Dynamic Response of Soft Poroelastic Bed to Nonlinear Water Wave—Boundary Layer Correction Approach

When an oscillatory water wave propagates over a soft poroelastic bed, a boundary layer exists within the porous bed and near the homogeneous water∕porous bed interface. Owing to the effect of the boundary layer, the conventional evaluation of the second kind of longitudinal wave inside the soft poroelastic bed by one parameter, ε1 = k0a, is very inaccurate so that a boundary layer correction approach for a soft poroelastic bed is proposed to solve the nonlinear water wave problem. Hence a perturbation expansion for the boundary layer correction approach based on two small parameters, ε1 and ε2 = k0∕k2, is proposed and then solved. The solutions carried out to the first three terms are valid for the first kind and the third kind of waves throughout the whole domain. The second kind of wave is solved systematically inside the boundary layer, whereas it disappears outside the boundary layer. The result is compared with the linear wave solution of Huang and Song in order to show the nonlinearity effect. The present study is very helpful to formulate a simplified boundary-value problem in numerical computation for soft poroelastic medium with irregular geometry.     

Analysis of liquid flow through ceramic porous media used for molten metal filtration

A two-dimensional mathematical model has been developed to study fluid flow inside ceramic foam filters, used for molten metal filtration, as a function of their structural characteristics. The model is based on the selection of a unit cell, geometric model, formed by two interconnected half-pores. The good agreement between experimental and computed permeabilities showed that the unit cell model approximates very well the effect of filter structure on the flow conditions inside the filter. The validity of the model is supported by the fact that permeabilities are calculated from directly measured structural parameters,i.e., without the introduction of any fitting variable, such as tortuosity. The laminar flow solutions for the Navier-Stokes equation, in steady state, were obtained numerically using the control-volume method. The boundary of the unit cell was represented through axisymmetrical, body-fitted coordinates to obtain a better representation of the complex pore shape. The generality of the model, to study fluid flow in reticulated media, was tested by comparing the computed specific permeabilities with values measured for ceramic foam filters and for the new ceramic filter of lost packed bed (CEFILPB). Such a comparison shows good agreement and discloses a fundamental property of the last kind of porous medium: the critical porosity. The model indicates how porosity and pore dimensions of reticulated filters may be tailored to meet specific fluid flow requirements.     

Effects of Weakly Nonlinear Water Waves on Soft Poroelastic Bed with Finite Thickness

Since porous material is usually of a finite thickness in nature, the effects of periodically nonlinear water waves propagating over a soft poroelastic bed with finite thickness are hence noticed and studied in this work. The water waves are simulated by potential theory while the porous bed is governed by Biot’s theory of poroelasticity herein. The conventional Stokes expansion of water waves based on a one-parameter perturbation expansion fails to solve the soft poroelastic bed problem; therefore, the boundary layer correction approach combined with a two-parameter perturbation expansion is proposed, which enables us to solve the problem of soft poroelastic bed with finite thickness. The results are compared to the similar problem with an infinite-thickness porous bed. The boundary effects of the impervious rock are significant on wave-induced pore water pressure and effective stresses, but are of very little significance on wave profiles at the free surface and the porous bed surface. However, the rigid boundary is insignificant to the pore water pressure and effective stresses when the thickness of porous bed is larger than about one wavelength.     

Microporodynamics of Bones: Prediction of the “Frenkel–Biot” Slow Compressional Wave

Understanding of ultrasonic wave propagation in bones is essential for further development of related techniques in clinical practice. As any other saturated porous medium, bone is characterized by different forms of longitudinal wave propagation, either undrained waves or fast and (Frenkel–Biot) slow compressional waves. We here study the wave propagation in the framework of poromicromechanics. A continuum micromechanics model allows for the prediction of the anisotropic poroelastic properties, Biot’s coefficients, and moduli, from tissue-specific composition data, on the basis of tissue-independent (“universal”) elastic properties of the elementary components of all bones. These poroelastic properties enter the governing equations for wave propagation in anisotropic porous media. They allow for the prediction of undrained, fast and slow waves, as is verified by comparison of model results with experimental findings.     

纳微米级孔隙气体流动数学模型及应用

对纳微米级孔隙多孔介质内的气体流动进行了研究.利用克努森数划分流态,绘制了流态图版,阐明了不同区域的流动特征.基于Beskok-Karniadakis模型,对渗透率校正系数进行了改进,引入多项式修正系数,将Beskok-Karniadakis模型简化为二项式方程,并利用最小二乘法分段拟合得出多项式修正系数的取值.模型对比显示,简化后的模型具有较高的精确度.应用此模型推导出了纳微米级孔隙气体流量的计算公式.进行了室内微观渗流模拟实验,得到气体平面单向渗流规律,与由纳微米级孔隙气体流量公式计算所得渗流特征进行对比,结果显示本模型与实验数据拟合较好.采用本模型进行编程计算,对其影响因素进行分析,发现气体流量随压力平方差增加而增大,且增加趋势越来越快,并随多孔介质渗透率和克努森扩散系数的增加而增大.      

Laminar Surface Water Flow over Vegetated Ground

This study examines low Reynolds number flow over vegetated sloping ground. Instead of using the traditional empirical formula related to resistance or frictional roughness, a new approach is presented by considering the flow inside the vegetation layer as porous media flow governed by Biot’s poroelastic theory as well as inside the soil layer. There is a discrepancy in the velocity distributions of flow over vegetative mantle area and bare area, respectively. Due to the change of the vegetation density, the effects of vegetation porosity and vegetation blockage on surface water flow are discussed.     

Turbulent Flow over a Channel with Fluid-Saturated Porous Bed

The characteristics of fully developed turbulent flow in a hybrid domain channel, which consists of a clear fluid region and a porous bed, are examined numerically using a model based on the macroscopic Reynolds-averaged Navier–Stokes equations. By adopting the classical continuity interface conditions, the present model treats the hybrid domain problem with a single domain approach, and the simulated results are noted to coincide with the existing experimental data and microscopic data. The effects of porosity ? and Darcy number Da on the flow properties over and inside the porous bed are further investigated in the selected ranges of 0.6 ? ? ? 0.8, and 1.6×10?4 ? Da ? 1.6×10?2. It has been demonstrated that the presence of the porous bed causes the significant reduction of the flow velocities inside the clear fluid region relative to that of a smooth impermeable bed, and also reduces the magnitude of the integral constant B of the velocity logarithmic distributions from its traditional value 5.25. Moreover, turbulent shear stress within the upper part of the porous bed increases significantly with the porosity ? and Darcy number Da. The thickness of turbulence penetration remains proportional to the values of porosity ? and Darcy number Da.     

Extended Boussinesq Equations for Water-Wave Propagation in Porous Media

This paper presents a new Boussinesq-type model equations for describing nonlinear surface wave motions in porous media. The mathematical model based on perturbation approach reported by Hsiao et al. is derived. The drag force and turbulence effect suggested by Sollitt and Cross are incorporated for observing the flow behaviors within porous media. Additionally, the approach of Chen for eliminating the depth-dependent terms in the momentum equations is also adopted. The model capability on an applicable water depth range is satisfactorily validated against the linear wave theory. The nonlinear properties of model equations are numerically confirmed by the weakly nonlinear theory of Liu and Wen. Numerical experiments of regular waves propagating in porous media over an impermeable submerged breakwater are performed and the nonlinear behaviors of wave energy transfer between different harmonics are also examined.     

Turbulent Flow Over and Within a Porous Bed

The characteristics of turbulent flow in open channels with a porous bed are studied numerically and experimentally. The “microscopic” approach is followed, by which the Reynolds-averaged Navier-Stokes equations are solved numerically in conjunction with a low-Re k-ε turbulence model above and within the porous bed. The latter is represented by a bundle of cylindrical rods of certain diameter and spacing, resulting in permeability K ranging from 5.5490×10?7 to 4.1070×10?4?m2 and porosity ? from 0.4404 to 0.8286. Mean velocities and turbulent stresses are measured for ? = 0.8286 using hot-film anemometry. Emphasis is given to the effect of Darcy number Da on the flow properties over and within the porous region. Computed and experimental velocities in the free flow are shown to decrease with increasing Da due to the strong momentum exchange near the porous medium/free flow interface and the corresponding penetration of turbulence into the porous layer for highly permeable beds. Computed discharge indicates the significant reduction of the channel capacity, compared to the situation with an impermeable bed. On the contrary, laminar flow computations, along with analytical solutions and measurements, indicate opposite effects of the porous medium on the free flow.     

Dynamic Analysis of Multilayered Soils to Water Waves and Flow

In nature, a soil profile generally consists of several heterogeneous layers. This study is aimed at discussing the interactive problem of oscillatory water waves and flow passing over multilayered soils. The soil behavior is considered as viscoelastic in the present mathematical model modified from Biot’s poroelastic theory. Employing this model, the dynamic response including the profiles of pore water pressure and effective stress in the multilayered soils is discussed. The results reveal that the perturbed pore pressure is different from that inside a single-layered soil where the thickness of the first soil layer is less than the water wavelength. The discrepancy of the vertical effective stresses between multilayered and single-layered soils is even much more apparent under the same conditions. Moreover, seepage force is examined and is found to be larger near the bed surface and the bottom of the first soil layer where soils are easily disturbed by external disturbance. The locations where soil failure might happen are found near the troughs of surface water waves.     

Laminar Water Wave and Current Passing Over Porous Bed

The problem of the dynamic interaction of water waves, current, and a hard poroelastic bed is dealt with in this study. Finite-depth homogeneous water with harmonic linear water waves passing over a semi-infinite poroelastic bed is investigated. In order to reveal the importance of viscous effect for different bed forms, viscosity of water is considered herein. In a boundary layer correction approach, the governing equations of the poroelastic material are decoupled without losing physical generality. The contribution of pressure effect and shear effect to the hard poroelastic bed, which is a valuable indication to the mechanism of ripple formation, is clarified in the present study. This approach will be helpful in saving time and storage capacity when it is applied to numerical computation.     

Water Well Resonance Induced by Preearthquake Signals

This study elucidates the water well resonance induced by preearthquake signals using an analytic approach. Weak pressure waves passing through a confined aquifer are considered as the incoming preearthquake signal. Owing to the hardness of the porous skeleton, the pressure waves are simply the limiting case of the second kind of dilatational waves of poroelasticity. Because the driving signals of a weak preearthquake pressure wave transmitting through a confined aquifer are too weak to significantly affect the solid skeleton, we believe that this phenomenon is attributed to the effect of resonant amplification of water levels in wells. The flow inside the well is assumed to be incompressible, inviscid, and irrotational, while that outside the well is treated as a porous-media flow with a rigid skeleton. The flows inside and outside the well are analyzed using the potential flow theory under the assumption of small-amplitude waves and Darcy’s law of porous-media flow, respectively. The well-posed boundary value problem is solved using the regular perturbation expansion based on a small gauge function k0R, where k0 = wave number and R = well radius. The results of this study demonstrate that the weak preearthquake longitudinal pressure wave is only a triggering mechanism for the resonance of transverse gravity surface water waves inside the well.     

3D Numerical Modeling of Flow and Sediment Transport in Open Channels

A 3D numerical model for calculating flow and sediment transport in open channels is presented. The flow is calculated by solving the full Reynolds-averaged Navier-Stokes equations with the k ? ε turbulence model. Special free-surface and roughness treatments are introduced for open-channel flow; in particular the water level is determined from a 2D Poisson equation derived from 2D depth-averaged momentum equations. Suspended-load transport is simulated through the general convection-diffusion equation with an empirical settling-velocity term. This equation and the flow equations are solved numerically with a finite-volume method on an adaptive, nonstaggered grid. Bed-load transport is simulated with a nonequilibrium method and the bed deformation is obtained from an overall mass-balance equation. The suspended-load model is tested for channel flow situations with net entrainment from a loose bed and with net deposition, and the full 3D total-load model is validated by calculating the flow and sediment transport in a 180° channel bend with movable bed. In all cases, the agreement with measurements is generally good.     

Earthquake Hydrodynamic Pressure on Dams

Hydrodynamic pressures on the vertical upstream face of straight dams during horizontal earthquakes were studied by Westergaad in 1933, and an analytical solution was obtained. Assuming that water is incompressible, an approximation can be made to reduce Westergaad’s mathematical formulation to the Laplace equation. The computer program SEEP2D, from the U.S. Army Corps of Engineers (COE), is available for the study of seepage flow in porous media; this flow can be expressed mathematically in a form of the Laplace equation. Therefore, we can use this computer program to study the hydrodynamic pressure on dams during a horizontal earthquake in the upstream/downstream direction. In practice, the proposed procedure is not limited to SEEP2D but can also be applied to any computer model capable of solving Laplace equations in bounded domains. Two examples are presented to show the application of the COE’s computer program, and the accuracy of the proposed method is discussed.     

Numerical Modeling of Bed Evolution in Channel Bends

A two-dimensional numerical model is developed to predict the time variation of bed deformation in alluvial channel bends. In this model, the depth-averaged unsteady water flow equations along with the sediment continuity equation are solved by using the Beam and Warming alternating-direction implicit scheme. Unlike the present models based on Cartesian or cylindrical coordinate systems and steady flow equations, a body-fitted coordinate system and unsteady flow equations are used so that unsteady effects and natural channels may be modeled accurately. The effective stresses associated with the flow equations are modeled by using a constant eddy-viscosity approach. This study is restricted to beds of uniform particles, i.e., armoring and grain-sorting effects are neglected. To verify the model, the computed results are compared with the data measured in 140° and 180° curved laboratory flumes with straight reaches up- and downstream of the bend. The model predictions agree better with the measured data than those obtained by previous numerical models. The model is used to investigate the process of evolution and stability of bed deformation in circular bends.     

Application of the porous medium combustion technology in the chamber reheating furnaces at Baosteel

The design of the porous medium combustion ( PMC) system which has been applied to chamber reheating furnaces is presented in this study and its main application effects are described in detail. Porous medium materials are mainly ceramic ball sucked granular bed porous media and foam ceramic porous media. This study investigates the foam ceramic porous medium and a schematic diagram of the combustion inside this porous medium. The PMC takes a solid medium as its main heat exchange way,thus greatly improving the heat transfer efficiency. Judging from the application effects,the following conclusions have been made: the PMC technology can save more than 25% of energy with remarkable effects; the furnace temperature uniformity can be significantly enhanced; the porous media combustion technology can make the heating furnace design in a more compact way,reduce the time for heating up the furnace, improve the heating rate and reduce energy consumption.     

Dynamic Axial Load Transfer from Elastic Bar to Poroelastic Medium

The time-harmonic response of a cylindrical elastic bar (pile) partially embedded in a homogeneous poroelastic medium and subjected to a vertical load is considered. The bar is modeled using 1D elastic theory valid for long bars in the low-frequency range, and the porous medium using Biot's 3D elastodynamic theory. The bar is bonded to the surrounding medium along the contact surface. The problem is formulated by decomposing the bar∕porous medium system into a fictitious bar and an extended porous medium. A Fredholm's integral equation of the second kind governs the distribution of axial force in the fictitious bar. The integral equation involves kernels that are displacement and strain influence functions of a poroelastic half-space subjected to a buried, uniform vertical patch load. The governing integral equation is solved by applying numerical quadrature. The solutions for axial displacement and axial force of the bar, and the pore pressure are also derived. Selected numerical results for vertical impedance, axial force, and pore pressure profiles are presented to portray the influence of bar stiffness and length∕radius ratio, frequency of excitation, and poroelastic properties.     

Furrow Irrigation Advance Simulation Using a Surface–Subsurface Interaction Model

A model for the simulation of furrow irrigation advance was developed based on the Saint-Venant equations for the one-dimensional surface flow and the two-dimensional Richards equation for porous media flow. Solutions are computed numerically using finite differences for the surface flow and finite elements for the subsurface flow. Computations are internally coupled through an iterative procedure. Infiltration is computed with the Richards equation every five nodes used in the surface flow computations and by linear interpolation at the remaining nodes. In addition, the Richards equation is solved at the boundaries of the surface flow domain and in the vicinity of the wave front. The time step is calculated using the Courant–Friedrich–Lewy condition and a stability criterion that accounts for friction effects. This combined criterion prevents numerical instabilities and convergence problems, especially in cases of high friction coefficient, low discharge rates, and/or high infiltration rates resulting generally in low flow depth and slow irrigation advance. The model was evaluated against an approach involving high resolution correspondence used in both surface and subsurface flow, using different soil types, inflow discharge, and stability criteria.     

Poromechanics Response of Inclined Wellbore Geometry in Fractured Porous Media

This paper presents the poromechanics/poroelastic analytical solution for stress and pore pressure fields induced by the action of drilling and/or the pressurization of an inclined/horizontal wellbore in fractured fluid-saturated porous media, or naturally fractured fluid-saturated rock formations. The model which is developed within the framework of the coupled processes in the dual-porosity/dual-permeability approach accounts for coupled isothermal fluid flow and rock/fractures deformation. The solution to the inclined/horizontal wellbore problem is derived for a wellbore drilled in an infinite naturally fractured poroelastic medium, subjected to three-dimensional in situ state of stress and pore pressure. The dual-porosity analytical solution is first reduced to the limiting single-porosity case and verified against an existing single-porosity solution. A comparison between single-porosity and dual-porosity poroelastic results is conducted and displayed in this work. Finally, wellbore stability analyses have been carried out to demonstrate possible applications of the solution.