The inertial effect on the natural convection flow within a fluid-saturated porous medium

The general momentum equation for fluid flow within a porous medium is supposedly valid for any fluid-porous medium configuration. One of the main concerns of using the general equations refers to the inclusion of both inertia terms, namely, the convective inertia term and the Forchheimer term. In this study, we go beyond the important discussion about the correctness of including both terms in the general momentum equations by focusing upon the effect of the convective inertia term on the heat transfer results. The fluid-porous medium system considered here is a cavity bounded by solid surfaces with vertical walls maintained at constant but different temperatures. The natural convection problem is solved numerically, and the results are compared with a general theory developed by using the method of scale analysis. It is demonstrated that the convective inertia term effect upon the heat transfer results is minor for 0.01 ≤ Pr ≤ 1, 10 ≤ Ra_D ≤ 10⁴, 10⁻⁸ ≤ Da ≤ 10⁻², and porosities 0.4 and 0.8. It is also shown that, contrary to the general belief, the convective inertial effect upon the heat transfer within the cavity is minimized when the Prandtl number is reduced.     

Scenarios of the onset of unsteady regimes in the problem of plane convective flow through a porous medium

The problem of plane convective flow through a porous medium in a rectangular vessel with a linear temperature profile steadily maintained on the boundary is considered. The onset of unsteady regimes is investigated numerically. It is shown that their onset scenarios depend on the vessel dimensions and the seepage Rayleigh number and may be as follows: the generation of stable and unstable periodic regimes as a result of a one-sided bifurcation, the generation of a stable periodic regime as a result of an Andronov-Hopf cosymmetric bifurcation, the formation of a chaotic attractor, the branching-out of a stable quasi-periodic regime from a point of a single-parameter family of steady-state regimes, and the generation of unstable periodic regimes as a result of disintegration of homoclinic trajectories. The specifics of most of the bifurcations mentioned above are attributable to the cosymmetry of the problem considered.     

Hydrodynamics of natural oscillations of neutrally buoyant bodies in a layer of continuously stratified fluid

The flow patterns induced by floats of different shapes (sphere, short and long cylinders) freely sinking to the neutral-buoyancy horizon in a continuously stratified fluid are investigated using optical methods. General flow elements, both large-scale (waves, vortices, hydrodynamic wake) and fine-scale (boundary layers, extended autocumulative jets), are distinguished. For large times, the float oscillation frequencies are of the order of or greater than the buoyancy frequency of the medium. This indicates the significant effect of the induced flows on the motion of the float.     

Lie-group method of solution for steady two-dimensional boundary-layer stagnation-point flow towards a heated stretching sheet placed in a porous medium

The boundary-layer equations for two-dimensional steady flow of an incompressible, viscous fluid near a stagnation point at a heated stretching sheet placed in a porous medium are considered. We apply Lie-group method for determining symmetry reductions of partial differential equations. Lie-group method starts out with a general infinitesimal group of transformations under which the given partial differential equations are invariant. The determining equations are a set of linear differential equations, the solution of which gives the transformation function or the infinitesimals of the dependent and independent variables. After the group has been determined, a solution to the given partial differential equations may be found from the invariant surface condition such that its solution leads to similarity variables that reduce the number of independent variables of the system. The effect of the velocity parameter λ, which is the ratio of the external free stream velocity to the stretching surface velocity, permeability parameter of the porous medium k ₁, and Prandtl number Pr on the horizontal and transverse velocities, temperature profiles, surface heat flux and the wall shear stress, has been studied.     

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.     

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.