

2013 year, number 6
A. A. Doinikov, A. Bouakaz
Keywords: ultrasound, echography, contrast agent, sonoporation
Abstract >>
The survey is devoted to a new field of bubble dynamics that studies the behavior of ultrasound contrast agents. This name denotes manmade encapsulated microbubbles applied in diagnostic and therapeutic ultrasonic medicine to enhance the quality of ultrasonic images and to deliver drugs to target sites in the human body. The survey analyzes theoretical models that are currently applied for the description of the bubble shell, the interaction of bubbles with blood vessel walls, and the acoustical action of bubbles on the cell membrane.

M. N. Davydov, V. K. Kedrinskii
Keywords: smoothed particle hydrodynamics (SPH) method, cavitationinduced fracture, shockwave loading
Abstract >>
It is demonstrated that the method of smoothed particle hydrodynamics can be used to study the flow structure in a cavitating medium with a high concentration of the gas phase and to describe the process of inversion of the twophase state of this medium: transition from a cavitating fluid to a system consisting of a gas and particles. A numerical analysis of the dynamics of the state of a hemispherical droplet under shockwave loading shows that focusing of the shock wave reflected from the free surface of the droplet leads to the formation of a dense, but rapidly expanding cavitation cluster at the droplet center. By the time t = 500 μs, the bubbles at the cluster center not only coalesce and form a foamtype structure, but also transform to a gas–particle system, thus, forming an almost free rapidly expanding zone. The mechanism of this process defined previously as an internal “cavitation explosion” of the droplet is validated by means of mathematical modeling of the problem by the smoothed particle hydrodynamics method. The deformation of the cavitating droplet is finalized by its decomposition into individual fragments and particles.

V. M. Sorokin, A. K. Yashchenko
Keywords: film membrane currentcarrying conductor, Ampère force, natural vibrations of membrane, damping of vibrations
Abstract >>
The dynamics of a circular film membrane with attached currentcarrying conductors in zero gravity is studied. Equations are derived which describe the vibrations of the membrane stabilized by the Ampère force. The spectrum of natural vibrations and their corresponding strains are calculated. Constrained vibrations of the membrane are studied. The effect of the geomagnetic field on the stability of the membrane and the damping of its vibration is investigated for unsteady modes of application of mechanical forces in zero gravity.

M. N. Kazeev, V. S. Koidan, V. F. Kozlov, Yu. S. Tolstov
Keywords: electric discharge, strong magnetic field, magnetic pulse welding, weld
Abstract >>
The results of a study of the feasibility of magnetic pulse welding of flat conductors are given. Various inductor circuits and sheet configurations are investigated experimentally. An optimized inductor circuit for accelerating flat conductors by a magnetic field is presented and the necessary diagnostic equipment is developed. Results of experiments on the acceleration of flat conductors and production of aluminum—aluminum and aluminum—steel welded joints are presented. The characteristics of the welds are investigated.

S. L. Davis^{}, T. B. Dittmann^{}, G. B. Jacobs^{}, W. S. Don^{}
Keywords: dispersion of particles, shock wave, highorder finitedifference monotonic scheme
Abstract >>
This paper discusses the particleladen flow development from a cloud of particles in an accelerated flow behind a normal moving shock. The effects of the aspect ratio of a rectangular and ellipsoidal cloud and the cloud's angle of attack with respect to the carrier flow are studied. Computations are performed with an inhouse highorder weighted essentially nonoscillatory (WENOZ) finitedifference schemebased Eulerian–Lagrangian solver that solves the conservation equations in the Eulerian frame, while particles are traced in the Lagrangian frame. Streamlined elliptically shaped clouds exhibit a lower dispersion than blunt rectangular clouds. The averaged and rootmeansquare locations of the particle coordinates in the cloud show that the cloud's streamwise convection velocity increases with decreasing aspect ratio. With increasing rotation angle, the crossstream dispersion increases if the aspect ratio is larger than unity. The particleladen flow development of an initially moderately rotated rectangle is qualitatively and quantitatively comparable to the dispersion of an initially triangular cloud.

S. Morsli, A. SabeurBendehina
Keywords: natural convection, undulated cavity, entropy generation, Bejan number
Abstract >>
The aim of the present work is to study the entropy generation in the natural convection process in square cavities with hot wavy walls through numerical simulations for different undulations and Rayleigh numbers, while keeping the Prandtl number constant. The results show that the hot wall geometry affects notably the heat transfer rate in the cavity. It has been found in the present numerical study that the mean Nusselt number in the case of heat transfer in a cavity with wavy walls is lower, as compared to heat transfer in a cavity without undulations. Based on the obtained dimensionless velocity and temperature values, the distributions of the local entropy generation due to heat transfer and fluid friction, the local Bejan number, and the local entropy generation are determined and plotted for different undulations and Rayleigh numbers. The study is performed for Rayleigh numbers 10^{3 }< Ra < 10^{5}, irreversibility coefficients 10^{–4 }< φ < 10^{–2}, and Prandtl numbers Pr = 0.71. The total entropy generation is found to increase with increasing undulation number.

E. Yu. Meshcheryakova
Keywords: ideal incompressible fluid, rotationally symmetric motion, nonstationary cylindrical vortex
Abstract >>
Equations of rotationally symmetric motion of an ideal incompressible fluid are considered. A class of solutions to these equations, described by a hyperbolic equation of the fourth order with one space variable, for which an initial boundaryvalue problem is formulated, is distinguished. The new class of exact solutions of the Euler equations was used to describe the a nonstationary cylindrical vortex in an ideal fluid.

S. Mukhopadhyay^{}, M. Golam Arif^{}, M. Wazed Ali^{}
Keywords: exponentially stretching, suction/blowing, velocity slip, mass transfer, similarity solutions
Abstract >>
The boundary layer flow and mass transfer toward an exponentially stretching porous sheet are analyzed in this paper. Velocity slip is considered instead of the noslip condition on the boundary. Selfsimilar equations are obtained by using similarity transformations. Numerical solutions of these equations are obtained by the shooting method. It is found that the fluid velocity and concentration decrease with increasing slip parameter. The fluid velocity decreases with increasing suction parameter.

Yu. N. Gordeev, D. O. Babaeva, E. B. Sandakov
Keywords: Perkins–Kern fracture, exact solution, formation fracturing fluid filtration
Abstract >>
An exact solution of the problem of hydraulic fracturing in a permeable medium with continuous fluid injection in a partially penetrated formation is constructed using the Perkins–Kern fracture model. The amount of fluid leakage from the fracture is determined using the pressure field of the fluid filtrate defined by the Shchelkachev equation (of the piezoconductivity type). Universal profiles of the fluid pressure in the fracture and the rate of fluid flow from it are obtained. It is shown that at the Perkins–Kern fracture tip, there is a dramatic increase in the leakage from the fracture.

A. I. Filippov, O. V. Akhmetova, I. F. Kabirov
Keywords: heatconducting medium, steadystate regime, filtration, temperature, averagely accurate asymptotic method
Abstract >>
The problem of the temperature field produced by sources whose position does not depend on the vertical coordinate and which are concentrated in a horizontal permeable layer surrounded by a heatconducting medium with radial steadystate fluid flow. The problem is solved using an averagely accurate asymptotic method. Analytical expressions for the zeroorder approximation and the first coefficient of the expansion. A condition is determined under which the averaged problem for the remainder term has a trivial solution.

G. Palani^{}, A. R. Ragavan^{}, E. Thandapani^{}
Keywords: magnetohydrodynamics, viscous dissipation, Nusselt number, free convection, vertical cone
Abstract >>
An analysis is presented to investigate the influence of viscous dissipation on a free convection flow over a vertical cone with a variable surface heat flux under the action of a transverse magnetic field. The heat transfer characteristics of the free convection flow are investigated numerically. Numerical solutions for transformed governing equations with a variable surface heat flux are obtained. Velocity, temperature, local shear stress, and heat transfer coefficients are calculated for various values of the problem parameters and presented in the graphical form. The effects of the magnetic parameter, the dissipation number, the powerlaw index, the angle between the cone generatrix and the vertical line, and the Prandtl number on the flow are discussed. For validation of the present numerical results, they are compared with available experimental data and are found to agree well.

N. I. Ostrosablin
Keywords: transversely isotropic medium, elasticity moduli, longitudinal normals, general solution, recursion operators, diagonalization of elliptic system
Abstract >>
A dynamic threedimensional system of linear equations in terms of displacements of the theory of elasticity of transversely isotropic media is given explicit expressions for phase velocities and polarization vectors of plane waves. All the longitudinal normals are found. For some values of the elasticity moduli, the system of equations is reduced to a diagonal shape. For static equations, all the conditions of the system ellipticity are determined. Two new representations of displacements through potential functions that satisfy three independent quasiharmonic equations are given. Constraints on elasticity moludi, at which the corresponding coefficients in these representations are real, different, equal, or complex, are determined. It is shown that these representations are general and complete. Each representation corresponds to a recursion (symmetry) operator, i.e., a formula of production of new solutions.

E. A. Ivanova, Ya. E. Kolpakov
Keywords: micropolar theory, piezoelectricity, piezoelectric effect, polar materials, spontaneous polarization
Abstract >>
A method for describing the piezoelectric effect in a polar material is proposed based on the use of a composite particle model with seven degrees of freedom and a nonzero dipole moment. Based on micropolar theory, a system of equations is obtained which differs from the classical theory of piezoelectricity in the presence of additional terms. It is shown that under certain assumptions, the proposed system of equations becomes the classical system but the piezoelectric moduli depend strongly on the spontaneous polarization vector. It is shown that for anisotropic media with different symmetries, the structure of the thirdrank piezoelectric tensors obtained using the proposed micropolar theory coincides with the structure of the tensors obtained using classical theory. For the media considered, dispersion relations are given and it is shown that in the proposed theory, unlike classical theory, the piezoelectric moduli are proportional to the spontaneous polarization.

Yu. N. Ovcharenko
Keywords: Vnotch, strain energy density, loading schemes of type I and type II, crack propagation direction, local fracture criterion
Abstract >>
Conditions of fracture of the local strain energy density, which were first formulated by Sih for a sharp Vnotch with an arbitrary tip angle, are proposed. The edges of the considered Vnotch are free from loading. If loading schemes of type I and type II are used, it is shown that the known brittle fracture conditions proposed by Sih contradict one of the basic postulates in fracture mechanics: the greater the intensity of stresses or elastic energy near the Vnotch tip, the greater the probability of crack propagation. The proposed new conditions of fracture (in a polar coordinate system) are obtained as a result of independent determination of the energy densities of changes in volume and shape. In this case, the abovementioned contradiction is eliminated.

V. A. Babakov, A. V. Shymanska
Keywords: dilatancy, hardening, quasilinear system, hyperbolic type, characteristics
Abstract >>
In the classical model of an ideal rigid–plastic material without hardening, the governing system of equations is a system of hyperbolic type, and, if hardening is taken into account, the type of the system of equations changes from hyperbolic to elliptical. In this case, the correlation between the experimentally observed strain localization lines and the characteristics of the quasilinear system is violated. It is shown that if dilatancy is taken into account, the system of equations remains hyperbolic.

I. P. Shatskii, V. V. Perepichka
Keywords: impact, elastic rod, viscoplastic resistance
Abstract >>
The wave problem of perturbation propagation along an elastic rod interacting with the medium is investigated using the model of viscoplastic friction. An exact solution of the problem is obtained for an arbitrary time of the loading period. Analysis of the results is performed.

V. M. Mirsalimov, B. E. Rustamov
Keywords: isotropic medium, cracklike cavity, end zones of cavity, traction, body forces, contact stress
Abstract >>
A mathematical model for the closure of a cracklike cavity with cohesive end zones in an isotropic medium is constructed using methods of elastic theory. It is assumed that the interaction between the surfaces of the cracklike cavity under the action of body and surface forces can lead to the formation of contact zones on their surfaces. Determination of the unknown parameters characterizing the closure of the cracklike cavity reduces to a system of singular integrodifferential equations. The integral equations are converted to a system of nonlinear algebraic equations which is solved by the method of successive approximations. The contact stresses, the interaction forces between the faces of the cracklike cavity, and the size of the contact zone in which the faces of the cracklike cavities are closed are determined.

