Onset of residual stress fields near solitary spherical inclusions in a perfectly elastoplastic medium

When computing residual stresses in deformable solids, one has to use the theory of elastoplastic solids, because the final level and distribution of residual stresses is determined exactly by the accumulated reversible strains. In turn, to compute the elastic strains, one needs to determine the displacement field. The problem of determining displacements in statically determinate problems of the theory of perfect elastoplastic solids was considered for the first time in [1, 2]. The techniques proposed there permitted solving the problem of finding the residual stresses near a cylindrical cavity in a perfectly elastoplastic medium [3]. It was shown that secondary plastic flow [4] may arise in the unloading processes, which significantly redistributes the final residual stresses. In the present paper, we consider the loading and unloading problems for a ball with a rigid or elastic spherical inclusion. We study the onset of secondary plastic flow under unloading and compute the residual stresses. Thus, we model the onset of the residual stress field near a more rigid inhomogeneity. The case of a softer inhomogeneity was essentially considered in [3], where the onset of the residual stress field near a continuity flaw was studied.     

Vibrational relaxation of diatomic molecules in a non-Boltzmann thermostat

The action of resonance IR laser radiation on a molecular gas leads, at high-power absorption intensity, to a breakdown in the equilibrium (Boltzmann) energy distribution in the internal degrees of freedom [1]. Under realistic conditions, molecular gases usually are (due to small amounts of impurities or isotopic components) multicomponent systems. In this case resonance IR laser radiation (or other methods of selective action), disturbing the distribution function of the primary gas, does not interact directly with impurities. The problem thus arises of determining the distribution function of the impurity gas interacting with the nonequilibrium (non-Boltzmann) thermostat. The present paper, devoted to the solution of this problem, treats the distribution function of harmonic oscillators A, consisting of a small amount of impurities in a system of harmonic oscillators B with given nonequilibrium distribution functions of vibrational energy. The behavior of a system in a nonequilibrium thermostat was first considered in [2, 3] where, as well as in [4, 5], it was shown that in a non-Maxwellian thermostat with a small amount of harmonic oscillator impurities, a Boltzmann distribution in harmonic oscillator vibrational energies is established under stationary conditions, with a temperature differing from the gas-kinetic temperature of the thermostat, defined in terms of the mean-square velocity. The behavior of a small amount of impurities (heavy monoatomic particles and harmonic oscillators) in a non-Maxwellian thermostat of a light gas was further investigated in [6–8]. Unlike the papers mentioned, the present one considers the behavior of a small amount of harmonic oscillator impurities in a thermostat with a Maxwellian velocity distribution and with a nonequilibrium (non-Boltzmann) distribution in vibrational energies.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 3–10, September–October, 1978.     

Destruction of coarse and fine water drops by monopulses of a ruby laser

In addition to the known method of evaporating water drops in the intensive radiation field of a CO₂ laser, papers have recently appeared wherein the destruction of water drops without the conversion of the light energy they absorbed into heat is investigated (surveys [1, 2], for example). Papers devoted to nonthermal methods of destroying a water aerosol, although still few in number, indicate the proposal of three methods of destroying the drops: optical breakdown in water, excitation of mechanical vibrations of the drops, and photochemical destruction of the water molecules [1, 2]. The optical breakdown phenomenon, when intense destructive shocks occur in a water drop subjected to a laser monopulse, has been investigated more fully than the other methods but also clearly insufficiently. Experiments on destroying millimeter- and micron-sized drops by ruby laser monopulses are described in this paper, values of the parameters characterizing this process are determined, and an approximate estimate of the energy and power of the laser pulses required to destroy a water aerosol in a track of definite length is also given.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 26–35, May–June, 1979.     

Motion of a magnetizable liquid in a rotating magnetic field

Moskowitz and Rosensweig [1] describe the drag of a magnetic liquid — a colloidal suspension of ferromagnetic single-domain particles in a liquid carrier — by a rotating magnetic field. Various hydrodynamic models have been proposed [2, 3] to describe the macroscopic behavior of magnetic suspensions. In the model constructed in [2] it was assumed that the intensity of magnetization is always directed along the field so that the body torque is zero. Therefore, this model cannot account for the phenomenon under consideration. We make a number of simplifying assumptions to discuss the steady laminar flow of an incompressible viscous magnetizable liquid with internal rotation of particles moving in an infinitely long cylindrical container in a rotating magnetic field. The physical mechanism setting the liquid in motion is discussed. The importance of unsymmetric stresses and the phenomenon of relaxation of magnetization are emphasized. The solution obtained below is also a solution of the problem of the rotation of a polarizable liquid in a rotating electric field according to the model in [3].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 40–43, July–August, 1970.     

Boundary layer on a blunt body in a flow of dusty gas

The problem of interaction of gas-dust flows with solid surfaces arose in connection with the study of the motion of aircraft in a dusty atmosphere [1–2], the motion of a gas suspension in power generators, and in a number of other applications [3]. The presence of a disperse admixture may lead to a significant increase in the heat fluxes [4] and to erosion of the surface [5]. These phenomena are due to the joint influence of several factors — the change in the structure of the carrier-phase boundary layer due to the presence of the particles, collisions of the particles with the surface, roughness of the ablating surface, and so forth. This paper continues an investigation begun earlier [6–7] into the influence of particles on the structure of the dynamical and thermal two-phase boundary layer formed around a blunt body in a flow. The model of the dusty gas [8] has an incompressible carrier phase. The method of matched asymptotic expansions [9] is used to obtain the equations of the two-phase boundary layer. In the frame-work of the refined classification made by Stulov [6], it is shown that the form of the boundary layer equations is different in the presence and absence of inertial precipitation of the particles. The equations are solved numerically in the neighborhood of the stagnation point of the blunt body. The temperature and phase velocity distributions in the boundary layer, and also the friction coefficients and the heat transfer of the carrier phase are found for a wide range of the determining parameters. In the case of an admixture of low-inertia particles that are not precipitated on the body, it is shown that even when the mass concentration of the particles in the undisturbed flow is small their accumulation in the boundary layer can lead to a sharp increase in the thermal fluxes at the stagnation point.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 99–107, September–October, 1985.I thank V. P. Strulov for a discussion.     

Distribution of radiant thermal flux over the surface of a sphere for hypersonic flow of a nonviscous radiating gas past the sphere

In the present study using the Newtonian approximation [1] we obtain an analytical solution to the problem of flow of a steady, uniform, hypersonic, nonviscous, radiating gas past a sphere. The three-dimensional radiative-loss approximation is used. A distribution is found for the gasdynamic parameters in the shock layer, the withdrawal of the shock wave and the radiant thermal flux to the surface of the sphere. The Newtonian approximation was used earlier in [2, 3] to analyze a gas flow with radiation near the critical line. In [2] the radiation field was considered in the differential approximation, with the optical absorption coefficient being assumed constant. In [3] the integrodifferential energy equation with account of radiation was solved numerically for a gray gas. In [4–7] the problem of the flow of a nonviscous, nonheat-conducting gas behind a shock wave with account of radiation was solved numerically. To calculate the radiation field in [4, 7] the three-dimensional radiative-loss approximation was used; in [5, 6] the self-absorption of the gas was taken into account. A comparison of the equations obtained in the present study for radiant flow from radiating air to a sphere with the numerical calculations [4–7] shows them to have satisfactory accuracy.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 44–49, November–December, 1972.In conclusion the author thanks G. A. Tirskii and É. A. Gershbein for discussion and valuable remarks.     

Increase in the density gradient in a thermal inhomogeneity through which a shock wave passes

The amplification of weak perturbations after passing through a shock wave was noted in [1]. In [2], the increase in the density gradient behind a shock wave which decays at the boundary of a weak inhomogeneity was calculated. Growth in the amplitude of acoustic perturbations interacting with a shock wave was demonstrated experimentally in [3]. In the present investigation, the density distribution behind a shock wave propagating through a gas at rest in which the density decreases (but the pressure is constant) was measured. The absolute value of the density gradient within a thermal inhomogeneity was found to increase as a result of the passage of a shock wave. The experimental data agree well with a calculation made under the assumption that the relative change in the density along the inhomogeneity is small. In contrast to [1], quadratic terms are taken into account in the calculation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 170–175, May–June, 1981.     

Green’s function for a prestressed thermoelastic half-space with an inhomogeneous coating

A mathematical model is developed for an inhomogeneous thermoelastic prestressed half-space consisting of a stack of homogeneous or functionally graded layers rigidly attached to a homogeneous base. Each component of the inhomogeneous medium is subjected to initial mechanical stresses and temperature. Successive linearization of the constitutive relations of the nonlinear mechanics of a thermoelastic medium is performed using the theory of superposition of small deformations on finite deformations with the inhomogeneity of the medium taken into account. Integral formulas are derived to explore dynamic processes in inhomogeneous prestressed thermoelastic media.     

Sound generation by a laser beam in a liquid with absorbing particles

Sound generation by a laser beam within a liquid, related to liquid boiling at absorption centers, has been studied relatively little. Acoustic effects upon liquid boiling in a laser beam were first reported in [1]. A change in the index of refraction of a liquid has been observed under the action of acoustical radiation of microbubbles formed on absorbing particles in the zone irradiated by a laser beam [2–4]. However direct measurements of acoustical radiation from a set of microbubbles uniformly distributed over the volume of laser beam-liquid interaction has yet to be performed, to the authors' knowledge. The present study is a preliminary report of results of an experimental study of this class of opticoacoustical phenomena.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 9–12, January–February, 1984.In conclusion, the authors consider it their pleasant duty to thank G. A. Askar'yan for evaluating the study and S. V. Luk'yanov for assistance in measuring the particle size distribution.     

Influence of an acoustic wave on a system of two spheres in a viscous fluid

In this article we formulate and solve the problem of the influence of radiation forces (forces created by the radiation pressure) on two spheres in a viscous fluid during the transmission of an acoustic wave. On the basis of these forces we investigate the nature of the interaction between the spheres as determined by the mutual disturbance of the flow fields around them as a result of interference between the primary and secondary waves reflected from the spheres. A previously proposed [2] approach is used in the investigations. The radiation force acting on one of the spheres is filtered by averaging the convolution of the stress tensor in the fluid with the unit normal to the surface of the sphere over a time interval and over the surface of the sphere. The stresses in the fluid are represented, to within second-order quantities in the parameters of the wave field, in terms of the velocity potentials obtained from the solution of the linear problem of the diffraction of the primary wave by the free spheres. The diffraction problem is formulated and solved within the framework of the theory of linear viscoelastic solids [6]. The case of an ideal fluid has been studied previously [3–5, 7]. Radiation forces are one of the causes of the relative drift of solid particles situated in a fluid in an acoustic field.S. P. Timoshenko Institute of Mechanics, Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 30, No. 2, pp. 33–40, February, 1994.     

Unsteady three-dimensional viscous shock layer in nonuniform gas flow in the neighborhood of a stagnation point

The combined influence of unsteady effects and free-stream nonuniformity on the variation of the flow structure near the stagnation line and the mechanical and thermal surface loads is investigated within the framework of the thin viscous shock layer model with reference to the example of the motion of blunt bodies at constant velocity through a plane temperature inhomogeneity. The dependence of the friction and heat transfer coefficients on the Reynolds number, the shape of the body and the parameters of the temperature inhomogeneity is analyzed. A number of properties of the flow are established on the basis of numerical solutions obtained over a broad range of variation of the governing parameters. By comparing the solutions obtained in the exact formulation with the calculations made in the quasisteady approximation the region of applicability of the latter is determined. In a number of cases of the motion of a body at supersonic speed in nonuniform media it is necessary to take into account the effect of the nonstationarity of the problem on the flow parameters. In particular, as the results of experiments [1] show, at Strouhal numbers of the order of unity the unsteady effects are important in the problem of the motion of a body through a temperature inhomogeneity. In a number of studies the nonstationary effect associated with supersonic motion in nonuniform media has already been investigated theoretically. In [2] the Euler equations were used, while in [3–5] the equations of a viscous shock layer were used; moreover, whereas in [3–4] the solution was limited to the neighborhood of the stagnation line, in [5] it was obtained for the entire forward surface of a sphere. The effect of free-stream nonuniformity on the structure of the viscous shock layer in steady flow past axisymmetric bodies was studied in [6, 7] and for certain particular cases of three-dimensional flow in [8–11].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 175–180, May–June, 1990.     

Dynamic compactness of coupled thermoelastic waves in continuously nonuniform anisotropic media

In the present work, the dynamic problem of coupled thermoelasticity with the most general type of nonuniformity and anisotropy is analyzed. The hyperbolic nature of the system of equations of coupled thermoelasticity is demonstrated, effects of extinction of separate waves by superposition of elastic and thermoelastic wave fronts are investigated, and the interrelationship of different orders of discontinuity of stresses, displacements, and temperature is determined. The case of the uncoupled problem of thermoelasticity is especially analyzed. Sufficient conditions are obtained for the dynamic density for wave processes in thermoelasticity, previously investigated for boundary value problems of hyperbolic systems of second order differential equations [1], andelastic stress waves [2] are obtained. The generally accepted system of tensor notation for the theory of thermoelasticity is used [3].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 154–163, May–June, 1981.     

Determination of the parameters of particles suspended in two-phase media by means of penetrating radiation

Determination of the concentration, size, and internal structure of microscopic particles suspended in two-phase media by means of contactless methods constitutes an important technological problem. If the particle sizes are on the order of the wavelength of light, methods based on light scattering by particles are widely used for this purpose. The most direct method consists in observing the optical signal scattered by an individual particle [1]. There are also several methods where the total signal from a large number of particles is recorded, but, in this case, multiple rescattering of light on particles must be negligible [2, 3]. At the same time, the complex relationship between the scattering amplitude and the refraction index, the shape of particles, etc., as well as the increasing background of multiply scattered light with greater thickness of the scattering layer, restrict the scope of application of such methods and make other measurement methods desirable, e.g., in the case of instrument calibration. Our aim is to point out the advisability of investigating two-phase media by means of penetrating radiation, which has been used successfully for radiation flaw detection [4] and for inspecting the composition and density of matter [5], We shall mention the most important advantages of the proposed method. First, the interaction between individual particles and nonrefracted radiation is described by simple expressions, which makes the interpretation of results much easier. Second, in using the most informative scheme whereby scattering media are investigated by transillumination, the background of multiply scattered radiation with a low information content (or, to borrow a term from radiation protection physics, the build-up factor [6]) increases with an increase in the scattering layer thickness much more slowly than it does for light. This makes it possible to use radiation methods for investigating optically dense two-phase media. We shall consider below the possibility of determining the distribution function of particle sizes by measuring the radiation attenuation as a function of the linear coefficient of attenuation inside the particles.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 11–14, May–June, 1979.     

Radiation of waves by a sphere harmonically oscillating to-and-fro in a viscous medium

The theory of the radiation of sound by a sphere in an ideal medium is presented in detail in [1–3]. The emission of waves by a sphere oscillating to-and-fro in a viscous incompressible liquid is analyzed in [4, 5]. The present paper gives a precise solution to the problem of the radiation of sound by a sphere oscillating in a viscous medium.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 101–106, September–October, 1970.     

Radiating hydrogen flow in axisymmetric nozzles

A considerable number of studies published in recent years have been devoted to the study of gas in channels and pipes. In view of the complexity of the question and the lack of analytic techniques, individual aspects of the problem are generally considered. The determination of the radiant field characteristics in regions of simple geometric form filled with a stationary radiating-absorbing medium has been carried out in several studies. The articles [1–3] are devoted to the calculation of the radiant field and the temperature field for a given flow of a perfect inviscid nonheat-conducting radiating gas with constant absorption coefficient. The flow is assumed to be irrotational [1, 2] or nearly potential [3]. The authors investigated the accuracy of the solution obtained with the aid of various approximate methods and found that the diffusion approximation yields a small error in calculating the radiation density field and the values of the radiant thermal fluxes for a quite broad class of wall reflecting properties. We may note also [4, 5], in which a calculation is made of one-dimensional steady flow of a viscous heat-conducting radiating perfect gas with constant transport coefficients.In [1–5] the absorption coefficient is considered constant. This assumption simplifies the solution process considerably, since as the independent variables we can take the corresponding optical thicknesses. The study [3] contains a remark that the calculation method proposed there may be used with a variable absorption coefficient. However, this possibility was not used in the calculations presented.For a constant absorption coefficient these studies yield a rather complete analysis of the methods for solving two-dimensional problems in geometrically simple regions in the absence of mechanical motion and one-dimensional problems with motion. They contain results obtained for the exact integral or integrodlfferential equations and present an analysis of the approximate methods. The study [3] considers broader possibilities of solving two-dimensional problems (using the Monte-Carlo method), but the flow is assumed known ahead of time.In the following we present a method for calculating the two-dimensional equilibrium flow of an inviscid non-heat-conducting radiating gas with variable absorption coefficient. As an example, we consider the flow of radiating-absorbing hydrogen in axisymmetric nozzles. It is assumed that the radiation is gray and is in local thermodynamic equilibrium. The transport equation is considered in the diffusion approximation. The nozzles examined have a semi-infinite cylindrical inlet section. The initial gas flow in the cylindrical section is supersonic. In the solution process we determine the radiation density field and all the flow parameters within the nozzle.The author wishes to thank Yu. D. Shmyglevskii for his continued interest in this study.     

Electrical breakdown in air in a transverse magnetic field

The electrical breakdown of gases in a transverse magnetic field is discussed in references [1–16]. Attention has mainly been concentrated on the case of coaxial electrode geometry [1–10]. The existing experimental data on breakdown between plane-parallel electrodes [11–14] relate to a narrow range of variation of the parameters characterizing breakdown (P, d, H, U). The author has made an experimental study of the process of electrical breakdown in air in a transverse magnetic field between plane-parallel electrodes of finite size in the pressure interval from 650 to 5·10^–3 mm Hg at gap lengths of from 1 to 140 mm and magnetic inductions from 0 to 10 600 G.     

Internal rotation in the hydrodynamics of weakly conducting dielectric suspensions

Hydrodynamic phenomena in weakly conducting single-phase media due to interphase electric stresses are reviewed in [1]. In the present paper, a model is constructed of a dielectric suspension with body couples due to the field acting on free charges distributed on the surface of the particles of the suspension. Averaging of the microscopic fields yields macroscopic equations for the field and the polarization of the dielectric suspension with allowance for the finite relaxation time of the distribution of the free charge on the phase interface. The developed model is used to consider the occurrence of spontaneous rotation of a dielectric cylinder in a weakly conducting suspension in the presence of an electric field; compared with the case of single-phase media [2], this is characterized by a significant reduction in the threshold intensity of the electric field with increasing concentration of the particles [3]. In the present model of a dielectric suspension, the destabilization of the cylinder is due to the occurrence of rotations of the particles of the suspension due to the interaction between the polarization and the motion of the medium. The relaxation equation for the polarization for the given model is analogous to the corresponding equation for media which can be magnetized [4–6].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 86–93, March–April, 1980.     

Numerical investigation of the propagation of a pulse of radiation with λ=10.6 μm through absorbing media

The passage of electromagnetic radiation through gaseous media is of special interest when reasonantly absorbing impurities are present in the gas. The interaction of radiation with such a medium can lead, for example, to a temporal decrease of the gas temperature or to its strong heating [1-3]. At the same time the index of refraction in the channel of the light beam is altered, which leads to a deviation of the light rays from the initial direction. The main characteristics of such thermal selfaction within the framework of linear absorption theory for steady and nonsteady processes have been discussed in [4-12]. Nonequilibrium processes in the medium upon absorption of resonant radiation were not taken into account. The effect of the kinetics of vibrational energy exchange on the state of a medium upon the propagation of radiation through a mixture of CO₂ and N₂ gases was first considered in [2, 13, 14]. However, the simplest models of vibrational energy exchange were used, and saturation of the absorbing transition P20 [10°0 00°1] in the CO₂ molecule was not taken into account. Thus linearized equations of vibrational kinetics were used in [13], and only one channel of relaxation of asymmetric vibrations of CO₂ and excited nitrogen was considered in [14]. The propagation of a pulse of radiation with =10.6 m through an absorbing medium is investigated and the influence of the saturation effect and nonlinear processes of vibrational energy exchange on the self-action of light beams of Gaussian profile is studied in this paper.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 14–19, May–June, 1984.     

Effect of a mobile load on a nonlinearly compressed strip with a rigid foundation

The two-dimensional stationery problem of the effect of a mobile load on a nonlinear compressed strip with a rigid foundation is studied. The case of linear loading and unloading of the medium was analysed in [1, 2]. In this work, unlike [1, 2], the wave process is studied taking into account the nonlinear loading of the strip material, the effect of the inelastic properties of the medium on the distribution of kinematic parameters and stresses in it is studied, and the form of the surface of the front of the wave reflected from the rigid foundation is determined.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 129–133, May–June, 1986.     

Flow around a sphere by a two-phase supersonic jet

Results are presented of a calculation of the flow around a sphere of a two-phase supersonic jet, discharging into a vacuum. Calculations were performed by the determination method with use of a difference grid constructed on the basis of characteristic ratios [1], The parameters of the unperturbed jet were determined with the two-velocity and two-temperature model of mutually penetrating flows of continuous media (gas and particles) [2, 3] by the network method [4]. In calculating the flow around the sphere, as in [5–7], it was assumed that the particles do not affect the gas flow in the shock layer. An analysis of the effect of particles on gasdynamic parameters in a shock layer was performed in [8].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 171–176, November–December, 1978.The authors are grateful to A. N. Nikulin for providing the program for calculation of flow about a blunt body by a uniform supersonic flow.