Blast wave propagation in air from a gaseous charge

In the point explosion problem it is assumed that an instantaneous release of finite energy causing shock wave propagation in the ambient gas occurs at a space point. The results of the solution of the problem of such blasts are contained in [1–4]. This point model is applied for the determination of shock wave parameters when the initial pressure in a sphere of finite radius exceeds the ambient air pressure by 2–3 orders of magnitude. The possibility of such a flow simulation at a certain distance from the charge is shown in papers [4, 5] as applied to the blast of a charge of condensed explosive and in [6, 8] as applied to the expansion of a finite volume of strongly compressed hot gas. In certain practical problems the initial pressure in a volume of finite dimensions exceeds atmospheric pressure by a factor 10–15 only. Such cases arise, for example, in the detonation of gaseous fuel-air mixtures. The present paper considers the problem of shock wave propagation in air, caused by explosion of gaseous charge of spherical or cylindrical shape. A numerical solution is obtained in a range of values of the specific energy of the charge characteristic for fuel-air detonation mixtures by means of the method of characteristics without secondary shock wave separation. The influence of the initial conditions of the gas charge explosion (specific energy, nature of initiation, and others) is investigated and compared with the point case with respect to the pressure difference across the shock wave and the positive overpressure pulse.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 110–118, May–June, 1986.     

Spherical shock wave reflection from a surface with a heated gas layer

The two-dimensional axisymmetric problem of the interaction between smallscale spherical shock waves initiated by a laser explosion and an absolutely rigid surface in the presence of a layer of hot gas is numerically investigated. A number of effects previously observed in physical and numerical experiments [5–8] are confirmed, in particular: the distortion of the reflected shock front and its acceleration on passage through the hot central zone of the laser explosion (lens effect), the strong deformation of this zone, and the formation of a precursor on the surface ahead of the shock wave interacting with the thermal layer. In addition, certain new anomalous effects are revealed: the formation of a pair of suspended shocks — one on the periphery of the hot central zone upon interaction with the reflected shock wave and the other behind the Mach stem in the triple point zone, etc.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 141–147, July–August, 1989.     

On the initial stage of a point explosion in a radiating gas

A study is made of the initial stage of a point explosion in a radiating gray gas whose absorption coefficient is approximated by the dependenceK=x()e ^–n ,where is the density and e is the internal energy of the gas. It is shown that for n > —1/3 the initial stage of the process differs significantly from the solution of the problem in not only the classical adiabatic case [1, 2] but also in the case of a medium with nonlinear thermal conductivity [2–4]. The supply of energy to the medium at a point leads to instantaneous heating of the complete medium. The form of this heating is found analytically. The method of matched asymptotic expansions is used to investigate the behavior of the solution in the neighborhood of the center. It is found that for definite conditions at the center of the perturbed region there are formed a shock wave and a region of reverse flow of the gas.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 75–82, May–June, 1980.I should like to thank V. P. Korobeinikov for interest in the work and a helpful discussion of it.     

Problem concerning a plane explosion in a heterogeneous atmosphere with account taken of the post-breakthrough stage

The problem is considered concerning a plane explosion in an exponential and standard atmosphere. The heterogeneity of the medium exerts an extremely marked influence on the gas flow. As shown in [1], under the conditions of an exponential atmosphere the upper part of the shock-wave front recedes to an infinite distance, after a finite time. This phenomenon has received the name breakthrough of the atmosphere. A numerical investigation of a powerful plane explosion in an exponential atmosphere at the stage before breakthrough is contained in [2]. In [3], asymptotic boundary conditions are proposed which permit the gas flow after breakthrough to be calculated. In the present paper, a numerical solution of this problem is obtained at an interval of time which exceeds by a factor of 10–15 the time of break-through. The effect of counterpressure and gravity is studied. Some results are given for a plane explosion in a standard atmosphere.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 124–131, May–June, 1976.The authors thank L. A. Chudov for attention to the project and for useful advice.     

Influence of viscosity on the flow over the sharp edge of bodies consisting of a spherical segment joined to an inverted cone

The results are given of an experimental investigation of the supersonic axisymmetric flow over a body consisting of a spherical segment joined to an inverted cone in the neighborhood of the point of inflection of the profile (Fig. 1a). For the limiting case of a cylinder with a flat end and M = 3, a study was made of the influence of the Reynolds number and the state of the boundary layer on the parameters of the local separation region formed near the inflection (Fig. 1b). It was found that there is an appreciable decrease in the length of the separation region and the pressure in it when the Reynolds number increases in the range Re = 10⁵– 10⁷ in the case of a laminar boundary layer on the flat end near the inflection point. A low level of the pressure on the surface of the body was achieved — of the order of thousandths of the pressure behind a normal shock. There was found to be a sharp increase in the pressure in the separation region when the boundary layer on the end becomes turbulent with transition to a flow regime that is self-similar with respect to the Reynolds number. Under conditions of a turbulent boundary layer, systematic experimental data on the pressure on the inverted cone near the point of inflection of such bodies were obtained and generalized.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 154–157, January–February, 1981.     

Calculation of reflection of a blast wave by a plane

Some results are given of calculation of the reflection of a blast wave by a rigid flat surface. A model of the explosion with a simple energy dissipation mechanism is considered, radiation being taken into account in the approximation of radiative heat conduction. The pressure distribution on the surface and the flow pattern in the region of propagation of the incident and reflected shock waves are obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 179–182, September–October, 1982.We thank L. A. Chudov for helpful discussions of the work.     

Oscillographic study of electrical explosion in copper and gold

An oscilloscope is used to measure electrical resistance as a function of enthalpy in copper and gold during the process of electrical explosion of wire samples. The enthalpy at the initial point of the explosion process was greater in value than at the melting point of the metal. The electrical explosion phenomenon is considered from the viewpoint of the kinetics of the liquid-metalvapor transition under impulse-heating conditions. The degeneration of the initial point of the electrical explosion for liquid-phase heating over periods less than 10^–7 sec is explained by disruption of the stability of homogeneous-vapor-nucleus formation.Translated from Zhurnal Prikladnoi Mekhaniki Tekhnicheskoi Fiziki, No. 3, pp. 54–58, May–June, 1974.     

Integral inequalities in the dynamics of a gravitating gas

In the framework of Newtonian mechanics, a study is made of the spherically symmetric problem of the adiabatic motion of a gravitating perfect gas in the presence of a shock wave produced by inhomogeneous gravitational collapse or a point explosion. The method of Golubyatnikov [1, 2] is used to construct a system of integro—differential inequalities that determine, in particular, the law of motion of the shock wave if the initial state of the gas is known. The investigated examples include some self-similar and nearly self-similar solutions to the problem of the gravitational contraction of dust with the formation of a strong shock wave, possibly with the release of energy; the self-similar problem of a point explosion in a gas at rest; and also the problem of the equilibrium of a gas sphere for =4/3 and arbitrary distribution of the entropy. In these cases, the inequalities reduce to algebraic relations and can be solved numerically.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 169–173, September–October, 1980.     

Propagation of blast waves with exponential heat release and internal heat conduction and thermal radiation

The problem of reactive blast waves in a combustible gas mixture, where the heat release at the detonation front decays exponentially with the distance from the center, is analyzed. The central theme of the paper is on the propagation of reactive blast into a uniform, quiescent, counterpressure atmosphere of a perfect gas with constant specific heats. The limiting cases of Chapman-Jouguet detonation waves are considered in the phenomenon of point explosion. In order to deal with this problem, the governing equations including thermal radiation and heat conduction were solved by the method of characteristics using a problem-specific grid and a series expansion as start solution. Numerical results for the distribution of the gas-dynamic parameters inside the flow field are shown and discussed.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

The determination of the crater for an explosion in ground with angular and curvilinear free boundaries

One of the simple mathematical models in the theory of the deformation of continuous media in an explosion is the solid—liquid model [1, 2]. This does not describe the dynamics of the ground and so enables us to determine only approximate characteristics of the crater. This model has now been used to study a wide range of problems in determining a crater in a continuous medium with various tensile properties and various positions of the explosive [3–5]. We consider below within the framework of the solid—liquid model boundary-value problems in determining a crater in the explosions of point explosives and uniformly distributed explosives on the surface and deep within an isotropic ground with angular and curvilinear free boundaries. The desirability of studying problems such as these was pointed out by Il'inski.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 3–9, January–February, 1985.     

On point blast theory

The problem of a spherical shock front generated in a point explosion and traveling in a homogeneous medium is analytically studied with account for counterpressure on the entire infinite interval of its existence. For this purpose, asymptotic representations of the excess pressure in the shock wave near and far away from the energy release point are matched. It is possible analytically to continue the four-term expansion for the far zone involving unknown constants, so that it rigorously coincides with the four-term power expansion of the solution for the singular point, that is, the blast center. The problem of determination of the unknown constants is mathematically closed by the derived entropy loss integral which expresses the global energy conservation law. The analytical dependence of the excess pressure in the shock wave on distance thus obtained is in good agreement with the results of numerical calculations.     

Explosion with plasma quasitrapping in a dipole field

Experiments using a powerful CO₂ amplifier were performed with the aim of developing a technique for simulating a space explosion in the magnetosphere of the Earth and other planets under laboratory conditions using laser plasma clouds. The amplifier radiation with an energy of about 300 J and a pulse duration of about 10^–7 sec focused on a Caprolon target of 4 mm diameter produced an exploding plasma in a dipole magnetic field with a characteristic dimension of 15 cm and a magnetic moment of 1.1·10⁷ Gs · cm³. The paper presents preliminary results of simulating a space explosion under quasitrapping conditions, where the energy of the explosion is much lower than the geomagnetic energy and the explosion point is located in the equatorial plane at a distance of two Earth's radii.     

Nonlinear waves and localized structures in two-phase flow through porous media

Three problems of two-phase flow through porous media are considered. In the first two flows in the region of near-critical saturations are investigated. Since under these conditions the active saturation and hence the phase permeability of one of the phases are small, it is important to take into account the delay in phase redistribution — such types of flow as nonlinear waves and localized structures become important. In the third problem it is assumed that the capillary jump is insignificant as compared with the phase pressures. It is shown that in this case localized structures may also occur.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 71–76, January–February, 1988.     

A spherical wave in a viscoelastic half-space

The propagation of spherical waves in an isotropie elastic medium has been studied sufficiently completely (see, e.g., [1–4]). it is proved [5, 6] that in imperfect solid media, the formation and propagation of waves similar to waves in elastic media are possible. With the use of asymptotic transform inversion methods in [7] a problem of an internal point source in a viscoelastic medium was investigated. The problem of an explosion in rocks in a half-space was considered in [8]. A numerical Laplace transform inversion, proposed by Bellman, is presented in [9] for the study of the action of an explosive pulse on the surface of a spherical cavity in a viscoelastic medium of Voigt type. In the present study we investigate the propagation of a spherical wave formed from the action of a pulsed load on the internal surface of a spherical cavity in a viscoelastic half-space. The potentials of the waves propagating in the medium are constructed in the form of series in special functions. In order to realize viscoelasticity we use a correspondence method [10]. The transform inversion is carried out by means of a representation of the potentials in integral form and subsequent use of asymptotic methods for their calculation. Thus, it becomes possible to investigate the behavior of a medium near the wave fronts. The radial stress is calculated on the surface of the cavity.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 139–146, March–April, 1976.     

Propagation of planar shock waves in an exponential atmosphere

We consider planar explosions in a medium with an exponential density distribution. In contrast to the so-called sectorial approximation [1] we take into account the overflow of energy from a lower region to an upper region, so that our solution of the problem considered here gives a truer picture of the flow of the gas at a later stage of a point explosion in a nonhomogeneous atmosphere. The numerical solution in both upper and lower regions of the flow merges into the corresponding limiting self-similar regime [2, 3]. The calculations are carried out up to a gap in the atmosphere [4]. The computational method is based on implicit difference approximations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza., No. 5, pp. 31–35, September–October, 1971.The authors are deeply grateful to L. A. Chudov for his constant interest in our work and for useful discussions, and they also wish to thank É. I. Andriankin for meaningful discussions of the paper.     

Stability of Hartmann flows

The stability of Hartmann flows for arbitrary magnetic Reynolds numbers is investigated in the framework of linear theory. The initial three-dimensional problem reduces to the equivalent two-dimensional problem. Perturbation theory is used to find asymptotic expressions for the eigenvalues. Distinguishing two types of disturbances — magnetic and hydrodynamic — is shown to be advantageous in a number of cases. Simple features of the stability are considered for particular cases. The well-know Lundquist result is generalized. An energy approach is applied to the problem of stability. The results of simulations involving the solution of the linear stability problem are described. A distinctive picture of stability is developed. There are several types of instability and they can develop simultaneously. The hydrodynamic and magnetic phenomena interact with each other in a very complex fashion. The magnetic field can either enhance flow stability or reduce it.Novosibirsk. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 6, pp. 17–31, November–December, 1972.     

Asymptotic theory of short separation regions on the leading edge of a slender airfoil

The two-dimensional flow of a viscous incompressible fluid near the leading edge of a slender airfoil is considered. An asymptotic theory of this flow is constructed on the basis of an analysis of the Navier—Stokes equations at large Reynolds numbers by means of matched asymptotic expansions. A central feature of the theory is the region of interaction of the boundary layer and the exterior inviscid flow; such a region appears on the surface of the airfoil in a definite range of angles of attack. The boundary-value problem for this region is reduced to an integrodifferential equation for the distribution of the friction. This equation has been solved numerically. As a result, closed separation regions are constructed, and the angle of attack at which separation occurs is found.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 42–51, January–February, 1981.I thank V. V. Sychev and Vik. V, Sychev for assistance.     

Container for Localization of an Explosion of a Compact High–Explosive Charge with an Inert Shell

Results of an experimental study of fragmentation effects in the explosion and the piercing power of the fragments of inert masses in the form of hemispherical aluminum and soft–steel shells enclosing the spherical charge of a high explosive under their action on flat steel, aluminum, steel–net, and claydite—concrete barriers are given. A design of the lightest spherical explosion–proof container with a load–carrying steel or glass–reinforced plastic shell protected by a splinter–proof layer capable of withstanding an explosion of a high–explosive charge (with a twofold safety factor) with an inert steel shell is proposed.     

Transition of nonone-dimensional flows produced by explosions into one-dimensional flows

A particular class of flows resulting from explosions is considered and two processes are analyzed, both independently and as coupled processes: the transition of the solution to the problem of nonpoint explosion to the corresponding point regime and the transition of the solution to the problem of an explosion with nonone-dimensional initial conditions to a corresponding one-dimensional solution (not necessarily a point solution).Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 93–99, July–August, 1983.     

Transition flow of a fibrous suspension in a pipe as the flow of an anisotropic fluid

The transition flow is considered of a fibrous suspension in a pipe. The flow region consists of two subregions: at the center of the flow a plug formed by interwoven fibers and fluid moves as a rigid body; between the solid wall and the plug is a boundary layer in which the suspension is a mixture of the liquid phase and fibers separated from the plug [1–3]. In the boundary region the suspension is simulated as an anisotropic Ericksen—Leslie fluid [4, 5] which satisfies certain additional conditions. Equations are obtained for the velocity profile and drag coefficient of the pipe, which are both qualitatively and quantitatively in good agreement with the experimental results [6–8]. Within the framework of the model, a mechanism is found for reducing the drag in the flow of a fibrous suspension as compared to the drag of its liquid phase.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 91–98, September–October, 1985.