Slow Motion of a Porous Eccentric Spherical Particle-in-Cell Models

A combined analytical?Cnumerical method is presented for the quasisteady axisymmetrical flow of an incompressible viscous fluid past an assemblage of porous eccentric spherical particle-in-cell models. The flow inside the porous particle is governed by the Brinkman model and the flow in the fictitious envelope region is governed by Stokes equations. In order to solve the Stokes equations for the flow field, a general solution is constructed from the superposition of the basic solutions in the two spherical coordinate systems based on both the porous particle and fictitious spherical envelope. Boundary conditions on the particle??s surface and fictitious spherical envelope that correspond to the Happel, Kuwabara, Kvashnin, and Cunningham/Mehta-Morse models are satisfied by a collocation technique. The drag of these eccentric porous particles relative to the drag experienced by a centered porous particle are investigated as functions of the effective distance between the center of the porous particle and the fictitious envelope, the volume ratio of the porous particle over the surrounding sphere and a coefficient that is proportional to the inverse of the permeability. In the limits of the motions of the porous particle in the concentric position with cell surface and near the cell surface with a small curvature, the numerical values of the normalized drag force are in good agreement with the available values in the literature.     

Slow Motion of a Porous Sphere Translating Along the Axis of a Circular Cylindrical Pore Subject to a Stress Jump Condition

The coupled flow problem of an incompressible axisymmetrical quasisteady motion of a porous sphere translating in a viscous fluid along the axis of a circular cylindrical pore is discussed using a combined analytical–numerical technique. At the fluid–porous interface, the stress jump boundary condition for the tangential stress along with continuity of normal stress and velocity components are employed. The flow through the porous particle is governed by the Brinkman model and the flow in the outside porous region is governed by Stokes equations. A general solution for the field equations in the clear region is constructed from the superposition of the fundamental solutions in both cylindrical and spherical coordinate systems. The boundary conditions are satisfied first at the cylindrical pore wall by the Fourier transforms and then on the surface of the porous particle by a collocation method. The collocation solutions for the normalized hydrodynamic drag force exerted by the clear fluid on the porous particle is calculated with good convergence for various values of the ratio of radii of the porous sphere and pore, the stress jump coefficient, and a coefficient that is proportional to the permeability. The shape effect of the cylindrical pore on the axial translation of the porous sphere is compared with that of the particle in a spherical cavity; it found that the porous particle in a circular cylindrical pore in general attains a lower hydrodynamic drag than in a spherical envelope.     

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.     

Slow Motion of an Assemblage of Porous Spherical Shells Relative to a Fluid

The body-force-driven motion of a homogeneous distribution of spherically symmetric porous shells in an incompressible Newtonian fluid and the fluid flow through a bed of these shell particles are investigated analytically. The effect of the hydrodynamic interaction among the porous shell particles is taken into account by employing a cell-model representation. In the limit of small Reynolds number, the Stokes and Brinkman equations are solved for the flow field around a single particle in a unit cell, and the drag force acting on the particle by the fluid is obtained in closed forms. For a suspension of porous spherical shells, the mobility of the particles decreases or the hydrodynamic interaction among the particles increases monotonically with a decrease in the permeability of the porous shells. The effect of particle interactions on the creeping motion of porous spherical shells relative to a fluid can be quite significant in some situations. In the limiting cases, the analytical solution describing the drag force or mobility for a suspension of porous spherical shells reduces to those for suspensions of impermeable solid spheres and of porous spheres. The particle-interaction behavior for a suspension of porous spherical shells with a relatively low permeability may be approximated by that of permeable spheres when the porous shells are sufficiently thick.     

Electrosolenoidal flows in a cylindrical cavity

The main difficulties in investigating three-dimensional magnetohydrodynamic (MHD) flows with vorticity arise, first, because it is necessary to solve an independent boundary-value problem in order to find the field of the electromagnetic forces and, second, because the regimes of these flows are strongly nonlinear for the majority of high-power technological MHD processes and a number of natural phenomena. Particular importance attaches to MHD flows generated by the interaction of an electric current applied to the fluid with the magnetic self-field. This class of MHD flows has become known as electrosolenoidal flows [1]. The presence of a definite symmetry in the distribution of the electromagnetic forces and the geometry of the region of the liquid conductor makes it possible to find a solution in self-similar form. The present paper is devoted to exact solutions of the nonlinear equations for axisymmetric electrosolenoidal flows of a conducting incompressible fluid in infinite cylindrical cavities.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 48–53, May–June, 1991.     

Steady rotation of a composite sphere in a concentric spherical cavity

The problem of steady rotation of a compositesphere located at the centre of a spherical container has beeninvestigated.A composite particle referred to in this paperis a spherical solid core covered with a permeable sphericalshell.The Brinkman’s model for the flow inside the composite sphere and the Stokes equation for the flow in the spherical container were used to study the motion.The torque experienced by the porous spherical particle in the presence ofcavity is obtained.The wall correction factor is calculated.In the limiting cases,the analytical solution describing thetorque for a porous sphere and for a solid sphere in an unbounded medium are obtained from the present analysis.     

Harmonic Vibrations of a Viscoelastoplastic Sandwich Cylindrical Shell

The free and forced harmonic vibrations of viscoelastoplastic sandwich shells are analyzed. An equation for approximate determination of the amplitudes of near-resonance vibrations is derived. As an example, the problem is solved for a sandwich circular cylindrical shell     

Vibrations of a Cylindrical Shell Filled with a Liquid

The concurrent effect of a harmonic excitation and an airflow on the vibrations and vibroaccelerations of a thin-walled cylindrical shell filled with a liquid is studied     

Nonlinear Vibrations of a Cylindrical Shell Containing a Flowing Fluid

The Bogolyubov-Mitropolsky method is used to find approximate periodic solutions to the system of nonlinear equations that describes the large-amplitude vibrations of cylindrical shells interacting with a fluid flow. Three quantitatively different cases are studied: (i) the shell is subject to hydrodynamic pressure and external periodical loading, (ii) the shell executes parametric vibrations due to the pulsation of the fluid velocity, and (iii) the shell experiences both forced and parametric vibrations. For each of these cases, the first-order amplitude-frequency characteristic is derived and stability criteria for stationary vibrations are established__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 4, pp. 75–84, April 2005.     

导电圆柱薄壳的热磁弹性效应分析

研究了磁场环境中受机械载荷作用的导电圆柱薄壳的热磁弹性问题．首先,根据电动力学方程和广义Ohm定律,得到了导电薄壳电流密度的分布,考虑到Joule热效应及热平衡方程,得到了导电薄壳的温度分布．其次,通过几何方程、物理方程、运动方程和电动力学方程导出了导电薄壳在机械场、电磁场以及温度场作用下的基本方程．最后,采用差分法及准线性化方法,得到了可以应用离散正交法求解的准线性微分方程组．对于导电圆柱薄壳,得到了Lorentz力表达式,并且推导了温度场积分特征值．讨论了导电圆柱薄壳应力、温度及变形随外加电磁参量的变化规律,并通过实例证实了可以通过改变电、磁、力场的参数来实现对薄壳的应力、应变、温度的控制．     

The Subharmonic Bifurcation of a Viscoelastic Circular Cylindrical Shell

In this paper the nonlinear dynamic behavior of a viscoelastic circular cylindrical shell under a harmonic excitation applied at both ends is studied. The modified Flugge partial differential equations of motion are reduced to a system of finite degrees of freedom using the Galerkin method. The equations are solved by the Liapunov–Schmidt reduction procedure. In order to study 1/2 and 1/4 subharmonic parametric resonance of the shell, the transition sets in parameter plane and bifurcation diagrams are plotted for a number of situations. Results indicate that, for certain static loads, the shell may display jumps due to the presence of dynamic periodic load with small amplitude. Additionally, different physical situations are identified in which periodic oscillating phenomena can be observed, and where 1/4 subharmonic parametric resonance is simpler than the 1/2-one.     

Turbulent jet impinging a cylindrical hot cavity

The possibility of improving the heat transfer is investigated numerically using finite volume method. The Reynolds number increase has a minor effect on flow structure but generates a systematic rise of Nusselt Number. The maximum heat exchange occurs when the cavity bottom is located at the potential core end. The main heat exchange occurs on the cavity bottom for every case. The stagnation Nusselt number is correlated according some problem parameters.     

Stress Distribution in a Composite Cylindrical Shell with a Large Circular Opening

The stress–strain distribution in a composite deep cylindrical shell is analyzed. The shell is weakened by a circular opening and loaded by an axial force. The problem is solved by the variational difference method. The analysis is carried out for an orthotropic shell with low shear stiffness     

Natural Vibrations of a Cylindrical Shell Reinforced with Two-Layer Rings

The vibrations of a cylindrical shell reinforced with ring ribs attached to the shell by means of elastic elements are studied. The problem is solved by the finite-element method. The shell and ribs are modelled by a plane four-node finite element, which is a combination of a four-node plane stress element and a four-node flexural element. The effect of the stiffness of the elastic elements on the natural frequencies and modes is examined __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 8, pp. 105–110, August 2005.