Thawing in saturated porous media

A mathematical model for thawing in a saturated porous medium is considered. The well-posedness of the corresponding mathematical problem is proved and similarity solutions are found.

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Sommario Si considera un modello matematico per to scongelamento in un mezzo poroso saturo. Viene dimostrata la buona posizione del corrispondente problema matematico e si trovano soluzioni di similarità.

     

Numerical investigation of the propagation of shock waves in rigid porous materials: flow field behavior and parametric study

A numerical parametric study of the flow field which develops when a planar shock wave impinge on a rigid porous material is presented. This study complements an earlier study (Levy et al. 1996a) where the values of some dominating parameters were estimated and the dependence of the resulting flow field on these values was not checked. Received 22 April 1996 / Accepted 5 January 1997     

Shock waves in saturated thermoelastic porous media

The objective of this paper is to develop and present the macroscopic motion equations for the fluid and the solid matrix, in the case of a saturated porous medium, in the form of coupled, nonlinear wave equations for the fluid and solid velocities. The nonlinearity in the equations enables the generation of shock waves. The complete set of equations required for determining phase velocities in the case of a thermoelastic solid matrix, includes also the energy balance equation for the porous medium as a whole, as well as mass balance equations for the two phase. In the special case of a rigid solid matrix, the wave after an abrupt change in pressure propagates only through the fluid.     

Plane waves in a semi-infinite fluid saturated porous medium

The field equations governing the propagation of waves in an incompressible liquid-saturated porous medium are investigated and a general solution is presented. It has been revealed that coupled longitudinal and transverse waves propagate in the porous medium. The propagation of transverse waves in the fluid phase is completely due to the interaction between the solid and fluid phases. The dispersion relationship and attenuation features are discussed. Unlike other investigations, all explicit forms of the arguments are derived. The reflection of the plane harmonic waves at the plane, traction-free boundary, which shows the influence of the dissipation on the velocity, and the attenuation coefficients of the reflected waves is studied. It is of interest that pore pressure is produced in the process of reflection, even in the case of the incidence of transverse waves.     

Linear waves in saturated porous media

The peculiarity of linear and nonlinear wave propagation in porous media saturated with liquid or gas has been investigated by the methods of multiphase media mechanics. It has been shown that for the analysis and interpretation of experimental data, it is expedient to build models taking into account the nonstationary powers of interaction between the solid and liquid phases and the viscouselastic behaviour of the porous media skeleton. Inertia and inertia-viscous powers principally influence wave attentuation in porous media. Two interphase mechanisms of momentum transfer (two stress tensors — in the solid phase and liquid) lead to two types of waves. Attenuation is determined not only by interphase friction, but also by dissipation resulting from intergrain friction in the solid phase, the influence of which multiplexly exceeds the liquid viscosity influence. The real decrement of attenuation may exceed the sphere restricted by the limiting curves corresponding to the frozen and equilibrium schemes of intergrain deformation. The attenuation of momentum perturbation has been studied. The method of discrete Fourier transform has been used. The analysis of experimental data contained in the literature and their comparison with the results of calculations has been carried out.     

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.     

Enhancement of the critical heat flux in saturated pool boiling using honeycomb porous media

Enhancement of the critical heat flux in pool boiling by the attachment of a honeycomb-structured porous plate on a heated surface is investigated experimentally using water under saturated boiling conditions. As the height of the honeycomb porous plate on the heated surface decreases, the CHF increases to 2.5 MW/m², which is approximately 2.5 times that of a plain surface (1.0 MW/m²). Automatic liquid supply due to capillary action and reduction of the flow resistance for vapor escape due to the separation of liquid and vapor flow paths by the honeycomb-structure are verified to play an important role in the enhancement of the CHF. A simplified one-dimensional model for the capillary suction limit, in which the pressure drops due to liquid and vapor flow in the honeycomb porous plate balances the capillary force, is applied to predict the CHF. The calculated results are compared with the measured results.     

Body waves in fractured porous media saturated by two immiscible newtonian fluids

A study of body waves in fractured porous media saturated by two fluids is presented. We show the existence of four compressional and one rotational waves. The first and third compressional waves are analogous to the fast and slow compressional waves in Biot's theory. The second compressional wave arises because of fractures, whereas the fourth compressional wave is associated with the pressure difference between the fluid phases in the porous blocks. The effects of fractures on the phase velocity and attenuation coefficient of body waves are numerically investigated for a fractured sandstone saturated by air and water phases. All compressional waves except the first compressional wave are diffusive-type waves, i.e., highly attenuated and do not exist at low frequencies.Now at Izmir Institute of Technology, Faculty of Engineering, Gaziosmanpasa Bulvari, No.16, Cankaya, Izmir, Turkey.     

Oblique reflection of shock waves from rigid porous materials

A study to determine the general gas dynamic behaviour associated with the impact of a shock wave on a porous wedge has been undertaken. A number of interesting features are noted. The pattern of wave reflection is shown to be significantly affected by the inflow of gas into the wedge. This has the effect of reducing the triple point trajectory angle for cases of Mach reflection and for strongly reducing the reflection angle in regular reflection. The permeability of the wedge has a significant effect on the strength of the reflected wave and in some cases this wave can be attenuated to the extent that it is almost eradicated. Pressure measurements taken under the wedge are characterized by oscillations which are of similar shape, for a given wedge, over a range of shock wave Mach numbers. It is shown that the wave transmitted into the wedge is attenuated to varying degrees depending on the material properties, and that for weak incident waves the mean propagation velocity can be less than the sound speed in the pore fluid. Photographs taken using a specially constructed wedge which allows the transmitted wave to be visualised, show that the transmitted wave is nearly plane.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Propagation of acceleration waves in incompressible saturated porous solids

Within the framework of the incompressible porous media model, the propagation properties of acceleration waves in liquid-filled porous solids is discussed. The incompressibility of the two constituents in the model forces the amplitudes of the longitudinal waves in the skeleton and in the liquid to satisfy a certain relation. The two propagation speeds are presented by examination for the existence of acceleration waves and only longitudinal and transverse waves are realizable in the incompressible two-phase porous materials.     

Fractal porous media II: Geometry of porous geological structures

Some geological structures are analysed and found to be fractal. An interesting feature is the very large range of scales involved; the spreading dimension is also measured for some of them. The consequences of these measurements on the analysis of transport processes in porous media are presented - the existence of fractal structures multiplies the variety of actual porous media.     

Propagation of nitromethane detonations in porous media

The characteristics of the propagation of a detonation in chemically sensitized nitromethane in a dense porous medium are investigated. By introducing liquid NM+15% (by weight) DETA into densely packed beds of solid spherical glass beads 66μm to 2.4 mm in diameter, a highly heterogeneous explosive mixture is obtained. The critical (i.e., failure) charge diameter of this mixture is systematically measured in unconfined charges over a wide range of bead sizes. Velocity measurements are also made for the various charges. It is found that there exists a critical bead size above which the critical diameter decreases with increasing bead size and below which it decreases with decreasing bead size. This result indicates an abrupt change in the mechanism of propagation at the critical bead size. Velocity measurements further support this by emphasizing the different behavior above and below the critical point.     

The effect of porosity on shock interaction with a rigid, porous barrier

This work investigates the pressure amplification experienced behind a rigid, porous barrier that is exposed to a planar shock. Numerical simulations are performed in two dimensions using the full Navier–Stokes equations for a M = 1.3 incoming shock wave. An array of cylinders is positioned at some distance from a solid wall and the shock wave is allowed to propagate past the barrier and reflect off the wall. Pressure at the wall is recorded and the flowfield is examined using numerical schlieren images. This work is intended to provide insight into the interaction of a shock wave with a cloth barrier shielding a solid boundary, and therefore the Reynolds number is small (i.e., Re = 500 to 2000). Additionally, the effect of porosity of the barrier is examined. While the pressure plots display no distinct trend based on Reynolds number, the porosity has a marked effect on the flowfield structure and endwall pressure, with the pressure increasing as porosity decreases until a maximum value is reached.      

Fluid penetration effects in porous media contact

The contact boundary conditions at the interface between two fluid-saturated porous bodies are derived. The general derivation is performed within the well-founded framework of the Theory of Porous Media (TPM) based on the constituent balance relations of mass, momentum, and energy accounting for finite discontinuities at the contact surface. Particular attention is drawn to the effects associated with the interstitial fluid flux across the interface. The derived contact conditions include two kinematic continuity conditions for the solid velocity and the fluid seepage velocity as well as two jump conditions for the effective solid stress and the pore-fluid pressure. As an application, the common case of biphasic porous media contact proceeding from materially incompressible constituents and inviscid fluid properties is discussed in detail.      

Combustion in a horizontal channel partially filled with a porous media

Experiments were carried out to investigate the combustion propagation phenomenon in a horizontal channel partially filled with ceramic-oxide spherical beads. A 1.22 m long, 43 mm nominally thick layer of spherical beads is located at the ignition end of a 2.44 m long, 76 mm square channel. Tests were performed with 6.4 and 12.7 mm diameter beads. A flame is ignited at the bead end wall by an automotive spark ignition system. Flame propagation and pressure measurements are obtained via ionization probes and piezoelectric pressure transducers mounted on the top and bottom surfaces of the channel. High-speed schlieren video was used to visualize the structure of the explosion front. Experiments were performed with a 31% nitrogen diluted stoichiometric methane–oxygen mixture at room temperature and at an initial pressure in the range of 15–50 kPa. For initial pressures of 15 and 20 kPa the flame accelerates to a velocity close to the speed of sound in the combustion products. For initial pressure of 30 kPa and higher DDT occurs in the gap above the bead layer. An explosion front propagating at a velocity just under the CJ detonation velocity is detected in the bead layer even though the bead layer pore size is much smaller than the detonation cell size. It is demonstrated that flame propagation within the bead layer is the driving force behind the very rapid flame acceleration observed, however the DDT event occurring in the gap above the bead layer is not affected by the bead layer porosity. Schlieren video indicates that the structure of the explosion front varies across the channel height and with propagation distance down the channel.     

On Darcy's law for growing porous media

The flow of a Newtonian fluid in porous media can be described using Darcy's law when inertial effects and deformations in the solid can be neglected and no mass interchange occur between the solid and the fluid components. Having in mind bio-medical applications, we analyze the correction to be considered when non-negligible mass exchanges between the constituents are present. This is done both on a thermodynamical basis and using a symmetry and frame indifferent argument.     

On the propagation of pressure waves in saturated porous media

The problem of the propagation of pressure waves through compressible porous media saturated with a slightly compressible fluid is considered. By using Darcy's law the problem is reduced to a mixed initial-boundary value problem for an equation of the heat conduction type with a nonlinear term. The method of quasi-characteristics is used to solve this equation numerically. Solutions of the wave propagation problem for media with different permeability coefficients are presented. A solution of the inverse problem of determining the permeability coefficient using wave-pulse test data is constructed on the basis of a set of solutions of the direct problem.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 81–84, November–December, 1996.     

A resistance model for flow through porous media

A new model for resistance of flow through granular porous media is developed based on the average hydraulic radius model and the contracting–expanding channel model. This model is expressed as a function of tortuosity, porosity, ratio of pore diameter to throat diameter, diameter of particles, and fluid properties. The two empirical constants, 150 and 1.75, in the Ergun equation are replaced by two expressions, which are explicitly related to the pore geometry. Every parameter in the proposed model has clear physical meaning. The proposed model is shown to be more fundamental and reasonable than the Ergum equation. The model predictions are in good agreement with the existing experimental data.