Jump conditions across strong compaction waves in gas saturated rigid porous media

Based on experimental results and some additional simplifying assumptions, the general macroscopic two phase equations governing the flow field which is developed in a gas saturated rigid porous medium domain were simplified to a form which enab led us to develop two analytical models for calculating the jump conditions across strong compaction waves.Predictions obtained by these two simplified analytical models are compared to the experimental results of Sandusky and Liddiard (1985) and to predictions of another more complicated model which was proposed by Powers et al. (1989). Fairly good to excelle nt agreements are evident.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.     

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.     

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     

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.

---

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.

     

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.     

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.     

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.     

Shock waves at microscales

We present a model for the effects of scale, via molecular diffusion phenomena, on the generation and propagation of shock waves. A simple parametrization of the shear stresses and heat flux at the wall leads to the determination of new jump conditions, which show that, for a given wave Mach number at small scales, the resulting particle velocities are lower but the pressures are higher. Also, the model predicts that the flow at small scale is isothermal and that the minimum wave velocity can be subsonic. Experiments with a miniature shock tube using low pressures to simulate the effects of small scale have shown qualitative agreement with the proposed model. In fact, the effects of scale appear even more important than what has been incorporated in the model.PACS: 47.40.-xReceived: 14 November 2002, Accepted: 2 April 2003, Published online: 18 June 2003     

Effective equations for two-phase flow in porous media: the effect of trapping on the microscale

In this article, we consider a two-phase flow model in a heterogeneous porous column. The medium consists of many homogeneous layers that are perpendicular to the flow direction and have a periodic structure resulting in a one-dimensional flow. Trapping may occur at the interface between a coarse and a fine layer. Assuming that capillary effects caused by the surface tension are in balance with the viscous effects, we apply the homogenization approach to derive an effective (upscaled) model. Numerical experiments show a good agreement between the effective solution and the averaged solution taking into account the detailed microstructure.     

Effects of an impermeable wall in dissipative dynamics of saturated porous media

A phase transition model for porous media in consolidation is studied. The model is able to describe the phenomenon of fluid-segregation during the consolidation process, i.e., the coexistence of two phases differing on fluid content inside the porous medium under static load. Considering pure Darcy dissipation, the dynamics is described by a Cahn–Hilliard-like system of partial differential equations (PDE). The goal is to study the dynamics of the formation of stationary fluid-rich bubbles. The evolution of the strain and fluid density profiles of the porous medium is analysed in two physical situations: fluid free to flow through the boundaries of the medium and fluid flow prevented at one of the two boundaries. Moreover, an analytic result on the position of the interface between the two phases is provided.     

A phase-field modeling approach of hydraulic fracture in saturated porous media

Continuum porous media theories, extended by a diffusive phase-field modeling (PFM) approach, introduce a convenient and efficient tool to the simulation of hydraulic fracture in fluid-saturated heterogeneous materials. In this, hydraulic- or tension-induced fracture occurs in the solid phase. This leads to permanent local changes in the permeability, the volume fractions of the constituents as well as the interstitial-fluid flow. In this work, the mechanical behaviors of the multi-field, multi-phase problem of saturated porous media, such as the pore-fluid flow and the solid-skeleton deformation, are described using the macroscopic Theory of Porous Media (TPM). To account for crack nucleation and propagation in the sense of brittle fracture, the energy-minimization-based PFM procedure is applied, which approximates the sharp edges of the crack by a diffusive transition zone using an auxiliary phase-field variable. Furthermore, the PFM can be implemented in usual continuum finite element packages, allowing for a robust solution of initial-boundary-value problems (IBVP). For the purpose of validation and comparison, simulations of a two-dimensional IBVP of hydraulic fracture are introduced at the end of this research paper.     

Rayleigh waves in orthotropic fluid-saturated porous media

In this paper, we are interested in the propagation of Rayleigh waves in orthotropic fluid-saturated porous media. This problem was investigated by Liu and Liu (2004). The authors have derived the secular equation of the wave but that secular equation is still in implicit form. The main aim of this paper is to derive explicit secular equation of the wave. By employing the method of polarization vector, the secular equations of Rayleigh waves in explicit form is obtained. This equation recovers the dispersion equation of Rayleigh waves propagating in pure orthotropic elastic half-spaces. Remarkably, the secular equation obtained is not a complex equation as the one derived by Liu and Liu, it is a really real equation.     

Homogenization of acoustic waves in strongly heterogeneous porous structures

We consider acoustic waves in fluid-saturated periodic media with dual porosity. At the mesoscopic level, the fluid motion is governed by the Darcy flow model extended by inertia terms and by the mass conservation equation. In this study, assuming the porous skeleton is rigid, the aim is to distinguish the effects of the strong heterogeneity in the permeability coefficients. Using the asymptotic homogenization method we derive macroscopic equations and obtain the dispersion relationship for harmonic waves. The double porosity gives rise to an extra homogenized coefficient of dynamic compressibility which is not obtained in the upscaled single porosity model. Both the single and double porosity models are compared using an example illustrating wave propagation in layered media.     

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.     

One-dimensional linear waves with axial and central symmetries in saturated porous media

The features of propagation of one-dimensional monochromatic waves and dynamics of weak perturbations with axial and central symmetries in liquid-saturated porous medium are investigated. Non-stationary interaction forces and viscoelastic skeleton characteristics are taken into account. The research is carried out within the two-velocity, two-stress tensor model by applying methods of multiphase media mechanics. The system of equations is solved numerically by applying Fast Fourier Transform (FFT) algorithm. The influence of geometry of the process on wave propagation behavior is studied.It is shown that the initial pressure perturbation splits into two waves: fast (deformational) wave and slow (filtrational) one. Each of them is followed by the balance wave: that is, rarefaction wave after compression wave and compression wave after rarefaction wave; at that slow wave and balance one following fast wave may interfere.     

Shock waves in aviation security and safety

Accident investigations such as of Pan Am 103 and TWA 800 reveal the key role of shock-wave propagation in destroying the aircraft when an on-board explosion occurs. This paper surveys shock wave propagation inside an aircraft fuselage, caused either by a terrorist device or by accident, and provides some new experimental results. While aircraft-hardening research has been under way for more than a decade, no such experiments to date have used the crucial tool of high-speed optical imaging to visualize shock motion. Here, Penn State's Full-Scale Schlieren flow visualization facility yields the first shock-motion images in aviation security scenarios: 1) Explosions beneath full-size aircraft seats occupied by mannequins, 2) Explosions inside partially-filled luggage containers, and 3) Luggage-container explosions resulting in hull-holing. Both single-frame images and drum-camera movies are obtained. The implications of these results are discussed, though the overall topic must still be considered in its infancy. Received 22 July 2001 / Accepted 19 July 2002 Published online 4 November 2002 Correspondence to: G.S. Settles (e-mail: gss2@psu.edu) An abridged version of this paper was presented at the 23rd International Symposium on Shock Waves at Fort Worth, Texas, from July 22 to 27, 2001.     

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.     

On the distance to blow-up of acceleration waves in random media

We study the effects of material spatial randomness on the distance to form shocks from acceleration waves, , in random media. We introduce this randomness by taking the material coefficients and – that represent the dissipation and elastic nonlinearity, respectively, in the governing Bernoulli equation – as a stochastic vector process. The focus of our investigation is the resulting stochastic, rather than deterministic as in classical continuum mechanics studies, competition of dissipation and elastic nonlinearity. Quantitative results for are obtained by the method of moments in special simple cases, and otherwise by the method of maximum entropy. We find that the effect of even very weak random perturbation in and may be very significant on . In particular, the full negative cross-correlation between and $ results in the strongest scatter of , and hence, in the largest probability of shock formation in a given distance x. Received November 6, 2001 / Published online September 4, 2002 Dedicated to Professor Ingo Müller on the occasion of his 65th birthday Communicated by Kolumban Hutter, Darmstadt     

Asymptotic analysis of surface waves at vacuum/porous medium and liquid/porous medium interfaces

Received November 1, 2001 / Published online February 4, 2002