A Magnetoelastic Field in a Ferromagnetic Medium with a Spherical Cavity

The problem on the stress–strain state of an infinite isotropic body made of a magnetically soft material and containing a spherical cavity is considered. It is assumed that the body is under an external magnetic field. The basic characteristics of the stress–strain state and the magnetic field induced are determined and their singularities near the cavity are studied. Graphs are presented for the total magnitoelastic and Maxwell stresses as functions of the magnetic induction, the angle of dip, and the mechanical and magnetic properties of the material     

Stability of a spherical cavity in a sound field

The linear theory of the stability of the spherical shape of a cavity and the stability of its radial oscillations in a sound field are discussed. An equation is derived for the amplitudes of the spherical harmonics with allowance for surface tension, viscosity, and compressibility of the surrounding liquid in the Herring-Flynn approximation. The radial pulsation stability is analyzed in the same approximation. The equations derived in the article are subjected to numerical analysis.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 109–114, November–December, 1973.     

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.     

Dynamics of a cavitational cavity in a non-newtonian fluid

The dynamics of a spherical cavity in a non-Newtonian fluid, described by the Reiner-Rivlin rheological equation [1], is investigated. The equation of radial cavity motion is obtained, where the gas in the cavity is subject to a polytropic law and surface tension is taken into account. The equation of cavity motion is solved numerically for a number of values of the transverse viscosity coefficient. The influence of the transverse viscosity on the collapse process of vapor and gas-filled cavities is shown. Numerical computations are also carried out for the rate of energy dissipation and the pressure distribution in the fluid.Translated from Izvestiya Akademiya Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 170–173, July–August, 1973.The authors are grateful to A. T. Listrove for attention to the research.     

Numerical simulation of the dynamics of a liquid in a moving axisymmetric cavity

The problem of the motion of an ideal liquid with a free surface in a cavity within a rigid body has been most fully studied in the linear formulation [1, 2]. In the nonlinear formulation, the problem has been solved by the small-parameter method [3] and numerically [4–7]. However, the limitations inherent in these methods make it impossible to take into account simultaneously the large magnitude and the threedimensional nature of the displacements of the liquid in the moving cavity. In the present paper, a numerical method is proposed for calculating such liquid motions. The results of numerical calculations for spherical and cylindrical cavities are given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 174–177, March–April, 1984.     

The separation effect during centrifuging

The article discusses the problem of the separation of particles of small spherical form from a disperse system enclosed in the cavity between two infinite coaxial cones, which are in permanent rotation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 188–192, September–October, 1973.In conclusion, the authors thank Yu. P. Gupalo for his critical observations.     

Numerical analysis of oscillations of a gaseous cavity in a compressible liquid

The radial oscillations of a gas-filled spherical cavity in an infinite compressible ideal liquid are investigated. The numerical solution of the equation of motion of a gaseous sphere is used for the comparison of acoustic and energy characteristics of underwater trotyl explosion and small-amplitude explosion sound sources (detonation of explosive gaseous mixture, expansion of a compressed inert gas).Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 176–182, March–April, 1971.     

Heat transfer in supersonic flow over a single spherical cavity

The flow and heat transfer on a plate with a single spherical cavity has been experimentally investigated for M=4 and Re_,L=3.1 · 10⁶. The flow pattern over the cavity has been obtained. Zones of enhanced heat transfer have been detected, and the heat transfer coefficients in and near the cavity have been determined. It has been established that a single spherical cavity has almost no effect on the integral heat flux.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 48–52, September–October, 1991.The authors are grateful to V. N. Brazhko for assistance in carrying out the experiments and to T. A. Ershova for assistance in analyzing the results.     

Microcavitation in the slow motion of a solid spherical particle along a wall in a fluid

In the slow motion of a spherical particle along a wall, a cavity in the form of a non-spherical bubble is detected visually in the narrow particle-wall clearance. The nondimensional parameters associated with cavity formation are formulated and the effect of these parameters on the particle motion is investigated.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, 2004, pp. 110–118. Original Russian Text Copyright © 2004 by Prokunin.     

Motion of a variable-volume sphere in an ideal fluid near a plane surface

The motion of a spherical cavity in a fluid is investigated. The radius of the sphere varies under the action of a constant pressure at infinity. The problems of the collapse of a cavity moving in an unbounded fluid and of the collapse of a cavity near a plane are solved in the exact formulation. The occurrence of an initial translational velocity or the presence of a solid surface, by contrast with the collapse of a sphere at rest in an unbounded fluid [1], yields a limiting radius at which the process of collapse ceases. A sphere initially at rest near a plane always comes into contact with the plane as a result of collapse. The radius and velocities at which the sphere arrives the plane are calculated for various initial distances from the latter. The possible mechanism of the action of a cavitation bubble on a solid surface is discussed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 94–103, September–October, 1971.     

Calculation of the explosion of hexogen in aluminum

A calculation is carried out for a spherical explosive charge in elastic-plastic materials with different yield points. Velocity and stress profiles are shown for several instants of time. The zone of increase of internal energy of the material, due to plastic flow, is shown. The values of the energy in the cavity and also the kinetic and plastic energies of the medium are calculated. Comparison with an experiment carried out with an explosion in aluminum [1] showed satisfactory agreement between the calculated and experimental velocity profile at the free surface.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 156–162, July–August, 1973.The authors thank V. N. Rodionov for interest in the work.     

Approximate method of determining liquid oscillation frequencies in cavities of revolution

Variational methods [1–4], which require the use of computers, are widely used at present for determining the oscillation frequencies of liquid partially filling an arbitrary cavity of revolution. A technique is given in [5] for the approximate solution of this problem for a cavity which differs little from a cavity for which the solution is known. In the present paper we obtain an approximate first-order differential equation for the frequency squared, using the filling level as the independent variable. Calculations were made using this method for several cavities (sphere, cylinder with spherical base, cone with varying apex angles, torus). Comparison of these results with the results obtained experimentally by other theoretical methods shows that the proposed method is sufficiently accurate for engineering applications.The author wishes to thank I. V. Kolin for carrying out the calculations.     

Approximate method of solving the problem of characteristic oscillations of a liquid in cavities of revolution

The problem of the characteristic oscillations of a liquid in axisymmetric cavities of rotation has been fairly fully studied [1–5], its solution in the general case being found by the variational method. Analysis of numerical results using the variational method shows that to achieve acceptable accuracy it is necessary to retain an appreciable number of coordinate functions, which entails the solution of a matrix eigenvalue problem of high order, this applying especially to the case when it is necessary to determine several eigenfrequencies and the shapes of the oscillations. In the present paper, a method proposed earlier by Shmakov [6] is developed, the velocity potential being sought in the form of a sun of two potentials. The first (base) potential is a solution to the problem of the characteristic oscillations of a liquid in a cavity whose free surface coincides with the free surface of the original cavity, and the second (correcting) potential is chosen in the form of a system of harmonic functions, this system being complete and orthogonal on the wetted surface of the cavity. Cavities of revolution are analyzed as examples, and a detailed investigation of numerical results is made for a spherical cavity. The numerical analysis shows that a sufficiently accurate result in the determination of a frequency is obtained if one term of the base problem is retained and only the correcting potential is used to make this more accurate. As a result, it is only necessary to solve an algebraic equation of first degree in the square of the frequency.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 3–8, September–October, 1983.     

Motion of a cylindrical cavity near a free boundary of a liquid

The dynamics of a cylindrical cavity in a liquid with no allowance for vertical displacement are considered in [1–3]. The present study investigates the pulsation motion of a cylindrical cavity near a free boundary of a liquid, allowing for displacement of the axis of the cavity in the vertical direction.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 173–176, November–December, 1988.     

Calculation of two-dimensional dispersion in a gas in unsteady flow in a porous medium

A two-dimensional problem of the flow of a gas containing an impurity through a porous medium is considered. At the initial time, the gas containing a uniformly distributed impurity is at a high pressure in a spherical cavity in a porous medium at a certain distance from a flat surface. It is assumed that for t > the motion of the carrier gas is described by the system of equations for flow in a porous medium and the dispersion of the impurity is described by the equations of convective diffusion and nonequilibrium adsorption. A numerical method for solving the problem is discussed. Some results of calculations are given. The influence of the flat surface on the flow of the gas and the dispersion of the impurity is analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 61–67, September–October, 1982.We thank V. N. Nikolaevskii for comments which permitted a significant improvement in the paper.     

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.     

Slender axisymmetric cavities in a supersonic flow

Slender axisymmetric cavities in a subsonic flow of compressible fluid were investigated in [1–4]. In [5] a finite-difference method was used to calculate the drag coefficient of a circular cone, near which the shape of the cavity was determined for subsonic, transonic, and supersonic water flows; however, in the supersonic case the entire shape of the cavity was not determined. Here, on the basis of slender body theory an integrodifferential equation is obtained for the profile of the cavity in a supersonic flow. The dependence of the cavity elongation on the cavitation number and the Mach number is determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 179–181, January–February, 1989.     

Some problems of axisymmetric cavitation flows

The equations for the shape of a slender axisymmetric cavity [1–3] are used to consider problems relating to pulsations of the cavity shape, the drag of a slender cavity-forming body, and the influence of surface tension on the shape of a steady cavity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 28–34, January–February, 1982.I thank V. P. Karlikov and Yu. L. Yakimov for helpful discussions of the results.     

Characterization of the panoramic annular lens

The panoramic annular lens (PAL) consists of a single piece of glass, with spherical surfaces, that produces a flat annular image of the entire 360-deg surround of the optical axis of the lens. This paper describes the attributes of the PAL and shows that the lens maps elements from object to image space via a constant aspect ratio polar mapping. A panoramic video system (PVS) is described to illustrate how the characterization can be applied in experimental mechanics for cavity inspection and measurement.Portions of this work were presented at the 1995 SEM Spring Conference and Exhibit, Grand Rapids, MI, June 12–14, 1995.     

Shock-initiated implosion of an elliptical cavity and detonation in a liquid layer

Many papers [1–9] have been devoted to the dynamical analysis of bubble implosion in a liquid layer. Experiments have shown that an initially circular cavity is displaced or transformed into an elliptical cavity during the implosion process due to instability, whereupon its further contraction produces cumulative jets. This problem is important in the study of surface wear in cavitation flow [7] and in the analysis of the impact sensitivity of liquid explosives [1–6]. The onset of accumulation is conveniently investigated by starting with an elliptical cavity or by displacing a circular cavity relative to the impact axis, thereby creating an asymmetrical pressure field about the center of the cavity. In the present article certain theoretical notions are advanced with regard to the onset of the cumulative jet in an elliptical or displaced cavity and its influence on the ignition of liquid explosives due to the formation of minute droplets [4] in the adiabatically heated gas inside the cavity. Experimental data on the jet formation time and the frequency of nitroglycerin detonations qualitatively support the theoretical predictions.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 78–85, September–October, 1971.