Non-linear study of electrohydrodynamic Rayleigh-Taylor instability in a composite fluid-porous layer

The non-linear electrohydrodynamic RTI in presence of electric field bounded above by porous layer and below by a rigid surface, have been studied based on electrohydrodynamic approximations in the effect similar to the Stokes and lubrication approximations. The non-linear problem is studied numerically in the present paper using the Adams-Bashforth predictor and Adams-Moulton corrector numerical techniques. In the conclusion, the non-linear problem discussed here is quite different from that of Babchin et al. (1983) [10] considering the plane Couette flow. The present problem is greatly influenced by the slip velocity at the interface between porous layer and thin film. It is not amenable to analytical treatment as that of Babchin et al. [10]. Therefore, numerical solutions have to be found. Fourth-order accurate central differences are used for spatial discretization using predictor and corrector numerical technique.     

内聚爆炸载荷下热塑性中厚球壳的变形和层裂

考虑温度和损伤对材料参数的影响,计入温度和损伤对材料塑性变形发展的耦合作用,以本构关系的内变量理论为基础得到了热塑性本构关系的普适显式表达式以及增量形式的热塑性本构方程,结合在实际中有重要意义的内聚爆炸载荷作用下的球壳层裂问题,建立了含损伤热塑性球壳破裂问题的完备方程组,使用有限差分方法,完成了对问题的数值模拟,并对结果进行了分析。     

Dynamic response in a bi-material spherical medium

Summary The elastodynamic problem of a bi-material spherical medium is solved under the condition that the external load applied is spherically symmetric. Exact and explicit formulas are provided for displacements and stresses induced by the propagating, reflected and transmitted waves. The D' Alembert solution is taken as a basic form, thereby reducing the boundary and interface conditions to ordinary differential equations and systems of ordinary differential equations. The integration constants contained in the solutions of the differential equations are fixed by a singularity extraction procedure, which removes from the solution those portions that are inadmissible to the wave motion problem. A number of numerical results are offered, to validate the analysis and to demonstrate the capability of the solution method in solving elastodynamic problems of engineering significance. Received 12 March 1996; accepted for publication 16 December 1996     

Dynamics of a spherical particle in a laminar boundary layer

The problem of the motion of an individual spherical particle in a laminar boundary layer is considered for small Reynolds numbers determined from the relative velocity and the transverse velocity gradient of the flow undisturbed by the particle. The dependence of the transverse force acting on the particle, which results from the nonuniformity of the free stream, on the distance of the particle from the surface of a flat plate is calculated. It is shown that the direction of the transverse force changes with the distance of the particle from the plate: near the surface the force is positive, i.e., directed away from the plate, and at greater distances negative.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 91–96, November–December, 1990.The author wishes to thank M. N. Kogan and N. K. Makashev for useful discussions.     

Instability of fluid motion in a thin spherical layer

We study flow stability in a thin spherical layer with respect to small disturbances. It is shown that for each given layer thickness there is a sequence of critical Reynolds numbers above which the motion is unstable. In its form, the critical disturbance is reminiscent of the secondary flow which develops upon loss of stability of the basic fluid flow between rotating cylinders (Taylor problem).The author wishes to thank M. I. Shliomis for his continued interest in this study.     

Averaging a granular medium with spherical packing

The problem of averaging three-component media consisting of rigid grains, a viscous or elastic deformable meterial occupying the intergranular gaps and an inviscid pore liquid (or gas) is examined. When the deformable material completely fills the gaps, the medium is reduced to two-component form. The volume of the interlayers is comparable with the volume of the grains (the grains are spherical and the distance between the nearest points on neighboring spheres is small as compared with the diameter).Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 74–81, May–June, 1990.     

Problem of filling of a spherical cavity in a Kelvin-Voigt medium

This paper is concerned with mathematical modeling and solution of the problem of the collapse of a spherical cavity in a viscoelastic medium under the action of constant pressure at infinity. A differential equation of motion for the cavity boundary is constructed and solved numerically. The existence of three modes of motion of the boundary is established, and a map of these modes in the plane of the determining parameters is constructed. Asymptotic forms of the solutions of the problem for all modes are constructed. The problem of cavity collapse with capillary forces taken into account is formulated and solved. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 5, pp. 93–101, September–October, 2008.     

Electromechanical nonstationary thickness vibrations of a piezoceramic layer

The methods of characteristics and difference schemes are used to study the nonstationary thickness vibrations of a piezoelectric layer polarized across the thickness and subjected to electrical and mechanical loads. The propagation of waves under loading of various types is studied. The dynamic electroelastic state of the layer is analyzed. It is established that the characteristics of the electroelastic state are in a linear relationship     

Tangential oscillations of a differentially rotating spherical fluid layer

The natural harmonic oscillations of a differentially rotating fluid layer under the action of a potential force are considered. The rise in the layer level is assumed to be negligible. The oscillations satisfy an ordinary second-order differential equation with singular coefficients that depend on the spatial coordinate. This equation is solved by the method of local separation of singularities based on the use of the properties of the Fuchs series for a bounded solution. Various laws for the latitude dependence of the angular rate of ocean rotation and the effect of these laws on the problem spectrum are considered. An equation is obtained for the streamlines of the oscillations investigated. Two cases in which the latitude dependence of the base flow velocity coincides with the real dependence for a celestial body are considered and the corresponding modes are found.     

Two-dimensional free boundary layer in a stratified medium

Expressions for the fluctuation characteristics of shear flow in a stratified medium are obtained on the basis of the equations for the single-point second-order moments of the velocity and temperature fields and then closure of those equations by means of semiempirical hypotheses. The Prandtl equation, with the influence or Archimedean forces taken into account, is used to analyze plane jet flows and wake flows of a body, Numerical computations are carried out for a plane wake, and the results are compared with the experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 71–79, July–August, 1977.     

Calculation of motion of a spherical drop in the Bingham medium

Mathematical modeling of the experimentally observed process of approaching of two identical oil drops located in an alcohol-water solution (matrix) with an identical density is performed. It is found that the drop moves in cycles consisting of the state at rest, acceleration, and deceleration; the cycle time is about 10⁻² s. Violation of the balance of forces on the drop boundary in the state at rest is caused by the fact that the shear stresses on this boundary cannot exceed the yield stress of the matrix, and the normal stresses are determined by solving the problem of the elasticity theory, because intermolecular bonds in the quiescent matrix make it similar to a solid. The results of drop motion calculations and experimental data agree well during the entire process of drop approaching, except for the final stage, which can be attributed to the neglect of hydrodynamic interaction of the drops.     

Motion through spherical droplet with non-homogenous porous layer in spherical container

The problem of the creeping flow through a spherical droplet with a nonhomogenous porous layer in a spherical container has been studied analytically. Darcy’s model for the flow inside the porous annular region and the Stokes equation for the flow inside the spherical cavity and container are used to analyze the flow. The drag force is exerted on the porous spherical particles enclosing a cavity, and the hydrodynamic permeability of the spherical droplet with a non-homogeneous porous layer is ca...     

Propagation of converging spherical deformation waves in a heteromodular elastic medium

The unsteady one-dimensional boundary-value problem of shock deformation of a medium bounded by a sphere is solved. The propagation of converging deformation wave fronts in an elastic material with different tensile and compressive strengths is studied. A boundary condition is obtained that provides the formation of a converging spherical shock wave with constant velocity. The impact conditions on the boundary of the heteromodular sphere are determined that can lead to the formation of a transition zone (a spherical layer of constant density) between the compression and tension regions.     

Transient response of a moving spherical shell in an acoustic medium

A ring-stiffened spherical shell is submerged in an acoustic medium. The shell is thin and elastic. The acoustic medium is inviscid, irrotational and compressible. The center of mass of the shell is subjected to a translational acceleration which is an arbitrary function of time. The absolute displacements of the shell are expressed in terms of the relative displacements and the displacement of the base of the shell, base being defined as the rigid ring placed at the equator. The motion of the acoustic medium is governed by the wave equation. The transient response of the shell is investigated numerically. The results are compared with the results of the in-vacuo response. The effects of the plane wave approximation and the base velocity on the transient response of the shell are studied. The numerical results show that the plane wave approximation accurately predicts the response of the shell in the acoustic medium for short times after excitation. The displacements of the shell in fluid are larger than those in vacuo. But when the base of the shell is restrained from translating, the displacements in fluid are smaller than those in vacuo. Therefore, base translation has a very significant effect on the transient response of the shells submerged in an acoustic medium.