Formation of the impermeable layer in the process of methane hydrate dissociation in porous media

The problem of decomposition of methane hydrate coexisting with water in a highpermeability reservoir is considered. The asymptotic solution is obtained for the decomposition regime in the negative temperature domain. Energy estimates presented show that an impermeable layer saturated with a hydrate-icemixture can be formed in reservoirs with initial positive temperature. The mathematical model of the process of hydrate decomposition is formulated under the assumption on the presence of such a layer in a high-permeability reservoir. In this case the problem is reduced to a purely thermal problem with two unknown moving boundaries. The water-ice phase transition takes place on the leading boundary, while hydrate dissociates at negative temperatures on the slower boundary. The conditions of existence of the layer saturated with a hydrate-ice mixture which is implemented in reservoirs with the high hydrate content are investigated.     

On the steady vibrations problem in linear theory of micropolar solid–fluid mixture

In this paper we study the steady vibrations problem in linear theory of isothermal micropolar solid–fluid mixture. With the help of fundamental solution we establish representations of Somigliana type. Then, using the potentials of single layer and double layer, we reduce the boundary value problems to singular integral equations for which the Fredholm’s theorems are valid. Existence and uniqueness results for interior and exterior problems are presented.     

Two-layer debris mixture flows on arbitrary terrain with mass exchange at the base and the interface

Granular-fluid gravity driven flow down arbitrary topographic terrain is modelled as a two-layer system of a solid-fluid mixture layer overlain by a slurry, consisting of a particle-laden fluid. The lower layer is dynamically treated as a two-phase flow with two constituent mass and momentum balance laws. By contrast, the slurry is described by mass and momentum balances for the mixture as a whole and a diffusive mass balance for the suspended particle phase. At the base, the mixture interacts with the stagnant base by solid-fluid deposition or erosion. At the mixture-slurry interface, solid and fluid mass exchanges are equally taken into account, but the free surface is treated as material and tractionless. The dynamical equations are formulated in three-dimensional form as general balance laws of mass and momentum in each layer. Intrinsic expressions of the jump conditions of mass and momentum are given for the basal and interface surfaces. The field equations are put into dimensionless form and presented relative to topography adjusted coordinates. These equations are further simplified and approximated by a depth-averaging procedure using an order parameter ${\varepsilon = H/L}$ , where H and L are typical thickness and length scales of the gravity current. Detailed proposals are worked out for the parameterizations of the solid and fluid mass flows across the basal surface and layer interface.     

Calculation of the wave motion on the uniformly charged interface between two immiscible viscous liquids on the basis of the boundary layer theory

A modified theory of the boundary layer associated with a periodic capillary-gravity wave on the uniformly charged interface between two immiscible viscous incompressible liquids is proposed. A model problem simpler than the exact problem is proposed for describing the boundary layer flows in the upper and lower liquids. The structure of the solution of this problem reflects the principal features of the exact asymptotic solution, namely, the rapidity of the decrease in the vortex part of the flow as a function of the depth and the insignificance of certain components. Estimates of the boundary layer thicknesses for which the difference between the exact asymptotic solution and the solution of the simplified model problem (formulated within the framework of the theory proposed) can be specified with a predetermined accuracy are obtained.     

Stress in elastic plates reinforced by fibres lying in concentric circles

We Consider fibre-reinforced elastic plates with the reinforcement continuously distributed in concentric circles ; such a material is locally transversely isotropic, with the circumferential direction as the preferred direction. For an annulus bounded by concentric circles, the exact solution of the traction boundary value problem is obtained. When the extension modulus in the fibre direction is large compared to other extension and shear moduli, the material is strongly anisotropic. For this case a simpler approximate solution is obtained by treating the material as inextensible in the fibre direction. It is shown that the exact solution reduces to the inextensible solution in the appropriate limit. The inextensible theory predicts the occurrence of stress concentration layers in which the direct stress is infinite ; for materials with small but finite extensibility these layers correspond to thin regions of high stress and high stress gradient. A boundary layer theory is developed for these regions. For a typical carbon fibre-resin composite, the combined boundary layer and inextensible solutions give an excellent approximation to the exact solution. The theory is applied to the problem of an isotropic plate, under uniform stress at infinity, containing a circular hole which is strengthened by the addition of an annulus of fibre-reinforced material.     

On geometrically exact post-buckling of composite columns with interlayer slip—The partially composite elastica

This paper is focused on the geometrically exact elastic stability analysis of two interacting kinematically constrained, flexible columns. Possible applications are to partially composite or sandwich columns. A partially composite column composed of two inextensible elastically connected sub-columns is considered. Each sub-column is modeled by the Euler–Bernoulli beam theory and connected to each other via a linear constitutive law for the interlayer slip. The paper discusses the validity of parallel and translational kinematics beam assumptions with respect to the interlayer constraint. Buckling and post-buckling behavior of this structural system are studied for cantilever columns (clamped-free boundary conditions). A variational formulation is presented in order to derive relevant boundary conditions in a geometrically exact framework. The exact post-buckling behavior of this partially composite beam-column is investigated analytically and numerically. The Euler elastica problem is obtained in the case of non-composite action. The “partially composite elastica” is then treated analytically and numerically, for various values of the interaction connection parameter. An asymptotic expansion is performed to evaluate the symmetrical pitchfork bifurcation, and comparisons are made with some exact numerical results based on the numerical treatment of the non-linear boundary value problem. A boundary layer phenomenon, similar to that also observed for the linearized bending analysis of partially composite beams, is observed for large values of the connection parameter. This boundary layer phenomenon is investigated with a straightforward asymptotic expansion, that also is valid for large rotations. Finally, the paper analyses the effect of some additional imperfection eccentricities in the loading mode, that lead to some pre-bending phenomena.     

The turbulent boundary layer of dissociated gas in the initial section of a tube

Many theoretical and experimental papers [1–4] have been devoted to investigating the turbulent boundary layer in the initial section of a channel. For the most part, however, the flow of an incompressible fluid with constant parameters is considered. There are many practical cases in which it is of interest to treat the development of the turbulent boundary layer of gas in the initial section of a pipe when conditions are strongly nonisothermal. A solution of a problem of this type, based on the theory of limit laws, is given in paper [1]. The present article extends this solution to the case of the flow of a high-enthalpy gas when the effect of gas dissociation on the turbulent boundary layer characteristics must be taken into account. We shall consider the flow of a mixture of i gases which is in a frozen state inside the boundary layer, and in an equilibrium state on its boundaries. Formulas are derived for the laws of friction and heat exchange, and a solution is given for the turbulent boundary layer equations in the initial section of the pipe when the wall temperature is constant and the gas flows at a subsonic velocity.Finally the authors are grateful to S. S. Kutateladze for discussing the paper.     

High accuracy non-equidistant method for singular perturbation reaction-diffusion problem

Singular perturbation reaction-diffusion problem with Dirichlet boundary condition is considered. It is a multi-scale problem. Presence of small parameter leads to boundary layer phenomena in both sides of the region. A non-equidistant finite difference method is presented according to the property of boundary layer. The region is divided into an inner boundary layer region and an outer boundary layer region according to transition point of Shishkin. The steps sizes are equidistant in the outer boundary layer region. The step sizes are gradually increased in the inner boundary layer region such that half of the step sizes are different from each other. Truncation error is estimated. The proposed method is stable and uniformly convergent with the order higher than 2. Numerical results are given, which are in agreement with the theoretical result.     

Heat and mass exchange in a turbulent boundary layer on a disintegrating plate surface

Heat- and mass-exchange processes in a turbulent boundary layer on a disintegrating surface during aerodynamic heating are investigated. The flow in the layer is considered frozen, and the gas composition is determined only by the reactions on the disintegration surface. The problem is solved under the usual assumptions for turbulent-boundary-layer theory. Computation of the disintegration of an asbestos-textolite surface is presented as an example.     

Nanofluid bioconvection: interaction of microorganisms oxytactic upswimming, nanoparticle distribution, and heating/cooling from below

The aim of this paper is to develop a theory describing the onset of convection instability (called here nanofluid bioconvecion) that is induced by simultaneous effects produced by oxytactic microorganisms, nanoparticles, and vertical temperature variation. The theory is developed for the situation when the nanofluid occupies a shallow horizontal layer of finite depth. The layer is defined as shallow as long as oxygen concentration at the bottom of the layer is above the minimum concentration required for the bacteria to be active (to actively swim up the oxygen gradient). The lower boundary of the layer is assumed rigid, while at the upper boundary both situations when the boundary is rigid or stress free are considered. Physical mechanisms responsible for the slip velocity between the nanoparticles and the base fluid, such as Brownian motion and thermophoresis, are accounted for in the model. A linear instability analysis is performed, and the resulting eigenvalue problem is solved analytically using the Galerkin method.     

A micropolar mixture theory of multi-component porous media

A mixture theory is developed for multi-component micropolar porous media with a combination of the hybrid mixture theory and the micropolar continuum theory. The system is modeled as multi-component micropolar elastic solids saturated with multi- component micropolar viscous fluids. Balance equations are given through the mixture theory. Constitutive equations are developed based on the second law of thermodynamics and constitutive assumptions. Taking account of compressibility of solid phases, the volume fraction of fluid as an independent state variable is introduced in the free energy function, and the dynamic compatibility condition is obtained to restrict the change of pressure difference on the solid-fluid interface. The constructed constitutive equations are used to close the field equations. The linear field equations are obtained using a linearization procedure, and the micropolar thermo-hydro-mechanical component transport model is established. This model can be applied to practical problems, such as contaminant, drug, and pesticide transport. When the proposed model is supposed to be porous media, and both fluid and solid are single-component, it will almost agree with Eringen＇s model.     

高温流体与变物性固体耦合系统温度场及热变形的数值计算

在腔体内部有高温流体,其外壳等固体材料的物性温度而为化的瞬态非线性问题中,其边界条件的确定十分困难。本文采用流一固“混合流”模式进行温度场的计算,由于方程计及了瞬态、复杂形状、浮动外边界条件等因系,采用变步长的控制容积法及时域有限元进行计算。对某个高温燃气配气阀的温度场及热变形进行了数值计算,得到与实测相符的结果。     

Calculation of neutral monotonic instability curves in the problem of concentration convection in a mixture with an infinite number of components

The Oberbeck-Boussinesq approximation for concentration convection in a mixture with an infinite number of components is constructed. The features of the formulation of the problem are described in detail. The large-parameter asymptotics are constructed for the linear problem of hydrodynamic stability. The problem is substantially simplified and equations not previously encountered in hydrodynamic stability theory are obtained. In the case of the non self-adjoint problem the asymptotics of the eigenvalues and eigenfunctions are obtained. Numerical results which, in particular, show that the spectrum of the boundary value problem is not connected are presented. The critical values obtained make it possible to solve the important practical problem of improving the process of mixture separation by the isoelectric focusing method.Rostov-on-Don. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 11–20, September–October, 1995.     

Chemically nonequilibrium laminar boundary layer in dissociated air

A difference scheme which permits computation without change in grid parameters over the entire range from equilibrium to frozen flow regimes is used to solve the equations of the chemically non-equilibrium boundary layer. Results are presented for the boundary layer in a mixture of N, O, NO, O₂, and N₂ with account for six reactions in the gaseous phase.In conclusion, I wish to thank G. I. Petrov, under whose guidance this study was carried out.     

Stability of a disperse-mixture flow in a boundary layer

The hydrodynamic stability of a dilute disperse mixture flow in a quasi-equilibrium region of a boundary layer with a significantly nonuniform particle concentration profile is investigated. The mixture is described by a two-fluid model with an incompressible viscous carrier phase. In addition to the Stokes drag, the Saffman lifting force is taken into account in the interphase momentum exchange. On the basis of a numerical solution of the boundary-value problem for a modified Orr-Sommerfeld equation, neutral stability curves are analyzed and the dependence of the critical Reynolds number on the governing parameters is studied. It is shown that taking into account the particle concentration nonuniformity in the main flow and the Saffman lifting force significantly changes the stability limits of the two-phase laminar boundary layer flow. The effect of these factors on the boundary layer stability is considered for the first time.     

On the flow of a fluid–particle mixture between two rotating cylinders, using the theory of interacting continua

Mixture theory is used to develop a model for a flowing mixture of solid particulates and a fluid. Equations describing the flow of a two-component mixture consisting of a Newtonian fluid and a granular solid are derived. These relatively general equations are then reduced to a system of coupled ordinary differential equations describing Couette flow between concentric rotating cylinders. The resulting boundary value problem is solved numerically and representative results are presented.     

Stability of viscoelastic rectangular plate with a piezoelectric layer subjected to follower force

The effects of a piezoelectric layer on the stability of viscoelastic plates subjected to the follower forces are evaluated. The differential equation of motion of the viscoelastic plate with the piezoelectric layer is formulated using the two-dimensional viscoelastic differential constitutive relation and the thin plate theory. The weak integral form of the differential equations and the force boundary conditions are obtained. Using the element-free Galerkin method, the governing equation of the viscoelastic rectangular plate with elastic dilatation and Kelvin–Voigt distortion is derived, subjected to the follower forces coupled with the piezoelectric effect. A generalized complex eigenvalue problem is solved, and the force excited by the piezoelectric layer due to external voltage is modeled as the follower tensile force; this force is used to improve the stability of the non-conservative viscoelastic plate. For the viscoelastic plate with various boundary conditions, the results for the instability type and the critical loads are presented to show the variations in these factors with respect to the location of the piezoelectric layers and the applied voltages. The stability of the viscoelastic plates can be effectively improved by the determination of the optimal location for the piezoelectric layers and the most favorable voltage assignment.     

Interfacial energy effects within the framework of strain gradient plasticity

In the framework of strain gradient plasticity, a solid body with boundary surface playing the role of a dissipative boundary layer endowed with surface tension and surface energy, is addressed. Using the so-called residual-based gradient plasticity theory, the state equations and the higher order boundary conditions are derived quite naturally for both the bulk material and the boundary layer. A phenomenological constitutive model is envisioned, in which the bulk material and the boundary layer obey (rate independent associative) coupled plasticity evolution laws, with kinematic hardening laws of differential nature for the bulk material, but of nondifferential nature for the layer. A combined global maximum dissipation principle is shown to hold. The higher order boundary conditions are discussed in details and categorized in relation to some peculiar features of the boundary surface, and their basic role in the coupling of the bulk/layer plasticity evolution laws is pointed out. The case of an internal interface is also studied. An illustrative example relating to a shear model exhibiting energetic size effects is presented. The theory provides a unified view on gradient plasticity with interfacial energy effects.