Dynamics of cavitational demolition in the interaction of a shock wave with a free surface

The problem of cavitation in the tension wave associated with the reflection of a shock wave from a free fluid surface is considered. A method of calculating the cavitation zone dynamics which makes it possible to determine the structure of the cavitation front, including for large space scales, is developed. A procedure for determining the dispersity of the fragment-drops of dispersed fluid, which takes into account the initial size distribution of the cavitation nuclei and the parameters of the incident shock wave, is proposed.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 73–80, November–December, 1992.     

Investigation of thermocapillary and thermogravitational convection in a fluid with local heating

The results of a numerical solution of the problem of the unsteady convective motion generated in a fluid layer by the formation at the initial instant of a heated zone in the form of a thin cylindrical column, extending from the surface into the interior of the fluid, are presented. The problem is formulated with allowance for both thermocapillary and thermogravitational convection. The influence of the thermocapillary and thermogravitational effects on the fluid motion for various layer thicknesses is subjected to parametric analysis.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 25–29, November–December, 1989.     

Sound absorption in a shock wave

It was shown in [1–4] that the reflection of a sound wave or its transmission through a shock front should be accompanied by attenuation or intensification of the wave is regarded as a discontinuity. In accordance with current representations [5, 6], a shock wave includes a viscous shock and a lengthy relaxation zone. Equilibrium is established with respect to translational and rotational degrees of freedom in the viscous shock and with respect to internal degrees of freedom in the relaxation zone. The result of the interaction of the shock and sound waves is determined by the relationship between the length of the sound wave and the width of the shock wave.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 90–94, May–June, 1986.     

Propagation of shock waves in free space

The problem of the exit of a shock wave from an axisymmetric channel and its propagation in a free space occupied by an ideal gas is examined. This problem has been studied earlier in [1], in which the shock wave front was considered planar, as well as in [2], in which the wave front was regarded as a surface of an ellipsoid of revolution. The solutions obtained in these studies assumed the presence of two regions in the wave-front surface: the region of the original shock wave and a region stemming from the decomposition of an infinitesimally thin annular discontinuity of the gas parameters, with the wave intensity over the front surface in each region being considered constant, i.e., the wave character of the process over the front was not considered. In this study a solution will be achieved by the method of characteristics [3–5] of the equations of motion of the shock-wave front, as obtained in [6, 7]. Flow fields are determined for the region immediately adjacent to the shock-wave front for a wide range of shock-wave Mach numbers M _a =1.6–20.0 for = 1.4. On the basis of the data obtained, by introduction of variables connected with the length of the undisturbed zone, as calculated from the channel cross-section along the x axis, together with the pressure transition at the wave front, relationships are proposed which approach self-similarity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 163–166, September–October, 1971.In conclusion, the author thanks S. S. Semenov for his valuable advice on this study.     

Interaction between a plane shock wave and a spherical volume of hot gas

The two-dimensional axisymmetric problem of the passage of a plane shock wave through a thermal is investigated. Two known effects are confirmed, namely, the intense distortion of the shock front on passage through the thermal and a change in the geometry of the gaseous element characteristic of the late stage of evolution of the thermal. Certain new effects are also detected: the formation of a pendant shock at the outer edge of the hot zone, cumulation of a secondary shock on the axis of symmetry at the top of the thermal, and straightening of the distorted front as it travels away from the heated zone.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 96–100, January–February, 1988.     

Approximation of the results of mathematical simulation of the effect of a shock wave on a cylinder

The results are given of a finite-difference calculation which augment previously known data and enable one in conjunction with the results of [1, 2] to approximate the time-dependent values of the pressure on the surface of a cylinder for the case when the shock front is parallel to the cylinder axis. The obtained approximation is valid in the interval of time from the instant at which the wave touches the cylinder until the disturbance reaches the rear stagnation point of the cylinder. The obtained expressions can be used in engineering calculations to determine the nonstationary distribution of the pressure over the surface of the cylinder and the force which acts in the direction of motion of the wave. The intensity of the wave and the specific heat ratio can vary in fairly wide ranges.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 179–184, July–August, 1980.I thank L. E. Taraskina for assistance in the calculations and the evaluation of the results.     

Amplification of intense blast pressure in a medium with this rarefied channels

It is known that a precursor is formed ahead of the wave front when a shock wave interacts with a hot thin surface layer. In this case for weak and moderate shock waves the maximum pressure at the measurement points on the surface is less than for shock waves propagating in the unperturbed medium. Below, it is shown, using estimates and numerical and laboratory simulation that precisely the opposite effect takes place in the near zone of an intense blast during the strong shock wave stage, i. e., the pressure at the measurement point may increase many times.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 143–149, January–February, 1996.     

Intensification of a detonation wave in the zone of secondary reactions in a two-phase medium

A method is proposed for the numerical calculation of one-dimensional nonsteady-state flows of a mixture of a gas with particles, based on the separation of a system of differential equations for a two-phase medium into two subsystems. The problem is solved concerning the propagation of a plane detonation wave in a mixture of a detonating gas with particles, behind the front of which secondary chemical reactions are taking place between the vapors of the particle material and the detonation products. The velocity profiles of the gas and of the thermodynamic functions behind the detonation wave front are determined, and also the dependence of the detonation velocity on the distance to the point of initiation. The conditions for intensification of the detonation wave are obtained in the zone of secondary reactions.Leningrad. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 92–96, September–October, 1972.     

Two-Phase Models of Formation of Cavitating Spalls in a Liquid

The dynamics of the structure of a liquid layer structure (with microbubbles of a free gas) behind a rarefaction wave front is studied numerically using the two-phase Iordansky–Kogarko–van Wijngaarden model and the frozen mass-velocity field model. An analysis of the initial stage of cavitation by the Iordansky–Kogarko–van Wijngaarden model showed that tensile stresses behind the rarefaction wave front relax quickly and the mass-velocity field in the cavitation zone turns out to be frozen. This effect is used to describe the late stage of the development of the cavitation zone. These models were combined to study the formation of cavitating spalls in a free-surface liquid under shock-wave loading.     

Regular reflection of a shock wave from a solid wall in a stream of fuel mixture

The two-dimensional stationary problem of regular reflection of a shock wave from a plane solid wall in a fuel gas mixture is examined in the case when the mixture is ignited at the intersection of the incident wave with the wall and a flame front is formed behind the reflected shock wave. The shock waves and the flame front are considered plane surfaces of discontinuity. The fuel mixture and the reaction products are considered perfect, inviscid, and non-heat-conducting gases.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 161–163, July–August, 1978.     

Pressure of an arbitrary acoustical wave on a plane

A study is made of the perturbed flow of a gas, brought about by a weak shock wave, falling on a fixed surface at an arbitrary angle. A solution determining the field of the velocities behind the front of the wave in an initially boundary-value problem with movable boundaries for a three-dimensional wave equation is obtained in the form of a double integral, containing an arbitrarily given function determining the parameters of the gas in the incident wave. The region of integration is a region included within an ellipse, whose relative eccentricity is equal to the sine of the angle of inclination of the front of the incident wave. A formula is obtained for the distribution of the pressure at the plane.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 114–116, January–February, 1975.     

Shock Compression of a Plate on a Wedged–Shaped Target

Problems of compression of a plate on a wedge–shaped target by a strong shock wave and plate acceleration are studied using the equations of dissipationless hydrodynamics of compressible media. The state of an aluminum plate accelerated or compressed by an aluminum impactor with a velocity of 5—15 km/sec is studied numerically. For a compression regime in which a shaped–charge jet forms, critical values of the wedge angle are obtained beginning with which the shaped–charge jet is in the liquid or solid state and does not contain the boiling liquid. For the jetless regime of shock–wave compression, an approximate solution with an attached shock wave is constructed that takes into account the phase composition of the plate material in the rarefaction wave. The constructed solution is compared with the solution of the original problem. The temperature behind the front of the attached shock wave was found to be considerably (severalfold) higher than the temperature behind the front of the compression wave. The fundamental possibility of initiating a thermonuclear reaction is shown for jetless compression of a plate of deuterium ice by a strong shock wave.     

Numerical investigation of the expansion of a cloud of dispersed particles or drops under the influence of an explosion

The results are given of a numerical investigation into the expansion of clouds of fine disperse particles or drops suspended in air under the influence of a blast wave. Two possible situations are simulated: an explosion in front of a cloud and an explosion in the region of a cloud (explosion with simultaneous formation of a drop region behind the shock front). The influence that the determining parameters have on the range and extension of the expansion zone is analyzed, and the results of the numerical experiments are generalized by means of empirical dependences.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 82–90, January–February, 1982.We thank K. I. Kozorezov for drawing our attention to the subject of the investigation and A. L. Gonor for a helpful discussion.     

Initial stage of the collision of blast waves

The collision of two blast waves is analyzed for the case of variable parameters of the gas behind the wave front and wave reflection at a plane, a cylindrical, and a spherical obstacle. The reflection of a blast wave from a nonmoving obstacle is investigated in detail. The problem of the collision of two shock waves with constant parameters behind the front is solved both in the symmetrical case (reflection from a nonmoving wall) and in the case of waves of different amplitudes by a system of algebraic relations for the compression shocks. The reflection of a strong point-source spherical shock wave from a wall has been treated in [1, 2]. The present article examines the initial stage of wave collision for an arbitrary distribution of the parameters behind the front.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 41–48, September–October, 1971.The authors are grateful to V. P. Korobeinikov for a discussion of the results and to V. P. Kolgan for furnishing the numerical solutions.     

Stability of an ionizing shock wave in an electromagnetic field

The stability of a plane shock wave, which is ionizing a gas, against small two-dimensional perturbations in the presence of a uniform electromagnetic field is analyzed. The applied electric field is assumed to be normal to the wave front while the magnetic field is parallel to the front and perpendicular to the plane in which the perturbations are propagating. The medium is assumed to be a two-parameter gas. The case of an ideal gas is analyzed in detail. The presence of an electric field component normal to the front leads to the formation of a surface charge at the front whose interaction with the electromagnetic field considerably affects the stability.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 134–142, November–December, 1978.In conclusion, the authors thank A. G. Kulikovskli for useful discussions of the present work.     

Propagation of magnetohydrodynamic shock waves in a medium of decreasing density

It is explained under what condition instability develops in the wave front when a shock wave travels in a medium whose density is decreasing. It is shown that under laboratory conditions the buildup of such an instability may be suppressed by a diffusion of wave front segments into the walls of the system. Such an instability can occur, for example, in certain astrophysical bodies.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 24–27, May–June, 1972.     

Reflection of a Dam–Break Wave at a Vertical Wall. Numerical Modeling and Experiment

Results of the experimental study and numerical modeling of the reflection of a dam–break wave at the vertical end wall of a channel are given. A wave forms with distance from a partition creating the initial level difference of the liquid. It is shown that a numerical calculation based on the Zheleznyak—Pelinovskii nonlinear dispersion model satisfactorily describes the height of the splash–up, the amplitude of reflected waves, and the wave velocity in front of the wall for smooth and dam–break waves. It is also shown that, for smooth and weakly breaking (without significant entrainment of air) incoming waves, the experimental values of the height of the splash–up at the wall agree well with relevant experimental and calculated data for solitary waves.     

Effect of the percolation heat transfer component on the temperature field and thawing dynamics of soils

The effect of the convective heat transfer component on the temperature field and thawing front dynamics of soils is investigated for high fluid percolation velocities in the thawed zone. The steady state interchange and approximate self-similarity methods are used to obtain upper and lower bounds of the solution of the Stefan problem with a convective heat transfer component in a porous medium. From the results of the calculations conclusions are drawn concerning the accuracy and limits of applicability of the solutions obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 166–171, March–April, 1987.     

The behavior of a gas bubble in a shock wave

The phenomenon of thermal relaxation of the gas bubbles in a fluid behind a shock front is analyzed. The approach to solving the problem of heat transfer between a gas bubble and a fluid developed by the author is used to obtain a solution describing the initial stage of bubble collapse behind the shock front.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 187–189, September–October, 1993.     

Wedging an Orthotropic Body by a Rectangular Wedge of Finite Length

Galin's method is used to derive equations that relate the basic parameters of the problem on wedging an orthotropic space by a rigid rectangular wedge. To eliminate the stress singularity at the wedging crack tips, a Leonov–Panasyuk–Dugdale prefracture zone is assumed to exist at the crack front. The equations are derived using the COD criterion