numerically study the dynamics of development of aluminum sulfide synthesis on explosive loading of a cylindrical ampoule on the basis of a phenomenologi.
ISSN 00125016, Doklady Physical Chemistry, 2010, Vol. 434, Part 2, pp. 172–176. © Pleiades Publishing, Ltd., 2010. Original Russian Text © S.A. Zelepugin, O.V. Ivanova, A.S. Yunoshev, V.V. Sil’vestrov, 2010, published in Doklady Akademii Nauk, 2010, Vol. 434, No. 5, pp. 643–647.
PHYSICAL CHEMISTRY
The Development of the Aluminum Sulfide Synthesis Reaction on Explosive Loading of a Cylindrical Ampoule S. A. Zelepugina, O. V. Ivanovaa, A. S. Yunoshevb, and V. V. Sil’vestrovb Presented by Academician A.G. Merzhanov April 20, 2010 Received January 20, 2010
DOI: 10.1134/S0012501610100052
In the scientific literature, much attention is paid to investigation of phase transitions on explosive load ing, in particular, solidphase chemical transforma tions under the action of shock waves. However, such transformations are studied mostly experimentally [1, 2], and their mathematical models are virtually unavailable. It is natural because chemical transfor mations are difficult to study in the course of explosive loading and reliable data on the dynamics of these phenomena are not always easy to obtain from experi mental results. Meanwhile, novel promising materials are more and more often produced and used in fast processes at high strain rates, pressures, and temperatures. These processes are accompanied by structural changes and sometimes chemical reactions. The currently widely used explosive technologies in metal working are most developed in forming, welding, cutting, hardening, and sealing, and many of these technologies have already been commercialized. At the same time, the effect of shock waves on solidphase reactions is still insufficiently studied and, by the present time, has not yet reached a technology level because of the lack of experimental data and also mathematical models that could take into account both the coupling of mechan ical and physicochemical processes, including their combined action, and the effect of each factor. The purpose of this work was to experimentally and numerically study the dynamics of development of aluminum sulfide synthesis on explosive loading of a cylindrical ampoule on the basis of a phenomenologi cal model of chemical transformations.
a
Department of Structural Macrokinetics, Tomsk Scientific Center, Siberian Branch, Russian Academy of Sciences, pr. Akademicheskii 10/3, Tomsk, 634021 Russia b Lavrent’ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, pr. Akademika Lavrent’eva 15, Novosibirsk, 630090 Russia
In this work, we proposed a new approach to numerical analysis of solidphase synthesis processes on explosive and shockwave loading on the basis of a developed mathematical model of a multicomponent medium. The time dependence of the pressure of the explosion products was described based on qualitative and quantitative agreement of the results of experi mentally and theoretically determining the parame ters of explosive loading of a cylindrical ampoule. The conditions were found for the transition from partial to complete conversion in the synthesis reaction in the shock front on reflection of the shock wave from the bottom cap of the ampoule. It was experimentally and theoretically established that, once the reaction in the shock wave is fully completed, the ampoule is broken down because of the formation of a gas phase and an increase in pressure, with the breakdown being initi ated in the bottom part of the ampoule. EXPERIMENTAL AND THEORETICAL DETERMINATION OF EXPLOSIVE LOADING PARAMETERS In the experiments, the material to be loaded was a mixture of an aluminum powder with a particle size less than 100 μm and a sulfur powder with a particle size of 100–300 μm. The powders were taken in the AltoS weight ratio 35 : 65, mixed, and compacted into eight 7.5mmhigh pellets 14.2 mm in diameter with a porosity of 0.15 (i.e., the pore volume was 15% of the total volume). The pellets were placed in a cylin drical steel ampoule 20 mm o.d. The ampoule with the mixture was loaded by shocking with a steel tube 37 mm o.d. with a wall 3 mm thick, which was accel erated by explosion products. The explosive was an ammonite 6ZhV–ammonium nitrate mixture in the weight ratio 1 : 1 with a density of 1.07 g/cm3. The explosive charge was 64 mm o.d. An assembly was placed in the field of two Orion 600 Xray tubes, using which the loading of the ampoule was photographed. Figures 1a and 1b present Xray images of the assembly before and during explosive loading, which
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(c) h, mm 0
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Fig. 1. The Xray images of the assembly with an external tube (a) before and (b) during explosive loading and (c) a computer image of an axial section of the assembly at the moment of time of 19 μs. h and r are the assembly height and radius, respectively.
were made by one of the Xray tubes. The exposure time was 1.5 ns. Analysis of the Xray images showed that the detonation velocity of the composite explosive was 3.3 km/s and the calculated Chapman–Jouguet pressure was 3.3–3.6 GPa, depending on an assumed value of the polytropic exponent of the detonation products of 2.2–2.5. The distance travelled by the det onation wave at the velocity 3.3 km/s from the top face of the striker (without considering the conical part of the ampoule cap) was 63.6 mm, and the tube rotation angle was 4.7° (Fig. 1b). After loading, molten sulfur exuded from the ampoule and there was a smell of hydrogen sulfide, which was indicative of aluminum sulfide synthesis reaction. The outer diameter of the ampoule after explosive loading was 19.2 ± 0.2 mm at the top and 20.2 ± 0.2 mm at the bottom. To determine the explosive loading parameters, we considered an axisymmetric problem in which a cylin drical steel tube (striker) accelerated by explosion products in the mode of sliding detonation of an explosive interacted with a cylindrical ampoule con taining a porous Al–S mixture. The behavior of a porous mixture on shockwave loading was numerically modeled using a model of a multicomponent medium [3–5]. Within this model, it was assumed that all the components occupied the same space as the mixture did and were thus present at each point of this space. The components interacted DOKLADY PHYSICAL CHEMISTRY
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with each other, exchanging with momentum, energy, and, if there were chemical reactions, mass. The con dition for the codeformation of the components was chosen to be equality of the pressures of the compo nents of the mixture [6]. For mathematical description of explosive loading, it was necessary to know not only the detonation velocity but also the time dependence of the pressure of the explosion products acting on the cylindrical tube (striker). In this work, we assumed that the deto nation process was steady; i.e., the rate of change (decrease) in the pressure of the explosion products with time was constant. Under such assumptions, the change in the pressure could be described by the equa tion P = P 0 – kt ( t = 0, …, Δt ), (1) which is an equation of a straight line with slope k and Pintercept P0. The slope k is found as P0 k = . Δt Then, the final form of the equations for the pres sure of the explosion products on the side wall of the cylindrical tube is P0 P = P 0 – t at 0 ≤ t ≤ Δt, Δt P = 0 at t > Δt, 2010
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Fig. 2. The view of the ampoule after explosive loading of the assembly without external tube.
Δ D Δt = , c = , c 2 where Δ is the explosive layer thickness, c is the esti mated average velocity of the unloading wave, and D is the detonation velocity. At the above values Δ = 13.5 mm and D = 3.3 km/s, the time duration of the pressure pulse is Δt ≈ 8.2 μs. The P0 value in the calcu lations was varied in order to reach agreement between the numerical and experimental results. Figure 1c shows the assembly section calculated by modeling the explosive loading at the moment of time of 19 μs counted from the moment at which the deto nation wave travelled through the top face of the outer tube (striker) at a given P0 of 4 GPa. Analysis of the calculation results showed that, by that moment of time, the distance travelled by the detonation wave at the velocity 3.3 km/s was 63 mm and the tube rotation angle was 4.76°. The obtained results of the numerical modeling of the explosive loading and the dynamics of the action of the explosion products on the striker were in qualitative and quantitative (with an accuracy of 1.3%) agreement with the experimental data. DEVELOPMENT OF THE SYNTHESIS REACTION ON EXPLOSIVE LOADING OF THE POROUS ALUMINUM–SULFUR MIXTURE In the explosive loading experiments, the material to be loaded was a mixture of ASD4 aluminum powder of grade PAP 2 (flakes 20 μm in diameter and several
microns in thickness) and a sulfur powder. The pow ders were mixed in an AGO2U planetary ball mill in the AltoS weight ratio 35 : 65, which corresponded to the stoichiometry of the formation of aluminum sulfide Al2S3. Then, the powders were compacted into eight 8mmhigh pellets 14 mm in diameter with a porosity of 0.393 ± 0.005. The pellets were placed in a 95mmlong cylindrical steel ampoule 20 mm o.d and 14 mm i.d. The ampoule was covered with caps at the end faces. The ampoule was loaded by exploding an explosive charge consisting of an ammonite 6ZhV– NaCl mixture in the weight ratio 1 : 1 with a density of 1.2 g/cm3. The explosive charge was 50 mm o.d. The measured detonation velocity was 2.8 km/s. During loading, the ampoule opened (Fig. 2). The explosive detonation travelled in the direction from the unopened cap. The ampoule opened initially in the bottom part and then along the entire length. After the experiment, on the inner surface of the ampoule, a lot of frozen drops up to 4 mm in diameter were detected, with all the large drops being on the side of the unopened cap. Xray diffraction analysis of the material from the ampoule showed that this is alumi num sulfide (the α and ω phases). For comparison with the results of this experiment, we numerically solved an axisymmetric problem of explosive loading of a cylindrical steel ampoule con taining a porous Al–S mixture. A synthesis reaction in a reacting porous multicomponent mixture can be described using a phenomenological model of chemi cal transformations with zeroorder kinetics without reverse transformations [5, 7]: ⎧ 0, if η = 1 or ( T i < T η and P < P η ) dη , = ⎨ dt ⎩ f ( P η ), if η < 1 and ( T i ≥ T η or P ≥ P η ) ⎧ K 0 , if P < P η , f ( Pη ) = ⎨ ⎩ K P K 0 , if P ≥ P η where η is the conversion; Ti is the temperature of the ith component of the mixture; P is the total pressure of the components; and Tη, Pη, Kp , and K0 are constants. We chose reaction initiation criteria in terms of tem perature, Tη of 933 K (aluminum melting point), and pressure, Pη of 2.5 GPa. The reaction rate K0 was taken to be 240.8 GJ/(kg s), and KP = 20.0 [8]. Figure 3 illustrates the time dependence of the conversion (mass fraction of reaction product) in the central and bottom parts of the ampoule. In the central part of the sample in 14 μs after the beginning of explosive loading, the reaction initiation criterion in terms of pressure remained valid and the chemical reaction began to occur at high rate (curve 1). The conversion reached 0.4 until the pressure decreased below the criterion Pη. After the pressure decrease in this part of the ampoule, the reaction initiation crite rion in terms of temperature continued to be valid, the reaction rate decreased, and the reaction was com
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pleted in 26.8 μs after the beginning of explosive load ing. In the bottom part of the ampoule (curve 2), the reaction started in 30.1 μs after the beginning of explo sive loading—because of reflection of the shock wave from the bottom cap of the ampoule and an increase in the pressure in this area—and was fully completed within 1 μs. It is in the reflected shock wave that the reaction in this part of the ampoule was initiated and occurred because the reaction initiation criteria in terms of either pressure or temperature in the trans mitted shock wave in this part of the ampoule were invalid. Unlike the rest of the ampoule, in the bottom part of the ampoule, the reaction was fully completed in the shock wave. Analysis of the theoretical and experimental results suggested the following dynamics of development of chemical transformations in the Al–S mixture in the cylindrical ampoule on explosive loading. In the top and central parts of the ampoule, the reaction is initi ated by a shockassisted mechanism [1], by which the reaction is initiated in the shock wave and continues and is completed behind the shock wave front. In this case, the amplitude and duration of the shock wave are insufficient for full completion of the chemical trans formation within the shock wave action time. In the bottom part of the ampoule, within the time of action of the transmitted shock wave, neither of the reaction initiation criteria is valid. The pattern of the process radically changes after the reflection of the transmitted shock wave from the bottom cap of the ampoule as a compression wave: a shockinduced mechanism of forced chemical transformations takes place [1], by which the chemical reaction is initiated, continues, and is fully completed within the shock wave at high pressures. Tentative thermodynamic calculations of the Al–S interaction using Terra program for the case of the pore space filled with argon at an initial porosity of 40% and a pressure of 0.1 MPa showed that the adia batic interaction temperature is limited by Al2S3 disso ciation and is 2940 K. The equilibrium composition of the interaction products at this temperature comprised a condensed compound, 64.0 mol % Al2S3, and gas eous substances—10.7 mol % Al, 3.9 mol % S, 9.8 mol % S2, 10.4 mol % AlS, and 1.0 mol % Al2S, with other components totaling less than 0.8 mol %. The volume of the forming gases exceeded the initial gas volume by a factor of 1057. If the final gas volume is compressed to the initial value at constant tempera ture, composition of substances, and their aggregation state, then, in the ideal gas approximation, the pres sure is about 0.1 GPa. However, experiments with inert porous mixtures on explosive loading under sim ilar conditions demonstrated that the pore volume becomes almost zero. Providing this, the estimated gas pressure should be at least one order of magnitude DOKLADY PHYSICAL CHEMISTRY
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η 1.0
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Fig. 3. The conversion η in the (1) central and (2) bottom parts of the ampoule versus time.
higher. Our estimates showed that the pressure in the ampoules should be no less than 1 GPa. Thus, based on a phenomenological model of chemical transformations, our experimental and the oretical studies into the dynamics of development of aluminum sulfide synthesis on explosive loading of a cylindrical ampoule have established a transition from partial to complete conversion in the synthesis reac tion in the shock front on reflection of the shock wave from the bottom cap of the ampoule. The high heat release rate during the chemical reaction in the bottom part of the ampoule causes the formation of a gas phase, which, in turn, leads to an increase in the pres sure in this area and to breakdown of the ampoule; it is in the bottom part of the ampoules that the breakdown is initiated. ACKNOWLEDGMENTS We thank A.N. Avramchik for help in performing thermodynamic calculations. This work was supported by the Russian Founda tion for Basic Research (project no. 08–08–12055), the Russian Foundation for Basic Research and the Tomsk Oblast Administration (project no. 09–08– 99059), and the Analytical Departmental Task Pro gram “Development of Scientific Potential of Higher Education” (projects no. 2.1.1/5993, 2.1.2/2509) of the Ministry of Education and Science of the Russian Federation. 2010
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4. Kuropatenko, V.F., Prikl. Mekh. Tekh. Fiz., 2005, vol. 46, no. 1, pp. 7–15. 5. Ivanova, O.V. and Zelepugin, S.A., Izv. Vyssh. Uchebn. Zaved., Fiz., 2008, vol. 51, no. 8/2, pp. 180–189. 6. Ivanova, O.V. and Zelepugin, S.A., Vestn. Tomsk. Gos. Univ., Mat. Mekh., 2009, no. 1. 7. Zelepugin, S.A., Nikulichev, V.B., Ivanova, O.V., and Zelepugin, A.S., Khim. Fiz., 2005, vol. 24, no. 10, pp. 76–82. 8. Zelepugin, S.A. and Nikulichev, V.B., Fiz. Goreniya Vzryva, 2000, vol. 36, no. 6, pp. 186–191.
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