Reflection of a shock wave from a rigid wall in a mixture of a liquid metal and solid particles

The problem of reflection of shock waves and expansion waves from a rigid wall in a mixture of liquid iron and small molybdenum crystals is considered. The study is performed within the framework of equilibrium and nonequilibrium approximations of mechanics of heterogeneous media with different pressures of the components. The mathematical model is verified by fitting the dependence of the equilibrium-frozen velocity of sound on the initial pressure in the mixture with available experimental data. In the equilibrium approach, the dependence of the type of the reflected wave on the type of the incident wave is determined. Direct numerical calculations within the framework of the nonequilibrium model of mechanics of heterogeneous media confirmed the validity of the reflection chart obtained. The possibility of significant compacting of molybdenum particles in reflected waves is revealed. Translated fromFizika Goreniya i Vzryva, Vol. 36, No. 4, pp. 97–107, July–August, 2000. This work was performed within the framework of the Integration Project No. 97-24 of the Siberian Division of the Russian Academy of Sciences.     

Scattering of a compressed stratified concentrated mixture

A mathematical model with allowance for phase compressibility is proposed to solve the problem of scattering of a stratified two-phase mixture. The wave structure of the flow is determined. The mathematical model is verified by the dependences of pressure at the shock-wave front and behind the compression wave and by the dependence of the delay on the spatial variable. __________ Translated from Fizika Goreniya i Vzryva, Vol. 42, No. 2, pp. 70–79, March–April 2006.     

Detonation of a mixture of RDX particles partially filling a cylindrical channel

Using a mathematical model of a two-phase, two-velocity medium, detonation in an annular layer of a suspension of volatile secondary explosives adjacent to the wall of a cylindrical channel is numerically investigated. The dynamics of formation and the special features of the structures of a two-dimensional reaction zone of a detonation wave in a gas mixture of RDX particles are discussed. A detonation regime with a vortex structure of the reaction zone is obtained in calculations for the first time. The geometrical limits of detonation in a channel are determined. Translated fromFizika Goreniya i Vzryva, Vol. 35, No. 4, pp. 79–87, July–August 1999.     

Ignition of a cloud of metal particles in the continuum regime. II. Nonadiabatic flow

The nonadiabatic motion of a gas mixture of magnesium particles behind the shock wave is considered within the framework of the general mathematical model of a reactive mixture of a gas, liquid drops, and solid particles. A classification of possible flow types of the mixture behind the front of a frozen shock wave is proposed. Ignition delays obtained by numerical methods are in good agreement with experimental data. The flow parameters obtained using the adiabatic and nonadiabatic models are compared. Translated fromFizika Goreniya i Vzryva, Vol. 35, No. 6, pp. 91–96, November–December 1999.     

Mathematical model of magnesium ignition in an extended range of parameters

A mathematical model of ignition of a magnesium particle with allowance for a heterogeneous chemical reaction is proposed. The model allows the final particle temperature after its ignition to be found and takes into account the region of the thermal influence of the particle on the gas. A stationary solution is found, which makes it possible to propose a classification of the thermal history of the particle-gas system. The mathematical model is consistent with experimental data on the dependence of the ignition delay on the gas pressure and particle radius and on the dependence of the limiting temperature on the particle radius and the ambient pressure. The mathematical model also reveals the effect of the size of the gas layer around the particle on the integral parameters of ignition. __________ Translated from Fizika Goreniya i Vzryva, Vol. 44, No. 5, pp. 64–71, September–October, 2008.     

Gas detonation in a channel with transverse ribs

Results of experiments on detonation propagation in a rectangular horizontal channel with high ribs on the lower wall are presented. The experiments were performed with acetylene-oxygen mixtures. An interval of initial pressures is found, in which low-velocity detonation with a steady velocity of 0.38–0.55 of the Chapman-Jouguet velocity without losses exists. This detonation wave is a system consisting of a shock wave and a flame. Owing to gas outflow to the layer occupied by the ribs, the flame is maintained at a constant distance from the shock wave, which is approximately equal to the free transverse size of the channel. This distance weakly decreases with increasing initial pressure and is almost independent of the burning rate of the gas at standard temperature. __________ Translated from Fizika Goreniya i Vzryva, Vol. 43, No. 5, pp. 82–86, September–October, 2007.     

Numerical study of the transfer of shock-wave loading to a screened flat wall through a layer of a powdered medium and a subsequent air gap

The two-velocity, two-temperature model with two stresses in a mixture of a gas and solid particles contacting each other is used to numerically study the dynamic effect of an air shock wave incoming onto a solid wall with a screening layer of a porous powdered medium at some distance from the wall. The process is described for the case of one-dimensional planar motion of the gaseous and disperse phases under the assumption of a viscoelastic behavior of the powder skeleton. The effect of stepwise shock waves onto the porous powdered screen is considered. The influence of parameters of the screening layer and the air gap on the dynamics of loading of the screened solid wall is analyzed. __________ Translated from Fizika Goreniya i Vzryva, Vol. 43, No. 1, pp. 132–142, January–February, 2007.     

Ignition of gaseous suspensions in an interacting continuum regime

A mathematical model is proposed for describing the flow of a mixture of gases and reactive solids including a heterogeneous chemical ignition reaction. The model is closed with an equation for the kinetics of oxide film growth. It is assumed that the heat of the chemical reaction can be released in both phases depending on the accommodation coefficients. The ignition of a motionless cloud of magnesium particles is studied in terms of this model. The model is tested with the use of experimental data on the maximum temperature of the medium as a function of the particle radius. Data on the dependence of the parameters of a heated particle cloud on the physical and chemical constants of the mixture and particles are presented. Translated fromFizika Goreniya i Vzryva, Vol. 34, No. 4, pp. 57–64, July–August 1998.     

Numerical study of heat waves in the oxidation of a magnesium wire

A mathematical model of ignition of magnesium samples is proposed based on the concept of the existence of thermal deceleration of a chemical reaction responsible for ignition. The model gives realistic values of temperatures after sample ignition and is in satisfactory agreement with experimental data on the dependence of the radius of a small particle on the limiting temperature of the ambient medium. It is shown that heat waves can be excited by heterogeneous oxidation of Mg wire located in the external flow. The range of parameters in which self-excited wave regimes are observed fits experimental data on oxidation of metal wires qualitatively and in order of magnitude. The problem of initiation of an ignition wave by the initial distributions of the sample temperature is solved numerically, and the stability of heat waves to small and finite perturbations is shown. Tranlated fromFizika Goreniya i Vzryva, Vol. 34, No. 6, pp. 29–38, November–December 1998.     

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.     

Mathematical modeling of a rotating detonation wave in a hydrogen-oxygen mixture

A two-dimensional unsteady mathematical model of spin detonation in an annular cylindrical ramjet-type combustor is formulated. The wave dynamics in the combustor filled by a hydrogen-oxygen mixture is studied numerically. __________ Translated from Fizika Goreniya i Vzryva, Vol. 43, No. 4, pp. 90–101, July–August, 2007.     

Surface layer dynamics in the pyrolysis of ammonium perchlorate-hydrocarbon binder propellants

Mixtures of ammonium perchlorate particles and polybutadiene binder appear to exhibit preferential accumulation of one or the other component on the pyrolyzing surface over a range of rocket-operating pressures. At low pressures, the surface layer is enriched with the oxidizer, and at high pressures, it is enriched with the binder. The degree of accumulation of the oxidizer is found to be higher for smaller particle size. These experimental data can be explained by the difference in activation energies for pyrolysis of the oxidizer and the binder. The particle size effect is explained by consideration of nearly identical surface temperatures for the oxidizer and binder in mixtures with fine particles, but different temperatures for those with coarse particles. The results obtained are important to the explanation of the mechanism of plateau burning rate exhibited by certain composite propellants. Translated fromFizika Goreniya i Vzryva, Vol. 36, No. 5, pp. 57–62, September–October, 2000.     

Numerical study of the effect of the parameters of a bulk layer and an incident shock wave on the pressure at a shielded flat wall

Results are presented from a numerical simulation to study the effect of the parameters of a porous, powdered layer and of an incident shock wave in air on the pulsed loading characteristics of a shielded flat wall. An analysis is made of the dependence of the total stress of the mixture and of the pressure of the pore gas at a rigid wall on the porosity of the medium, density of the material, particle diameter, depth of the shielding layer, and depth of the actuating shock wave. The depth of the screen is found to have the most significant effect on the amplitude of the total pressure of the powdered medium at the solid wall behind a reflected shock. A formula is obtained for estimating the number of maxima in the total pressure of the mixture at the wall during reflection of a shock wave from it. Translated fromFizika Goreniya i Vzryva, Vol. 35, No. 2, pp. 105–113, March–April 1999.     

Mathematical model for the ignition of a mixture of a liquid fuel and solid particles in air

A point mathematical model is developed, which describes the ignition in air of composite mixtures of the fine aluminum particles and drops of a hydrocarbon fuel and a gaseous oxidizer. The generalized overall reaction of combustion of hydrocarbon vapors, the difference in temperature between the components, and the build-up of an oxide film on a metallic particle are taken into account. In the particular case of a mixture containing drops of a hydrocarbon fuel, the model is adapted to the experimental data on the dependence of the ignition delay on the ambient temperature. In the case of a composite mixture containing both solid particles and drops, the induction time of “thermal explosion” with oxidizer excess depends to a greater extent on the concentration and sizes of fuel drops than on the amount of aluminum particles. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Fizika Goreniya i Vzryva, Vol. 33, No. 3, pp. 86–94, May–June, 1997.     

Modeling of the interaction between an air shock wave and a porous screen

Some specific features of the reflection of air shock waves from a rigid wall coated with the layer of a porous substance is studied numerically. A mathematical two-speed model with two stress tensors that has been constructed by methods of the mechanics of multiphase media is used for studying the wave processes in saturated porous media. The numerical-modeling technique based on the Lax-Wendroff two-step scheme is developed. The processes of passage of a “ledge”-type wave through the “gas-porous medium” interface and of reflection from a rigid wall covered with a porous material are considered, the effect of the porous-medium and wave parameters on the reflection is analyzed, and the numerical results are compared with the experimental data obtained by other authors. Translated fromFizika Goreniya i Vzryva, Vol. 36, No. 4, pp. 87–96, July–August, 2000. This work was supported by the Russian Federation President’s Foundation for State Support of Leading Scientific Schools of the Russian Federation (Grant No. 96-15-96001), the Foundation of the Ministry of Education of the Russian Federation for Fundamental Natural Sciences (Grant No. 97-0-4.2-130), and the Russian Foundation for Fundamental Research (Grant No. 98-01-00831).     

Mathematical model of continuous detonation in an annular combustor with a supersonic flow velocity

A two-dimensional unsteady mathematical model of a continuous spinning detonation wave in a supersonic incoming flow in an annular combustor is formulated. The wave dynamics in a combustor filled by a gaseous hydrogen-oxygen mixture is studied. The possibility of continuous spin detonation with a supersonic flow velocity at the diffuser entrance is demonstrated numerically for the first time; the structure of transverse detonation waves and the range of their existence depending on the Mach number are studied. __________ Translated from Fizika Goreniya i Vzryva, Vol. 44, No. 6, pp. 83–91, November–December, 2008.     

Tests of a solid state laser pumped by radiation from a converging shock wave

A neodymium glass laser pumped optically by radiation from a strong converging shock wave in argon is tested. A condensed explosive charge with an inner cylindrical hollow is used to initiate the converging shock. A mathematical model confirms the feasibility of optical pumping by radiation from a converging shock with lasing. Translated fromFizika Goreniya i Vzryva, Vol. 35, No. 2, pp. 114–119, March–April 1999     

Effect of a low-amplitude shock wave with residual pressure on hexagonal boron nitride

We have performed shock-wave loading of hexagonal boron nitride under pressures of10.8–16 GPa in the range of initial temperatures of20–500°C in flat recovery ampoules allowing one to sustain residual pressures of ∼1 GPa. To form a plane shock wave, a gas gun was used. Application of a residual pressure under the action of a shock wave with an intensity of16 GPa increased the yield of wurtzite boron nitride by4 to5 times. This explained on the basis of the assumption of wurtzite formation from the amorphous phase in high-temperature zones of adiabatic shear in the residual regime. Center of High Dynamic Pressures, Mendeleevo 141570. Translated from Fizika Goreniya i Vzryva, Vol. 33, No. 5, pp. 122–127, September–October, 1997.     

Ignition and combustion of magnesium particles in a nonuniform thermal field

A distributed two-dimensional mathematical model of ignition and combustion of magnesium particles with allowance for the heterogeneous chemical reaction and for the region of the thermal influence of the particle on the gas is developed. Problems of particle ignition under the action of uniform and nonuniform thermal fields in a rectangular microchannel are solved. __________ Translated from Fizika Goreniya i Vzryva, Vol. 45, No. 2, pp. 48–57, March–April, 2008.     

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.