Mathematical modeling of accidental gas explosions

Results are presented from mathematical modeling of the detonation of gas clouds in the form of cylinders with different ratios of height to radius. It is shown that the parameters of the resulting air shock wave depend significantly on the shape of the cloud. The trotyl equivalents of the explosion are obtained on the basis of maximum excess pressure and the impulse of excess pressure in the wave. This information can be used to analyze the consequences of accidents and substantiate standards on explosion-proofing. N. é. Bauman Moscow State Technical University, 107005 Moscow. Translated from Fizika Goreniya i Vzryva, Vol. 31, No. 6, pp. 155–165, November–December, 1995.     

Optical methods of studying the explosion of shaped charges

This article describes a group of optical methods for studying the explosion of shaped charges, including modifications of established methods (slit photorecording, the luminous points method, laser probing) and two new methods — measurement of wave velocities with transducers based on optical fibers and laser visualization of the shaped-charge jet. Optical methods are used to study such jets under laboratory conditions. Characteristic distortions of the symmetry of the detonation front and their effect on the jet are discussed, the probable character of breakup of the jet is established, and the distribution of the jet particles with respect to size is determined along with the maximum values of average limiting tension for copper. Scientific-Research Institute of Machine Design, 125212 Moscow. Translated from Fizika Goreniya i Vzryva, Vol. 31, No. 6, pp. 147–154, November–December, 1995.     

Detonation Velocity of Emulsion Explosives Containing Cenospheres

The detonation velocity of an emulsion explosive containing hollow alumosilicate microspheres (cenospheres) as the sensitizer is measured. The size of the microspheres is 50–250 μm. The relations between the detonation velocity and the charge density and diameter are compared for emulsion explosives containing cenospheres or glass microballoons as the sensitizer. It is shown that for a 55 mm diameter charge, the maximum detonation velocity of the composition with cenospheres of size 70–100 μm is 5.5–5.6 km/sec, as well as for 3M glass microballoons. The critical diameter for the emulsion explosive with cenosphere is 1.5–2 times larger than that for the emulsion explosive with glass microballoons and is 35–40 mm. __________ Translated from Fizika Goreniya i Vzryva, Vol. 41, No. 5, pp. 119–127, September–October, 2005.     

Detonation of a coal-air mixture with addition of hydrogen in plane-radial vortex chambers

Results of an experimental study of continuous and pulsed detonation of a coal-air mixture with addition of hydrogen in plane-radial vortex chambers 204 and 500 mm in diameter are presented. The tested substance is pulverized activated charcoal. A method of coal powder supply through narrow channels by means of adding the gas at the injector entrance is found. Stable regimes of continuous spin detonation with one or two transverse detonation waves moving with velocities of 1.8–1.6 km/sec are obtained for the first time in the combustor 204 mm in diameter. The frequency of pulsed detonation with radial waves is 4–4.8 kHz. The limits of continuous detonation in the combustor 500 mm in diameter are extended: regimes of continuous spin detonation with a large number (5–8) of transverse waves moving with velocities of 1.8–1.5 km/sec are obtained, the amount of hydrogen added to coal is reduced to 2.8%, and combustion of coarser fuel particles is ensured owing to an increased residence time of the mixture in the combustor. The wave structure and the flow in the vicinity of the waves are reconstructed in the combustor plane.     

Critical diameter for and fluctuations in detonation of solutions of dinitrotoluene in nitroglycol

The critical detonation diameters of nitroglycol and solutions of dinitrotoluene in nitroglycol in paper shells are measured. The frequency of the detonation fluctuations is determined. Data with glass and paper shells are the same. The frequency of the fluctuations is independent of the concentration of the solution at ≈7 MHz. The detonation parameters of these solutions are compared with systems which detonate in a low-frequency (≈2 MHz) spin regime. When the dinitrotoluene content of the solution is ≤15%, the critical detonation diameter is constant and equal to that for nitroglycol, but as the dinitrotoluene concentration is raised, the critical detonation diameter increases. The experimental results are in good agreement with theory. Translated fromFizika Goreniya i Vzryva, Vol. 35, No. 3, pp. 97–102, May–June 1999.     

Detonation characteristics of emulsion explosives

The detonation properties of a water-emulsion explosive are studied. The shock adiabat is determined for a density of 1.38 g/cm³. The critical diameter and the detonation velocity are found as functions of the initial density of the charge and the shock heating temperature is calculated.D. I. Mendeleev Moscow Institute of Chemical Technology, Moscow, 125190. Translated from Fizika Goreniya i Vzyrva, Vol.30, No. 3, pp. 86–91, May–June, 1994.     

Detonation combustion of coal

Results of an experimental study of continuous spin detonation of a coal-air mixture with addition of a certain amount of hydrogen in a plane-radial vortex chamber 500 mm in diameter are presented. The tested substance is fine-grained cannel coal from Kuzbass, which has a particle size of 1–7 μm and contains 24.7% of volatiles, 14.2% of ashes, and 5.1% of moisture. Stable regimes of continuous spin detonation with transverse detonation waves having velocities of 1.86–1.1 km/s with respect to the cylindrical wall of the combustor are obtained for the first time. The mass fraction of hydrogen is 1.5–0.88% of the air flow rate and 50–3.4% of the coal consumption rate. The maximum specific coal consumption rate of 106 kg/(s · m²) is obtained.     

Detonation of nitrobenzene and propargyl alcohol

Detonation of mononitrobenzene and propargyl alcohol at reduced pressure is recorded for the first time in 10-mm-diameter steel tubes with a wall thickness of 13 mm with high-power initiation. The detonation velocities of nitrobenzene equal 25–50% of the ideal value obtained from thermodynamic calculations. The conditions for stationary detonation propagation are examined and the critical porosities for these materials are computed based on calculations of the fraction of material that is heated and burnt up during detonation. The computations are in good agreement with experiment. Translated fromFizika Goreniya i Vzryva, Vol. 35, No. 1, pp. 89–97, January–February 1999.     

Equation of State of Explosion Products on the Basis of a Modified Van der Waals Model

A semi-empirical model is proposed for the equation of state of high explosives in a range of pressures and temperatures typical of detonation processes. A possibility of formation of solid phases (e.g., graphite or diamond) in the gas is implied. The model can be used to calculate all thermodynamic quantities for arbitrary molecular compositions and to calculate the thermodynamically equilibrium molecular (and phase) composition. An iterative scheme of calculations is proposed. The model contains several empirical functions whose form can be changed without violating the overall calculation scheme. A particular set of these functions is considered as an illustration. Some results calculated for a number of high explosives containing four elements (C, H, N, and O) are presented. The calculated results are compared with available experimental data. __________ Translated from Fizika Goreniya i Vzryva, Vol. 42, No. 1, pp. 87–99, January–February, 2006.     

Specific Features of Synthesis of Detonation Nanodiamonds

It is demonstrated that the Chapman-Jouguet parameters for high explosives used in nanodiamond synthesis are located in the region of liquid nanocarbon; therefore, the chemical reaction zone of the detonation wave involves formation of carbon nanodroplets, which are later crystallized into nanodiamonds on the segment of the isentrope of expansion of detonation products, passing through the region of stability of nanodiamonds in the pressure range of 16.5–10 GPa and the temperature range of 3400–2900 K. Soot in the resultant mixture is the product of amorphization of nanodroplets rather than graphitization of ultrafine diamonds. The influence of detonation conditions of high-explosive charges in an explosive chamber on nanodiamond synthesis is analyzed. __________ Translated from Fizika Goreniya i Vzryva, Vol. 41, No. 5, pp. 104–116, September–October, 2005.     

Interaction of detonation and rarefaction waves in aluminum particles dispersed in oxygen

The problem of interaction of a plane detonation wave with an adjacent rarefaction wave is studied on the basis of a mathematical model of detonation of aluminum particles dispersed in oxygen. The numerical solution is obtained within the framework of the one-velocity two-temperature approximation of the mechanics of heterogeneous media for the Chapman–Jouguet regime and strong and weak detonation regimes. It is shown that the Chapman–Jouguet regime and weak regimes with an internal singular point are self-sustained. Three intervals of the relaxation parameter (the ratio of the characteristic times of thermal relaxation and combustion) are determined. The detonation/rarefaction wave interaction results in the Chapman–Jouguet regime in the first interval, in decomposition of the detonation wave into a shock wave and a lagging combustion front with further loss of stability in the second interval, and in a weak detonation regime in the third interval. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Fizika Goreniya i Vzryva, Vol. 33, No. 2, pp. 102–110, March–April, 1997.     

Detonation of propane-air mixtures under injection of hot detonation products

The tube for spontaneous detonation (Institute of Technical Physics, Russian Federal Nuclear Center, Snezhinsk) was used to study the initiation and development of detonation in propane-air mixtures under injection of hot detonation products into them. The full picture of this phenomenon was recorded: the injection of hot detonation products into the main tube of the facility with the formation of a mixture of the starting propane-air composition with the hot products; the initiation of a local explosion in this mixture and the subsequent development of a detonation in it; detonation transfer to the region of the cold starting reactants (or detonation failure at the interface). The detonation was found to exist for an initial volume concentration of propane of 3.3 to 5%. The following critical (by the moment of the local explosion) parameters were determined: a mass fraction of hot detonation products of 6–9%, an energy input density due to product injection of 145–195 J/g, and an input energy power of 70–50 J/(g · msec). __________ Translated from Fizika Goreniya i Vzryva, Vol. 42, No. 3, pp. 100–109, May–June, 2006.     

Initiation of detonation in vacuum suspensions of RDX particles

The initiation of detonation in a vacuum suspension of volatile secondary explosives is studied numerically. A mathematical model of a two-phase, two-velocity medium takes into account the nonuniform temperature inside the particles as the gas flows around them. The formation dynamics of the reaction zone of a nonstationary detonation wave with a collisionless structure in a vacuum suspension of RDX particles is discussed. The critical size of the initiation region and of the energies for excitation of plane, cylindrical, and spherical detonations are determined as functions of the initial mass concentration and diameter of the particles. Translated fromFizika Goreniya i Vzryva, Vol. 34, No. 4, pp. 65–71, July–August 1998.     

Characteristic regimes of multifront-detonation propagation along a convex surface

Experimental results of multifront-detonation diffraction on a convex curvilinear surface are given. An estimate of the minimum gas-layer thickness, which is necessary for the external circumferential rotation of a multifront wave, is proposed. The characteristic propagation regimes are established in annular channels: complete destruction of detonation and combustion, high-speed combustion, galloping detonation, and multifront detonation. Translated fromFizika Goreniya i Vzryva, Vol. 35, No. 5, pp. 86–92, September–October 1999.     

Formation of carbon clusters in deflagration and detonation waves in gas mixtures

Numerical and experimental results of studying the formation of carbon clusters due to propagation of deflagration and detonation waves in enriched acetylene-oxygen and acetylene-air mixtures are described. Experiments are performed in tubes of different diameters (including tubes filled by a porous medium) with wide-range variations of the initial pressure and the fuel-to-oxidizer ratio. A large variety of carbon clusters formed in different regimes of burning of the mixture is found. A typical size of condensed carbon particles is 15–100 nm. In the case of detonation in a porous medium, the size of carbon particles is 15–45 nm; in some tests, large individual fullerene-type particles 150, 400, and 950 nm in size are formed. The fraction of condensed carbon in the total amount of carbon in the initial mixture is found to depend on the wave type; detonation is characterized by the minimum “yield” of condensed carbon. The amount of condensed carbon increases with increasing acetylene concentration in the mixture and initial pressure. The size of carbon particles in the case of deflagration is greater than that in the case of detonation. Cooling of reaction products decelerates condensation and interrupts the growth of carbon particles. __________ Translated from Fizika Goreniya i Vzryva, Vol. 44, No. 3, pp. 81–94, May–June, 2008.     

A generalized dependence of the critical detonation diameter of porous substances on the density

A generalized dependence of the detonation diameter of closed-porosity explosives on the relative density is obtained in the form of anU-shaped curve. The right branch of the curve can be described within the framework of the theory of V. S. Trofimov. The linear rate of chemical conversion of a substance at an interface is approximately proportional to the pressure. It is shown that despite its purely approximate character, the qualitative theory of Yu. B. Khariton yields the same values of the average reaction rates as the theory of V. S. Trofimov if the coefficient in Khariton’s formula is assumed to be equal to 5. It is noted that in almost all cases the gasification rate of explosives in a detonation wave is greater by a factor of 2–3 than the usual burning rates, which were obtained by extrapolation of the quantities measured in a constant-pressure shell. We propose a mechanism of forced gasification of explosives by a shock-heated gas which fills the pores. The left part of the curve is described under the assumption that the specific combustion surface of low-density explosives is limited by the shock-compression energy supplied to form a heated layer necessary to ignite a detonating substance. Mendeleev Chemical Engineering University, Moscow 125047. Translated from Fizika Goreniya i Vzryva, Vol. 33, No. 2, pp. 111–123, March—April, 1997.     

Nonclassical steady-state detonation regimes in pressed TNETB

The reaction zones and the dependence of the velocity of steady-state detonation waves on the initial density of pressed TNETB are studied using a VISAR interferometer. It is shown that, in the range of initial densities of TNETB 1.56–1.77 g/cm³, the propagation of a steady-state detonation wave is possible without the range of elevated pressures (chemical spike) in the reaction zone predicted by the classical theory. The dependence of the detonation velocity on the initial density shows singularities which indicate that a steady-state underdriven regime can occur in this range of initial densities. Based on the well-known theoretical concepts of the hot-spot decomposition mechanism of heterogeneous explosives, it is shown that the possibility of the existence of a steady-state detonation wave without a chemical spike, in particular, underdriven detonation, and the effect of the internal structure of the charge on the detonation regime are explained by the decomposition of explosives at the shock-wave front. __________ Translated from Fizika Goreniya i Vzryva, Vol. 43, No. 6, pp. 97–103, November–December, 2007.     

Detonation-wave profile in the explosive compression of cylindrical ampules

Experimental data on the geometric configuration of detonation waves in powder compaction in cylindrical steel ampules by a coaxial external ammonite charge are outlined. A polynomial approximating the geometric configuration of the detonation wave is obtained. Translated from Fizika Goreniya i Vzryva, Vol. 29, No. 5, pp. 85–88, September–October, 1993.     

Detonation combustion of gas mixtures using a hypervelocity projectile

This paper considers, from a unified point of view, problems of initiation of detonation combustion of a gaseous mixture using a hypervelocity projectile (HVP), The consideration is based on the energy criterion forHVP-induced detonation initiation. Experimental results are given that support the correctness of the criterion in a wide range of diameters (5–250 mm),HVP velocities (800–3500m/sec), and compositions of explosive mixtures (from active fuel-oxygen to hard-to-detonate fuel-air mixtures). The processes ofHVP interaction with an explosive mixture are classified. The previously unknown effect of jet formation of a detonation wave from a ballistic wave (at velocities less than the detonation velocities) was discovered for anHVP with a plane bow. Lavrentśev Institute of Hydrodynamics, Siberian Division, of the Russian Academy of Sciences, Novosibirsk 630090. Translated from Fizika Goreniya i Vzryva, Vol. 33, No. 5, pp. 85–102, September–October, 1997.     

Research on the thermal ionization model of detonation products by quantum mechanics methods

A thermal ionization model of gaseous detonation products, improved by using quantum mechanics methods, is described. The main attention is focused on the calculations of the potential energy and partition functions of detonation products using the ab initio quantum mechanics method, which are then used to solve the Saha equation for the detonation products in the thermodynamically equilibrium state. After that, the electrical conductivity and other physical parameters of detonation products in the H₂/O₂ and C₂H₂/O₂ systems are obtained. A comparison of the results calculated by the improved thermal ionization model with the results computed by the simple thermal ionization model and experimental data shows that the improved thermal ionization model ensures better agreement with experimental data. __________ Translated from Fizika Goreniya i Vzryva, Vol. 44, No. 1, pp. 113–122, January–February, 2008.