Mater. Sci. 10 (2003) 236. [22] M.H. Keshavarz, H.R. Pouretedal, Thermochim. Acta 414 (2004) 203. [23] H. Hurwitz, M.J. Kamlet, Isr. J. Technol. 7 (1968) 431. [24] R.L. Rothstein, R. Petersen, Propellants Explosives 4 (1979) 56. [25] R.L. Rothstein, Propellants Explosives 6 (1981) 91. [26] J.R. Stine, J. Energ. Mater. 8 (1990) 41. [27] J.R. Stine, Mater. Res. Soc. Symp. 296 (1993) 3. [28] B.M. Rice, J. Hare, Thermochim. Acta 384 (2002) 377.
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[29] P. Politzer, J.S. Murray, M.E. Grice, M. Desalvo, E. Miler, Mol. Phys. 91 (1997) 923. [30] B.M. Rice, V.V. Pai, J. Hare, Combust. Flame 118 (1999) 445. [31] M.H. Keshavarz, M. Oftadeh, High Temp. High Press., in press. [32] A.I. Aniskin, in: Proceedings of the Eighth All-Union Symposium on Detonation, Taskent, 1986. [33] R. Charet, Acta Astron. 1 (1974) 893. [34] N.A. Imkhovik, V.S. Soloviev, in: Proceedings of the Ninth All-Union Symposium on Detonation, Suzdal, 1989. [35] M. Cowperthwaite, in: Tenth Symposium (International) on Detonation, Boston, 1993.
Brief Communication
New method for predicting detonation velocities of aluminized explosives Mohammad Hossein Keshavarz ∗ Department of Chemistry, Malek-ashtar University of Technology, Shahin-shahr, P.O. Box 83145/115, Islamic Republic of Iran Received 8 June 2004; received in revised form 6 February 2005; accepted 29 March 2005 Available online 27 April 2005
Abstract A simple procedure for determining detonation velocities of aluminized explosives, which have significantly nonideal behavior, is introduced. It is shown how only the atomic composition and condensed phase heat of formation of explosives, as compared with complicated computer programs, are sufficient for reliable, simple prediction of detonation velocity. Detonation velocities can be predicted by assuming that aluminum powder, based on oxygen content and the different pathways of decomposition of explosives, partially interacts with detonation products. Detonation velocities calculated by this procedure for aluminized nonideal explosives are in good agreement with experimental values, that is, results computed using BKWS-EOS. 2005 The Combustion Institute. Published by Elsevier Inc. All rights reserved.
1. Introduction Detonation parameters such as detonation velocity and detonation pressure are performance parameters and represent the effectiveness of different explosives; they can be calculated using different computer programs, e.g., BKW [1], RUBY [2], TIGER [3], CHEQ [4], and CHEETAH [5]. The heat of formation and density of the explosive substance and the equation of state (EOS) of the detonation products are usually needed for the calculations. There are several EOSs, among which BKW-EOS is used extensively to calculate detonation properties [1]. BKWC-EOS [5], BKWR-EOS [6], and BKWS-EOS [7] are three different parameterizations of BKW-EOS. * Fax: +98 0312 522 5068.
E-mail addresses: [email protected], [email protected].
Aluminum powder is used in explosives to enhance air blast, increase bubble energies in underwater weapons, raise detonation temperature, and create incendiary effects. It increases the heat of detonation and acts as an intermediate sensitivity agent. For many years, researchers have investigated the role of aluminum powder in explosives with the goal of producing utilitarian explosive mixtures containing aluminum powder [8–14]. Aluminized composite explosives are classified as nonideal explosives: the amount of material reacted may be a function of reaction zone length. The degree of heterogeneity and the secondary exothermic reactions occurring in the detonation products expanding behind the detonation zone are two important characteristics of nonideal explosives. Partial equilibrium rather than a complex reaction mechanism can be used to predict the detonation properties of nonideal explosives by specifying the initial amount of aluminum assumed to react. As physical separation
0010-2180/$ – see front matter 2005 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.combustflame.2005.03.011
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M.H. Keshavarz / Combustion and Flame 142 (2005) 303–307
of the fuel and oxidizer in aluminized explosives results in extension of the chemical reaction zone, they are often poorly modeled by Chapman–Jouguet theory. Thus, a nonideal explosive can have Chapman– Jouguet detonation pressure and velocity significantly different from those expected from equilibrium and steady state calculations using a computer program such as BKW [1]. Fairly accurate data are highly desired in the calculation of the various detonation parameters of ideal and nonideal explosives. There is a continuing need for simple, reliable prediction of detonation performance rather than complicated computer programs. This study had as its original purpose the development of a simple, reliable method, as compared with complex computer programs, for calculating detonation velocities of aluminized explosives with nonideal behavior. A new equation is introduced to correlate detonation velocity with elemental composition and condensed-phase heat of formation, as well as the initial density, of the explosive. The calculated detonation velocity is then compared with measured values and the predictions of BKWS-EOS using full and 50% interactions of aluminum with detonation products. It should be noted that the predicted results are comparable to the output of complex computer programs, and accuracy is not necessarily enhanced by greater complexity.
2. Detonation velocities of aluminized explosives Some empirical equations have been developed for predicting Chapman–Jouguet (C-J) detonation pressures and velocities of pure explosives and mixtures of different classes of explosives [15–27]. Detonation velocity is one the most important detonation parameters and can be measured directly with high accuracy to within a few percent at various charge diameters and extrapolated to an “infinite diameter.” Various studies show that the detonation velocity of aluminized explosives depends on elemental composition, oxygen balance, heat content, and initial density of the mixture. The heat of formation is a measure of the energy content of an energetic material and usually enters into the calculation of explosive properties such as detonation velocity and pressure. Condensed-phase heats of formation of explosives can be calculated for some classes of explosives [28–31]. All chemical bonds present in the reacting explosive are broken, resulting in the formation of monatomic species, which subsequently recombine to form stable products. For mixtures of highly volatile aluminum explosives, significant difficulties lie in the uncertainty in the amount of aluminum oxidized at the Chapman–Jouguet point. Because it is
not clear to what degree the aluminum is oxidized at the Chapman–Jouguet point for aluminized composite explosives, thermodynamic calculations of detonation parameters were carried out by assuming a specific degree of oxidation of aluminum [32–35]. Detonation pressure and velocity increase with an increase in the amount of gaseous products, prevention of oxidation of aluminum causes an increase in the number of gaseous molecules. On the other hand, complete oxidation of aluminum can force oxygen to react with oxygen rather than carbon, producing hot gas phase as a result of the large negative heat of formation of Al2 O3 . Experimental values reported for the detonation velocity of TNT/Al demonstrate that increasing the percentage of aluminum does not result in an appreciable change in the detonation velocity values. Because TNT is very oxygen deficient, it can be assumed that the least amount of aluminum can react with the detonation products of TNT. Some pathways for decomposition of ideal and less ideal explosives recently suggested [22] depend on the oxygen content of the explosive. It can be assumed that partial oxidation of aluminum will occur in any mixture of aluminum with Ca Hb Nc Od explosives based on the oxygen balance of the explosive. Different aluminum oxidation pathways can be introduced under the following conditions: 1. If d a, only 10% of Al reacts. 2. If d > a and b/2 > d − a, only 25% of Al is oxidized. 3. If d a + b/2 and d 2a + b/2, only 50% of Al reacts. It is possible to represent the detonation velocity of an explosive as a function of its composition on the basis of an approach proposed earlier, e.g., by Stine [26,27] and Rothstein and Petersen [24,25], to define and evaluate in a fairly simple and straightforward manner the detonation velocity at theoretical maximum density. The presence of a higher percentage of aluminum in the mixture increases the initial density and, in most cases, decreases the detonation velocity. To express the detonation velocity of nonideal aluminized explosives as a function of basic parameters, namely, elemental composition, oxygen balance, heat content, and initial density of the mixture, various combinations of the parameters mentioned were studied and optimized with experimental data. The results show that the detonation velocity of aluminized explosives is reliably predicted by D (km/s) = 2.693ρ0 − 0.2391a + 0.2810b + 0.4750c + 0.8382d − 0.2765e × OxAl − 0.0045Hf ,
(1)
M.H. Keshavarz / Combustion and Flame 142 (2005) 303–307
where ρ0 is the initial density of the mixture (g/cm3 ), Hf is the condensed-phase heat of formation of the mixture (kcal/mol), and OxAl is the amount of oxidized aluminum based on the above-described conditions. a, b, c, d, and e are the numbers of moles of carbon, hydrogen, nitrogen, oxygen, and aluminum, respectively, in 100 g of mixture. The procedure of Kamlet and Hurwitz [18], for determining adjustable
305
parameters, was used to find constants for the suggested correlation. The heat of formation and other necessary data for calculations are listed in Table 1. Detonation velocities calculated for aluminized explosives are listed in Table 2 and compared with the results obtained with BKWS-EOS using full and partial equilibrium as well as measured values. Only 50% of the aluminum is
Table 1 Parameters used in calculations Explosive
Chemical formula
% Al
Condensed-phasea Hf (kcal/mol)
H-6 HBX-1 HBX-3 HMX/Al (90/10) HMX/Al (80/20) HMX/Al (70/30) HMX/Al (60/40) RDX/Al (90/10) RDX/Al (80/20) RDX/Al (70/30) RDX/Al (60/40) RDX/Al (50/50) TNETB/Al (90/10) TNETB/Al (80/20) TNETB/Al (70/30) TNT/Al (89.4/10.6) TNT/Al (78.3/21.7) TNT/Al (67.8/32.2)
C1.89 H2.59 N1.61 O2.01 Al0.74 Ca0.005 Cl0.009 C2.06 H2.62 N1.57 O2.07 Al0.63 Ca0.005 Cl0.009 C1.66 H2.18 N1.21 O1.60 Al1.29 Ca0.005 Cl0.009 C1.216 H2.432 N2.432 O2.432 Al0.371 C1.08 H2.16 N2.16 O2.16 Al0.715 C0.944 H1.888 N1.888 O1.888 Al1.11 C0.812 H1.624 N1.624 O1.624 Al1.483 C1.215 H2.43 N2.43 O2.43 Al0.371 C1.081 H2.161 N2.161 O2.161 Al0.715 C0.945 H1.89 N1.89 O1.89 Al1.11 C0.81 H1.62 N1.62 O1.62 Al1.483 C0.675 H1.35 N1.35 O1.35 Al1.853 C1.399 H1.399 N1.399 O3.264 Al0.371 C1.244 H1.244 N1.244 O2.902 Al0.715 C1.088 H1.088 N1.088 O2.539 Al1.11 C2.756 H1.969 N1.181 O2.362 Al0.393 C2.414 H1.724 N1.034 O2.069 Al0.804 C2.090 H1.493 N1.896 O1.791 Al1.193
20 17 35 10 20 30 40 10 20 30 40 50 10 20 30 10.6 21.7 32.2
−0.81 −2.54 −2.53 5.44 4.83 4.22 3.63 5.95 5.29 4.63 3.97 3.31 −27.75 −24.66 −21.58 −5.91 −5.17 −4.48
a Heats of formation of pure explosives were obtained from [7].
Table 2 Comparison of detonation velocities calculated using the new correlation, Eq. (1), those obtained using BKWS-EOSa , and measured values [7] Name
ρ0 Dexp (g/cm3 ) (km/s)
Dnew (km/s)
% Deviation (new)
DBKWS-EOS % Deviation (km/s), BKWS-EOS, full full
H-6 HBX-1 HBX-3 HMX/Al (90/10) HMX/Al (80/20) HMX/Al (70/30) HMX/Al (60/40) RDX/Al (90/10) RDX/Al (80/20) RDX/Al (70/30) RDX/Al (60/40) RDX/Al (50/50) TNETB/Al (90/10) TNETB/Al (80/20) TNETB/Al (70/30) TNT/Al (89.4/10.6) TNT/Al (78.3/21.7) TNT/Al (67.8/32.2)
1.75 1.71 1.84 1.76 1.82 1.86 1.94 1.68 1.73 1.79 1.84 1.89 1.75 1.82 1.88 1.72 1.8 1.89
7.39 7.30 7.06 8.25 7.97 7.62 7.40 8.03 7.72 7.43 7.12 6.81 8.25 7.99 7.70 7.08 6.98 6.93
6.44 0.17 0.80 0.59 4.02 4.73 3.92 0.00 0.60 1.93 1.09 0.00 −1.55 0.01 1.82 −0.47 0.97 1.70
7.22 7.18 6.27 8.32 7.93 7.27 6.86 8.02 7.60 7.03 6.42 5.78 7.85 7.53 6.99 7.02 6.59 4360
7.9 7.31 7.12 8.3 8.3 8 7.7 8.03 7.77 7.58 7.2 6.81 8.12 7.99 7.84 7.05 7.05 7.05
−8.6 −1.8 −11.9 0.2 −4.5 −9.1 −10.9 −0.12 −2.2 −7.3 −10.8 −15.1 −3.3 −5.8 −10.8 −0.4 −6.5 5.94
a Using full and partial (50%) interactions of aluminum with detonation products.
DBKWS-EOS % Deviation (km/s), BKWS-EOS, partial partial 7.49 7.38 6.91 8.41 8.22 7.82 7.46 8.08 7.81 7.49 6.93 6.02 7.91 7.73 7.43 7.12 6.94 −15.7
−5.2 0.96 −2.9 1.3 −1.0 −2.3 −3.1 0.6 0.5 −1.2 −3.8 −11.6 −2.6 −3.3 −5.2 1.0 −1.6 −4.8
306
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assumed to interact with combustion products in the case of partial equilibrium. As indicated in Table 2, the new manually calculated detonation velocity surprisingly agrees very well with experimental data, as compared with that calculated using the complicated EOS, namely, BKWS-EOS. Comparison of the calculated results with experimental data and BKWS-EOS results listed in Table 2 may be taken as appropriate validation of the simple correlation introduced for use with aluminized explosives.
mentally or estimated by theoretical methods, the results of this work are remarkable.
Acknowledgment I thank the research committee of Malek-ashtar University of Technology (MUT) for supporting this work.
References 3. Conclusions The equilibrium composition of detonation products can be determined from the condition of total isobaric–isothermal potential minimum at the condition of elements mole number conservation. Partial equilibrium rather than a complex reacting mechanism can be used to predict the detonation properties of nonideal explosives if the initial amount of aluminum that is assumed to react is specified. During detonation transformation of nonideal explosives, powdered aluminum can participate in chemical reactions proceeding inside the detonation wave. The present method is exceedingly simple and, at the same time, gives results that are comparable to values predicted using other methods involving equations of state of the products. Taking into consideration the few percent deviations generally attributed to experimental measurements, the agreement between calculated and measured temperatures is also satisfactory. The motivation behind this work was to propose a procedure that could be used to determine the detonation velocity of aluminized explosives. A simple correlation complementing the computer output was introduced for manual calculation of the detonation velocities of aluminized explosives using the condensed-phase heat of formation and atomic composition of mixed explosives. Given the chemical formula of a real or hypothetical mixture of aluminum and CHNO explosives, one can estimate the detonation velocities of aluminized explosives to within a few percent. Because the contribution of |Hf | in Eq. (1) is small relative to the elemental composition of aluminized explosives, this permits a simple calculation of the detonation velocity of explosives even when the condensed-phase heats of formation are relatively uncertain. As indicated in Table 2, excellent agreement is obtained between measured and calculated values for detonation velocity for all aluminized explosives, as compared with values computed using BKWS-EOS. As the data necessary for this method comprise only the approximate heat of formation of CHNO explosive, which can be determined experi-
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