On the Chebyshev collocation spectral approach to stability of fluid flow in a porous medium

In this paper, the temporal development of small disturbances in a pressure‐driven fluid flow through a channel filled with a saturated porous medium is investigated. The Brinkman flow model is employed in order to obtain the basic flow velocity distribution. Under normal mode assumption, the linearized governing equations for disturbances yield a fourth‐order eigenvalue problem, which reduces to the well‐known Orr–Sommerfeld equation in some limiting cases solved numerically by a spectral collocation technique with expansions in Chebyshev polynomials. The critical Reynolds number Re_c, the critical wave number α_c, and the critical wave speed c_c are obtained for a wide range of the porous medium shape factor parameter S. It is found that a decrease in porous medium permeability has a stabilizing effect on the fluid flow. Copyright © 2008 John Wiley & Sons, Ltd.     

Enhancement of shock waves in a porous medium saturated with a liquid containing soluble-gas bubbles

Evolution of a moderate-intensity shock wave and its enhancement after reflection from a rigid surface embedded in a porous medium are studied experimentally. The medium is saturated with a liquid that has bubbles of a soluble gas. A physical mechanism of shock wave enhancement in a saturated porous medium is proposed. Experimental data on the amplitude and velocity of reflected waves are compared with results of theoretical modeling. The process of gas bubble dissolution behind a shock wave is studied.     

Convective stability of a binary mixture in a fractured porous medium

The effect of the gravity field and the concentration and thermal gradients on the convective stability of a mixture in a nonhomogeneous porous medium containing a system of thin highly permeable fractures separating relatively impermeable blocks is analyzed. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.1, pp. 88–97, January–February, 1994.     

Free convection from one thermal and solute source in a confined porous medium

This paper reports a numerical study of double diffusive natural convection in a vertical porous enclosure with localized heating and salting from one side. The physical model for the momentum conservation equation makes use of the Darcy equation, and the set of coupled equations is solved using the finite-volume methodology together with the deferred central difference scheme. An extensive series of numerical simulations is conducted in the range of −10 ⩽ N ⩽ + 10, 0 ⩽ R _t ⩽ 200, 10⁻² ⩽ Le ⩽ 200, and 0.125 ⩽ L ⩽ 0.875, where N, R _t , Le, and L are the buoyancy ratio, Darcy-modified thermal Rayleigh number, Lewis number, and the segment location. Streamlines, heatlines, masslines, isotherms, and iso-concentrations are produced for several segment locations to illustrate the flow structure transition from solutal-dominated opposing to thermal dominated and solutal-dominated aiding flows, respectively. The segment location combining with thermal Rayleigh number and Lewis number is found to influence the buoyancy ratio at which flow transition and flow reversal occurs. The computed average Nusselt and Sherwood numbers provide guidance for locating the heating and salting segment.     

Optical studies of local flow behaviour of a non-Newtonian fluid inside a porous medium

In this study the local flow of a polymeric solution inside a porous medium is studied visually. While the flow is quite uniform for low volume flow rates it shows pronounced nonuniformity for higher volume flow rates. That is to say, only certain preferred passages are taken and these passages change in time (they fluctuate). This flow irregularity is the reason for increased resistance. Received: 28 April 1997 Accepted: 30 December 1997     

Numerical simulation of three-dimensional natural convection inside a heat generating anisotropic porous medium

Natural convection in anisotropic heat generating porous medium enclosed inside a rectangular cavity has been studied. A 3D finite volume based code is developed using the Darcy approximation and validated using experimental results of natural convection around an enclosed rod bundle. Subsequently, detailed simulation is carried out for a cavity, filled with orthotropic porous medium. The effects of heat generation, geometry and anisotropy are studied. Anisotropy is found to be of significant importance for both maximum value and distribution of temperature.     

Theoretical investigation on submicron particle penetration through circular tubes inside a porous medium

The analytical infinite series solution of submicron particle transport in a circular tube bounded by a porous wall, such as a pinhole, is determined under the slip velocity boundary condition, and the solution is verified by using the experimental data in the previous studies for the specific cases. The results show that particle penetration rate increases with the increase of the porous parameter, the axial pressure drop, and the pinhole radius, whereas it decreases with increasing the pinhole length. The penetration rate of nano-particles are more sensitive to the variation of these parameters. However, the differences between the penetrations of particles ranging from 0.3 μm to 1 μm are not evident because the diffusion becomes weak gradually in this size range. In addition, a further comparison is performed between the analytical solution and the existing studies, and approximate expressions are presented for accurate calculation of particle penetration rate through pinholes appearing in porous materials including filter devices and masks.     

On the two-dimensional deformation of a semi-infinite porous elastic medium

On the basis of Biot's theory the two-dimensional problem of deformation of a semi-infinite porous elastic medium, the bounding surface of which is subjected to an arbitrary pressure is considered by the use of stress function and Laplace-Fourier integral transforms. Solutions are obtained for the case that the upper boundary is either permeable or impermeable. As an example, the distribution of stresses and the consolidation settlement have been obtained when a uniform load is applied on one half of the surface, the remaining half being unloaded. The consolidation settlement is evaluated numerically for the permeable case only and is exhibited graphically. The solution of the problem of constant strip load considered by earlier workers has also been deduced.     

Propagation of shock waves in a porous medium saturated by a liquid with bubbles of a soluble gas

The process of evolution and reflection of shock waves of moderate amplitude from a rigid boundary in a porous medium saturated by a liquid with bubbles of a soluble gas is studied experimentally. Experimental values of the amplitude and velocity of the reflected wave are compared with the calculated results obtained using mathematical models. The process of dissolution of gas bubbles in the liquid behind the shock wave is studied. Kutateladze Institute of Thermal Physics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 5, pp. 91–102, September–October, 2000.     

On the stability of gas bubbles in liquid-gas solutions

It was shown some time ago by use of diffusion theory that a gas bubble in a liquid-gas solution was unstable. This problem has been reconsidered recently in two papers both of which propose to develop a stability analysis solely from thermodynamic considerations. The first of these studies purports to find stability for a gas bubble in a liquid-gas solution. Some possible sources of error in this analysis are mentioned here. The second study considers a particular system of a bubble in a liquid drop immersed in a second liquid in which the gas is insoluble. A condition of stability is then found. This system is reconsidered here simply in terms of the ideas of diffusion theory. The stability conditions may then be stated in simple physical terms.     

Mixed convection flow over a vertical wedge embedded in a highly porous medium

 The steady mixed convection flow over a vertical wedge with a magnetic field embedded in a porous medium has been investigated. The effects of the permeability of the medium, surface mass transfer and viscous dissipation on the flow and temperature fields have been included in the analysis. The coupled nonlinear partial differential equations governing the flow field have been solved numerically using the Keller box method. The skin friction and heat transfer are found to increase with the parameters characterizing the permeability of the medium, buoyancy force, magnetic field and pressure gradient. However the effect of the permeability and magnetic field on the heat transfer is very small. The heat transfer increases with the Prandtl number, but the skin friction decreases. The buoyancy force which assists the forced convection flow causes an overshoot in the velocity profiles. Both the skin friction and heat transfer increase with suction and the effect of injection is just the reverse. Received on 21 May 1999     

Investigation of the flow stability of liquids with incipient gas bubbles in porous media

The stability of the steady-state flow regimes of a liquid with dissolved gas in a porous medium is investigated in the region of the saturation pressure. It is shown that under certain conditions periodic and stochastic self-oscillations caused by the accumulation in the porous medium and subsequent entrainment of the very small gas bubbles formed as a result of pressure reduction may arise. Experimental data that confirmed the theoretical results are presented. Ufa. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 66–73, March–April, 1994.     

Effect of vibration on the stability of a plane displacement front in a porous medium

The effect of linearly polarized vibration on the stability of a plane displacement front in a porous medium is studied. The problem of the stability of the motion of a plane displacement front traveling at a constant velocity U under the action of vibration normal to the front is considered. It is shown that under the action of vibration the dynamics of the plane displacement front can be described by the Mathieu equation with a dissipative term. Using the standard averaging method, in the case of high-frequency vibration it is revealed that vibration can only increase the stability of the system. It is found that the vibration stabilizes the plane displacement front with respect to part of the perturbation spectrum.     

On the unsteady flow of a compressible liquid through a porous medium

Summary The unsteady flow of a compressible liquid in a porous medium can be described in terms of a non-linear partial differential equation for the liquid pressure or a linear differential equation for the density if gravitational effects are negligible. In gravitational flow fields the formulation yields non-linear equations for both density and pressure. A transformation is given which shows that in the absence of gravitational effects, the solution of the non-linear boundary value problem in terms of the pressure involves no more labour than the solution of the linear problem in terms of the density, contrary to a misconception in the petroleum literature. Furthermore this transformation offers in addition the solution to a heretofore unsolved problem in gravity flow.This research was supported in part by the Office of Naval Research under Contract Nonr-222(04).     

Interaction of two spark-generated bubbles near a confined free surface

In this paper, the oscillation of two spark-generated bubbles placed on a vertical column in close proximity to a confined free surface is considered. The confined free surface is accorded by the top opening of different configurations. These configurations include (i) a centrally perforated horizontal flat plate (\({\theta=90^{\circ})}\), (ii) vertically placed cylinder (\({\theta=0^{\circ})}\) and (iii) nozzle (\({\theta >0^{\circ})}\). The main objective of the present work is to study the effects of key parameters such as the nozzle geometry, the locations of the energy input (i.e., initial position of the bubbles with respect to each other and relative to the free surface) on the dynamics of the two bubbles and the free surface. It was found that the lifetime of the upper bubble decreases from the vertical cylinder to the flat plate case. In addition, by reducing the inter-bubble distance, the lifetime of the upper bubble becomes longer and the repulsion between two bubbles during the expansion phase is stronger. Finally, by reducing the upper bubble-free surface distance, the repulsion between two bubbles during expansion phase increases, the tendency of the upper bubble to rebound and initiate another oscillation cycle decreases, and the amplitude of elevation of the free surface increases.     

On countercurrent capillary imbibition in a hydrophilic porous medium

The model of two-phase flow proposed in [1] is used to investigate the imbibition of a wetting phase in a hydrophilic sample. It is shown that during a certain interval of time the amount of imbibed liquid depends linearly on t (t is the time), which agrees with the results of laboratory and theoretical investigations [2–8]. The obtained results permit conclusions to be drawn about the distribution of the phases over the field and about the influence of the ratio of the viscosities and the degree of inhomogeneity of the permeability of the sample on the intensity of countercurrent imbibition.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 141–144, March–April, 1980.We thank M. I. Shvidler for helpful discussions.