Behavior of the vorticity vector in a supersonic nonuniform swirl flow of a combustible gas behind a moving curvilinear shock or detonation wave

Expressions for components of the vorticity vector behind a curvilinear shock or detonation wave propagating in a supersonic nonuniform flow of a combustible gas are derived. Plane and axisymmetric gas flows are considered. The free stream in the general case is a vortex flow with a specified distribution of parameters. Formulas for the vorticity components in the plane of the flow for axisymmetric flows are found to have the same form as formulas for steady axisymmetric flows. As in the case of steady flows, the normal-to-wave component of vorticity is demonstrated to remain continuous across the discontinuity surface; in the case of axisymmetric flows, the ratio of the tangential component of vorticity aligned in the plane of the flow to density also remains continuous, though the quantities themselves become discontinuous. __________ Translated from Fizika Goreniya i Vzryva, Vol. 45, No. 2, pp. 68–75, March–April, 2008.     

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.     

Effect of the degree of dispersion on the detonation wave structure in pressed TNETB

A VISAR interferometer was used to study the reaction zone in steady-state detonation waves in pressed TNETB at different initial densities (1.23–1.71 g/cm³) and degrees of dispersion (5 and 80 μm) of the initial powdered high explosive (HE). The initial density range in which a pressure rise was observed instead of the theoretically predicted chemical spike is shown to depend on the degree of dispersion of the HE. The unusual change in the parameters in the reaction zone is explained by the heterogeneous structure of pressed HEs, whose decomposition has a local nature and proceeds partially at the compression wave front. A technique for recording wave profiles using LiF windows was developed, which confirmed that all qualitative features observed when using aluminum foils ≈200 μm thick and a water window reliably reflect the detonation wave structure. __________ Translated from Fizika Goreniya i Vzryva, Vol. 43, No. 5, pp. 90–95, September–October, 2007.     

Interaction of rarefaction waves with a finite-thickness layer near a rigid boundary. Equilibrium approximation

Interaction of a rarefaction wave with a layer of solid particles near the end face of a shock tube is considered. A one-dimensional unsteady approximation of mechanics of heterogeneous media with identical pressures of the phases and with allowance for a finite volume concentration of particles in the layer is used as a mathematical model. The wave pattern of the flow and the mechanism of wave interaction with the layer, including the dynamics of the layer boundary depending on the layer thickness and rarefaction-wave width, are determined. The mathematical model proposed is verified against the dependence of the layer-boundary coordinate on time and also the dependence of the velocity of upward motion of the layer on the difference in pressures between the high-pressure and low-pressure chambers. __________ Translated from Fizika Goreniya i Vzryva, Vol. 43, No. 5, pp. 126–135, September–October, 2007.     

Transport equation for gas-dynamic perturbations in a spatially nonuniform self-igniting medium

An approach is developed to describe the formation and propagation of small gas-dynamic perturbations in a spatially nonuniform self-igniting medium for arbitrary chemical-reaction kinetics. An asymptotic equation describing the variation in the amplitude of the gas-dynamic perturbation along the characteristic is derived, and the conditions of its applicability are defined. Zel’dovich’s spontaneous flame wave is shown to be a natural zeroth approximation to the solution of the equations of gas dynamics. A method is proposed to determine the point in space at which a shock wave is formed. __________ Translated from Fizika Goreniya i Vzryva, Vol. 44, No. 3, pp. 72–80, May–June, 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.     

Bubble detonation as a self-sustained solitary wave with energy release

Previous experiments have shown that a bubble detonation wave is a resonant or self-sustained solitary wave in a bubble medium. Bubble detonation is modeled by a solitary wave with energy release in bubbles. The equation describing a solitary wave of small amplitude is shown to be an analog of nonlinear Boussinesq equation of the fourth order. A comparison of the solution obtained with averaged experimental pressure profiles shows that the analytical solution is suitable for describing bubble detonation waves with a finite pressure amplitude. In the model proposed, the time of action of solitary-wave compression on a separate bubble is several times the bubble oscillation period. This result agrees with experimental data and confirms the presence of a collective resonant effect in a bubble medium. Satisfactory agreement is obtained between experimental and theoretical data on the pressure profile and extent and velocity of bubble detonation waves. __________ Translated from Fizika Goreniya i Vzryva, Vol. 43, No. 6, pp. 104–111, November–December, 2007.     

Model of Vapor—Air Gasification of a Solid Fuel in a Filtration Mode

A two-temperature mathematical model of steady filtration combustion of a solid fuel in open systems is proposed. Air or a mixture of air with water vapors is considered as a gaseous oxidizer. The model takes into account that the heat capacities of the phases depend on temperature and composition and that the reactor length is finite and allows obtaining the composition of gaseous combustion products. Calculated results on gasification of a mixture of carbon with an inert component are presented. It is demonstrated that thermodynamic calculations are important for obtaining the upper estimate of gasification efficiency. Even a sufficiently long reactor becomes “short” in the regime of transient combustion waves, which results in more intense entrainment of heat by combustion products and, as a consequence, in lower efficiency of the process. __________ Translated from Fizika Goreniya i Vzryva, Vol. 42, No. 1, pp. 65–72, January–February, 2006.     

Radiographic study of interaction of shock and detonation waves in a high explosive

Collisions of shock and detonation waves in an HMX-based high explosive are experimentally studied with the use of flash radiography. Based on X-ray patterns, specific features of the wave-interaction process are identified, and qualitative differences are found in detonation formation and evolution in an explosive precompressed by a weak shock wave and in an undisturbed explosive. __________ Translated from Fizika Goreniya i Vzryva, Vol. 43, No. 3, pp. 132–138, May–June, 2007.     

Combustion of bulk density powder mixtures in a coflow of inert gas: 4. Ti-Si and Zi-Al systems

Combustion of bulk density Ti-Si and Zi-Al mixtures an a coflow of argon was studied in the presence/absence of (1) applied pressure difference δP along the direction of wave propagation, (2) thermal treatment of green samples in vacuum, and (3) blowing agent (borax). The data on variation of the burning velocity U _c were rationalized in terms of the convection-conduction combustion theory for heterogeneous condensed systems. For Parts 1–3, see Int. J. SHS, 2008, vol. 17, no. 2.     

Numerical Study of Formation of a Detonation Wave in a Supersonic Flow over a Wedge by an H2-O2 Mixture with Nonequilibrium Excitation of Molecular Vibrations of Reagents

Specific features of formation of an oblique detonation wave in a supersonic hydrogen-oxygen mixture flow over a plane wedge are analyzed. Preliminary excitation of molecular vibrations of H₂ is shown to lead to a noticeable (severalfold) decrease in the induction-zone length and the distance at which the detonation wave is formed. These effects are manifested even if H₂ molecules are excited in a narrow region in the vicinity of the flow centerline. The reason for these effects is intensification of chain reactions in the H₂-O₂ (air) mixture owing to the presence of vibrationally excited hydrogen molecules in the flow. __________ Translated from Fizika Goreniya i Vzryva, Vol. 42, No. 1, pp. 78–86, January–February, 2006.     

Wave formation in a high-velocity symmetric impact of metal plates

The impact of metal plates is considered within the framework of the model of a viscous incompressible fluid. The beginning of the wave-formation process in the model is equivalent to the initial stage of origination of instability of a steady flow in Landau’s scenario. To establish the correspondence between the model and the real process, a series of experiments is performed on a symmetric impact of plates made of an aluminum alloy with identical impact angles and different velocities of the contact point. At high values of the Reynolds number and, hence, at high velocities of the contact point, wave excitation is shown to have a soft character; at lower values of Reynolds number, there exists a metastability region where the wave-excitation regime is rather hard; at even lower Reynolds numbers, no action can lead to wave formation, as it follows from the theory. Thus, Landau’s model of origination of instability of a steady fluid flow is found to agree with the process of wave formation in an oblique impact of metal plates. __________ Translated from Fizika Goreniya i Vzryva, Vol. 42, No. 5, pp. 132–137, September–October, 2006.     

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.     

Flame spread over a liquid surface in a channel of finite section under oncoming air-flow conditions

The propagation of a combustion wave over a shallow hot liquid (n-butanol) blown over by an air flow was studied experimentally. The flame spread was accompanied by pulsations, whose amplitude depended on the oncoming gas velocity. Dependences of the average flame speed on temperature and oncoming gas velocity were obtained. The average speed was found to be independent of the liquid depth ahead of the flame within the experimental error. __________ Translated from Fizika Goreniya i Vzryva, Vol. 44, No. 1, pp. 29–34, January–February, 2008.     

Transformation of shock waves at the interface of bubble media

The transition of shock waves from a bubble medium into a liquid or into another bubble medium with different properties is considered experimentally. Data on the structure, velocity, and pressure in the shock wave incident onto the interface, transmitted wave, and reflected wave are obtained. Experimental results are compared with numerical data. __________ Translated from Fizika Goreniya i Vzryva, Vol. 42, No. 2, pp. 97–104, March–April, 2006.     

Experimental investigation of gasless detonation in metal-sulfur compositions

Samples of zinc-sulfur and manganese-sulfur mixtures are shocked using an explosive pentolite charge to investigate if a shock-initiated reaction is able to support continued shock wave propagation. Samples of two different nominal densities (62 and 86% of theoretical maximum density) are prepared as weakly confined cylinders 50 mm in diameter and are instrumented along their length (⩽280 mm) with sensitive piezoelectric pins. Experimental results showed that the shock wave transmitted into the sample by the explosive rapidly decays to an acoustic wave in all four sample types. Furthermore, in denser samples, the part of the sample farthest from the explosive is recovered intact and unreacted, which clearly indicates that the wave is unable to trigger reactions after 100 mm of travel along the sample. Thus, it is concluded that insufficient reaction energy is transmitted forward to the shock wave to prevent its decay as it travels along the sample. __________ Translated from Fizika Goreniya i Vzryva, Vol. 45, No. 2, pp. 116–123, March–April, 2009.     

Electromotive force for solid-flame combustion of heterogeneous systems in loose and pressed states

By an example of condensed 3Zr + 2WO₃ and Al + Ni systems, it is demonstrated that the electromotive force of solid-flame combustion measured by probing in loose systems is significantly higher than that in the same systems in a pressed state. An explanation for this phenomenon is offered, based on the difference in electrical conductivity in different zones of the combustion wave in loose and pressed condensed systems. __________ Translated from Fizika Goreniya i Vzryva, Vol. 42, No. 4, pp. 71–77, July–August, 2006.     

Reflection of a shock wave in a dusty cloud

The problem of shock-wave passage along a cloud of particles adjacent to a solid surface is studied numerically and analytically. The wave pattern of the flow near the shock wave reflected from this surface is analyzed within the framework of the equilibrium approximation of mechanics of heterogeneous media. The conditions of the transition from regular to irregular reflection from the substrate of the refracted shock wave inside the cloud are obtained analytically. The results of numerical simulations of a nonequilibrium flow in the two-velocity two-temperature approximation are compared with data obtained in the equilibrium approximation. Nonequilibrium and equilibrium flows are found to become more similar as the particle size decreases. __________ Translated from Fizika Goreniya i Vzryva, Vol. 43, No. 1, pp. 121–131, January–February, 2007.     

Experimental study of shock-wave magnetic cumulation

Experiments with aluminum, copper, and silicon powders are performed to study the mechanism of shock-wave magnetic cumulation. For all substances examined, the magnetic field as a function of the cavity area is described by a power dependence with a constant exponent α. The value of α depends substantially on the substance porosity and particle size. For copper and silicon powders and for small-size aluminum powder, the value of α is consistent with the ratio of the particle velocity u to the wave velocity D, as is predicted by a simple model of magnetic cumulation. For the fine and coarse aluminum powders, the value of α is noticeably smaller than the ratio u/D. The lower effectiveness of magnetic compression can be attributed to insufficiently high electrical conductivity (fine powder) and the emergence of conductivity with incomplete compression of the substance (coarse powder). In the first case, diffusion losses of the magnetic flux in the compressed substance are fairly noticeable. In the second case, the work against the magnetic forces is performed by a layer in the shock-transition region, which has a lower particle velocity. The mechanism of magnetic cumulation involves substance metallization under shock compression and expelling of some portion of the magnetic flux to the non-conducting region ahead of the shock front. The two-stage mechanism of cumulation known in the literature (metallization in the elastic precursor and subsequent compression of the field in the main wave) is not validated by experiments with measurements of the particle and wave velocities and electrical conductivity and by experiments on magnetic cumulation. __________ Translated from Fizika Goreniya i Vzryva, Vol. 44, No. 2, pp. 106–116, March–April, 2008.