Numerical Simulation of Thermal and Concentration Natural Convection in a Porous Cavity in the Presence of an Opposing Flow

Two-dimensional steady-state thermal concentration convection in a rectangular porous cavity is simulated numerically. The temperature and concentration gradients are horizontal and the buoyancy forces act either in the same or in opposite directions. The flow through the porous medium is described by the Darcy-Brinkman or Forchheimer equations. The SIMPLER numerical algorithm based on the finite volume approach is used for solving the problem in the velocity-pressure variables.Numerous series of calculations were carried out over the range Ra _t =3·10⁶ and 3·10⁷, 10^-6 < Da < 1, 1 < N < 20, Le=10 and 100, where Ra, Da, Le, and N are the Rayleigh, Darcy, and Lewis numbers and the buoyancy ratio, respectively. It is shown that the main effect of the presence of the porous medium is to reduce the heat and mass transfer and attenuate the flow field with decrease in permeability. For a certain combination of the Ra, Le, and N numbers the flow has a multicellular structure. The mean Nusselt and Sherwood numbers are presented as functions of the governing parameters.     

Gradient plasticity with the tangential-subloading surface model and the prediction of shear-band thickness of granular materials

An extended gradient elastoplastic constitutive equation is formulated, which is capable of describing the plastic strain rate due to the rate of stress inside the yield surface and the inelastic strain rate due to the stress rate component tangential to the subloading surface by incorporating the tangential-subloading surface model. Based on the extended constitutive equation, the post-localization analysis of granular materials is performed to predict the shear-band thickness. It is revealed that the shear-band thickness is almost determined by the gradient coefficient characterizing the inhomogeneity of deformation, although the stress–strain curve is strongly dependent on material properties.     

理想弹塑性材料平面应力Ⅰ型裂纹尖端的弹塑性场

本文参照文献[1,2,3],重新研究了理想弹塑性材料平面应力Ⅰ型裂纹问题。构造了一种不存在应力间断线的裂纹尖端局部应力场,并导出了塑性区中的奇异塑性应变场。     

On applications of the microlocal parameter method in modelling of temperature distributions in composite cylinders

Summary The problems of transient heat conduction in a periodically stratified medium consisting of a large number of alternating concentric cylinders of two homogeneous isotropic rigid materials and in a rotationally periodic cylinder consisting of a large number of circular homogeneous isotropic rigid sectors are considered. The equations of the homogenized models with microlocal parameters are derived by using the homogenization procedure given in [17]. The obtained models take into account certain microlocal effects connected with the microperiodic structure of the considered composites. Some examples of the application of the presented models to the problems of temperature distributions in composite cylinders are detailed. Received 10 March 1997; accepted for publication 23 October 1997     

Variational principles of time-dependent fluid flows through porous media with discontinuous reservoir properties

The use of variational principles as the initial basis for constructing continuum models was investigated by Sedov and his disciples. In this study the variational formalism is developed for calculating time-dependent fluid flows through porous and fractured-porous media with inhomogeneous, discontinuous, and, in particular, piecewise-constant properties. It is proved that, in the case of a medium with discontinuous properties, from the basic variational relation W = 0 there follows not only the differential equations of the flow models but also the conditions on the surfaces of discontinuity of the reservoir properties. This clears the way for the generalization and effective use of direct variational methods for calculating flow fields in complex-structure reservoirs. The methods proposed are illustrated by particular examples.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, 2004, pp. 115–123.Original Russian Text Copyright © 2004 by Volnitskaya.     

Modeling the deformation of rock with rough surfaces of block contact under quasistatic and dynamic loading conditions

The effect of layers consisting of small particles or asperities on contact surfaces on the deformation of a block medium as a whole and the failure of the blocks constituting the medium was studied experimentally. The samples were subjected to quasistatic uniaxial compression perpendicular to the contact surfaces. Numerical modeling was performed of wave propagation during pulse loading of a pair of blocks having rough surfaces of contact and made of a material with elastic characteristics close to the characteristics of marble and limestone. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 173–178, May–June, 2007.     

Layered model of electrorheological fluid under flow

We present a theoretical model of the behavior of a concentrated electrorheological fluid (ERF) which explicitly takes into account the effects of conductivity. The increase in shear viscosity under an electric field is due to a layered structure between the electrodes, made up of the remnants of particle chains adhering to the electrodes by electrostatic image forces, and a freely flowing liquid layer where all the shear flow is concentrated. This layered model can explain the variation of electric current with shear rate, as well as the rheological response of a dynamic yield stress proportional to the square of the applied electric field.     

Saturated steam relative permeabilities of unconsolidated porous media

This paper presents a method and describes an experimental device for determining the steam-water relative permeabilites of unconsolidated porous media. The experimental conditions are as close as possible to those of geothermal reservoirs. The relative permeabilities have been obtained at 180 and 150?C. Their variations versus liquid saturation are quite classical. The air-water relative permeabilities have been measured also at room temperature. The values obtained under these three conditions are almost identical. However, the air-water relative permeability differs slightly from that of steam at 180 and 150?C. We think this discrepancy is acceptable in practice, as it is easier to determine the relative permeabilities for an air-water flow at room temperature than for a steam-water flow at high temperature and pressure.     

各向异性体内含任意孔洞对反平面波散射的边界元方法

本文借助于广义格林公式导出了用位移表示的各向异性介质中SH波入射时的边界积分方程.根据本文作者在文献[8]给出的基本解,求解了各向异性介质中孔洞对SH波的散射问题.边界积分方程的离散基于常数元模式.文中给出了一个圆柱、一个椭圆柱和两个椭圆柱形式的孔洞周围的位移场和应力场的数值结果.最后,对入射波频率较高时的情形作了说明.     

The horizontal intrusion layer of melt in a saturated porous medium

This article presents a theory of how the melt region advances as an intrusion layer along the top boundary of a solid phase-change material that is heated from the side. The phase-change material fills the pores of a solid matrix. We show that the thickness of the horizontal melt layer increases as x^3/5, where x is the horizontal distance measured by from the leading edge of the layer. The total length of the intrusion layer increases as t^3/4, and as T_max^5/4. Finite-difference simulations of convection melting in the Darcy-Rayleigh number range of 200–800 agree with the theoretical results. We also show that in a rectangular porous medium heated from the side, the size of the entire melt region is dominated by the melting contributed by the horizontal intrusion layer, if the time is great enough so that the group (Ste Fo)^3/4 is greater than 1.