Numerical Simulation of Turbulent Flow and Heat Transfer in a Three-Dimensional Channel Coupled with Flow Through Porous Structures

This study investigates numerically the turbulent flow and heat transfer characteristics of a T-junction mixing, where a porous media flow is vertically discharged in a 3D fully developed channel flow. The fluid equations for the porous medium are solved in a pore structure level using an Speziale, Sarkar and Gatski turbulence model and validated with open literature data. Overall, two types of porous structures, consisted of square pores, are investigated over a wide range of Reynolds numbers: an in-line and a staggered pore structure arrangement. The flow patterns, including the reattachment length in the channel, the velocity field inside the porous medium as well as the fluctuation velocity at the interface, are found to be strongly affected by the velocity ratio between the transversely interacting flow streams. In addition, the heat transfer examination of the flow domain reveals that the temperature distribution in the porous structure is more uniform for the staggered array. The local heat transfer distributions inside the porous structure are also studied, and the general heat transfer rates are correlated in terms of area-averaged Nusselt number accounting for the effects of Reynolds number, velocity ratio as well as the geometrical arrangement of the porous structures.     

The evaluation of the influence of various parameters on the velocity of elastic wave propagation in a rock medium

A full waveform recording in a borehole during acoustic logging makes it possible to determine the elastic parameters of a medium under in-situ conditions.The velocity of elastic wave propagation in rocks and elastic moduli are influenced by factors connected with its macrostructure and microstructure, as well as with rock overburden and porous pressure and temperature.The results of the calculations of the relationships between the elastic and reservoir parameters of sedimentary rocks are presented in this paper. The theoretical Kuster and Toksöz model has been applied.The influence of the porosity, the pore space coefficient, and the saturation of different media of porous rocks on elastic moduli and on compressional and shear wave propagation have been considered in this model. The complex composition of the skeleton and the influence of clay material in the porous rock are taken into account.     

Analytical Determination of Flow Patterns in a Double Porosity Medium Containing Ellipsoidal Occluded Macro-Voids

This article presents the analytical study of fluid flow in a porous medium presenting pores of two different length scales: at the smallest or microscopic scale, the presence of connected voids confers a porous medium structure to the material investigated, while at the upper or mesoscopic scale, occluded macro-pores are present. This microstructure is employed to represent the progressive opening of inter-aggregate pore spaces observed in natural compacted montmorillonites polluted by heavy metal ions. Three-dimensional analytical expressions are rigorously derived for the pore fluid velocity and excess pore fluid pressure within the porous matrix, around an occluded ellipsoidal inter-aggregate void. The eccentricity ratio is employed to characterize the geometrical shape of the ellipsoidal void, while its size is characterized by the macro-porosity. Confrontations are made with numerical solutions in order to investigate the applicability of the analytical pressure and velocity solutions to microstructures of finite size.     

Analysis of hydrodynamic and thermal dispersion in porous media by means of a local approach

A pore scale analysis is implemented in this numerical study to investigate the behavior of microscopic inertia and thermal dispersion in a porous medium with a periodic structure. The macroscopic characteristics of the transport phenomena are evaluated with an averaging technique of the controlling variables at a pore scale level in an elementary cell of the porous structure. The Darcy–Forchheimer model describes the fluid motion through the porous medium while the continuity and Navier–Stokes equations are applied within the unit cell. An average energy equation is employed for the thermal part of the porous medium. The macroscopic pressure loss is computed in order to evaluate the dominant microscopic inertial effects. Local fluctuations of velocity and temperature at the pore scale are instrumental in the quantification of the thermal dispersion through the total effective thermal diffusivity. The numerical results demonstrate that microscopic inertia contributes significantly to the magnitude of the macroscopic pressure loss, in some instances with as much as 70%. Depending on the nature of the porous medium, the thermal dispersion may have a marked bearing on the heat transfer, particularly in the streamwise direction for a highly conducting fluid and certain values of the Peclet number.     

一维流体饱和粘弹性多孔介质层的动力响应

本文研究了不可压流体饱和粘弹性多孔介质层的一维动力响应问题。基于粘弹性理论和多孔介质理论,在流相和固相微观不可压、固相骨架服从粘弹性积分型本构关系和小变形的假定下,建立了不可压流体饱和粘弹性多孔介质层一维动力响应的数学模型,利用Laplace变换,求得了原初边值问题在变换空间中的解析解,并利用Laplace逆变换的Crump数值反演方法,得到原动力响应问题的数值解。数值研究了饱和标准线性粘弹性多孔介质层的动力响应,分析了固相位移、渗流速度、孔隙压力及固相有效应力等的响应特征。结果表明,与不可压流体饱和弹性多孔介质相同,不可压流体饱和粘弹性多孔介质中亦只存在一个纵波,并且固相骨架的粘性对动力行为有显著的影响。     

Effect of Inertial Terms on Fluid–Porous Medium Flow Coupling

The study considers an effect of the nonlinear inertial terms in the Brinkman filtration equation on the characteristics of coupled flows in a pure fluid and porous medium in the frameworks of two independent problems. The first problem is the forced boundary-layer flow overlying the Darcy–Brinkman porous medium. The Prandtl theory is used, and the self-similar equations are built to describe it. It is shown that the inertial terms have a valuable effect on the boundary-layer structure because of the large velocity gradient in the transition zone. The boundary-layer thickness in a porous medium rapidly grows at large Reynolds numbers. The velocity magnitude and gradient at the interface also change. The second independent problem is an analysis of the inertial terms effect on the flow stability. The neutral curves of the full and linearized flow models are built using the shooting method. They have different short-wave asymptotic, but there are no significant changes in the critical Reynolds numbers and corresponding wave numbers.     

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.     

Squirt-Flow in Fluid-Saturated Porous Media: Propagation of Rayleigh Waves

Propagation of attenuated waves is studied in a squirt-flow model of porous solid permeated by two different pore regimes saturated with same viscous fluid. Presence of soft compliant microcracks embedded in the grains of stiff porous rock defines the double-porosity formation. Microcracks and pores respond differently to the compressional effect of a propagating wave, which induces the squirt-flow from microcracks to pores. Elastodynamics of constituent particles in porous aggregate is represented through a single-porosity formulation, which involves the frequency-dependent complex moduli. This formulation is deduced as a special case of double-porosity formation allowing the wave-induced flow of pore-fluid. This squirt-flow model of porous solid supports the attenuated propagation of two compressional waves and one shear wave. Superposition of these body waves, subject to stress-free surface, defines the propagation of Rayleigh wave. This wave is governed by a complex irrational dispersion equation, which is solved numerically after rationalising into an algebraic equation. For existence of Rayleigh wave, a complex solution of the dispersion equation should represent a leaky wave, which decays for propagation along any direction in the semi-infinite medium. A numerical example is solved to analyse the effects of squirt-flow on phase velocity, attenuation and polarisation of the Rayleigh waves, for different combinations of parameters. Numerical results suggest the existence of an additional (second) Rayleigh wave in the squirt-flow model of dissipative porous solids.     

Evolution of a wave pulse propagating through a porous obstacle

This paper studies the evolution of a wave pulse during propagation through a porous obstacle located in a gas and saturated with it. The cases of open and closed boundaries of the porous obstacle are considered. The effect of the parameters of the porous medium such as the initial value of the gas volume fraction and pore size and interfacial heat transfer on the evolution of the wave pulse was analyzed.     

Removal of Particle Bridges From a Porous Material by Ultrasonic Irradiation

Particle bridge formation during the flow of a liquid with particles through a porous material is a fouling mechanism that can block the pores and, hence, decrease the permeability of the material. Ultrasonic irradiation of the material is a cleaning method that can restore the permeability. We make a numerical study of this cleaning method using the lattice-Boltzmann method. We start from a pore blocked by two spherical particles attached to the pore wall by colloidal adhesion forces, thus forming a particle bridge. Next we calculate the hydrodynamic force exerted by a high-frequency acoustic wave on the two particles. By comparing the hydrodynamic force and the adhesion force we investigate, whether the particle bridge will be removed by the ultrasonic irradiation. A sensitivity study is carried out to investigate the influence of some relevant parameters, such as the acoustic wave amplitude, the acoustic frequency, the fluid flow velocity and the ratio of particle diameter and pore diameter. An upscaling procedure is applied to translate the microscopic results for the removal of the particles at the pore level to the permeability improvement of the material at the macroscopic level. A comparison is made between numerical results and experimental data. The agreement is reasonable.     

波浪与外壁开孔双筒柱群的相互作用

应用速度势的特征函数展开和透空壁内两壁间压力差和流体速度成正比的线性模型,建立 了波浪与外壁开孔同轴双筒桩柱群相互作用的线性解析解. 应用这一模型进行了数值计算, 用以检验孔隙系数对双筒柱上的波浪力和波面高度的影响. 结果表明,外壁孔隙系数的增加 对减小波浪力和柱外波面高度有很大影响.     

A mixture theory analysis for the surface-wave propagation in an unsaturated porous medium

The mixture theory is employed to the analysis of surface-wave propagation in a porous medium saturated by two compressible and viscous fluids (liquid and gas). A linear isothermal dynamic model is implemented which takes into account the interaction between the pore fluids and the solid phase of the porous material through viscous dissipation. In such unsaturated cases, the dispersion equations of Rayleigh and Love waves are derived respectively. Two situations for the Love waves are discussed in detail: (a) an elastic layer lying over an unsaturated porous half-space and (b) an unsaturated porous layer lying over an elastic half-space. The wave analysis indicates that, to the three compressional waves discovered in the unsaturated porous medium, there also correspond three Rayleigh wave modes (R1, R2, and R3 waves) propagating along its free surface. The numerical results demonstrate a significant dependence of wave velocities and attenuation coefficients of the Rayleigh and Love waves on the saturation degree, excitation frequency and intrinsic permeability. The cut-off frequency of the high order mode of Love waves is also found to be dependent on the saturation degree.     

Air shock wave interaction with an obstacle covered by porous material

The interaction between an air shock wave and a rigid wall covered by a porous screen is investigated numerically and experimentally. A mathematical two velocity with two stress tensors model is used for studying the wave processes in saturated porous media. The process of reflection of a step-type wave from a rigid wall covered with a porous layer is considered, the effect of the porous medium and wave parameters on the reflection is analyzed, and the numerical results are compared with the experimental data.Received: 30 July 2002, Accepted: 24 December 2002, Published online: 27 May 2003     

A linear dynamic model for a saturated porous medium

A linear isothermal dynamic model for a porous medium saturated by a Newtonian fluid is developed in the paper. In contrast to the mixture theory, the assumption of phase separation is avoided by introducing a single constitutive energy function for the porous medium. An important advantage of the proposed model is it can account for the couplings between the solid skeleton and the pore fluid. The mass and momentum balance equations are obtained according to the generalized mixture theory. Constitutive relations for the stress, the pore pressure are derived from the total free energy accounting for inter-phase interaction. In order to describe the momentum interaction between the fluid and the solid, a frequency independent Biot-type drag force model is introduced. A temporal variable porosity model with relaxation accounting for additional attenuation is introduced for the first time. The details of parameter estimation are discussed in the paper. It is demonstrated that all the material parameters in our model can be estimated from directly measurable phenomenological parameters. In terms of the equations of motion in the frequency domain, the wave velocities and the attenuations for the two P waves and one S wave are calculated. The influences of the porosity relaxation coefficient on the velocities and attenuation coefficients of the three waves of the porous medium are discussed in a numerical example.     

Analysis of the Propagation of Sound Waves in Partially Saturated Soils by Means of a Macroscopic Linear Poroelastic Model

In this paper, the propagation of sound waves in partially saturated soils is investigated. A macroscopic linear model that is based on the two-component model of Biot and on the Simple Mixture Model by Wilmanski is used. For the construction of the model by a micro-macro transition, see Albers, Géotechnique, 2007. We investigate a porous medium consisting of a deformable skeleton and two compressible, chemically non-reacting, pore fluids (liquid and gas). The wave analysis of the poroelastic model reveals the number of acoustic waves and the dependence of velocities and attenuations of these waves on the initial saturation and frequency. There appear four body waves: three longitudinal waves, P1, P2, P3, and one shear wave, S. The P2-wave shows a similar feature as in air–water mixtures: from the theory of suspensions, it is well known that the existence of air bubbles in water reveals a minimum in the sonic velocity. This is also the case for the P2 -speed in the unsaturated porous medium. The P1-velocity increases very abruptly for a certain degree of saturation. This provides the hope for the development of a nondestructive testing method.     

A stochastic model for the permeability characteristics of saturated cemented porous media undergoing freezing

As the temperature of a saturated porous medium drops, the water in the pores starts to freeze. Since the temperature at which the phase change takes place is dependent on the pore size, the permeability of the medium changes continuously. Simultaneously, due to the expansion of water on freezing, it is forced to migrate through the pore body thus inducing stresses in material matrix. The stresses developed and the consequent frost damage are therefore dependent on the change in the permeability characteristics of the medium on freezing. This paper deals with the numerical prediction of permeability characteristics of porous cemented media saturated with water undergoing progressive freezing.A bond percolation model is used to generate the pore structure according to an assumed poresize distribution. Permeability of the medium at various temperatures is computed by solving the network problem. The computed results are compared with other analytical and experimental results. The proposed model predicts a threshold temperature below which permeability drops to zero. This phenomenon is crucial in developing a deeper understanding of the mechanism of frost damage to cemented porous materials such as bricks, stone, concrete, etc.     

Waves in partially saturated porous media

The propagation of compressional waves in a porous medium is investigated in case the pore liquid contains a small volume fraction of gas. The effect of oscillating gas bubbles is taken into account by introducing a frequency-dependent fluid bulk modulus, which is incorporated in the Biot theory. Using a shock tube technique, new experimental data are obtained for a porous column subjected to a pressure step wave. An oscillatory behaviour is observed, consisting of two distinct frequency bands, which is predicted by the theoretical analysis.     

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.     

孔隙深度对多孔储液介质摩擦学性能的影响研究

多孔储液介质凭借其独特的孔隙结构可以储存并释放润滑介质,具备良好的自润滑性能. 利用计算流体力学(CFD)方法研究了孔隙深度对多孔储液介质摩擦界面流体压力分布的影响;考虑气-液界面的弯月面力作用,研究了不同孔隙深度的多孔储液介质气-液承载模型以及气-液二相的最小压差分布规律. 基于模拟计算结果,采用3D打印技术制备了不同孔隙深度的多孔储液介质,进一步考察了孔隙深度对其摩擦学性能的影响. CFD模拟结果表明合理设计孔隙深度能够增强多孔储液介质的流体动压润滑效应,孔隙深度较低会使得润滑升力不足,孔隙深度过高又会使得孔隙中流体产生回流循环,削弱楔形效应. 气体进入多孔储液介质摩擦副表面后,在孔隙中形成气-液二相受压承载,其最大承载力随着孔隙深度的增加先升高后趋于平稳,但孔隙深度越小,对润滑作用的积极效果越显著. 摩擦试验表明多孔储液介质的摩擦系数随着孔隙深度的增加呈先降低后增加的趋势,与模拟计算结果一致. 因此合理设计多孔储液介质的孔隙深度,能优化多孔储液介质的润滑性能.