Limit thermodynamic model for compositional gas–liquid systems moving in a porous medium

It is shown that a multicomponent two-phase system moving through a porous medium may be described by a limit model in which the thermodynamic subsystem is totally separated from the hydrodynamics. The limit corresponds to a contrast phase mobility and a fast pressure relaxation process. The obtained limit thermodynamic model includes several differential thermodynamic equations and describes the equilibrium in an open system. The model is validated by comparing with the full compositional flow simulations. A numerical solution to the limit thermodynamic model is constructed. An application to the gas-condensate systems is compared to the full compositional model.     

Geometrical Representation of the Motion of a Body Through a Medium

The paper presents a complete qualitative analysis of the model plane-parallel motion of a body (plate) through a resisting medium with jet or detached flow. A simplified system is analyzed on the phase plane. A geometrical interpretation is given to the motion of the plate     

Quasi-optimal deceleration of rotational motion of a dynamically symmetric rigid body in a resisting medium

We study the problem of quasi-optimal (with respect to the response time) deceleration of rotational motion of a free rigid body which experiences a small retarding torque generated by a linearly resisting medium. We assume that the undeformed body is dynamically symmetric and its mass is concentrated on the symmetry axis. A system of nonlinear differential equations describing the evolution of rotation of the rigid body is obtained and studied.     

Mathematical model of heat and mass transfer in a bidisperse porous material

A model of heat and mass processes in a body with two types of pores is considered. This model describes the initial stage of substance penetration into the porous system (or the inverse process, namely, substance extraction from the system) and takes into account convective transport in large channels. A kinetic function of impregnation (extraction) of the porous medium and the substance flux density are found for a problem with additional conditions.     

A linear dynamic model for a saturated porous medium

A linear isothermal dynamic model for a porous medium saturated by a Newtonian fluid is developed in the paper. In contrast to the mixture theory, the assumption of phase separation is avoided by introducing a single constitutive energy function for the porous medium. An important advantage of the proposed model is it can account for the couplings between the solid skeleton and the pore fluid. The mass and momentum balance equations are obtained according to the generalized mixture theory. Constitutive relations for the stress, the pore pressure are derived from the total free energy accounting for inter-phase interaction. In order to describe the momentum interaction between the fluid and the solid, a frequency independent Biot-type drag force model is introduced. A temporal variable porosity model with relaxation accounting for additional attenuation is introduced for the first time. The details of parameter estimation are discussed in the paper. It is demonstrated that all the material parameters in our model can be estimated from directly measurable phenomenological parameters. In terms of the equations of motion in the frequency domain, the wave velocities and the attenuations for the two P waves and one S wave are calculated. The influences of the porosity relaxation coefficient on the velocities and attenuation coefficients of the three waves of the porous medium are discussed in a numerical example.     

Mathematical Model of a Biological Medium with Account for the Active Interactions and Relative Displacements of Cells That Form It

A three-phase continuum model of a biological medium formed by cells, extracellular fluid, and an additional phase responsible for independently controlled active force interaction between the cells is obtained. The model describes the reconstruction of biological tissues with account for the active stresses exerted at intercellular interactions. The constitutive relation for the active stress tensor takes into account different mechanisms of cell interactions, including the chaotic and directed cell activities as the active stresses are created, as well as the anisotropy of their development due to cell density distribution inhomogeneity. On the basis of the model, the problem of forming a cavity within an initially homogeneous cell spheroid due to the loss of stability of the homogeneous state is solved. The constitutive relation for the medium strain rate due to cell rearrangements takes into account two mechanisms of relative cell motion: related to cell adhesion and cellmotility. The participation of differentmechanisms of cell interaction in the self-organization of the biological system that consists of mechanically active cells is investigated.     

On stretching of a bar capable of undergoing phase transitions

The dynamic processes in an elastic bar composed of a material, which is capable of undergoing phase transitions, are under consideration. We use a model of an elastic body with non-convex strain energy potential. The bar with variable cross-sectional area is considered. Propagation of the phase boundary along the bar loaded with time-dependent tensile forces is investigated. It is assumed that the phase boundary moves at a variable speed. The problem is solved analytically by using two approaches, namely, the full dynamic approach and the quasi-static (kinetic) approach. The results obtained by means of these two methods are compared.     

Stability of spatial motion of a body of revolution in an elastoplastic medium

A previously constructed model that describes the spatial motion of a body of revolution in an elastoplastic medium (without flow separation and with nonsymmetric separation of the medium flow taken into account) is used to study the Lyapunov stability of rectilinear motion of a body in the case of frozen axial velocity on a half-infinite time interval. Some stability criteria are obtained and the influence of tangential stresses is analyzed.     

Sliding a body on snow

Snow is considered as an ideal nonlinear elastoplastic medium. A body performs planeparallel motion on snow. The area of its contact with snow is a part of a rectangular plate. The contact zone changes during the motion of the body. Steady motions are found from the derived equations of motion in the case when the constant external forces and the moment exerted on the body are given. The inverse problem of determining the forces and moments is solved for a given steady motion of a vehicle.     

One-dimensional steady-state flows of a rotating gas and zonal wind

A thin layer of an ideal gas on a solid gravitating sphere is considered with allowance for inertia forces. Flows are initiated by heating the solid spherical surface nonuniformly in latitudes. A solution in the form of a one-dimensional flow directed along the meridians is obtained. Assuming that the gas density is independent of the latitude, an exact solution is obtained for the one-dimensional flow in question. This solution has all the features of zonal winds existing in many planets of the Sun system including the possibility of existence of supperrotation, i.e., the regime for which the atmosphere moves more rapidly than the solid body of the planet.     

Evolution of a heavy rigid body rotation under the action of unsteady restoring and perturbation torques

The paper develops an approximate solution to the system of Euler’s equations with additional perturbation term for dynamically symmetric rotating rigid body. The perturbed motions of a rigid body, close to Lagrange’s case, under the action of restoring and perturbation torques that are slowly varying in time are investigated. We describe an averaging procedure for slow variables of a rigid body perturbed motion, similar to Lagrange top. Conditions for the possibility of averaging the equations of motion with respect to the nutation phase angle are presented. The averaging technique reduces the system order from 6 to 3 and does not contain fast oscillations. An example of motion of the body using linearly dissipative torques is worked out to demonstrate the use of general equations. The numerical integration of the averaged system of equations is conducted of the body motion. The graphical presentations of the solutions are represented and discussed. A new class of rotations of a dynamically symmetric rigid body about a fixed point with account for a nonstationary perturbation torque, as well as for a restoring torque that slowly varies with time, is studied. The main objective of this paper is to extend the previous results for problem of the dynamic motion of a symmetric rigid body subjected to perturbation and restoring torques. The proposed averaging method is implemented to receive the averaging system of equations of motion. The graphical representations of the solutions are presented and discussed. The attained results are a generalization of our former works where µ and M_i are independent of the slow time τ and M_i depend on the slow time only.

     

Self-similar degeneration of the turbulent wake behind a body towed in a passively stratified medium

A mathematical model of the far turbulent wake behind a towed body in a passively stratified medium, based on the known semi-empirical e-? model of turbulence, is considered. A grouptheoretical analysis of the model is performed. With the help of the method of B-determining equations, the model is reduced to a system of ordinary differential equations, which is solved numerically. The resultant solution is compared with a self-similar solution obtained by direct numerical integration of the differential equations at large distances from the body.     

Motion of a cylinder in a viscous electroconductive medium with a magnetic field

The method of force sources is used to consider the planar problem of the motion of a circular cylinder in a viscous electroconductive medium with a magnetic field. The conventional and magnetic Reynolds numbers are assumed to be small. Expressions are obtained for the hydrodynamic reaction forces of the medium, acting on the moving cylinder. It is shown that as a result of the flow anisotropy in the medium, caused by the magnetic field, in addition to the resistance forces on bodies moving at an angle to the field, there are deflecting forces perpendicular to the velocity vector. The velocity field disturbances at great distances from the moving cylinder are determined.The problems of viscous electroconductive flow about solid bodies in the presence of a magnetic field constitute one of the divisions of magnetohydrodynamics. Motion of an electroconductive medium in a magnetic field gives rise to inductive electromagnetic fields and currents which interact with the velocity and pressure hydrodynamic fields in the medium [1, 2]. Under conditions of sufficiently strong interaction, the number of independent flow similarity parameters in MHD is considerably greater than in conventional hydrodynamics. This circumstance complicates the theoretical analysis of MHD flow about bodies, and therefore we must limit ourselves to consideration of individual particular flow cases.Here we consider the linear problem of the motion of an infinite circular cylinder in a viscous incompressible medium with finite electroconductivity located in a uniform magnetic field.There are many studies devoted to the flow of a viscous electroconductive medium with a magnetic field about solid bodies (see, for example, [3–5]). Because of this, some of the results obtained here include previously known results, which will be indicated below. In contrast to the cited studies, the examination is made by the method of force sources, suggested in [6]. This method permits obtaining integral equations for the distribution of the forces acting on the surface of the moving body. Their solution is obtained for small Reynolds and Hartmann numbers. Then the nature of the velocity disturbances at great distances from the body are determined. These results are compared with conventional viscous flow about a cylinder in the Oseen approximation.     

A numerical method for flows in porous and homogenous fluid domains coupled at the interface by stress jump

A numerical method was developed for flows involving an interface between a homogenous fluid and a porous medium. The numerical method is based on the finite volume method with body‐fitted and multi‐block grids. A generalized model, which includes Brinkman term, Forcheimmer term and non‐linear convective term, was used to govern the flow in the porous medium region. At its interface, a shear stress jump that includes the inertial effect was imposed, together with a continuity of normal stress. Furthermore, the effect of the jump condition on the diffusive flux was considered, additional to that on the convective part which has been usually considered. Numerical results of three flow configurations are presented. The method is suitable for coupled problems with regions of homogeneous fluid and porous medium, which have complex geometries. Copyright © 2006 John Wiley & Sons, Ltd.     

Integrable systems in the dynamics on the tangent bundle of a two-dimensional sphere

A mechanical system whose phase space is the tangent bundle of a two-dimensional sphere is studied. The potential nonconservative systems describing a geodesic flow are classified. A multiparameter family of systems possessing a complete set of transcendental first integrals expressed in terms of finite combinations of elementary functions is found. Some examples illustrating the spatial dynamics of a rigid body interacting with a medium are discussed.     

Macrokinetic model of the trapping process in two-phase fluid displacement in a porous medium

A microinhomogeneity-averaged model of the kinetics of the trapping process is proposed for a porous medium in which two fluids are mutually displaced. The traps are treated as a new hydrodynamic phase, and the trapping process as a phase transition. Kinetic relations for the average trapping process are obtained. The structure and quantitative values of the kinetic coefficients are obtained for a model of a porous medium in the form of a system of doublets. The dependence of the characteristic time of the process on the degree of inhomogeneity of the medium is investigated. A variant of the macroscopic model of the process of two-phase flow, in which the kinetic relations obtained are used as the closing relations, is proposed.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 92–101, May–June, 1995.     

Constitutive relations for a growing masonry with setting mortar

A model is proposed for averaging a periodic block structure, namely, a growing brick masonry body with setting interlayers of bonding mortar. The brick (block) material is assumed to be elastic, and the setting mortar is described by the model of an inhomogeneously aging viscoelastic medium. The obtained system of constitutive relations describes an anisotropic inhomogeneously aging viscoelastic medium and contains a small parameter that is the ratio of the hardening interlayer thickness to the brick thickness. Also presented is an example of solving the problem of erecting a brickwork (wall) deviating from the vertical in the gravity field.     

Stability of a Uniform Rotation of an Asymmetric Rigid Body in a Resisting Medium under a Constant Moment

International Applied Mechanics - The conditions of asymptotic stability of the uniform rotation of an asymmetric absolutely rigid body in a resisting medium are obtained in the form of a system of...     

Quadratic Boundedness of Motions of a Quasilinear Discrete System with Uncertain Perturbation

A problem is solved on the quadratic boundedness of motions of a quasilinear uncertain system. The sufficient boundedness conditions are established. The result is illustrated by an example of studying the rotary motions of a rigid body in a medium with uncertain resistance.