Stokes flow past a porous spheroid embedded in another porous medium

A study is made with an analysis of an incompressible viscous fluid flow past a slightly deformed porous sphere embedded in another porous medium. The Brinkman equations for the flow inside and outside the deformed porous sphere in their stream function formulations are used. Explicit expressions are investigated for both the inside and outside flow fields to the first order in small parameter characterizing the deformation. The flow through the porous oblate spheroid embedded in another porous medium is considered as the particular example of the deformed porous sphere embedded in another porous medium. The drag experienced by porous oblate spheroid in another porous medium is also evaluated. The dependence of drag coefficient and dimensionless shearing stress on the permeability parameter, viscosity ratio and deformation parameter for the porous oblate spheroid is presented graphically and discussed. Previous well-known results are then also deduced from the present analysis.     

An overview on nonlinear porous flow in low permeability porous media

This paper gives an overview on nonlinear porous flow in low permeability porous media, reveals the microscopic mechanisms of flows, and clarifies properties of porous flow fluids. It shows that, deviating from Darcy's linear law, the porous flow characteristics obey a nonlinear law in a low-permeability porous medium, and the viscosity of the porous flow fluid and the permeability values of water and oil are not constants. Based on these characters, a new porous flow model, which can better describe low permeability reservoir, is established. This model can describe various patterns of porous flow, as Darcy's linear law does. All the parameters involved in the model, having definite physical meanings, can be obtained directly from the experiments.     

On the permeability of fibre-reinforced porous materials

Biological tissues can be considered as composite materials comprised of a porous matrix filled with interstitial fluid and reinforced by impermeable collagen fibres. Motivated by studies on fluid flow in articular cartilage, we would like to quantify the undeformed configuration permeability of fibre-reinforced composite materials. If there is a sufficient scale separation between the internal structure of the porous matrix and the arrangement of the fibres, the matrix can be taken as a porous continuum at the fibre scale. In this case, the fibres can be treated as inclusions in a porous continuum, and the overall permeability of the composite can be evaluated using homogenisation procedures. For an isotropic homogeneous matrix, the symmetry of the system is governed by the orientation of the fibres. Here, we propose to retrieve the overall permeability through geometrical considerations and directional averaging methods. The special case of transverse isotropy is discussed in detail, with particular attention to the sub-cases of aligned fibres and fibres lying on a plane.     

On the motion of a fluid-saturated porous solid

Two-parameter structure model of a porous solid is proposed as an approximation of a real porous structure and the macroscopic mass and momentum balance equations are derived for such a medium filled with liquid. The approach presented leads to the equations of motion for a fluid-saturated porous medium with coupling terms via cross-mass couplings. The linear form of these equations is equivalent to the well-known Biot equations.     

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.     

Macroscopic thermodynamics of porous media

A macroscopic thermodynamical theory of unsaturated porous media is studied. The porous media under consideration contain air, liquid water and its vapour encountering phase changes. To the classical state quantities, viz. temperature and densities, we add the volume fractions. These fractions are submitted to constraints, for instance their values lie between 0 and 1. The constraints are taken into account by the free energies which become non-smooth functions. The constitutive laws are obtained by classical thermodynamics and a careful treatment of the non-smooth functions. The constitutive laws account for experimental properties of unsaturated porous media: hysteresis of the sorption and desorption, capillary suction ...     

Plastic yielding in cyclically loaded porous materials

The present paper focuses on plastic yielding of cyclically loaded porous materials. Unit cell models are employed to observe the evolution of the yield surface of porous materials under cyclic loading conditions. Non-linear isotropic as well as non-linear kinematic hardening matrix materials are considered. The yield surfaces computed with the unit cell models are compared to predictions of a micro-mechanical porous plasticity model that incorporates hardening. It is found that, in the case of kinematic hardening, the porous plasticity model underestimates the yield strength for larger hydrostatic stresses. An improvement of the model is proposed, so that a reasonable micro-mechanical approach to model porous materials under cyclic loadings is found.     

Experimental study of the effect of a passive porous coating on disturbances in a hypersonic boundary layer. 1. Effect of the porous coating length

The effect of passive porous coatings of different lengths on the second mode of disturbances in a hypersonic boundary layer is considered. The experiments are performed in a flow with a free-stream Mach number M_∞ = 5.8 and five values of the unit Reynolds number around a sharp cone with an apex half-angle equal to 7°, which is aligned at a zero angle of attack. One half of the model surface along its generatrix is covered by a porous material, and the other part is a solid surface. Pressure fluctuations on the model surface are measured. It is found that application of a passive porous coating can either decrease or increase the amplitude of the second mode. The length of the passive porous coating corresponding to the maximum efficiency of its action on flow disturbances and the coating length that increases the amplitude of the second mode are found.     

Elasto-viscoplastic-viscous theories of granular and porous media

The mechanics of granular and porous media is considered in the light of the modern theories of structured continuum. The basic laws of motion are presented and several constitutive relations are derived. The special case of elastic porous media is considered in detail and the basic field equations are derived and the possible application of the results to soil dynamics is pointed out. The theory of the flow of granular media is also considered and basic equations of motion are derived where the results of Goodman and Cowin are recovered. The viscoplastic flow of porous media is studied and the possible application to soil mechanics is also discussed.     

Difference between the longitudinal Frenkel-Biot waves in water-and gas-saturated porous media

The problem of the propagation of longitudinal Biot waves in a porous medium saturated with a weakly compressible liquid (water) or a gas is considered theoretically. The frequency dependence of the phase velocities and damping coefficients is investigated numerically. It is shown that for a certain relationship between the parameters of the porous medium and the saturating fluid there is a “critical” frequency at which the properties of longitudinal waves of both kinds are identical. An analytical expression for this “critical” frequency is obtained. It is shown that for a gas-saturated porous medium, at a certain frequency, in both longitudinal waves the relative gas-matrix motion changes type. Assuming that the saturating-gas behavior corresponds to an adiabatic equation of state, an estimate is obtained for the threshold pore pressure necessary for the restructuring of the relative motion. The wave associated with matrix deformation is shown to have a high damping coefficient in a porous medium saturated with a weakly compressible liquid (water in the case considered) but to be only weakly damped in a gas-saturated porous medium.     

疏松金属材料冲击温度理论分析

以热力学原理和固态物质的三项式物态方程为基础,由密实物质的冲击绝热线和热力学状态,通 过等容线法推导出了疏松金属材料的冲击温度理论计算方法。以铁为例,分析了几种物理参数对该模型计算 结果的影响。计算和分析结果显示,利用新模型得到的计算结果与已有实验结果吻合较好,误差均在5%以 内。疏松金属材料的冲击温度受Grneisen系数、电子Grneisen系数影响不大,而密实度、冲击压力和电子 比热系数则会对疏松金属材料冲击温度产生较大影响。     

Equations of the mechanics of porous media saturated with liquid and gas

The approach proposed by Podil'chuk [1] is used to derive a system of equations of motion for saturated porous media, allowance being made for the mutual influence of the solid, liquid, and gas phases. The permeabilities of the anisotropic porous medium are assumed to depend on the direction. It is shown that when there are no gas phases and the liquid is incompressible the system of equations reduces to the general equations of the theory of elasticity of an anisotropic body with fictitious stress components. For a porous medium saturated with liquid, the relationships between the permeabilities and the anisotropy constants are obtained. The motion of liquid in an elastic porous medium in the form of an orthotropic cylindrical region with a cavity in the form of a circular cylinder is considered as an example.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 82–87, July–August, 1981.     

Non-Newtonian effects of second-order fluids on double-layered porous Rayleigh-step bearings

Theoretical study of double-layered porous Rayleigh-step bearings with second-order fluid as lubricant is presented. An approximate method for the solutions of the governing fluid film equations for a porous region is proposed. The expressions for the pressure distribution, load capacity and frictional coefficient are obtained in compact form. Calculations of the dimensionless load capacity, frictional force and frictional coefficients are presented for specific values of the material parameters. It is found that the double porous layer yields an increase in the load capacity and ensures decrease in frictional force at the porous lining as compared with the conventional porous Rayleigh-step bearings. The maximum dimensionless load-carrying capacity is found to occur at a slightly larger step ratio as compared with the conventional porous Rayleigh-step bearings.     

Wave trapping by porous barrier in the presence of step type bottom

The present study deals with the trapping of oblique wave by porous barrier located near a rigid wall in the presence of a step type bottom bed. The solution of the physical problem is obtained using the eigenfunction expansion method and multi-mode approximation associated with modified mild-slope equation. Assuming that the porous structure is made of materials having fine pores, the mathematical problem is handled for solution by matching the velocity and pressure at interface boundaries. Various numerical results are computed and analyzed to understand the role of bed profiles, structural porosity, depth ratio, oblique angle of incidence, distance between barrier and step edge and, the distance between the porous barrier and rigid wall in optimizing wave reflection and load on the structure/rigid-wall. A comparison of results on wave trapping by porous barriers over flat and undulated bed reveals that for the same distance between the porous barrier and rigid wall, more number of times optimum reflection occurs in case of undulated bed. The present study is likely to be of immense importance in the design of coastal structures for protecting coastal infrastructures.     

On the theory of porous elastic rods

We consider the direct approach to the theory of rods, in which the thin body is modelled as a deformable curve with a triad of rigidly rotating orthonormal vectors attached to every material point. In this context, we employ the theory of elastic materials with voids to describe the mechanical behavior of porous rods. First, we derive the dynamical nonlinear field equations of the model. Then, in the framework of linear theory, we prove the uniqueness of the solution to the associated boundary-initial-value problem. We identify the relevant field quantities from the theory of directed curves by comparison with the three-dimensional equations of straight porous rods. Finally, for orthotropic and homogeneous rods, we determine the constitutive coefficients in terms of the three-dimensional elasticity constants by solving several problems in the two different approaches.     

Effects of a magnetic field on the onset of convection in a porous medium

The stability of a conducting fluid saturating a porous medium, in the presence of a uniform magnetic field, is investigated using the Brinkman model. In the first part of the paper constant-flux thermal boundary conditions are considered for which the onset of convection is known to correspond to a vanishingly small wave number. The external magnetic field is assumed to be aligned with gravity. Closed form solutions are obtained, based on a parallel flow assumption, for a porous layer with either rigid-rigid, rigid-free or free-free boundaries. In the second part of the paper, the linear stability of a porous layer, heated isothermally from below, is investigated using the normal mode technique. The external magnetic field is applied either vertically or horizontally. Solutions are obtained for the case of a porous layer with free boundaries. Results for a pure viscous fluid and a Darcy (densely packed) porous medium emerge from the present analysis as limiting cases.     

Flow through isotropic granular porous media

A generalization of the Navier-Stokes equation is developed to include laminar flow through a rigid isotropic granular porous medium of spatially varying permeability. The model is based on a theory of interspersed continua and the mean geometrical properties of an idealized granular porous microstructure. The derived momentum transport equations are applicable to granular porous media over the entire porosity range from zero through unity. No restriction with respect to flow velocity is imposed, except for the assumption of laminar flow within the pores. The results provide useful and versatile equations and substantiate many of the empirical equations currently in use. One of the major advantages of the generalized momentum equation is its adaptability to numerical simulation.     

SPH-based numerical treatment of the interfacial interaction of flow with porous media

In this paper, the macroscopic equations of mass and momentum are developed and discretized based on the smoothed particle hydrodynamics (SPH) formulation for the interaction at an interface of flow with porous media. The theoretical background of flow through porous media is investigated to highlight the key constraints that should be satisfied, particularly at the interface between the porous media flow and the overlying free flow. The study aims to investigate the derivation of the porous flow equations, computation of the porosity, and treatment of the interfacial boundary layer. It addresses weak assumptions that are commonly adopted for interfacial flow simulation in particle-based methods. As support to the theoretical analysis, a two-dimensional weakly compressible SPH model is developed based on the proposed interfacial treatment. The equations in this model are written in terms of the intrinsic averages and in the Lagrangian form. The effect of particle volume change due to the spatial change of porosity is taken into account, and the extra stress terms in the momentum equation are approximated by using Ergun's equation and the subparticle scale model to represent the drag and turbulence effects, respectively. Four benchmark test cases covering a range of flow scenarios are simulated to examine the influence of the porous boundary on the internal, interface, and external flows. The capacity of the modified SPH model to predict velocity distributions and water surface behavior is fully examined with a focus on the flow conditions at the interfacial boundary between the overlying free flow and the underlying porous media.